Patent Publication Number: US-11639001-B2

Title: Robotic system and method for reorienting a surgical instrument

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. Non-Provisional patent application Ser. No. 16/409,024, filed May 10, 2019, which is a continuation of U.S. Non-Provisional patent application Ser. No. 15/401,567, filed Jan. 9, 2017, now U.S. Pat. No. 10,314,661, which is a continuation of U.S. Non-Provisional patent application Ser. No. 14/841,062, filed Aug. 31, 2015, now U.S. Pat. No. 9,566,125, which is a divisional of U.S. Non-Provisional patent application Ser. No. 13/958,070, filed on Aug. 2, 2013, now U.S. Pat. No. 9,119,655, which claims the benefit of U.S. Provisional Patent App. No. 61/679,258, filed on Aug. 3, 2012, and U.S. Provisional Patent App. No. 61/792,251, filed on Mar. 15, 2013, the advantages and disclosures of each of the above-referenced applications are hereby incorporated by reference in their entirety. 
    
    
     FIELD 
     This disclosure relates generally to surgical robotic systems and methods for controlling a surgical manipulator to reorient a surgical instrument based on determined forces and torques applied to a virtual rigid body. 
     BACKGROUND 
     Recently, medical practitioners have found it useful to use robotic devices to assist in the performance of surgical procedures. A robotic device typically includes a moveable arm that comprises one or more linkages. The arm has a free, distal end that can be placed with a very high degree of accuracy. A surgical instrument designed to be applied to the surgical site is attached to the free end of the arm. The practitioner is able to precisely position the arm so as to by extrapolation, precisely position the surgical instrument at the site on the patient at which the instrument is to perform a medical or surgical procedure. One advantage of using a robotic system to hold the instrument is that the system arm, unlike the arms and hands of a surgeon, are not subjected to muscle strain or neurological actions like twitching. Thus, in comparison to when an instrument is hand-held and therefore hand positioned, using a medical robotic system it is possible to hold an instrument steady, or move the instrument along a defined path with a higher degree of accuracy. 
     Further some robotic surgical systems are designed to be used with surgical navigation systems. A surgical navigation system is a system that is able to generate data that provides a relatively precise indication of the surgical instrument relative to the location of the patient against which the instrument is applied. When a surgical robotic system is provided with the data indicating the position of the instrument relative to the patient, the robotic system may be able to position the instrument to ensure that it is applied to the tissue of the patient against which the instrument is supposed to be applied. This substantially eliminates the likelihood that the instrument will be applied to tissue against which the instrument should not be applied. 
     Some medical robotic systems are designed to work in what is referred to as a “semi-autonomous” mode. In this mode of operation, the robotic system actuates the arm so as to cause the instrument to move against the patient&#39;s tissue in a preprogrammed path. This is useful if, for example, the instrument is some sort of cutting device and the goal of the particular procedure is to remove a pre-defined section of the patient&#39;s tissue. By way of reference, if a robotic system operates in an “autonomous” mode of operation, the robot, once actuated, performs the procedure with essentially no input from the surgeon. In a “semi-autonomous” mode of operation, the practitioner is able to assert commands to control the operation of the robot. For example, some semi-autonomous robots are constructed so that, in order for the robot to displace the instrument, the practitioner must actuate a command by continually depressing a control button or switch associated with the robot. Upon the negation of the actuate command by the practitioner, the advancement of the instrument by the robot at least temporarily stops. 
     Some robotic systems are not traditional robots in that once activated, they do not automatically move the attached instrument along a pre-programmed path of travel. These systems include control systems through which the practitioner enters commands indicating where the attached instrument is to be positioned. Based on these practitioner-entered commands, this type of system actuates the system&#39;s arm/arms to cause the essentially simultaneous, real time, movement of the instrument. These robotics systems are considered to operate in a manual mode. 
     To date though, it has been difficult to provide a robotic system able to, during the performance of a single procedure, switch between semi-autonomous and manual modes of operation. For example, it is believed that many times a surgeon may want to initially manually operate the instrument in order to remove a large mass of tissue. This part of the procedure is sometimes referred to as debulking. Then, to remove tissue to define the surfaces of the remaining tissue, the surgeon may want the robotic system to semi-autonomously perform fine positioning of the instrument. This part of the procedure is sometimes known as the finishing cut. 
     Moreover, there are times when it may be desirable to switch from semi-autonomous positioning of the instrument back to manual positioning. For example, in an orthopedic joint replacement procedure, the practitioner may want the instrument, a cutting tool, to move in a programmed path in order to precisely shape the bone to which the instrument is applied. This precise bone shaping facilitates the precise fitting of the implant to the face of the bone exposed by the cutting tool. However, there may be a situation in which, after the procedure begins, it becomes apparent that the instrument may collide with an object at the surgical site against which such contact is undesirable. This object may be tissue that has moved into the surgical site or a second instrument positioned at the site. In this situation, it should be possible for the practitioner to momentarily interrupt the programmed movement of the tool, manually control the tool to reposition the instrument, and then return the tool to the programmed movement. 
     SUMMARY 
     A robotic system comprising is provided according to a first aspect. The robotic system includes a surgical instrument and an energy applicator extending from the surgical instrument, and wherein the surgical instrument and the energy applicator define a common axis; a surgical manipulator comprising a plurality of links and a plurality of actuators configured to move the plurality of links to position the surgical instrument and energy applicator; a force/torque sensor coupled to the surgical manipulator and being configured to generate an output in response to forces and torques applied to the surgical instrument by a user; and at least one controller configured to: define a centering point that intersects the common axis; model the surgical instrument and the energy applicator as a virtual rigid body; determine forces and torques to apply to the virtual rigid body, wherein the forces and torques to apply to the virtual rigid body are determined, in part, based on the output generated by the force/torque sensor; and control the surgical manipulator to: advance the energy applicator based on the determined forces and torques applied to the virtual rigid body; and reorient the surgical instrument such that the common axis pivots about the centering point during advancement of the energy applicator. 
     A method of operating a robotic system is provided according to a second aspect. The robotic system comprises a surgical instrument and an energy applicator extending from the surgical instrument, wherein the surgical instrument and the energy applicator define a common axis, a surgical manipulator comprising a plurality of links and a plurality of actuators configured to move the plurality of links to position the surgical instrument and energy applicator, a force/torque sensor coupled to the surgical manipulator and being configured to generate an output in response to forces and torques applied to the surgical instrument by a user, and at least one controller, the method comprising the at least one controller: defining a centering point that intersects the common axis; modeling the surgical instrument and the energy applicator as a virtual rigid body; determining forces and torques for applying to the virtual rigid body, wherein the forces and torques for applying to the virtual rigid body are determined, in part, based on the output generated by the force/torque sensor; and controlling the surgical manipulator for: advancing the energy applicator based on the determined forces and torques applied to the virtual rigid body; and reorienting the surgical instrument such that the common axis pivots about the centering point during advancing of the energy applicator. 
     A robotic system is provided according to a third aspect. The robotic system comprises a surgical instrument and an energy applicator extending from the surgical instrument; a surgical manipulator comprising a plurality of links and a plurality of actuators configured to move the plurality of links to position the surgical instrument and energy applicator; a force/torque sensor coupled to the surgical manipulator and being configured to generate an output in response to forces and torques applied to the surgical instrument by a user; and at least one controller to control operation of the surgical manipulator in a manual mode in which a user applies forces and torques to the instrument to advance the energy applicator, whereby in the manual mode, the at least controller is configured to: model the surgical instrument and the energy applicator as a virtual rigid body; determine forces and torques to apply to the virtual rigid body, wherein the forces and torques to apply to the virtual rigid body are determined, in part, based on the output generated by the force/torque sensor; control the surgical manipulator to advance the energy applicator based on the determined forces and torques applied to the virtual rigid body; enable reorientation of the surgical instrument in response to actuation of a button; monitor the output of the force/torque sensor in response to the user applying reorienting forces and torques to the surgical instrument; and control the surgical manipulator to reorient the surgical instrument based on the determined forces and torques applied to the virtual rigid body. 
     According to a fourth aspect, a method is provided for operating the robotic system of the third aspect. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is pointed out with particularity in the claims. The above and further features and advantages of this invention are understood from following Detailed Description taken in conjunction with the following drawings in which: 
         FIG.  1    is an overview of how a manipulator of this invention is used to position and advance a surgical instrument on a patient; 
         FIG.  2    is a perspective view of a manipulator of this invention to which both a surgical instrument and a navigation tracker are attached; 
         FIGS.  2 A and  2 B  are, respectively, top and side views of a pendant used to regulate the operation of the manipulator; 
         FIG.  3    is front view of the manipulator; 
         FIG.  4    is a perspective view of the arms of the manipulator; 
         FIG.  5    is an alternative perspective view of the manipulator arms; 
         FIG.  6    is a side view of the manipulator arms wherein the lower arm is seen in the foreground; 
         FIG.  7    is a top view of the manipulator arms; 
         FIG.  8    is a side view of the end effector and a surgical instrument, here a powered drill, attached to the end effector; 
         FIG.  9    is a front view of the end effector and attached surgical instrument; 
         FIG.  10    is perspective view of the end effector and attached surgical instrument; 
         FIG.  11    is a block diagram of a number of the processors that collectively cooperate to control the actuation of the manipulator and attached surgical instrument; 
         FIG.  12    is a diagrammatic illustration of the different coordinate systems associated with the patient and the elements that regulate the actuation of the manipulator; 
         FIG.  13 A through  13 E  form a block diagram of software modules that are run to regulate the actuation of the manipulator; 
         FIG.  14    is a block diagram of the components forming one of the joint actuators; 
         FIG.  15 A  is a side view of a bone depicting how tool paths are formed to define the sections of the bone to which the surgical instrument is applied; 
         FIG.  15 B  is a top view of a bone depicting the arrangement of the tool maps; 
         FIG.  15 C  illustrates how a single tool path may comprises a set of path segments of different length and orientation; 
         FIGS.  16 A- 16 D  depict the sub-modules internal to the tool path force calculator; 
         FIG.  17    diagrammatically depicts how a tool path segments are averaged by the rolling average filter; 
         FIGS.  18 A through  18 D  are a set of diagrammatic depictions of how the points and boundaries used by the orientation regulator are generated; 
         FIG.  19    is a graphical depiction the relationship between the offset of the instrument from the target orientation and the force that the orientation regulator determines should be applied to the virtual rigid body to compensate for the offset; 
         FIGS.  20 A,  20 B and  20 C  are diagrammatic depictions of the energy applicator repositioning that is performed by the cut guide; 
         FIGS.  21 A,  21 B and  21 C  form a flow chart of the process steps executed by the cut guide; 
         FIG.  22    is an illustration of how a boundary defining tile closest to the energy applicator may not be the tile that the applicator will most likely intersect, 
         FIGS.  23 A and  23 B  are diagrammatic depictions of the velocity changes the instrument and energy applicator undergo as a consequence of the cut guide&#39;s prevention of the movement of the energy applicator beyond the defined boundary; 
         FIG.  23 C  is a diagrammatic depiction of the change in position of the instrument and energy application as a consequence of the cut guide&#39;s prevention of the movement of the energy applicator beyond the defined boundary; 
         FIG.  24    is a flow chart of the process by which joint limit constraining force may be generated; 
         FIG.  25    is a flow chart of the process by which an interference angle constraining force may be generated; 
         FIG.  26    is a flow chart of the process by which a workspace constraining force may be generated; 
         FIG.  27    is a block diagram of the inputs into and output from the instrument manager; 
         FIG.  28 A- 28 G  collectively form a flow chart of process steps executed by the manipulator when engaged in semi-autonomous advancement of the instrument; 
         FIGS.  29 A and  29 B  are, respectively, top view and side view diagrammatic depictions of the initial orientation of the instrument when in the semi-autonomous mode; 
         FIGS.  30 A and  30 B  are, respectively, top and side view diagrammatic depictions of how, based on the force and torque commands output by the tool orientation force regulator the manipulator orients the instrument and energy applicator so the common axis extends through the centering point; 
         FIG.  31    is a diagrammatic depiction of how, as the energy applicator advances along the tool path, based on the force and torque commands output by the tool orientation force regulator, the orientation of the common axis is held relatively close to the centering point; 
         FIGS.  32 A,  32 B and  32 C , are, respectively, top, side and cross section views of how, even with the presence of a obstruction  828  above the tool path, the manipulator is able to adjust the orientation of the instrument to hold the energy applicator on the tool path while maintaining the common axis within the reference surface aperture; 
         FIGS.  33 A and  33 B  are, respectively, top and side views of how the manipulator adjusts the orientation of the instrument to hold the energy applicator on the tool path while maintaining the common axis within the reference surface aperture; 
         FIG.  33 C  is a diagrammatic depiction of how, as the energy applicator advances along the tool path, based on the force and torque output by the tool orientation regulator, the orientation of the common axis shifts to maintain the axis in the reference surface aperture. 
         FIGS.  34 A,  34 B and  34 C  are a second set of cross-sectional views that depict how the position of the orientation reference surface and the aperture defined in the surface are reset during the operation of the manipulator. 
         FIGS.  35 A,  35 B, and  35 C  are a second set of cross section views that depict how the position and orientation of the reference surface and aperture defined by in the reference surface are reset during operation of the manipulator; and 
         FIGS.  36 A,  36 B and  36 C  are a sequence of drawings depicting how the boundary defining where the energy applicator is to be applied is modified during the course of a surgical procedure. 
     
    
    
     DETAILED DESCRIPTION 
     I. Overview 
     This invention relates generally to a new and useful surgical manipulator that positions a surgical instrument or tool on or in the patient. The surgical manipulator positions the surgical instrument so that the end of instrument that is to be applied to the tissue is only applied to the tissue to which the instrument should be applied. 
     The manipulator can be operated in either a manual mode or a semi-autonomous mode. When the manipulator is operated in the manual mode, the manipulator monitors the forces and torques the practitioner places on the instrument in order to position the instrument. These forces and torques are measured by a sensor that is part of the manipulator. In response to the practitioner applied forces and torques, the manipulator essentially moves the instrument in real time. The movement of the instrument by the manipulator can therefore be considered to be movement of the instrument that emulates the desired positioning of the instrument by the practitioner. 
     When the manipulator is in the manual mode, the manipulator determines the relative location of the instrument to a boundary. This boundary defines the limits of the tissue beyond which the instrument should not be placed. In the event it appears that the practitioner wants to position the instrument beyond the boundary, the manipulator does not allow this movement of the instrument. For example, should the manipulator determine that the practitioner&#39;s repositioning of the instrument is resulting in the instrument approaching a boundary which the instrument should not cross, the manipulator prevents the instrument from movement beyond the boundary. 
     The practitioner may continue to attempt to reposition the instrument to a location beyond which the tip should not be applied. The manipulator does not move the tip such that the tip is repositioned beyond the boundary. The manipulator does, however, reorient the instrument according to the force detected from the practitioner. This reorienting of the instrument without allowing tip repositioning indicates to the practitioner that the instrument tip has reached a boundary that should not be crossed. The manipulator still does not respond to move the tip along the boundary. 
     When the manipulator is operated in a semi-autonomous mode, the manipulator calculates the forces and torques necessary to move the instrument along a predefined path of travel. Based on these forces and torques, the manipulator moves the instrument along the predefined path of travel. 
     It is a further feature that the practitioner is able to engage in some manual adjustment of the position of the instrument while the manipulator moves the instrument during the semi-autonomous operation. One such adjustment is that the practitioner can adjust the orientation of the instrument while the instrument moves along the programmed path of travel. 
     In some versions, when the manipulator advances the instrument, it does so based on a determination of forces and torques that need to be applied to a virtual rigid body. This virtual rigid body is a model of the instrument and the energy applicator. Based on these forces and torques, the manipulator advances the instrument. When the manipulator operates in the manual mode, a component of these forces and torques are forces and torques that, as a consequence of their being applied to the virtual rigid body, result in the manipulator positioning the instrument in such a manner that the instrument does not cross the boundary. When the manipulator operates in the semi-autonomous mode, forces and torques applied to the virtual rigid body include additional components. In response to the presence of these additional force and torque components, the manipulator advances the instrument so the energy applicator moves along the predefined tool path. 
     In some versions, the manipulator includes a number of interconnected links. These links may be connected together in series and/or parallel. In one embodiment of this invention, these links form two parallel four bar linkages. The instrument is connected to the distal end of the links. Generally, each pair of adjacent links is connected by a joint. The position of the links is set by actuators associated with the joints. 
       FIGS.  1  and  2    illustrate an exemplary manipulator  50  used to apply a surgical instrument  160  to a patient  600 . Manipulator  50  includes an end effector  110  that is the component of the manipulator to which the surgical instrument  160  is attached. Manipulator  50  positions the end effector  110  to position and orient the surgical instrument  160  so that the instrument performs the intended medical/surgical procedure on the patient. The manipulator  50  is used in conjunction with a surgical navigation system  210 . The surgical navigation system  210  monitors the position of the end effector  110  and the patient  600 . Based on this monitoring, the surgical navigation system  210  determines the position of the surgical instrument  160  relative to the site on the patient to which the instrument is applied. 
     A hand-held pendant  190  ( FIG.  2 A ) is also attached to manipulator  50 . Pendant  190  is used in some operating modes to regulate operation of the manipulator and instrument  160 . 
     Manipulator  50  of this invention can operate in a manual mode. When the manipulator operates in the manual mode, the manipulator responds to the forces and torques the practitioner places on the instrument  160  to position the instrument. In response to these forces and torques, the manipulator mechanically moves the instrument in a manner that emulates the movement that would have occurred based on the forces and torques applied by the practitioner. As the instrument  160  moves, the surgical manipulator  50  and surgical navigation system  210  cooperate to determine if the instrument is within a defined boundary. Often, but not always, this boundary is within the patient and beyond which the instrument should not be applied. Based on these data, the manipulator  50  selectively limits the extent to which the instrument  160  moves. Specifically, the manipulator constrains the manipulator from movement that would otherwise result in the application of the instrument outside of the defined boundary. Thus, should the practitioner apply forces and torques that would result in the advancement of the instrument beyond the boundary, the manipulator does not emulate this intended positioning of the instrument. 
     The manipulator  50  can also operate in a semi-autonomous mode. To operate the manipulator  50  in this mode, a path of travel along which the instrument  160  should be applied to the tissue is generated. At least the basic version of this path is generated prior to the start of the procedure. Based on these forces and torques, as well as other data, the manipulator generates data describing a commanded pose to which the instrument should be advanced. (“Pose” is understood to be the position and orientation of the system component being discussed.) Once the commanded pose is generated, the manipulator advances the instrument to that pose. As when in the manual mode, when the instrument is operated in the semi-autonomous mode, the manipulator does not advance the instrument  160  beyond the boundary. 
     II. Hardware 
     As seen in  FIGS.  2  and  3   , the manipulator  50  includes a cart  52 . Cart  52  includes a wheel mounted frame (frame not illustrated). A shell  56  is disposed over the frame. 
     Manipulator  50  includes lower and upper arms  68  and  70 , respectively. Arms  68  and  70  extend upwardly from shoulders  67  and  69 , respectively. The shoulders  67  and  69  are located above cart shell  56 . Each shoulder  67  and  69  and associate arm  68  and  70 , respectively, collectively have three degrees-of-freedom relative to a horizontal base plane of the cart  52 . Shoulder  69 , the shoulder to which upper arm  70  is mounted, is located above shoulder  67 , the shoulder to which lower arm  68  is mounted. Both shoulders  67  and  69  are rotatably attached to the cart frame. Each shoulder  67  and  69  rotates around an axis that extends perpendicular to the horizontal base plane of the cart  52 . The rotation of each shoulder  67  and  69  results in the like displacement of the associated arm  68  or  70 , respectively. As is apparent below, the shoulders need not always move in unison or have the same end position. The angular position of each shoulder  67  and  69  relative to a reference location on the cart  52  is referred to as the joint angle of the shoulder. 
     As seen in  FIGS.  4  and  5   , each arm  68  and  70  includes a four-bar linkage. In these Figures, the arms are in their nominal home positions. Each arm  68  and  70  includes an upper link  74  that is pivotally mounted to the shoulder  67  or  69 . While upper links  74  are able to pivot, in  FIGS.  4  and  5    they are shown extending above the shoulders and approximately perpendicular to the ground plane. A driver link  76  is also pivotally mounted to shoulder  67  or  69 . Driver link  76  is mounted to the shoulder  67  or  69  so as to pivot around the same axis around which upper link  74  pivots. Each driver link extends rearwardly away from the associated shoulder  67  or  69 . Here, “rearward” is the direction away from the patient. “Forward” is in the direction of towards the patient. In the depicted version, the driver links  76 , unlike the other links, are not generally in the form of straight beams. Instead, each driver link  76  is formed with a bend (bend not identified). The bent shape of the driver links  76  facilitates the clearance of links about the shoulders  67  and  69 . 
     A four-bar link  78  is pivotally mounted to the rear free end of each driver link  76 . Four bar link  78  extends upwardly from the associated driver link  76  and is generally parallel with the upper link  74 . A driven link  80  is the remaining rigid link of each arm  68  and  70 . Each driven link  80  has an upper section, not identified, that is pivotally attached to the free end of the associated proximal four bar link  78 . Each driven link  80  is also pivotally attached to the free end of the associated upper link  74 . Each driven link  80  has a forward section, not identified, that extends outwardly beyond the upper link  74 . Owing to shoulders  67  and  69  being of different heights above ground level, the drive link  80  integral with upper arm  70  is located above the drive link integral with lower arm  68 . 
     Each link  74 ,  76 ,  78  and  80 , like each shoulder  67  and  69 , rotates. The connection between two links is referred to as a joint. The angle between two links is the joint angle of the joint connecting the links. 
     A rigid coupler  88 , also part of the manipulator  50 , extends between the distal ends of the driven links  80 . As seen in  FIGS.  6  and  7   , a wrist  82  connects coupler  88  to lower arm driven link  80 . Wrist  82  is connected to the lower arm driven link  80 . Wrist  82  is a three degree of freedom wrist. A wrist  84  connects coupler  88  to the distal end of the upper arm driven link  80 . Wrist  84  is a two degree of freedom wrist. A description of some of the features of this type of manipulator as well as a description of an alternative set of links that can be used to position the end effector  110  is contained in U.S. Pat. No. 7,950,306, MANIPULATOR, issued May 31, 2011 the contents of which are explicitly incorporated herein by reference. 
     Three actuators  92 ,  94  and  96 , one of each shown diagrammatically in  FIG.  13 D , are associated with each arm  68  and  70 . Each actuator  92  is mounted to the cart frame adjacent the shoulder  72  integral with the associated arm  68  or  70 . 
     Actuators  94  and  96  are mounted in the shoulder  67  or  69  integral with the associated arm  68  or  70 . Actuator  94  is connected to the upper link  74  to selectively pivot the upper link. Actuator  96  is connected to the driver link  76  to pivot the driver link  76 . The pivoting of the driver link  76  results in the displacement of the attached four bar link  78 . The movement of the four-bar link  78  results in the pivoting of the attached driven link  80 . Specifically, the driven link  80  pivots about the axis around which the driven link  80  is attached to the associated upper link  74 . These particular gear assemblies are essentially “zero backlash” gear assemblies. There is essentially no looseness between interlocking gears. This feature of the gears contributes to the precision positioning of the shoulders  72  and links  74 ,  76 ,  78  and  80 . 
     Arms  68  and  70  and coupler  88  collectively form an over actuated mechanism. This means the actuation of one link must be accompanied by the corresponding movement of one or more of the other actuated links. 
     A number of components are associated with each actuator  92 ,  94  and  96 .  FIG.  14    arbitrarily shows the components associated with actuator  94 . Specifically, the actuator includes a permanent magnet synchronous motor  101  attached to a structural frame  87  internal to the shoulder  67  or  69 . The motor  101  is not attached directly to the frame  87 . Instead a torque sensor  89  is located between the frame  87  and motor  101 . 
     Associated with the motor  101  is the below described rotary encoder  114 . A brake  103  locks rotation of the motor shaft when the motor is not powered. The locked/unlocked states of the brakes  103  are controlled by the manipulator controller  124 . When the manipulator  50  is powered down, manipulator controller  124  sets the brakes  103  from the unlocked to the locked state. Thus, when manipulator  50  is powered down, brakes  103  are the components integral with shoulders  67  and  69  and arms  68  and  70  that prevent movement of the arms. 
     A reduction gear  105  converts the rotational movement of the output shaft of the motor rotor (not illustrated) into rotational moment that drives the shoulder  67  or  69  or link  74  or  76  to which the motor is attached. In some versions, the reduction gear is a harmonic gear drive. Output shaft  107  of the reduction gear assembly  105  is shown connected to upper link  74 . In some versions, the motor, the rotary encoder, the brake and reduction gear assembly are a single unit. 
     While not shown, integral with each actuator is a transfer gear assembly. The transfer gear assemblies integral with actuators  92  comprises the gears that rotate the associated shoulder  67  or  69 . The transfer gear assemblies integral with actuators  94  comprise the gears that pivot the upper links  74 . The transfer gear assemblies integral with actuators  96  comprise the gears that pivot the driver link  76 . The transfer gear assemblies are essentially “zero backlash” gear assemblies. This means there is essentially no looseness between interlocking gears. This feature of the gear assemblies contributes to the precise positioning of shoulder  67  and  69  and arms  68  and  70 . 
     Associated with each arm  68  and  70  are three of the above mentioned rotary encoders  112 ,  114  and  116 . One of each shown in  FIG.  13 D . Each rotary encoder  112 ,  114  and  116  is a sensor that monitors the angular position of one of the three motor driven components of the arm  68  or  70  with which the encoder is associated. Rotary encoder  112  monitors the rotation of the arm shoulder  67  or  69 . Rotary encoder  114  monitors the rotation of the arm upper link  74 . Rotary encoder  116  monitors the rotation of the arm driver link  76 . 
     In the described version, each rotary encoder  112 ,  114  and  116  monitors the rotation of the shaft integral with the motor  101  internal to the associated actuators  92 ,  94  and  96 , respectively. (Motor shafts not illustrated). The rotation of each actuator motor shaft is directly proportional to the rotation of the shoulder or arm link driven by the motor. Each rotary encoder  112 ,  114  and  116  monitors both the extent to which the rotor of the associated motor shaft is rotated as well as the direction of rotation (clockwise or counterclockwise). 
     In other versions, each encoder  112 ,  114  and  116  monitors the extent of rotation and rotational direction of one of the gears of the transfer gear assembly that connects the motor shaft to the shoulder or arm link the motor displaces. There is a first order linear relationship between the degrees of rotation of this gear and the joint angle of the joint set by the associated motor. Alternatively, each encoder  112 ,  114  and  116  is a sensor that directly measures the joint angle of the joint with which the sensor is associated. 
     In some versions, encoders  112 ,  114  and  116  are absolute encoders. An absolute encoder, upon start up of the manipulator  50 , generates signals that immediately indicate the position of the component (motor rotor shaft or gear shaft) the encoder monitors. In other versions, the encoders are incremental encoders. Upon start up of the manipulator  50 , an incremental encoder is set to a zero state. Once set at the zero state, the incremental encoder provides data indicating the extent to which the component the encoder monitors is displaced. With this type of encoder, prior to the use of the manipulator, the arms  68  and  70  may be moved to a home or zero state position. Once the arms are so moved, the incremental counts maintained by the encoders are zeroed out. After the zeroing processing, the incremental counts output by the motor are used to provide an inferential indication of the position of the arms  68  and  70 . 
     In some versions, rotary encoders  112 ,  114  and  116  are multi-turn absolute encoders. This type of absolute encoder, after measuring a full rotation of 360°, outputs a signal indicating that the further present rotational angle is in addition to the first, or additional 360° of rotation. For example, when the encoder during the third rotation of the shaft being monitored measures a rotation of 10°, the encoder outputs a signal indicating that the shaft has undergone 730° of rotation. 
     Manipulator  50  includes two additional encoders, encoder  117  and  118 . Encoders  117  and  118  are associated with the driven link  80  integral with upper arm  70 . In  FIG.  13 D , encoders  117  and  118  are depicted internal to the upper arm driven link  80 . Encoders  117  and  118  generate signals representative of the angular position of wrist  84  relative to the upper arm driven link  80 . As discussed above, wrist  84  rotates in two degrees of freedom relative to the adjacent driven link. Each encoder  117  and  118  generates signals representative of the angular position of the wrist around one of the axes around which the wrist rotates. 
     The end effector  110  is rigidly attached to coupler  88 . In some versions, the end effector is removably attached to coupler  88 . While not shown or described in detail, it should be understood that the end effector  110  includes a coupling assembly  111 , identified in  FIG.  10   , which firmly and releasably holds the surgical instrument  160  to the coupler  88 . The coupling assembly  111  is designed to ensure that when the instrument is subjected to significant forces, these forces do not cause the slippage of the surgical instrument  160  relative to the end effector  110 . The end effector may be capable of movement in one or more degrees of freedom. Such end effectors may include the surgical instruments disclosed in U.S. patent application Ser. No. 13/600,888, entitled, “Surgical Instrument Including Housing, a Cutting Accessory that Extends from the Housing and Actuators that Establish the Position of the Cutting Accessory Relative to the Housing”, hereby incorporated by reference. 
     Also mounted to coupler  88  is a sensor  108 , seen symbolically in  FIG.  13 D . Sensor  108  is configured to output variable signals that are a function of the force and torque to which the end effector  110  is disposed. While the exact structure of sensor  108  is not described herein, it should be understood that the sensor is a six degrees of freedom sensor. Sensor  108  thus outputs signals representative of three mutually orthogonal forces and three torques about the axes of the forces that are applied to the instrument or energy applicator. 
     Also mounted to cart  52 , is a manipulator controller  124  and joint motor controllers  126 , which are depicted in block form in  FIG.  11   . Manipulator controller  124  can be a high speed general purpose digital computer. One such computer is the iHawk computer available from Concurrent Computer having a x8 SuperMicro motherboard. This computer has dual quad core processors. In some versions, the manipulator controller has less or more processing cores. In still other versions, the manipulator controller  124  has 16 or more processing cores. Manipulator controller  124 , typically also has multiple graphical processing units. In one embodiment, manipulator controller  124  determines the location to which the surgical instrument  160  should be moved based on data from force/torque sensor  108 , encoders  112 ,  114 ,  116 ,  117  and  118 , surgical navigation system  210 , as well as other information. Based on this determination, manipulator controller  124  determines the extent to which each arm-forming link needs to be moved in order to reposition the surgical instrument  160 . The data regarding where the links are to be positioned are forwarded to the joint motor controllers  126 . 
     Each joint motor controller  126  regulates the application of energization signals to a single one of the joint motors  101 . The primary function of the joint motor controller  126  is to apply energization signals to the associated motor  101  so that the motor drives the associated joint to an angle that approaches the below discussed commanded joint angle. The signal from the rotary encoder  114  is employed as a feedback signal representative of the actual joint angle to perform this type of motor regulation. Some controllers  126  calculate the energization signals using cascaded position, speed, and current control loops. Each control loop is often implemented using proportional-integral-derivative control. A signal representative of the feed forward torque is often added to the input of the current control loop to improve the responsiveness of the controller  126 . 
     Internal to the joint motor controller  126  is a drive circuit (not illustrated). A power signal from a power supply integral with the manipulator (power supply not illustrated) is applied to the drive circuit. This drive circuit, in response to the last control loop output signal, converts the power signal into an appropriate energization signal that is applied to the motor  101 . In many versions of manipulator  50  the energization signal is in the form of a three phase pulse width modulated (PWM) voltage signal. This signal often has a voltage amplitude of between 10 and 200 Volts and a PWM frequency between 20 and 200 kHz. The drive circuit supplies back to the current control loop the signal representative of the current drawn by the motor  101 . This signal is output to other software modules run on the manipulator controller  124  as the measured motor current signal. 
     When motor  101  is a permanent magnet synchronous motor, controller  124  also regulates the application of the energization signals so the driven currents are in correct phase with rotor position. This is known as motor commutation. Some controllers perform commutation control based on field oriented control techniques. To perform this regulation of the current signals, the joint motor controller  126  relies on the signals that indicate the position of the motor rotor. Signals from the rotary encoders  112 ,  114  and  116 , are used as a feedback signal. In one version, REL-230-36 Motor Controllers from Harmonic Drive LLC of Peabody, Mass. are employed as joint motor controllers  126 . 
     A touch screen display  128  or other user input/output unit is also mounted to cart  52 . Display  128  is attached to a user interface  130  also attached to the cart. One such user interface  130  is the C6320 Touch Screen from Beckhoff Automation of Verl, Germany. User interface  130  controls the presentation of information on the display  128  and initially processes user-generated commands entered over the display. The majority of these commands are applied to the manipulator controller  124 . 
     User interface  130  is the manipulator processor to which the signals output by pendant  190  are transmitted. 
     Cart  52  includes a tool controller  132 . Tool controller  132  supplies energization signals to the surgical instrument  160 . Tool controller  132  typically includes: a power supply; power control circuit; a user interface; an application specific data processing unit (components not illustrated). The power supply converts the line voltage into power signals that can be applied to the surgical instrument  160 . The power controller circuit selectively applies the power signals to the power generating unit integral with the instrument  160 . The user interface  130  allows the practitioner to enter instructions regarding how he/she wants the instrument to function. The tool controller  132  receives the instructions entered over the user interface and other data necessary to operate the instrument. Based on these data, the tool controller  132  outputs energization signals that cause the instrument to operate in the manner instructed by the practitioner. A more detailed discussion of a tool controller is contained in U.S. Pat. No. 7,422,582, CONTROL CONSOLE TO WHICH POWERED SURGICAL HANDPIECES ARE CONNECTED, THE CONSOLE CONFIGURED TO SIMULTANEOUSLY ENERGIZE MORE THAN ONE AND LESS THAN ALL OF THE HANDPIECES, the contents of which are incorporated herein by reference. 
     In some versions, the manipulator display  128  functions as the user interface and output display for the tool controller  132 . Commands to set and adjust the operational settings of the tool controller  132  and instrument  160  are forwarded from the user interface  130  to the tool controller  132 . 
     Surgical instrument  160 , seen in  FIGS.  8 - 10   , includes a shell  162  that is the outer body of the instrument. Internal to the shell  162  is a power generating unit  163 , represented by a dashed rectangle in  FIG.  9   . The power generating unit  163  converts the electrical power received from the tool controller  132  into an appropriate form of power. If for example, instrument  160  is a motorized surgical instrument, power generating unit  163  is the instrument motor. If the instrument vibrates, power generating unit  163  is the component that converts the electrical energy that causes the desired mechanical vibrations. If the instrument  160  outputs light (photonic) energy, the power generating unit is the unit that converts the electrical energy into light energy. 
     Six control buttons are mounted to instrument shell  160 . Two buttons, buttons  164  and  174  are mounted to the opposed sides of the shell  160 . Buttons  164  and  174  are normally open momentary contact switches that are connected in parallel. When the practitioner wants to actuate the instrument  160 , the practitioner depresses either one of the buttons  164  or  174 . The open/closed state of the circuit regulated by buttons  164  and  174  are monitored by the user interface  130 , connections not shown. Interface  130  forwards these state data to the manipulator controller  124 . Manipulator controller  124 , based in part on the state of these control members, sends commands to the tool controller  132 . Based on these commands, the tool controller  132  selectively applies energization signals to the power generating unit  163  internal to instrument  160 . The two buttons  164  and  174  are provided so the practitioner can actuate the instrument  160  by depressing a button located on either side of the instrument. 
     Buttons  166 ,  168  and  170  are located on the front face of the instrument shell  162 . Buttons  166 ,  168  and  170  are provided to facilitate operation of the surgical navigation system  210 . This particular operation of the surgical navigation system is not part of the present invention. 
     The sixth button, button  172  is mounted to the top of the instrument. Button  172  is a momentary contact push button switch. As discussed below, button  172  is depressed when the practitioner wants to change the orientation of the instrument when in the semi-autonomous mode. As will be apparent below, the changing of the orientation of the instrument means the repositioning of the instrument and energy applicator  184  so that the both devices pivot around the distal end tip of the energy applicator while the distal end tip of the energy applicator  184  continues to advance along the planned path while in the semi-autonomous mode. 
     A switch  176 , seen in  FIG.  8   , is pivotally mounted to instrument shell  162 . Switch  176  is mounted to the proximally directed side of the shell  162 . Switch  176  is a normally open momentary contact switch. Switch  176  is the control member the practitioner depresses when he/she wants to manually set the pose of the instrument. It should be understood that the “pose” of a component is the position and orientation of the component. The open/closed states of button  172  and switch  176  are monitored by manipulator controller  124  and user interface  130 , connections not shown. 
     Extending forward from instrument shell  162  is the energy applicator  184 . The energy applicator  184  is the component that applies the energy output by the instrument power generating unit  163  to the site at which the procedure is being performed on the patient. If the power generating unit  163  is a motor, the energy applicator  184  may be a drill, a saw blade or a bur. If the power generating unit is an ultrasonic vibrator, the energy applicator  184  is a tip. If the power generating unit outputs photonic energy, the energy applicator  184  is some sort of member that is transparent to the wavelength of light emitted by the power generator. Generally, the distal end of the energy applicator  184 , often referred to as the distal end tip, is the portion of the instrument energy applicator  184  that is applied to the tissue on which the procedure is to be performed. 
     Many instruments  160  include a coupling assembly, represented by ring  182  in  FIG.  9   . The coupling assembly releasably holds the energy applicator  184  to the shell  162  and releasably connects the energy applicator  184  to the power generating unit  163 . 
     One motorized surgical instrument that may function as instrument  10  as well as a complementary energy applicator  184  are disclosed in U.S. Pat. No. 6,562,055, CUTTING ATTACHMENT FOR SURGICAL HANDPIECE DESIGNED TO BE SELECTIVELY COUPLED TO THE HANDPIECE, the contents of which are explicitly incorporated herein by reference. 
     For the manipulator  50  to emulate the positioning of the instrument by the practitioner, it should be appreciated that the instrument and energy applicator  184  are modeled as a virtual rigid body. This virtual rigid body is considered to have a virtual mass. The virtual mass of the virtual rigid body is typically within the same order of magnitude as the actual mass of the instrument  160  and energy applicator  184 . Owing to mechanical and electrical limitations, often the virtual mass is greater than the actual mass. By extension, it is understood that the virtual rigid body has its own center of mass. In  FIG.  8    this is represented by point  165  which is a point internal to the handpiece shell  162 . This is a point that would be perceived as the center of mass of the actual instrument. Often, but not always, this point is on or within the instrument. Here “center of mass” is understood to be the point around which the instrument and energy applicator  184  would rotate if a force is applied to another point of the instrument. The center of mass of the virtual rigid body is close to, but is often not the same as, the actual center of mass of the instrument  160  with the energy applicator  184  attached. 
     The center of mass of the virtual rigid body can be determined empirically. Once the instrument and energy applicator  184  are attached to the manipulator, the position of the center of mass can be reset to accommodate the preferences of the individual practitioners. 
     Pendant  190 , now described by reference to  FIGS.  2 A and  2 B , is also used to regulate operation of the manipulator  50 . Pendant  190  as seen in  FIG.  2 A , includes a shell  191  shaped to be held in one hand. Three normally open control members are mounted to shell. These control members are used to regulate semi-autonomous operation of the manipulator  50 . One control member, trigger  194  is located on the underside of the shell. Trigger  194  is depressed to place the manipulator in the mode in which the manipulator performs semi-autonomous advancement of the instrument  160 . The two additional control members, buttons  193  and  195 , are located on the top surface of the shell  191 . Buttons  193  and  195  regulate the rate at which the manipulator  50 , when in the semi-autonomous mode, advances the instrument. One of the buttons, button  193 , is depressed to slow the rate of semi-autonomous instrument advancement. Button  195  is depressed to advance the rate of semi-autonomous advancement. The speed at which the instrument engages in semi-autonomous advancement is referred to as the feed rate of the instrument. Ergonomically, pendant  190  is designed so that the practitioner can, with the thumb and fingers of one hand depress trigger  194  and, at the same time, depress either button  193  or button  195 . 
     Pendant  190  includes additional control members (not identified). These members allow the practitioner to enter commands and data into the surgical navigation system  210 . A cable  197  connects pendant  190  to cart  52 . 
     The surgical navigation system  210  used with manipulator  50  of this invention is now described by reference to  FIGS.  1 ,  11  and  13 D . Surgical navigation system  210  includes one tracker, tracker  212 , that is firmly affixed to the patient  600 . Often tracker  212  is firmly affixed to a section of bone adjacent where the tissue to which the instrument energy applicator  184  is to be applied. 
     A second tracker, tracker  214 , seen in  FIG.  1   , is firmly attached to the end effector  110 . Since the instrument positioned by the manipulator  50  is firmly attached to the end effector, tracker  214  is sometimes referred to as the tool tracker. 
     A localizer  216  receives signals from or transmits signals to the trackers  212  and  214 . If the localizer  216  receives light signals from the trackers  212  and  214 , the localizer may be called a camera. The surgical navigation system also includes a navigation processor  218 . If the localizer  216  receives signals from the trackers  212  and  214 , the localizer outputs to the processor  218  signals based on the position and orientation of the trackers to the localizer (localizer to processor  218  connection not shown). If the trackers  212  and  214  receive signals from the localizer  216 , the trackers output to the processor  218  signals based on the position and orientation of the trackers to the localizer. Based on the received signals, navigation processor  218  generates data indicating the relative positions and orientations of the trackers  212  and  214  to the localizer  216 . In some versions, the surgical navigation system  210  could include the trackers, sensor system, localizer, and/or computer system disclosed in U.S. Pat. No. 7,725,162 to Malackowski et al., issued on May 25, 2010, entitled, “Surgery System”, hereby incorporated by reference. 
     As discussed below, prior to the start of the procedure, additional data are loaded into the navigation processor  218 . Based on the position and orientation of the trackers  212  and  214  and the previously loaded data, navigation processor  218  determines the position of the distal end of instrument energy applicator  184  and the orientation of the instrument relative to the tissue against which the energy applicator  184  is to be applied. Navigation processor  218  forwards these data to the manipulator controller  124 . 
     The navigation processor  218  also generates image signals that indicate the relative position of the instrument energy applicator  184  to the surgical site. These image signals are applied to an interface  220 , also part of the surgical navigation system  210 . Interface  220 , based on these signals, generates images that allow the practitioner to view the relative position of the instrument energy applicator  184  to the surgical site. Interface  220  includes a touch screen or other input/output device that allows entry of commands. 
     Manipulator controller  124  and navigation processor  218  cooperate to position the end effector  110  so that the energy applicator  184  is appropriately positioned at the site at which the procedure is to be performed on the patient  600 . As part of this positioning, manipulator controller  124  does not position the energy applicator  184  outside of defined boundaries. To perform this process, controller  124  and processor  218  collectively keep track of the poses of a number of different system components and the patient  600 . Each component pose can be considered tracked relative to a world coordinate system. The world coordinate system has an origin and an orientation (i.e., a set of X- Y- and Z-axes) that, for the procedure being performed, are both static. The coordinate system of the manipulator  50  is the world coordinate system, MNPL, as seen in  FIG.  12   . In one version, the origin of manipulator coordinate system MNPL is a point along the axis through the shoulder  69  associated with upper arm  70 . This point is the intersection of the axis around which the shoulder  69  rotates and the axes around which the arm links  74  and  76  rotate. In  FIG.  12   , to distinguish between the structure of the manipulator upper arm  70  and the manipulator coordinate system MNPL, the coordinate system is shown in dashed lines. 
     A second static coordinate system that is associated with this invention is the coordinate system of the localizer  216 , LCLZ. 
     Each tracked component has its own coordinate system separate from coordinate system MNPL and coordinate system LCLZ. Each of these coordinate systems has an origin that can be identified as a point relative to the origin of the manipulator coordinate system MNPL. A vector defines the position of the origin of each of these coordinate systems relative to another one of the other coordinate systems. The location of a coordinate system is thus understood to be the location of the origin of the coordinate system. Each of these coordinate systems also has an orientation that, more often than not, is different from the orientation of manipulator coordinate system MNPL. The orientation of a coordinate system can be considered the angular positions of the X-, Y- and Z-axes of the coordinate system relative to the corresponding axes of the manipulator coordinate system MNPL. A rotation matrix describes the orientation of a coordinate system relative to another coordinate system. The rotation matrix consists of the unit vectors of the axis of one coordinate system expressed in the other coordinate system. The position vector and the rotation matrix that define the relation of one coordinate system to another collectively form the homogenous transformation matrix. The symbol  i   i-1 T is the notation for the homogenous transformation matrix that identifies the position and orientation of coordinate system i with respect to coordinate system i−1. 
     Two components of the system that have their own coordinate systems are the bone tracker  212  and the tool tracker  214 . In  FIG.  12    these coordinate systems are represented as, respectively, bone tracker coordinate system BTRK and tool tracker coordinate system TLTR. 
     Navigation system  210  monitors the position of the patient  600  by monitoring the position of bone tracker  212 , the tracker firmly attached to bone of the patient  600 . The patient&#39;s coordinate system is considered to be the bone coordinate system BONE, the coordinate system of the bone to which the bone tracker  212  is firmly attached. Prior to the start of the procedure, pre-operative images of the location of the site on the patient at which the procedures are performed are generated. These images may be based on MRI scans, radiological scans or computed tomography (CT) scans of the surgical site. These images are mapped to the bone coordinate system BONE using methods not material to the present invention. These images are fixed in the bone coordinate system BONE. 
     During the initial phase of the procedure, the bone tracker  212  is firmly affixed to the bone of the patient. Using process steps not part of the present invention, the pose of coordinate system BONE is mapped to coordinate system BTRK. Given the fixed relationship between the bone and the bone tracker  212 , the pose of coordinate system BONE remains fixed relative to coordinate system BTRK throughout the procedure. The pose-describing data are stored in memory integral with both manipulator controller  124  and navigation processor  218 . 
     In addition to coordinate system MNPL, there are additional coordinate systems associated with the manipulator  50 . The end effector  110  has its own coordinate system, coordinate system EFCT. There is also a coordinate system associated with the virtual model of the instrument  160 . This coordinate system has its origin at the center of mass of the virtual rigid body. Given the origin of this coordinate system, this coordinate system is referred to as coordinate system CMVB. The Z-axis of instrument coordinate system CMVB is centered on the longitudinal axis that extends through the instrument  160  and the energy applicator  184 . The energy applicator  184  has its own coordinate system, system EAPP. The origin of the coordinate system EAPP is the distal end tip of the energy applicator  184 . The Z-axis of the energy applicator  184  coordinate system EAPP is aligned with the longitudinal axis of the energy applicator  184 . This Z-axis extends outwardly away from the distal end tip of the energy applicator  184 . This is why in  FIG.  12    the Z-axis of coordinate system EAPP is shown with an orientation that is generally in the negative direction of the Z-axes of the other coordinate systems. An additional coordinate system associated with manipulator  50  is the previously described coordinate system of the tool tracker  214 , system TLTR. 
     Not depicted in  FIG.  12    are representations of some of the minor coordinate systems. As discussed below, these coordinate systems are only referenced occasionally during the operation of the manipulator. These coordinate systems are not illustrated in  FIG.  12    to reduce the complexity of this Figure. 
     It should be appreciated that, upon assembly of the components of this invention for use, the poses of coordinate system EFCT, the virtual rigid body coordinate system CMVB, the energy applicator coordinate system EAPP and the tool tracker coordinate system TLTR are fixed relative to each other. Accordingly, upon assembly of the components, the poses of these coordinate systems relative to each other are determined. These coordinate system and pose data are stored in a memory integral with the end effector  110 , coupling assembly  111 , instrument  160  or energy applicator  184 . There may be some versions where these data are stored in the memory integral to the manipulator controller  124 . 
     III. Software 
       FIG.  13 A through  13 E  depict basic software modules executed by the manipulator controller  124  and navigation processor  218 .  FIGS.  13 A through  13 E  also represent how the software modules interact with hardware to actuate the manipulator so surgical instrument  160  is displaced. 
       FIG.  13 A  depicts some software modules run on the navigation processor  218 . One of these modules is the boundary generator (BDNRY GNRTR)  232 . Boundary generator  232  is a software module that generates a map that defines one or more boundaries between the tissue to which the instrument energy applicator  184  should be applied and the tissue to which the energy applicator  184  should not be applied. This boundary is typically generated when energy applicator  184  is used to remove a volume of tissue. These types of energy applicators include, but are not limited to: burs; drill bits; saw blades; ultrasonic vibrating tips; electrode tips; RF electrodes; cauterizing and ablation tips; and light emitting tips. 
     An input into the boundary generator  232  includes the preoperative images (PRE-OP IMGS) of the site on which the procedure is to be performed. If the manipulator is used to selectively remove tissue so the patient can be fitted with an implant, a second input into the boundary generator  232  is a map of the shape of the implant. The initial version of this map may come from an implant database (IMPNT DB). This is because the shape of the implant defines the boundaries of the tissue that should be removed to receive the implant. This relationship is especially true if the implant is an orthopedic implant intended to be fitted to the bone of the patient. 
     A third input into boundary generator  232  is the surgeon&#39;s settings (SRGN STNGS). These settings include the practitioner&#39;s settings indicating to which tissue the energy applicator  184  should be applied. If the energy applicator  184  is used to remove tissue, the settings identify the boundaries between the tissue to be removed and the tissue that remains after application of the energy applicator  184 . If the manipulator  50  is used to assist in the fitting of a orthopedic implant, these settings define where over the tissue the implant should be positioned. These settings may be entered preoperatively using a data processing unit. Alternatively, these settings may be entered through an input/output unit associated with one of the components of the system such as with navigation interface  220 . 
     Based on the above input data and instructions, boundary generator  232  generates a map that defines the instrument energy applicator  184  boundaries. 
     In practice, prior to the start of the procedure an initial version of the map may be set by the practitioner at the surgical site. At the start of the procedure, data that more precisely defines the implant that is to be actually fitted to the patient is loaded into the boundary generator  232 . These data may come from a storage device associated with the implant such as a memory stick or an RFID tag. For ease of understanding the invention, these data can be considered a component of the implant database data supplied to the boundary generator  232 . These data are based on post manufacture measurements of the specific implant. These data provide a definition of the shape of the specific implant that, due to manufacturing variations, may be slightly different than the previously available stock definition of implant shape. Based on this implant-specific data, the boundary generator  232  generates a final definition of the cutting guide, the boundaries between the tissue to be removed and the tissue that should remain in place. Implants that could be implanted into the patient include those shown in U.S. patent application Ser. No. 13/530,927, filed on Jun. 22, 2012 and entitled, “Prosthetic Implant and Method of Implantation”, hereby incorporated by reference. The implants disclosed in this patent application could thus be used to define the cutting guide and thereafter be implanted in the patient after the appropriate amount of material, such as bone, is removed. Other implants are also contemplated. 
     In one version, the boundary generator  232  generates the boundary between the tissue that is to be excised and the tissue that is to remain in place as a set of contiguous defined surface areas. In one more specific version, these surface areas are polygons. More particularly, these surface areas are triangles. The corners of each polygon are defined by points in the bone coordinate system BONE. In  FIG.  15 A , surface  242  is the boundary between where tissue is to be removed and the tissue that is to remain in place. Sometimes the boundary is referred to as a mesh. An individual area section that defines a portion of the boundary or mesh is referred to as a tile. 
     A tool path generator (TOOL PATH GNRTR)  234  is a second software module run on the navigation processor  218 . Tool path generator  234  receives the same general inputs as those applied to the boundary generator  232 . Based on these inputs, the tool path generator  234  generates a tool path  248  as seen in  FIGS.  15 A and  15 B .  FIG.  15 A  represents a bone  202 , a section of which is to be removed to receive an implant. Surface  242  is a boundary beyond which the energy applicator  184  should not be applied. Surface  242  is therefore also the outline of the bone  202  remaining after the removal procedure, the bone to which the implant is to be mounted. Dashed line  244  represents the perimeter of the bone that is to be removed using manipulator  50 . In  FIG.  15 A  the tool path is represented by the back and forth line  248 . The smoothness and quality of the finished surface depends in part of the relative positioning of the back and forth line  248 . More specifically, the closer together each back and forth pass of the line, the more precise and smooth is the finished surface. 
     In addition, the configuration of the tool path  248  also contributes to the quality of the finished surface. For example, in one path configuration, the circumference of the surface boundary is cut first with the tool path migrating inward toward the center. In this configuration, there is no allowance for the outflow of the removed material. In another configuration, the tool path starts at the center of the section of bone to be removed and proceeds in an outward direction. In this way, the removed material has outflow path and does not interfere with the removal process. 
     In  FIG.  15 A  the tool path  248  is shown as only being within the perimeter of the tissue being removed. The location of the tool path  248  is a function of the geometry of the distal end of the energy applicator  184 . For example, the center of the distal end of the energy applicator  184  may be the origin of coordinate system EAPP. In this implementation, when the tool path is generated, the tool path generator  232  accounts for the fact that the energy applicator  184  actually extends beyond the origin of coordinate system EAPP. If the energy applicator  184  is a spherical bur, this means that the tool path segments closest to boundary  242  are typically spaced away from boundary a distance at least equal to the radius of the bur head. 
     Tool path  248  is not plotted in a single plane. In  FIG.  15 B  tool path  248  is shown as comprising a number of layers wherein top most segments are shown as set of solid connected lines and dashed lines represent segments located below the top segments. 
     As seen in  FIG.  15 C , the tool path  248  includes a number of path segments. Each segment includes the set of points along which the origin of coordinate system EAPP should travel. As seen in the Figure, individual segments  256 ,  262  and  266  may be straight or curved. Each segment  256 ,  262  and  266  has an origin and a terminus. Point  258 , is both the origin of tool path  248  and the origin of segment  256 . The terminus of one segment will be the origin of the abutting segment. Thus, point  260  is both the terminus of segment  256  and the origin of segment  262 . Point  264 , is the terminus of segment  262  and the origin of segment  266 . Point  268  is the terminus of segment  266 . Point  268  may also be the terminus of tool path  248  and the origin of another tool path that is not illustrated. In  FIG.  15 C , segment  266  is depicted as a sequence of dashed lines, from origin to terminus, of decreasing size. This is to diagrammatically depict that the path in addition to having X and Y components, has a Z component that is into or out of the page on which  FIG.  15 C  is depicted. 
     Tool path generator  234  receives as inputs the image of the tissue, data defining the shape of the boundary, and the surgeon&#39;s setting regarding the location of the boundary. For an orthopedic surgical procedure, the boundary is typically the shape of the implant; the surgeon setting is often the position of the implant. Based on these data, the tool path generator  234  defines the tool path  248 . Each tool path segment  256 ,  262  and  266  is defined as a vector or a curve that extends between points present in bone coordinate system BONE. It should be understood that the path segments are defined in three dimensions. This is because the instrument energy applicator  184  is not just applied in a single plane to the tissue. The energy applicator  184  also moves up or down in order to contact tissue in the plane above or below the plane in which it is presently located. 
     Once a procedure begins, the tool path generator  234  receives additional data. These data are the data from the below described removed material logger  275  that identifies the sections of the tissue to which the energy applicator  184  has been applied. Based on these data, the tool path generator  234  revises the path segments of the tool path. These revisions are performed to avoid the generation of path segments that would have the energy applicator  184  transit through spaces left void as a consequence of the previous removal of tissue. Adaptation or revision of the cutting path may include a high velocity jump wherein the energy applicator  184  jumps across a known gap in the volume of removed tissue (also referred to as a sub-volume) at a high velocity. Revision of the cutting path may also include a circuitous path that routes around areas where bone has been previously removed. Further, adaptation of the cutting path may also include sub-volume areas that are labeled as complete and would not be part of any autonomous cutting path if that mode was used to complete any part of the remaining bone removal. 
     A localization engine  270  is a third software module that can be considered part of the surgical navigation system  210 . In some versions, the localization engine  270  is run on the manipulator controller  124 . Components of the localization engine  270  may also run on navigation processor  218 . Localization engine  270  receives as inputs the signals localizer  216  outputs as a function of the signals received from trackers  212  and  214 . Based on these signals received from the bone tracker  212 , localization engine  270  determines the pose of the bone coordinate system BONE relative to the localizer coordinate system LCLZ. Based on the signals received from the tool tracker  214 , the localization engine  270  determines the pose of the tool tracker coordinate system TLTR relative to the localizer coordinate system LCLZ. 
     The localization engine  270  forwards the signals representative of the poses of trackers  212  and  214  to a coordinate transformer  272 . Coordinate transformer  272  is a navigation system software module that runs on navigation processor  218 . Coordinate transformer  272  is a software module that references the data that defines the relationship between the preoperative images of the patient and the patient tracker  212 . Coordinate transformer  272  also stores the data indicating the pose of the instrument energy applicator  184  relative to the tool tracker  214 . 
     Navigation processor  218  includes the removed material logger  275 . The removed material logger  275  contains a map of the volume of the tissue to which the energy applicator  184  is to be applied. Often this is a map of a volume of tissue that is to be removed. In  FIG.  13 A , this map is shown being based on the preoperative images of the patient. Other data that goes into maintaining this map may come from the data describing the shape of the implant and the personal setting of the surgeon, connections not shown. Other sources of data for defining this volume including mapping data obtained at the start of the procedure. These data may be obtained by applying a pointer to landmarks on the tissue to which the energy applicator  184  is to be applied. 
     Logger  275  also collects data identifying the on-patient locations to which the energy applicator  184  is applied. In one implementation of this invention, these data are the data that describes the locations to which the end effector and, by extension, the energy applicator  184 , have advanced. These data may be based on the below described data from the manipulator that tracks the movement of the arms  68  and  70 . These data may be based on the commanded or measured pose data. Alternatively, these data may be generated based on the data describing the movement of the tool tracker. Logger  275  transforms these data regarding movement of the end effector and the tool tracker into data that defines where, relative to the bone  202 , the energy applicator  184  has moved. Logger  275  stores these data. 
     Based on these data, the logger  275  generates image data suitable for presentation on one of the displays that indicates the extent to which the energy applicator  184  has been applied to the tissue. These image data may be presented on navigation interface  220 . The images present by the logger may indicate surface sections of tissue to which the energy applicator  184  has not been applied and sections of tissue to which the energy applicator  184  has been applied. The images presented by the logger also identify the sections of tissue to which it is not necessary to apply the energy applicator  184 ; the tissue outside of the boundary area. This tissue includes tissue beyond the boundaries exposed by the removal of tissue. 
     Logger  275  provides data indicating the sections of the tissue to which the energy applicator  184  has and has not been applied to the tool path generator  234 . 
     As mentioned above, the pose of coordinate system EAPP is typically fixed relative to coordinate system TLTR. The location of patient&#39;s tissue and the representation of the tissue are typically fixed relative to the bone tracker coordinate system BTRK. 
     During the procedure, the coordinate transformer  272  receives the data indicating the relative poses of the trackers  212  and  214  to the localizer  216 . Based on these data and the previous loaded data, the coordinate transformer  272  generates data indicating the relative position and orientation of both the origin of coordinate system EAPP, and the bone tracker coordinate system, BTRK to the manipulator coordinate system MNPL. Based on these data, coordinate transformer  272  generates data indicating the position and orientation of the distal end of the energy applicator  184  relative to the tissue against which the instrument is applied. Image signals representative of these data are forwarded to interface  220  enabling the surgeon to view this information. 
     Two additional sets of software modules are run on the manipulator controller  124 . One set of software modules perform behavior control. Behavior control is the process of generating instructions that indicate the next commanded pose for the energy applicator  184 . 
     The second set of software modules perform what is known as motion control. One aspect of motion control is the control of the manipulator  50 . In the below discussed motion control process, the motion control process receives data defining the next commanded pose of the energy applicator  184  from the behavior control process. Based on these data, the motion control process determines the next position of the joint angles of manipulator  50 . A second aspect of motion control is the providing feedback to the behavior control modules based on the constraints of the manipulator. These constraints include the joint angle limits of the manipulator and the goal of insuring that plural links do not move closer than a minimum distance towards each other. A further component of this feedback control is the ensuring that the energy applicator  184  is kept within a defined workspace boundary. Movement of energy applicator  184  is limited to the area within this workspace boundary to ensure that the dexterity of the instrument  160  is not diminished. The motion control modules also monitor the state of the manipulator  50  to detect if external forces/torques are being applied to or objects are in contact with the manipulator  50  or instrument  160 . 
     Feedback data generated by the motion control processes are applied to the behavior control processes. Based on these data, the behavior control processes adjusts the manipulator&#39;s movement of the instrument and energy applicator  184 . The behavior control processors perform this adjustment by using these data as variables for establishing the next commanded pose for the energy applicator  184 . Once this next commanded pose is established, the motion control processes cause the manipulator  50  to advance the energy applicator  184  towards this position. 
       FIG.  13 B  depicts the software modules that form the behavior control processes. One of these modules is the tool path force calculator (TOOL PATH FRC CLCLTR)  278 . Tool path force calculator  278  calculates two variables. A first one of these variables are the forces and torques that when applied to the virtual rigid body, results in the advancement of the distal end of the energy applicator  184 . The second one of these variables are forces and torques applied to the virtual rigid body to maintain the orientation of the instrument  160  within an acceptable range of orientations. Tool path force calculator  278  includes a number of sub modules. 
     One of the modules that form the tool path force calculator  278  is the feed rate calculator  284 , as seen in  FIG.  16 A . Feed rate calculator  284  determines the velocity, referred to as the instrument feed rate, at which the distal end of the energy applicator  184  should move as it travels along an individual path segment. The primary input into the feed rate calculator  284  is the defined feed rate (DEFINED F.R.) In its most fundamental form, the defined feed rate is a scalar value. In practice, the manipulator controller  124  is often provided with plural defined feed rates. A specific defined feed rate is assigned to each path segment. This feed rate assignment may be performed preoperatively. The feed rates can then be adjusted at the start of or during the procedure. Two or more contiguous path segments may be assigned the same defined feed rate. These feed rates are generated based on variables such as: the shape of the void space; the type of energy applicator  184 ; the health of the patient; the nature of the tissue to which the energy applicator  184  is applied; and the geometry of the path segment. In practice, the defined feed rate is typically between 5 and 400 mm/sec. 
     In practice, the defined feed rate is generated by the tool path generator  234 , connection not shown. 
     Feed rate calculator  284  adjusts the defined feed rate to produce the instrument feed rate. In one version, this adjustment is performed by multiplying the defined feed rate by a number of coefficients. Each coefficient is generally between 0 and 1.0. Coefficients may have values that exceed 1.0. Each of these coefficients changes as a function of a variable that is also applied to the feed rate calculator  284 . The first of these variables is the user adjustment (USER ADJUST) of the feed rate. This is the adjustment of the feed rate that the practitioner performs, in real time, as the procedure progresses. The practitioner makes this adjustment of the feed rate by depressing pendant buttons  193  and  195 . The feed rate calculator  284  outputs a coefficient as a function of the practitioner entered command to increase or decrease the instrument feed rate. 
     A second variable used to selectively scale the defined feed rate is force and torque to which the energy applicator  184  is exposed (SNSD F/T). The energy applicator  184  is rigidly attached to the instrument  160  and the instrument is rigidly attached to the end effector  110 . Accordingly, the signals output by the end effector force/torque sensor  108  are the signals representative of the forces and torques to which energy applicator  184  is exposed. Feed rate calculator  284  sets the instrument rate based on the principle that there is relationship between the amount of force/torque that the manipulator applies to the instrument and energy applicator  184  and the rate of instrument advancement. Generally, it is a goal of modern medical practice to minimize the heating of tissue that is not being removed. One reason for this goal is to minimize the attendant damage this needless heating can cause to the tissue. Accordingly, manipulator  50  of this invention is configured to, when it is determined that an appreciable amount of force and/or torque is applied to the instrument or energy applicator  184 , slow the advancement of the instrument along the path segment. 
     One example of where this adjustment of instrument feed rate is useful is when the energy applicator  184  travels across a path segment through both cortical bone and cancellous bone. Cortical bone, the outer bone, is relatively hard. Cancellous bone, the inner bone, is more porous and less resistant to removal than cortical bone. Accordingly, if the energy applicator  184  moves across both types of bone at a constant speed, more force/torque is needed to be applied to move the applicator across the cortical bone than the cancellous bone. This means that, without adjustment of instrument speed, the cortical bone would be subject to more potentially damage inducing heating than the adjacent section of cancellous bone. This feature of the manipulator of this invention minimizes this potential for the unwanted heating by slowing the rate of advancement for the instrument energy applicator  184  when the force/torque sensor  108  provides signals indicating that the amount of force/torque required to advance the instrument increases. 
     Once the energy applicator  184  moves from cutting the cortical bone to cancellous bone, the force/torque required to advance the instrument decreases. In this situation, the rate at which the instrument is advanced can be speeded up without appreciably increasing the extent to which the bone to which the energy applicator  184  is applied is heated. The feed rate calculator  284  therefore increases the calculated rate of the advancement of the instrument. This reduces the amount of time it takes to perform the procedure on the patient. This is desirable because it is a further goal of modem surgical practice to minimize the time it takes to perform the procedure on the patient. One reason this time minimization is desired is because it lessens the amount of time the patient&#39;s internal tissue is exposed and open to infection. Also, performing the procedure as quickly as possible lessens both the likelihood of surgeon fatigue and the amount of time the patient must be held under anesthesia. 
     Feed rate calculator  284  determines a force/torque adjustment coefficient as based on one, two or three of: (1) the magnitude of a six component vector comprised of the individual force and torque components; (2) the magnitude of a three component vector comprised of the individual force components; and (3) the magnitude of a vector comprised of any combination of individual force and/or torque components. Alternatively, the coefficient is based on one or more of the largest force or torque components. Based on one or more of these variables, feed rate calculator  284 , by reference to data in an associated look-up table  286 , determines a force/torque adjustment coefficient. 
     In addition to adjusting the instrument feed rate, the speed of the energy applicator  184  may also be varied. More specifically, where the energy applicator  184  is a bur, the speed of the cutting teeth of the bur may be adjusted and optimized to improve the accuracy of the tissue removal and to minimize heat generation at the tissue. The optimal speed of the bur cutting teeth is a factor of cutter rotational speed and cutter diameter, which are optimized based on the tooth geometry and the type of material being removed. 
     A third variable upon which the instrument feed rate is adjusted is the curvature of the path segment (PATH CRVTR). This adjustment is performed to ensure that when the instrument is displaced along a curved path of travel, the instrument is not displaced at such a high rate of speed that the momentum causes the energy applicator  184  to move away from the path of travel. Generally, when the path of travel is linear or has a relatively small curvature, the defined feed rate is not adjusted based on the curvature. When the feed rate calculator  284  receives an indication that the instrument energy applicator  184  is traveling along a path segment with a relatively large curvature, or a small radius, the calculator downwardly adjusts the defined feed rate, based on this variable in order to produce the instrument feed rate. 
     The feed rate calculator  284  receives an indication of the curvature, the PATH CRVTR variable, of the path along which the energy applicator  184  is traveling from a curvature calculator  291  ( FIG.  16 B ). As discussed below, the curvature calculator  291  is another sub-module component of the tool path force calculator  278 . Based on this input variable, the feed rate calculator  284  refers to one of the look up tables  286  to determine a coefficient that reflects the extent to which the defined feed rate should be adjusted. Generally, when the path of travel is linear or has a curvature approaching zero, the defined feed rate is not adjusted based on the curvature. The coefficient is at or near 1.0. When the feed rate calculator  284  receives an indication that the instrument energy applicator  184  is traveling along a path segment with a relatively large curvature, the calculator downwardly adjusts the defined feed rate, based on this variable in order to produce the instrument feed rate. The retrieved coefficient decreases from unity. In some versions, if the curvature is 0.05 mm −1  or lower, feed rate calculator  284  does not attenuate the instrument feed rate based on the curvature of the segment along which the energy applicator  184  is advancing. 
     A fourth variable upon which the defined feed rate is adjusted to produce the instrument feed rate is instrument power (INST POWER). This variable is the amount of power the instrument applies through the energy applicator  184  to the patient. Instrument power is employed as an input variable for adjusting instrument feed rate because generally as the power the instrument applies to the tissue increases, the extent to which the tissue is heated by this power is increased. As discussed above, it is desirable to minimize the extent to which the tissue is subjected to the potentially damaging heating. There may also be situations in which, the large outputting of power by the instrument indicates that manipulator is entering a state in which, if instrument feed rate is not reduced, the performance of the energy applicator  184  will drop. For example, if a large amount of power needs to be applied to the bur, this increase in power may indicate that the bur may be entering a state in which it is having difficulty removing the material it should remove. To ensure that the bur performs as expected, it is then desirable to reduce the rate of advancement of the bur. This can help improve the accuracy with which material is removed. Improving the accuracy of tissue removal enhances the surface finish and definition of the tissue that remains after application of the bur. 
     Accordingly, when there is an indication that the power applied by the instrument  160  increases, feed rate calculator  284  outputs a reduced instrument feed rate. 
     In constructions in which the instrument  160  is a motorized tool, the power variable can be the amount of torque output by the tool motor. 
     Generally, there is a directly proportional relationship between the current applied to the tool and the torque output by the tool. Accordingly, a measure of the current drawn by the tool is employed as the instrument power variable. The instrument power signal representative of this variable is generated by the tool controller  132  and applied to the manipulator controller  124 . More particularly, a circuit internal to the instrument controller  132  that monitors the current drawn by the instrument outputs a signal representative of the current drawn by the instrument. This signal is the root signal upon which either an analog or digital INST POWER signal applied to feed rate calculator  284  is generated. 
     The feed rate calculator  284 , based on the INST POWER signal and by reference to one of the look up tables  286 , determines a coefficient that indicates the extent to which the defined feed rate should be scaled based on the instrument power to determine the instrument feed rate. 
     A fifth variable that is used as a factor for adjusting the defined feed rate to produce the instrument feed rate is tissue temperature (TISSUE TEMP.) This is due to the above mentioned goal of modern surgical practice to minimize the extent that the patient&#39;s uncut tissue is heated. Temperature sensor  97  provides an indication of the tissue temperature (TISSUE TEMP). In the Figures temperature sensor  97  is shown only symbolically in  FIG.  16 A . Typically, the sensor  97  is mounted to the instrument  160 . Again, the signal output by sensor  97  may be representative of the temperature of the tissue or the temperature of the energy applicator  184 . Often the signal output by the temperature sensor  97  is routed through tool controller  132  to manipulator controller  124 . In addition to the temperature of the uncut tissue, another factor for adjusting the defined feed rate may include the temperature of the chips removed by the energy applicator  184 . The chips from and material removed are often referred to as “slurry.” The temperature of the slurry may be measured in any suitable manner including temperature sensor  97 . 
     Feed rate calculator  284 , based on the temperature represented by the TISSUE TEMP signal and by reference to one of the look-up tables  286 , determines the appropriate tissue temperature feed rate adjustment coefficient. If the TISSUE TEMP signal indicates that the tissue temperature is within an acceptable range, this coefficient may be at or near 1.0. Alternatively, if the TISSUE TEMP signal indicates that the tissue or energy applicator  184  temperature is approaching or above a level at which there may be appreciable damage to the tissue, the retrieved coefficient may decrease from unity. 
     A sixth variable employed by the feed rate calculator  284  to generate the instrument feed rate is the computed force (CMPTD FORCE). As discussed below, this computed force is the force that is applied to the virtual rigid body. In response to this force, the motion control processes advance energy applicator  184  along the tool path. The computed force is computed by another one of the behavior control process software modules. This computed force, (which can include torque components), serves as an input variable from which a commanded position for the end effector is determined. 
     Feed rate calculator  284  generates the instrument feed rate so there is an inverse relationship between the computed force and the instrument feed rate. In the event the computed force is increased to effect the desired advancement of the energy applicator  184 , feed rate calculator  284  reduces the instrument feed rate. This reduction of instrument feed rate reduces the likelihood that the manipulator will advance the energy applicator  184  at a speed above which the accuracy of the application of the energy applicator  184  to the tissue will be adversely affected. 
     In some versions of this invention, the feed rate calculator, based on the magnitude of the computed force and reference to one of the look up tables  286 , determines a coefficient. This coefficient represents the extent to which the defined feed rate should be scaled as a function of the magnitude of the computed force. 
     Feed rate calculator  284  multiplies the defined feed rate by the above six coefficients. The product of this process is the instrument feed rate. This is the rate at which the energy applicator  184  should be advanced along the current path segment. 
     An additional input into feed rate calculator  284  is a signal asserted from a below discussed force overrider  375 , also a component of the tool path force calculator  278 . In response to the assertion of a signal from the force overrider  375 , feed rate calculator  284  outputs a zero speed instrument feed rate. Often feed rate calculator  284  ramps the instrument to the zero speed feed rate. Once the force overrider  375  stops asserting the signal to the feed rate calculator  284 , based on the input of other commands from the practitioner, the feed rate calculator  284  returns to outputting a non zero speed instrument feed rate. 
     A path interpolator (PATH INTRPLTR)  288 , seen in  FIG.  16 B , is another sub-module component of the tool path force calculator  278 . Path interpolator  288  determines target positions for coordinate system EAPP. The pose of distal end of the instrument energy applicator  184  is understood to be fixed relative to coordinate system EAPP. These target positions are points along which the distal end of energy applicator  184  should travel to perform the desired task. Inputs into the path interpolator include: the data defining the origin and terminus of a path segment; the data indicating if the segment is straight or curved and, if curved, the characteristics of the curve. Another input into the path interpolator  288  is the instrument feed rate from feed rate calculator  284 . This is the rate at which the instrument should travel along the path segment as determined by the feed rate calculator  284 . 
     Based on the above input variables, the path interpolator  288  determines the target position of the distal end of the energy applicator  184  according to the following steps: 
     1) The origin of coordinate system EAPP is assumed to be at an initial position. The initial position is a position along the path segment over which the energy applicator  184  should travel. If the energy applicator  184  is at the beginning point of the segment, this point is the initial position of coordinate system EAPP. Both the initial position and the target position are points in the bone coordinate system BONE.
 
2) Based on the instrument feed rate, the distance along which the energy applicator  184  would travel along the segment in a single time frame is calculated. In some versions, the period of a time frame is 0.1 to 2 milliseconds.
 
3) Based on the initial position, the length of the calculated distance and the location of the segment terminus, path interpolator  288  generates data defining the target position. A further variable used to determine target positions are data from the tool path generator describing the characteristics of the path segment: straight or curved; and, if curved, the radius of curvature.
 
4) Steps 1 through 3 are repeated until it is determined that the coordinate system EAPP has reached the terminus of the path segment. After the calculation of the first target position spaced from the segment origin, the target position calculated in each frame is employed as the initial position upon which the calculation of the next frame&#39;s target position is based.
 
5) Once the target position equals the terminus position for a path segment, interpolator  288  repeats steps 1 through 4 to generate a set of target positions that are located along the new segment.
 
     During the time period of a single frame, the distance the energy applicator  184  is able to travel may be greater than the distance to the terminus position for the current segment. If the path interpolator  288  determines that the energy applicator  184  would be in this state, the interpolator, for a time point starting when it is determined that the energy applicator  184  would be at the terminus of the current path segment, generates data indicating where the energy applicator  184  should be located at along the next path segment at the end of that frame. 
     The target positions are output from the path interpolator  288  to a series of cascaded running average filters  290 , (RNING AVG FILTER), also a component of the tool path force calculator  278 . The running average filters  290  average the individual target positions to produce filtered target positions. The particular running average filters employed in this invention are finite impulse response filters. The running average filters generate filtered target positions as a function of time, the length of the filter. This time period is typically between 5 and 50 milliseconds. Consequently, the resulting distance filtered is a function of filter time period and instrument feed rate. 
     Cascaded running average filters are employed in this process to ensure that higher order derivatives of the target positions are continuous. In some versions, three cascaded filters are employed. This makes the resulting filtered path have continuous derivatives up through jerk. This filtering essentially ensures that the actuators are not driven beyond their capabilities to advance the energy applicator  184  along the tool path  248 . 
     The filtering performed by these filters is illustrated by reference to  FIG.  17   . Here, points  294  and  302  represent, respectively, the initial and final target positions of the energy applicator  184  as it moves along path segment  297 . Point  302  is also the initial position along from which the energy applicator  184  moves as it travels along path segment  310 . Path segment  297  is completely linear. In the running average process, filters average the locations of a number of points along the portion of the path being averaged to determine a mean location. Points  296  and  298  are two spaced apart target positions along path segment  297 . If target positions between points  296  and  298  form a straight line and the distance between the points is greater than the distance the energy applicator  184  travels during the length of the filter, the results of this running average form a straight line. As in any filter, there is a lag in time between the input of these positions to the output of the equivalent filtered output positions. 
     During this running average process, it should be understood that, to produce the filtered target position equivalent to point  296  data, regarding the unfiltered target positions behind point  296  are input variables into the filters. 
     Target position  302  is the origin of path segment  310 . Path segment  310  is linear and angles away from path segment  297 . The running average filter  290  eventually produces filtered target positions from target position  299 , a point on path segment  297  and target position  303 , a point on path segment  310 . The resultant averaged target positions are represented by segment  314 . These filtered target positions are based on the assumption that the distance between target positions  299  and  303  is greater than the distance the energy applicator  184  travels during the length of the filter. Here, point  312  is identical in position to point  299 . Point  316  is identical in position to point  303 . Point  318  is identical to point  305 . The set of filtered target positions between filtered target positions points  312  and  316  defines a curve. This curve represents the averaged transition from the target positions defining segment  297  to the target positions defining segment  310 . From filtered target position  316  to filtered target position  318  the set of target positions is linear. This is because during this portion of the averaging process no points other than those along path segment  310  are input into the averaging equation. 
     Target position  320  is the terminus of straight segment  310  and the origin of curved segment  330 . Based on the locations of the points bounded by and including target position  320  and target position  332 , a point in the middle of curved segment  330 , filters  290  produce another set of averaged target positions. These averaged target positions are represented by segment  340 . Segment  340  extends between filtered target position  338  and filtered target position  342 . Given that target position  320  is the terminus of linear path segment  310 , the corresponding filtered target position, point  338  is slightly displaced from the actual position. In locations where the target positions to be filtered define a curve, the filtered versions of these target positions typically define a curve which has a larger radius than the radius of points being filtered. 
     For some procedures it is desirable to substantially minimize the difference between the filtered and unfiltered target positions. One such procedure is the forming of bores in bones. Another procedure is the precise shaping of bone to facilitate precise seating of an implant. For these procedures, the manipulator is set to reduce the defined rate that is applied to the feed calculator  284 , (process not shown). This results in the generation of filtered target positions that define path segments that are essentially identical to the path segments defined by the unfiltered set of target positions. 
     The filtered target positions are applied to the curvature calculator  291 . The curvature calculator  291 , based on data defining multiple spaced apart filtered target positions, determines the curvature of the current filtered path. Data representative of this curvature are forwarded to the feed rate calculator  284  as the PATH CRVTR variable. 
     The filtered target positions are also forwarded to a target location coordinate transformer  354 , also a sub-module component of the tool path force calculator  278 . Coordinate transformer  354  maps each filtered target position, which is in coordinate system BONE into coordinate system MNPL. This filtered target position of the origin of coordinate system EAPP is applied to an energy applicator force calculator  358 , also part of tool path force calculator  278 . 
     A second input into calculator  358  is a representation of the actual position of coordinate system EAPP. In many implementations of this invention, the commanded position is employed as the representation of the actual position. The commanded position is the position component of the commanded pose. One advantage of employing the commanded position as the representation of actual position is that it is a leading indicator of the actual position. This feed forward effect facilitates responsive control of the movement of the instrument. This fosters movement of the energy applicator  184  that only minimally deviates from the tool path. 
     When manipulator  50  is first activated, the initial commanded pose is determined by solving the forward kinematics of the end effector  110 . This process is understood to mean determining the pose of coordinate system CMVB as a function of the joint angles of the shoulders  67  and  69  and arms  68  and  70 . This pose is relative to coordinate system MNPL. Since the origin of coordinate system EAPP is fixed relative to coordinate system CMVB, the forward kinematic solution of the virtual rigid body results in a like determination of the first initial pose of coordinate system EAPP in coordinate system MNPL. 
     Energy applicator force calculator  358  determines a set of forces and torques that would be applied to the virtual rigid body. In response to the application of these forces and torques to the virtual rigid body, motion control processes cause manipulator  50  to advance coordinate system EAPP along the tool path  248 . The forces and torques applied to the virtual rigid body that results in the setting of the orientation of the instrument are not material to the calculations performed by the calculator  358 . 
     After this first determination of the initial pose of the origin of energy applicator coordinate system EAPP, manipulator controller  124  assumes that at the end of each frame, the origin of coordinate system EAPP moved to the commanded pose calculated at the start of the frame. This commanded pose is generated by a below described cut guide  390 . The commanded position component of the commanded pose is supplied by the cut guide  390  to the energy applicator force calculator  358 . 
     Accordingly, two inputs into the energy applicator force calculator  358  are the commanded position of coordinate system EAPP and the next targeted position of this coordinate system. This latter position is the input from the target location coordinate system transformer  354 . Both these positions are points in coordinate system MNPL. A third input into the tool tip force generator is the velocity of coordinate system CMVB at the start of the frame, velocity V 0 . The means by which velocity V 0  is calculated is discussed below. The fourth input into the energy applicator force calculator  358  is the velocity at which the energy applicator  184  should move as it advances along the path, velocity V 1 . Velocity V 1  is a vector based on the target position from the previous frame and the current target position. Velocity V 1  is the velocity relative to the manipulator coordinate system MNPL. Velocity V 1  therefore includes the effects of the movement of bone coordinate system BONE relative to the manipulator coordinate system MNPL. Velocities V 0  and V 1  are understood to include both linear and rotational components. 
     Energy applicator force calculator  358  calculates a force that would move the origin of coordinate system EAPP from its current position to the filtered target position. In one version of this invention, calculator  358  determines this force by determining the impulse that needs to be applied to the virtual rigid body at the origin of coordinate system EAPP. The impulse, I, is the change of momentum that is applied to an object. Accordingly, impulse/change of momentum in its most general form, I, is calculated according to the formula
 
 I=∫Fdt=m ( v   FNL   −v   INTL )  (1)
 
     Here, F is force; m is the mass of the object to which the impulse is applied; v INTL  is the initial velocity; and v FNL  is the final velocity. The object is to calculate the force that would need to be applied to the distal end tip of the energy applicator  184 , which is the origin of coordinate system EAPP, to cause the applicator to advance to velocity V 1 . Equation (1) assumes that the velocities are those present at the center of mass of the object to which the force is applied and the velocities are the velocities present at this point. While the initial velocity V 0  is that of coordinate system CMVB and is known, the final velocity V 1  is the velocity of the energy applicator  184 . 
     Force F is applied to the virtual rigid body. As mentioned above, force F is not applied to the origin of coordinate system CMVB; this force is applied to the origin of coordinate system EAPP. To account for these factors, the impulse equation is rewritten as follows: 
     
       
         
           
             
               
                 
                   
                     
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     Here, D xyz  is the direction in which the impulse is to be applied. Direction D xyz  includes two unit vectors. One of these unit vectors defines the direction along which the force is to act. The second unit vector defines the direction around which the torque is to act. Often, it is only necessary to calculate the force component. To accomplish this, the torque component of vector D xyz  is set to the null vector. Force F EAPP  is a scalar force along direction D xyz . Jacobian J SA  is the Jacobian matrix from the origin of coordinate system CMVB expressed in coordinate system CMVB to the origin of the energy applicator coordinate system EAPP along the direction D xyz . Because Jacobian J SA  only maps to the component along direction D xyz , J SA  is a non-square Jacobian. Matrix M is the mass/inertia of the virtual instrument. Direction D xyz  is computed by the energy applicator force calculator  358 . The variables upon which direction D xyz  is based are the commanded position and filtered target position of the energy applicator  184 . By employing the direction D xyz  vector, Equation (2) is reduced from six equations and six unknowns to one equation with one unknown. 
     It is further necessary to account for two additional factors. One is that instrument and energy applicator  184  are modeled as a rigid body and the velocities are specified in a non-inertial coordinate system. This body is therefore subjected to inertial forces. The effect of these inertial forces, which include torques, must be modeled. These inertial forces are calculated according to the following formula: 
                     F   inertial     =     [             -   ω     ×   V                 -   ω     ×   I   ⁢   ω           ]             (   3   )               
Here, F inertial  is a vector consisting of the inertial forces and torques. Velocity V is the velocity of coordinate system CMVB. Rotational velocity ω is the rotational velocity of coordinate system CMVB. Inertia I is the virtual inertia tensor in coordinate system CMVB. Both velocities ω and V are expressed in coordinate system CMVB
 
     The second additional factor is that environmental forces discussed below, collective force F ENV , act on the virtual rigid body. Components of the environmental force include a joint limit force, an interference limit force, a workspace boundary force and a damping force. An additional component of the environmental force is external forces applied to the manipulator  50 , the instrument  160  and the energy applicator  184 . The external forces include the effect of the resistance of the tissue to which the energy applicator  184  is applied. Another component of the external force is the force the practitioner places on the instrument. The components of environmental force F ENV  are discussed in detail below. 
     Accordingly, force F EAPP  is calculated according to the formula: 
                       (       J   SA     ⁢     M     -   1       ⁢     J   SA   T       )     ⁢     F   EAPP       =             D     x   ⁢   y   ⁢   z       ⁢     V   1       -       J   SA     ⁢     V   0           Δ   ⁢   t       -       J   SA     ⁢       M     -   1       (       F   inertial     +     F   ENV       )                 (   4   )               
Here, F inertial  are the inertial forces acting on the instrument and energy applicator  184 . Force F ENV  is received from a below discussed environmental force summer  379  and is expressed in coordinate system CMVB. Time period Δt is equal to the integration time period employed by the below discussed integrator  386 .
 
     In practice, if the energy applicator  184  is simply repositioned based on the calculation of velocity vectors the position of the energy applicator  184  has a tendency to drift from the path segment along which the applicator should advance. This drift occurs due to such factors as rounding errors, machine precision and the inherent limits associated with discrete time modeling. Drift can also occur as a consequence of the micro-environmental disturbances in the vicinity of the instrument. To compensate for this drift, a correction force is added to the calculation of the force applied to the virtual rigid body. The general description of these forces is: 
                 ϵΔ   ⁢   d       Δ   ⁢     t   2         +       C   ⁢     F   EAPP         Δ   ⁢   t             
Distance Δd is defined to be the negative of the magnitude of the distance the energy applicator  184  has drifted from the path segment. In one implementation, distance Δd is computed by determining the negative of the magnitude of the distance between the actual position and the target position. In one implementation, the commanded position is employed as the representation of the actual position of the energy applicator  184 . Coefficients E and C are scale factors. When the above terms are added to Equation (4), the final form of the equation to solve for the force applied to the virtual rigid body at the origin of coordinate system EAPP is:
 
                       (         J     S   ⁢   A       ⁢     M     -   1       ⁢     J     S   ⁢   A     T       +     I   ⁢     c     Δ   ⁢   t           )     ⁢     F   EAPP       =             D     x   ⁢   y   ⁢   z       ⁢     V   1       -       J     S   ⁢   A       ⁢     V   0           Δ   ⁢   t       -       J     S   ⁢   A       ⁢       M     -   1       (       F   inertial     +     F   ENV       )       -       ϵΔ   ⁢   d       Δ   ⁢     t   2                   (   5   )               
Matrix I is the identity matrix.
 
     The energy applicator force calculator  358  therefore solves for force F EAPP , the force along direction D xyz  applied to the virtual rigid body at the origin of coordinate system EAPP. In response to the presence of force F EAPP , the motion control processes cause the manipulator  50  to advance energy applicator  184  along the path segment at the appropriate velocity. As mentioned above F EAPP  is scalar. Force transformer module  362  transforms this scalar to force F INST . Force F INST  is the vector of forces and torques applied to the virtual rigid body at the origin of coordinate system CMVB to advance the energy applicator  184  at the desired velocity. These forces and torques are calculated according to the following equation:
 
 F   INST   =J   SA   T   F   EAPP   (6)
 
Force F INST  is a vector consisting of three separate forces and three separate torques applied to the virtual rigid body at the origin of coordinate system CMVB. Force F INST  is expressed in coordinate system CMVB.
 
     The forces and torques comprising F INST  are applied from force transformer module  362  to a force summer  380 . As described below, the force summer  380  is another one of the behavior control modules that runs on the manipulator controller  124 . 
     Tool path force calculator  278  also includes an instrument orientation regulator  368  seen in  FIG.  16 C . Orientation regulator  368  determines the forces and torques that need to be applied to the virtual rigid body to ensure that, as the manipulator  50  moves the instrument  160 , the instrument maintains an acceptable orientation relative to the tissue against which the energy applicator  184  is applied. Instrument orientation regulation is desirable because as discussed above, the energy applicator force calculator  358  generates data defining forces and torques applied to the virtual rigid body that result in the advancement of the energy applicator  184  when in the semi-autonomous mode. External forces and torques are also applied to the manipulator  50 , instrument  160  and energy applicator  184 . In response to these external forces, manipulator  50  computes additional forces and torques that are applied to the virtual rigid body. The application of either one of these sets of forces and torques to the virtual rigid body can result in the manipulator  50  positioning the instrument so that the instrument appreciably drifts from an acceptable range of orientations. Should the instrument drift from this range of orientations, the efficiency of the energy applicator  184  may be reduced. Also, as a result of this orientation drift, the instrument may move to a position in which it could potentially abut other tissue or other instruments adjacent the tissue against which the energy applicator  184  is applied. This contact could inhibit the further advancement of the energy applicator  184 . 
     Orientation regulator  368  determines the restoring forces and torques that need to be applied to the virtual rigid body to prevent this drift. 
     In most versions, orientation regulator  368  is set to operate when the manipulator advances the instrument in the semi-autonomous mode. When commands are first entered to begin semi-autonomous advancement of the instrument, orientation regulator  368  defines a reference surface  369  that is located above the distal end of the energy applicator  184 , as shown in  FIG.  18 A . To perform this process, orientation regulator  368  is required to know the actual pose of the instrument. In some versions, the commanded pose is employed as the representation of the actual pose. In the Figures, surface  369  is depicted as a plane but in practice is not so limited. Reference surface  369  is typically located approximately 5 to 20 cm above the distal end of the energy applicator  184 . In some versions, the reference surface is positioned to intersect the origin of coordinate system CMVB. If the reference surface is a plane, upon manipulator initialization, regulator  368  often defines the plane as being perpendicular to the longitudinal axis of the instrument  160 . The orientation regulator  368  then defines an aperture  370  in the reference surface  369 , as shown in  FIG.  18 B . Aperture  370  is typically, but not limited to, a circle. The aperture  370  is centered around the point where the longitudinal axis of the instrument or energy applicator  184  intersect the reference surface  369 . In the described version, these axes are assumed to be linear and are collectively referred to as the “common axis”. In the figures, this point of intersection is called out as centering point  371 . If aperture  370  is in the form of a circle, the aperture may have a radius of between 2 to 5 cm. Surface  369  and aperture  370  are typically fixed relative to the coordinate system BONE. This ensures that the representation of these geometric landmarks move with the patient. The surface  369  and aperture  370  are typically defined in either manipulator coordinate system MNPL or bone coordinate system BONE. 
     At the start of the frame, the orientation regulator  368  has the data describing the commanded pose of the instrument  160 . Owing to the repositioning of the instrument  160  by the manipulator  50 , the common axis may be displaced from the centering point  371  as seen in  FIG.  18 D . This displacement occurs because neither aperture  370  nor centering point  371  moves with the displacement of the instrument and energy applicator  184 . If the instrument  160  is so displaced, orientation regulator  368  determines an orientation restoring force that, applied to the virtual rigid body, results in manipulator  50  moving the instrument so that the common axis moves towards the centering point  371 . 
     The process by which orientation regulator  368  determines the orientation restoring forces and torques start with the orientation regulator determining the point along the common axis that intersects the reference surface  369 . Orientation regulator  368  determines the current location of the common axis based on representation of the actual pose, the commanded pose. Orientation regulator  368  then determines the distance from this point to the centering point  371 . Based on these data, the orientation regulator  368  determines the restoring forces and torques that would pivot instrument  160  towards centering point  371 . In one version, these forces and torques are determined according to the following formula:
 
 F   R_MAG   =f (DIST INST-CP )+ f ( V   INST-CP )  (7)
 
In some cases:
 
 f (DIST INST-CP )= K   ORNT DIST INST-CP   (7A)
 
 f ( V   INST-CP )= D   ORNT   V   INST-CP   (7B)
 
Here, F R_MAG  is the magnitude of the restoring force applied to the virtual rigid body along the reference surface  369  to pivot the instrument towards the centering point. Force F R_MAG  would act along the vector from the point where the instrument axis intersects reference surface  369  to the centering point  371 . In Equation (7), force F R_MAG  has a distance component and a velocity component. Distance DIST INST-CP  is the distance between the point where the common axis intersects reference surface  369  and centering point  371 . Distance DIST INST-CP  is a positive scalar. Velocity V INST-CP  is the time derivative of distance DIST INST-CP .
 
     Coefficient K ORNT  is a spring coefficient. This coefficient may be variable. One reason for this is that when the common axis is very close to the centering point  371 , it may not be necessary to apply an appreciable restoring force to the instrument. This is because, while it is desirable that the common axis be located on the centering point  371 , it is not a requirement for the operation of the manipulator. Accordingly, when the common axis is relatively close to the centering point  371 , spring constant K ORNT  may be relatively low or even zero. If the common axis is spaced further from centering point  371 , it may be desirable to increase the application of these restoring forces and torques. 
     Coefficient D ORNT  is a damping coefficient. The damping coefficient may be variable. In some versions, this coefficient is a function of distance DIST INST-CP  and/or velocity V INST-CP . Varying coefficient D ORNT  may be desirable to enhance the stability of the movement of the instrument. 
     In  FIG.  19    the magnitude of the distance component of the force in Equation (7) is shown. In this Figure, there is a steep increase in the application of the force from inflection point  377  to peak  378 . Inflection point  377  is located at the perimeter of aperture  370 . Accordingly, should the common axis continue beyond this location, the orientation regulator  368  generates data indicating that a significant restoring force needs to be applied to the virtual rigid body to maintain the instrument within the aperture. The magnitude of this restoring force significantly increases as the instrument moves incrementally beyond aperture  371 . 
     Orientation regulator  368  may determine that the instrument has moved an appreciable distance beyond aperture  370 . This is the distance at which peak  378  is located. If orientation regulator  368  determines this condition exists, the regulator  368  no longer generates data indicating that a large restoring force should be applied. This is because there may be instances, when the instrument is being displaced in a semi-autonomous mode, it is desirable to move instrument outside the normal range of orientations. For example, there may be an obstacle that blocks advancement of the energy applicator  184  along the programmed path segment. This obstacle might be a protruding tissue or a surgical instrument. So that this obstacle does not block the advancement of the energy applicator  184 , the instrument may need to assume an orientation outside of the normal range of orientations. Alternatively, the practitioner may attempt to force the reorientation of the instrument  160  without first depressing button  172 . Should this event occur, the fact that the orientation regulator  368  allows the instrument to move outside of the normal range of orientations allows the practitioner to engage in such reorienting of the instrument. 
     Accordingly, as the instrument moves more than 0.5 to 2.0 cm beyond the aperture, the magnitude of the distance component ramps down to nominal levels. This level may equal zero. Prior to allowing this force to fall to zero, the manipulator may present a message on the user interface requesting that the practitioner confirm that the orientation regulator  368  at least temporarily suspend regulation of instrument orientation. While awaiting this confirmation, the manipulator may suspend advancement of the energy applicator  184  along the path segment. 
     Once orientation regulator  368  starts to generate data indicating that only a nominal/zero orientation restoring force F R_MAG  should be applied to the virtual rigid body, the practitioner may manually reorient the instrument so that the axis is at or in close proximity to the aperture  370 . Should this event occur, the orientation regulator  368  may return to outputting data indicating that a more than nominal restoring force should be applied. In some constructions of the manipulator  50 , for the orientation regulator  368  to return to outputting a more than nominal orientation restoring force, the practitioner is required to press and release button  172 . Orientation regulator  368  redefines the reference surface  369 , the aperture  370  and centering point  371  based on instrument orientation when button  172  is released. Once these landmarks are redefined, the orientation regulator  368  returns to outputting more than nominal orientation restoring forces. 
     In practice, orientation regulator  368  does not actually execute Equation (7) to determine the orientation restoring force F R_MAG . Instead, the orientation regulator  368  maintains look up tables of restoring forces (tables not illustrated). The inputs to determine the appropriate restoring force are representations of distance DIST INST-CP  and velocity V INST-CP . 
     Once restoring force F R_MAG  is determined, orientation regulator  368  converts this force into a vector. Orientation regulator  368  performs this conversion by multiplying force F R_MAG  by the unit direction vector from the point where the instrument axis intersects the reference plane  368  to the centering point  371 . The unit direction vector is expressed in coordinate system MNPL. This multiplication produces a force vector F RSTR  also in coordinate system MNPL. This vector defines the restoring force that is applied to the virtual rigid body where the longitudinal axis of the body instrument intersects the reference surface  369 . This point is not the origin of coordinate system CMVB. 
     Orientation regulator  368  therefore converts force F RSTR  into the equivalent forces and torques that should be applied to the virtual rigid body at the origin of coordinate system CMVB. This conversion is performed according to the following formula:
 
 F   ORNT   =J   ORNT   −T   F   RSTR   (8)
 
Force F ORNT  is the force and torque vector that is applied to the origin of coordinate system CMVB to reposition the instrument axis towards the centering point. This force is expressed in coordinate system CMVB. Jacobian J ORNT  is the Jacobian from where the instrument axis intersects the reference surface  369  expressed in coordinate system MNPL to the origin of coordinate system CMVB expressed in coordinate system CMVB. These forces and torques, which are in the coordinate system CMVB are also applied by the tool path force calculator  278  to total force summer  380 .
 
     Orientation regulator  368  receives as inputs other signals. These signals include signals from instrument button  172  and the below discussed force overrider  375 . The responses of the orientation regulator  368  to the assertion and negation of these signals is discussed below. 
       FIG.  16 D  illustrates another module integral to the tool path force calculator  278 , the force overrider  375 . One input into force overrider  375  are signals representative of the forces and torques applied to force torque sensor  108 . A second input into force overrider  375  are signals representative of the force F INST  that application of which to the virtual rigid body results in the advancement of the energy applicator  184  on the tool path. These signals are from the energy applicator force calculator  358 . These signals are shown coming from the force transformer  362 . A third input into the force overrider  375  is force F ORNT , collectively the forces and torques the tool orientation force regulator  368  determines would maintain the instrument axis within aperture  370 . A fourth input into force overrider is signals representative of the power applied by the energy applicator  184 . For an instrument having a motor as a power generating unit, the torque produced may function as indicia of instrument power. The current drawn by the instrument may be employed as a representation of the power applied by the energy applicator  184 . In  FIG.  16 D  this is why the signal ENGRY APP PWR is shown coming from the tool controller  132 . 
     Each of these signals is thus representative of a force or torque that is applied to or output by the instrument  160  and/or energy applicator  184 . Force overrider  375  compares each of these forces/torques to one or more limit values. If one set of these forces/torques exceeds a lower limit value, the force overrider deactivates the instrument and stops the advancement of the instrument. Depending on which set of force/torques exceeded the limit value, the force overrider may not deactivate the instrument and stop advancement until the limit value is continuously exceeded for a set time period. This delay may be programmed into the force overrider  375  to minimize the instances of momentary spikes in applied or output force/torque interrupting operation of the manipulator. This delay period is typically between 10 and 500 milliseconds. The deactivation of the instrument is represented by the assertion of a signal to an instrument manager  702  ( FIG.  27   ). In response to the receipt of this signal, instrument manager  702  sends a command to the tool controller  132 . This command causes the controller  132  to negate the application of energization signals to the instrument power generating unit  163 . The cessation of movement along the tool path is represented by the assertion of a signal to the feed rate calculator  284 . In response to this signal, the feed rate calculator  284  ramps the instrument feed rate to zero. 
     If one set of these forces/torques exceeds a higher limit level, force overrider  375  causes the manipulator to transition from semi-autonomous operation to manual mode operation. As with the lower limit level, the force overrider  375  may not cause this transition of the manipulator  50  until after the particular force/torque limit is exceeded for a continuous time period. This time period is typically less than the time period associated with the corresponding force/torque lower limit. This time limit is lower because the sensing of higher magnitude applied or output force/torque means that there is a greater likelihood that the manipulator may be in an undesirable state. Reducing the time period before which the force overrider  375  responds to this force/torque information essentially ensures that when the higher limit level is exceeded, the overrider takes the corrective action associated with this condition instead of responding to the lesser corrective action associated with the lower limit force/torque level being exceeded. 
     To reset the operation of the manipulator to the manual mode, the force overrider  375  asserts signals to the energy applicator force calculator  358  and the tool orientation regulator  368 . When energy applicator force calculator  358  receives this command signal from overrider  375 , the calculator ramps force F INST  to zero. When tool orientation regulator receives this command signal from overrider  375 , the regulator ramps force F ORNT  to zero. 
     From the above, it is now understood that tool path force calculator  278  produces information regarding the forces and torques that are applied to the center of mass of the virtual rigid body to: (1) move the energy applicator  184  along the path segment; and (2) maintain the instrument within an acceptable range of orientations. Data describing both these forces and torques are applied to a total force summer  380 . The forces and torques used to advance the energy applicator  184  and maintain tool orientation are calculated separately. Accordingly, in  FIG.  13 B , these two sets of forces and torques are depicted as two separate addends into force summer  380 . 
     Force summer  380  is a separate behavior control software module run on the manipulator controller  124 . An additional addend into force summer  380  is the environmental force F ENV  output from environmental force summer  379 . Force summer  380 , based on these three inputs, produces two sums: forces F TTL ; and torques T TTL . These sums are, respectively, the totals of the forces and torques that the manipulator would apply to the center of mass of the virtual rigid body. Both forces F TTL  and torques T TTL  are expressed in coordinate system CMVB. In both the manual or semi-autonomous modes of operation, manipulator  50  advances instrument  160  as a function of these total forces and torques. 
     An acceleration calculator  384 , another behavior control software module run on the manipulator controller  124 , receives the total force and torque vectors, respectively, F TTL  and T TTL  from force summer  380 . In  FIG.  13 B  a single connection from summer  380  to calculator  384  is shown. Acceleration calculator  384  determines the extent to which the origin of coordinate system CMVB should be accelerated based on the application of forces F TTL  and torques T TTL . This acceleration is both translational and rotational. As mentioned above the instrument and the energy applicator  184  are modeled as a virtual rigid body. The equations of motion for this body are:
 
 F   TTL   =m{dot over (V)}+ω×V   (9)
 
 T   TTL   =I{dot over (ω)}+ω×Iω   (10)
 
Here: m is the virtual mass of the virtual rigid body; V is the linear velocity of coordinate system CMVB; {dot over (V)} is the linear acceleration of coordinate system CMVB; ω is the rotational velocity of coordinate system CMVB; {dot over (ω)} is the rotational acceleration of coordinate system CMVB. These velocities and accelerations are expressed in coordinate system CMVB. Tensor I is the virtual inertia tensor of the virtual rigid body expressed in coordinate system CMVB.
 
     Therefore, acceleration calculator  384  is also loaded with the virtual mass and virtual inertia of the virtual rigid body. This value is typically constant. Acceleration calculator  384  assumes that linear velocity V and angular rotation ω are the immediately past calculated values for these variables. Acceleration calculator  384 , given the above known variables is therefore able to solve for both the linear and rotational accelerations, respectively, {dot over (V)} and {dot over (ω)}. It should be appreciated that V and w are vectors. 
     Vectors {dot over (V)} and {dot over (ω)} are both applied to an integrator  386 , another behavior control software module run on the manipulator controller  124 . Integrator  386  also receives from the below described cut guide  390  a commanded pose and a commanded velocity for coordinate system CMVB expressed in coordinate system MNPL. These commanded pose and commanded velocity data are used by the integrator  386  as the initial conditions for the integrations for the current frame. The integrator  386  converts the velocity from coordinate system MNPL to coordinate system CMVB. This conversion is necessary to employ the velocity as an initial condition in the integrations. 
     For the first frame integrations upon manipulator initialization, as previously described, the commanded pose is based on the data from the below discussed forward kinematics module  562 . The commanded velocity is set to zero. 
     Integrator  386  performs a first integration to determine both the linear and rotational velocities, V and ω, of coordinate system CMVB. Integrator  386  then rotates linear velocity V into its equivalent in manipulator coordinate system MNPL. The integrator  386  may then limit the magnitude of these velocities to ensure that the motion of the manipulator is within the operational limits of the manipulator. This velocity limiting may also be performed to ensure that the rate at which the manipulator advances the instrument does not exceed the desired rates for the procedure. Integrator is able to independently limit the magnitudes of the linear and rotational velocities. 
     These velocities are then integrated to determine the new position of the origin of the coordinate system CMVB in coordinate system MNPL. 
     Integrator  386  also converts the rotational velocities to quaternion rates. These quaternion rates are expressed in coordinate system MNPL. The quaternion rates are integrated to obtain the quaternions. The quaternions are then used to form the rotation matrix of the new orientation of the coordinate system CMVB in the manipulator coordinate system MNPL. Collectively, this rotation matrix and the vector defining the position of the coordinate system CMVB in the manipulator coordinate system MNPL form the homogenous transformation matrix of the coordinate system CMVB with respect to manipulator coordinate system MNPL. This transformation matrix specifies a pose of the virtual rigid body. This pose is applied to the below described cut guide. 
     Integrator  386  also monitors the state of switch  176 . When the integrator  386  determines that switch  176  has been transitioned from the asserted to the not asserted state, the integrator momentarily ramps down the signals indicating the velocities V and a to zero. This ramping down is performed prior to the second integration to both the linear and rotational velocity. Integrator  386  does not hold the velocity to zero. This allows other forces such as the below described back drive forces and joint limit forces to continue to influence the movement of the manipulator after switch  176  is no longer asserted. 
     In some versions, integrator  386  does not directly ramp the velocity to zero. Instead, when switch  176  is no longer asserted, the velocity is indirectly driven to zero by momentarily increasing the below described damping force applied to force summer  379 . 
     The results of the velocity and position integrations are applied to a cut guide  390 . Cut guide  390  is a behavior controller software module that runs on the manipulator controller  124 . The cut guide  390  is the software module that, when the manipulator is operated in the manual mode, prevents the manipulator from positioning the energy applicator  184  beyond the boundaries of the volume in which the applicator is to be applied. Cut guide  390  is thus the software module that ensures that the manual mode positioning of the energy applicator  184  is boundary constrained. 
     When the manipulator  50  is operated in the semi-autonomous mode the path segments along which the energy applicator  184  advances are inherently within the boundaries of the volume in which the energy applicator  184  should be applied. Cut guide  390  remains the initial recipient of the pose generated by the integrator  386 . Thus, when the manipulator  50  operates in the semi-autonomous mode, cut guide  390  functions as a safety that prevents unintended movement of the energy applicator  184  beyond the defined boundary. 
     One input into cut guide  390  is the pose generated by integrator  386 . This integrator-generated pose is of the origin of coordinate system CMVB relative to coordinate system MNPL. A second input is the velocity, linear and rotational, generated by integrator  386 . A third input into the cut guide  390  is the data from the boundary generator  232  that define the boundaries between the volume where the energy applicator  184  is and is not to be applied. In  FIGS.  20 A,  20 B and  20 C , these boundaries are called out by line segments  452 ,  454  and  456 .  FIGS.  20 A- 20 C  are understood to be two-dimensional section views through a three-dimensional surface. 
     Cut guide  390  also receives a fourth input from coordinate system transformer  272 . These are data defining transformations of coordinate systems relative to each other. These include transformations relating coordinate systems CMVB, EAPP, BONE and MNPL. 
     The above pose and velocity inputs are initially expressed in coordinate system MNPL. Cut guide  390  transforms each of these inputs into coordinate system BONE, step  482 . This transformation is performed because the boundaries beyond which the energy applicator  184  should not be applied are typically fixed in coordinate system BONE. For ease of processing, it is therefore more convenient to perform the following analyses in bone coordinate system BONE. 
     The operation of the cut guide  390  is initially explained by reference to the flow charts of  FIGS.  21 A- 21 C . While not shown as a step, cut guide  390 , based on the previous commanded pose, calculates the previous commanded position of the origin of coordinate system EAPP. Based on the integrator-generated pose, the cut guide  390  calculates an integrator-generated position of the origin of coordinate system EAPP. 
     In a step  484 , cut guide  390  identifies any boundary-defining tiles the energy applicator  184  could cross during the frame. This step is often described as a broad phase search. Step  484  is performed by identifying the set of tiles that are within a defined distance of the previous commanded position of the energy applicator  184 . In  FIG.  20 A , this is point  458 . This distance is a function of: the dimensions of the energy applicator  184 ; the velocity of the energy applicator  184  relative to the tiles (the velocity of advancement during the past frame is acceptable); the time period of the frame; a scalar defining a characteristic size of the boundary defining sections; and a rounding factor. 
     As a result of the execution of broad phase search, step  484 , cut guide  390  may determine that, in the frame for which this analysis is being performed, all of the tiles are outside of the defined distance, step  486 . This means that, by the end of frame for which this analysis is being performed, the energy applicator  184  will not have advanced to a location beyond the boundary. This is illustrated by  FIG.  20 A  where the integrator-defined position of the energy applicator  184 , point  460 , is spaced well away from the closest boundary. 
     Since the continued advancement of the energy applicator  184  is within the boundary of the volume in which the energy applicator  184  is to be applied, the cut guide  390  does not modify either the pose or the velocity of coordinate system CMVB as generated by the integrator  386 . In a step  488 , the cut guide  390  outputs a commanded pose and a commanded velocity. If this version of step  488  is executed as a result of it being determined that all the boundary tiles are outside of the defined distance, the pose and velocity generated by integrator  386  are output by the cut guide  390  as a commanded pose and a commanded velocity. 
     As part of the execution of the above version and the other below described versions of step  488 , cut guide  390  transforms the commanded pose and velocity from coordinate system CMVB so this pose and velocity are expressed in coordinate system MNPL. The commanded velocity, it is understood is a vector that comprises both linear and rotational components. 
     As a result of the execution of step  484 , cut guide  390  may alternatively identify a broad set of boundary-defining tiles that are within the defined distance of the energy applicator  184 . In a step  490 , the cut guide  390  then identifies a narrow set of boundary-defining tiles that are within the broad set of tiles that the energy applicator  184  could cross. This step is often referred to as the narrow phase search. This narrow phase search can be performed by initially defining a bounding volume. This bounding volume extends between what are considered to be initial and final positions of the energy applicator  184 . If this is the first execution of step  490 , the initial position is set to the previous commanded position; the final position is set to the integrator-generated position. 
     In its most elemental form, this bounding volume is a line segment between the initial and final positions of the energy applicator  184 . The bounding volume may have a cross sectional area geometry that is constant along the length of the volume. The bounding volume may have a cross sectional section that comprises one or more borders that is curved and/or straight in shape. The bounding volume may have a shape that is function of the shape of the energy applicator  184  and the initial and final orientations of the energy applicator  184 . 
     Once the bounding volume is defined, as part of the narrow phase search of step  490 , the cut guide  390  determines which, if any, of the broad set of tiles are intersected by this volume. The tiles intersected by the bounding volume are the narrow set tiles. 
     As a result of evaluation of step  490  it may be determined that none of the broad set of tiles are intersected by the bounding volume; the narrow set is an empty set. This is the evaluation of step  492 . If this evaluation tests true, cut guide  390  interprets this condition as indicating that the final position of the energy applicator  184  is within the volume defined by the boundaries. If the energy applicator  184  is so located, cut guide  390  proceeds to the above-described step  488 . If this is the first execution of step  490 , in this version of step  488 , the pose and velocity generated by integrator  386  are output by the cut guide  390  as a commanded pose and a commanded velocity. 
     Alternatively, as a result of the evaluation of step  492  it may be determined that the bounding volume crosses one or more tiles; the narrow set contains one or more tiles. If this is the determination of the evaluation of step  492 , the cut guide  390  interprets this condition as indicating that the final position of the energy applicator  184  is beyond a boundary. This condition is illustrated by  FIG.  20 B . Here point  462  is the initial position of the energy applicator  184 . Point  469  is the final position. 
     If the condition of  FIG.  20 B  exists, a step  493  is performed to determine which of the narrow set of tiles the energy applicator  184  would cross first. If the bounding volume is a line, the cut guide  390 , for each tile, determines the percentage of distance the energy applicator  184  will advance during the frame prior to the crossing of the applicator with the tile. The tile crossed at the lowest percentage of distance is the tile understood to be crossed first. If the bounding volume has a non-zero cross sectional area, processes not part of this invention are used to determine crossing distances. 
     By reference to  FIG.  22    it can be seen that the boundary defining tiles closest to the energy applicator  184  may not be the tiles that the energy applicator  184  could cross. Here as a result of the process of step  484 , it was initially determined that tiles  506 - 522  are within distance d, a volume represented by dashed circle  501 , the distance the energy applicator  184  could potentially move within the time frame. 
     The closest tile to the energy applicator  184  is tile  518 . However, the energy applicator  184  is moving along a trajectory that is, for purposes of illustration, straight and downward in  FIG.  22   , towards point  469 . Therefore, in the evaluation of step  493 , cut guide determines that tile  512  is the tile the bounding volume would intersect. 
     Once cut guide  390  generally determines which boundary-defining tile the energy applicator  184  will cross, in a step  494  cut guide  390  determines a time t CNTC  and a point P CNTC . Time t CNTC  is the time period relative to the start of the frame, when the energy applicator  184  will cross the boundary. This time is determined based on the percentage of distance the energy applicator  184  will advance during the frame prior to contacting the boundary. This determination is made based on the assumption that, during any given frame, the velocity of the energy applicator  184  is constant. Point P CNTC  is the point in coordinate system BONE where the energy applicator  184  will cross the tile. This point is determined by calculating where the path of advancement of the energy applicator  184  crosses the tile. Both calculations use as input variables the initial and final positions of the energy applicator  184  and data defining the perimeter of the boundary tile. These location-specifying data are in coordinate system BONE. 
     Also as part of step  494 , cut guide  390  determines the pose of coordinate system CMVB and the velocity of this coordinate system at time t CNTC . This pose is calculated based on the initial pose of coordinate system CMVB, the initial velocity of this coordinate system and time t CNTC . If this is the first execution of step  494 , cut guide  390  assigns the previous commanded pose of coordinate system CMVB to be the initial pose. If this is the first execution of step  494 , cut guide  390  assigns the previous commanded velocity of coordinate system CMVB to be the initial velocity. Both the linear and rotational velocities of coordinate system CMVB are assumed to be constant throughout the frame. Therefore, both the initial linear and rotational velocities are assumed to be the linear and rotational velocities at time t CNTC . The above determinations are made with reference to coordinate system BONE. 
     Also as part of step  494 , the linear and rotational velocities of coordinate system EAPP are determined at time t CNTC . These velocities are based on the velocities of coordinate system CMVB and the fixed pose of coordinate system EAPP relative to coordinate system CMVB. The linear and rotational velocities of coordinate system EAPP are calculated with reference to coordinate system BONE. 
     Cut guide  390  also defines a boundary contact coordinate system, step  496 . This coordinate system is defined so as to have a z-axis that is orthogonal to the surface section of the boundary that would be crossed by the energy applicator  184 . As part of the process of defining the boundary contact coordinate system, the position and orientation of this coordinate system relative to the coordinate system BONE is determined. The origin of this coordinate system is point p CNTC . 
     Cut guide  390  then determines a force F BNDR  applied to the virtual rigid body at the origin of coordinate system EAPP to stop the unwanted progression of the energy applicator  184  beyond the boundary. The method by which force F BNDR  is determined is explained by initial reference to  FIG.  23 A . This Figure represents the velocities of coordinate system CMVB and the energy applicator  184  as the applicator moves towards boundary. For ease of illustration, velocities along only the X- and Z-axes of the boundary contact coordinate system are illustrated. As seen in  FIG.  23 A , the energy applicator  184  moves at high velocities to the right in the x-axis and downwardly in the z-axis. Simultaneously, the virtual rigid body, more particularly the origin of coordinate system CMVB, moves at slower velocities to the left in the X-axis and upwardly along the Z-axis. Owing to the orientation and relative magnitude of these velocities, what is occurring in this motion is that the energy applicator  184  is rotating counterclockwise relative to the coordinate system CMVB while there is some minor displacement of the virtual rigid body. 
     Cut guide  390  determines a boundary constraining force applied to the origin of coordinate system EAPP that prevents the energy applicator  184  from advancing in the z-axis of the boundary contact coordinate system. 
     Accordingly, in step  530 , the cut guide  390  transforms the positions and velocities of coordinate system EAPP and the pose and velocities of coordinate system CMVB into the boundary contact coordinate system. In a step  532 , the cut guide determines a scalar force F BNDR  that, if applied to the origin of coordinate system EAPP at time t CNTC , would stop the advancement of the applicator in the direction normal and towards the boundary. As represented by arrow  457  in  FIG.  23 B , force F BNDR  acts along the z axis in the boundary contact coordinate system. Cut guide  390  may use one of a number of different methods to determine the magnitude of force F BNDR . 
     For example, it is possible to use an impulse method to compute force F BNDR . In one such method, a version of Equation (5) with components expressed in the boundary contact coordinate system is employed to determine F BNDR . In this application of Equation (5), F BNDR  is substituted for F EAPP . In this case velocity V 1  is the desired velocity of the energy applicator  184  at time t CNTC . Therefore, the Z-component of velocity V 1  is zero. This is because the goal of this application of the Equation is to determine the force that, if applied to the origin of coordinate system EAPP, would cause the Z-axis velocity to drop to zero relative to the boundary. The other components of velocity V 1  are not relevant. This is due to the choice of the direction vector D xyz  discussed below. Velocity V 0  is the velocity of coordinate system CMVB at the start of the frame. Time t CNTC  is employed as Δt. The linear component of direction vector D xyz  is the unit vector defining the normal direction of the surface of the boundary at point P CNTC . This vector is therefore [0, 0, 1]. The rotational component of vector D xyz  is set to the null vector. In this application of Equation (5) J BNDRY  replaces J SA . Jacobian J BNDRY  is the Jacobian from the origin of coordinate system CMVB to the origin of the boundary coordinate system along direction vector D xyz . 
     In this application of Equation (5) mass matrix M is expressed in boundary contact coordinate system. Force F cg     ext    is the output of force summer  380 . For forces F inertial  and F cg     ext    to be used they must first be expressed in the boundary contact coordinate system. Components C and ϵ are often set to zero. This eliminates the need to determine Δd. 
     There may be situations in which the energy applicator  184  simultaneously contacts plural boundary-defining tiles. When the energy applicator  184  is so positioned, the plural tiles simultaneously apply plural forces to the energy applicator  184 . Collectively, these forces must displace the energy applicator  184  along a path that does not cross any of the tiles. Performing the calculations to determine the force that would need to be applied to the origin of coordinate system EAPP to ensure this movement is a linear complementarity problem. This problem is of the form in which, for each force and velocity pair, the force must be equal to or greater than zero and the velocity also equal to or greater than zero. To solve this problem, it is therefore necessary for the Jacobian matrix of this version of Equation (5) to include extra rows. 
     It should be understood also that this impulse is applied to a point on the virtual rigid body, the origin of energy applicator  184  coordinate system EAPP that is spaced from the origin of coordinate system CMVB. Once F BNDRY  is determined, this scalar force is converted to an equivalent set of boundary constraining forces and torques, F B_C , that would need to be applied to the virtual rigid body at the origin of coordinate system CMVB, step  534 . This conversion may be according to the following formula:
 
 F   B_C   =J   BNDRY   T   F   BNDRY   (11)
 
Force F B_C  is expressed in the boundary contact coordinate system.
 
     Force F B_C  is then summed with F cg     ext   . Using the methods described with reference to Equations (9) and (10), cut guide  390  determines the new accelerations of the coordinate system CMVB, step  536 . The above sum of forces and torques are substituted for F TTL  and T TTL  in these applications of the Equations. 
     Based on these acceleration values, using the methods employed by the integrator  386 , the cut guide  390  determines the velocities of coordinate system CMVB at time t CNTC , using an integration interval ending at time t CNTC , step  538 . If this is the first execution of this step, the beginning of the frame is the beginning of integration interval. If this is a subsequent execution of this step, this integration interval starts at a time after the beginning of the frame. 
     Next, a second execution of the methods employed by the integrator  386  is performed to determine the velocities and pose of coordinate system CMVB at the end of the frame. This second execution is performed using an integration interval extending from time t CNTC  to the end of the frame. 
     The above integrator processes performed by the cut guide  390  are performed in the boundary contact coordinate system. During a single iteration of the boundary constraining force generating process, the pose of boundary contact coordinate system is fixed relative to coordinate system BONE. Therefore, by performing these processes in the boundary contact coordinate system, the movement of the patient&#39;s anatomy is taken into account when calculating the boundary constraining forces. Often it is assumed that the boundary contact coordinate system is an inertial coordinate system with constant velocity and no acceleration relative coordinate system MNPL during the integration interval. The outputs of these integrator processes are then converted from boundary contact coordinate system to coordinate system BONE. 
     At this time in the boundary constraining process, the pose of coordinate system CMVB at time t CNTC  becomes the new initial pose of this coordinate system. From this pose, a new initial position of coordinate system EAPP is determined. This position is the position of the energy applicator  184  adjacent but not over the boundary. In  FIG.  20 B , this is point  464 . The pose of coordinate system CMVB at the end of the frame becomes the new final pose of this coordinate system, step  540 . From this pose a new final position of coordinate system EAPP is determined, step  542 . In  FIG.  20 B  this position is represented by point  468 . It should be understood that, as a result of the application of F B_C , to the virtual rigid body, the position of coordinate system EAPP moves along, but does not cross, the boundary. In  FIG.  20 B , this is represented as the advancement of the energy applicator  184  from point  464  to point  468   
     It should further be appreciated that as a result of the application of F B_C , there will be appreciable change in the position of coordinate system CMVB. This difference is represented by the differences in position of point  165  from  FIG.  23 B to  23 C . In comparison to the depiction in  FIG.  23 B , in  FIG.  23 C , coordinate system CMVB is displaced both downwardly and to the right more than it would if not subject to the boundary constraining forces. This is represented by the dashed line representation of the instrument  160  and energy applicator  184 . 
     In  FIG.  20 B , the energy applicator  184  is shown advancing on a path approximately parallel and adjacent to boundary  454 . Energy applicator  184  of the virtual rigid body advances along this path until the end of frame. 
     After the advancement of the energy applicator  184  is constrained to prevent the applicator from crossing one boundary, there is a possibility that, within the same time frame, the energy applicator  184  could cross a second boundary. This scenario is depicted in  FIG.  20 C . Here point  470  is the previously commanded position, the first initial position, of the energy applicator  184 . Point  472  represents the integrator-generated position, the first final position, if advancement of the energy applicator  184  is not boundary constrained. It can be seen that point  472  is beyond a boundary. Cut guide  390  therefore determines a boundary constraining force that would need to be applied to the virtual rigid body to prevent the energy applicator  184  from crossing boundary  454 . 
     Point  471 , is the point adjacent boundary  454  where, by applying a first boundary constraining force, cut guide  390  prevents the energy applicator  184  from crossing boundary  454 . Point  471  is therefore the second initial position of the energy applicator  184  in the frame. 
     Point  476  represents the second final position of the energy applicator  184  if the virtual rigid body is only subjected to a single boundary constraining force. In  FIG.  20 C  it is observed that the path of travel between points  471  and  476  crosses boundary  456 . Cut guide  390  is therefore further configured to prevent one boundary constraining diversion of the energy applicator  184  from causing the applicator to cross another boundary. 
     Cut guide  390  prevents this trespass by, after step  542  is executed, performing a subsequent narrow phase search of the tiles, step  490  is reexecuted. Prior to performing this subsequent narrow phase search, step  490 , the cut guide executes a step  543 . In step  543  the cut guide  390  evaluates whether or not the cut guide  390  has performed a maximum number of allowed recalculations of the boundary constraining force F BNDRY  that can be applied to the origin of coordinate system EAPP. The purposes of performing step  543  are discussed below. If the cut guide has not performed the maximum number of recalculations of the boundary constraining force, cut guide proceeds to the subsequent step  490  reexecution of the narrow phase search. 
     In this subsequent narrow phase search process, the newly defined initial and final positions of the energy applicator  184  are, in step  490 , employed to define a new bounding volume. Again also in step  490  a determination is made regarding whether or not this volume intersects any boundaries. During a subsequent execution of step  492 , the evaluation may indicate that the set of tiles the bounding volume crosses is the empty set. As with the first execution of step  492 , if this evaluation tests true, the cut guide  390  interprets the results as indicating that, should the energy applicator  184  advance to the final position, the applicator will not cross the boundaries. This is the evaluation result the cut guide would make with regard to the advancement of the energy applicator  184  from point  464  to  468  in  FIG.  20 B . 
     As a result of this subsequent evaluation of step  492  testing true, cut guide  390  executes a version of step  488 . It should be understood that this execution of step  488  is occurring after a second or later execution of step  492 . Accordingly, in this version of step  488 , the cut guide  390  outputs the last determined end of frame pose and last determined end of frame velocity of coordinate system CMVB to be, respectively, the commanded pose and commanded velocity of this coordinate system. 
     In the second narrow phase search of energy applicator  184  advancement of  FIG.  20 C , the bounding volume is between points  471  and  476 . This volume crosses boundary  456 . The subsequent evaluation of step  492  will test false. Consequently, steps  493 ,  494 ,  496 ,  530 ,  532 ,  534 ,  536 ,  538 ,  540 ,  542  and  543  are reexecuted. As a result of the reexecution of these steps, the cut guide  390  determines the characteristics of a subsequent boundary constraining force that needs to be applied to the virtual rigid body. Cut guide  390  then determines a subsequent final position to which the energy applicator  184  would advance upon the application of this subsequent boundary constraining force. 
     In  FIG.  20 C  it is seen that it is necessary to apply a subsequent boundary constraining force to the virtual rigid body to prevent the energy applicator  184  from, at point  474 , crossing the boundary. As a consequence of the application of this subsequent boundary constraining force, the energy applicator  184 , advances to point  478 . The final pose of coordinate system CMVB when the energy applicator  184  is at this point  478  is the end-of-frame commanded pose output by the cut guide  390 . 
     Thus, for a single time frame in which the energy applicator  184  is advanced, the cut guide  390  may perform multiple analyses to determine the positions of the energy applicator  184  relative to the boundaries. If necessary, the cut guide  390  applies multiple boundary constraining forces to the virtual rigid body to prevent the energy applicator  184  from crossing boundaries. 
     In some versions, the cut guide is limited in the number of times, in a single frame it can generate data regarding a boundary constraining force that should be applied to the virtual rigid body. This is due to limitations in the processing capability of manipulator controller  124 . In some versions, the cut guide is limited to between 4 and 16 iterations and more often 6 to 12 iterations per frame. This is why the cut guide executes the evaluation of step  543 . If the cut guide determines that it has performed the maximum number of boundary constraining force generations, the cut guide executes a version of step  488 . In this version of the execution of step  488 , the last initial pose and velocity are output as, respectively, the commanded pose and the commanded velocity for coordinate system CMVB. This is because this pose and velocity are the last pose and velocity stored by the cut guide  390  for the state in which the energy applicator  184  is within the boundaries. 
     The commanded pose and commanded velocity of coordinate system CMVB relative to coordinate system MNPL are the final output of the behavior control processes. 
     The commanded pose of coordinate system CMVB is applied to the inverse kinematics module  542  shown in  FIG.  13 C . The inverse kinematics module  542  is one of the motion control modules executed by the manipulator controller  124 . Based on the commanded pose and preloaded data, the inverse kinematic module  542  determines the desired joint angle of the joints of the manipulator  50 . The preloaded data are data that define the geometry of the links and joints. In some versions, these data are in the form Denavit-Hartenberg parameters. 
     There are constructions of this invention in which a closed form solution to the inverse kinematics is not known. This is often the case with overactuated parallel mechanisms such as the mechanism described in this application. In such situations, the inverse kinematics are solved using numerical methods such as the iterative Newton Raphson method. The inverse kinematics model calculates the joint angles for both the active and passive joints of the manipulator. The active joints are the joints the angles of which are driven by joint actuators. The passive joints are the joints the angles of which are set as a result of the positioning of the active joints. The passive joints are: the joints between the upper links  74  and the driven links  80 ; the joints between the four bar links  78  and the driven links  80 ; and the joints between the driven links  80  and coupler  88 . 
     Each desired joint angle for an active joint is applied to the associated joint motor controller  126 . The joint motor controller  126  regulates the positioning of the joint. These joint angles applied to controllers  126  are referred to as commanded joint angles. 
     While not illustrated, it should be understood that some manipulators include modules that perform load balancing and/or arm compensation. This is true of manipulators that include parallel arms. These modules are almost always provided if the manipulator includes overactuated parallel arms. The load balancing is performed to ensure that the arms share the load associated with advancing the instrument to the commanded poses. This load balancing is performed to minimize the extent to which each arm resists the movement of the other arm. Load balancing is also performed to redistribute torque among the actuators. The torque is redistributed to minimize the instances in which any individual actuator is required to apply a significant percentage of the total torque output by the manipulator. 
     Arm compensation is performed because one arm is typically positioned to regulate the positioning of the other arm. For example, often at least some of the commanded joint angles of the lower arm  68  are often finely adjusted to ensure precise positioning of the passive joint angles associated with the upper arm  70 . The design of the load balancing and arm compensation modules is specific to the nature of the links integral with the manipulator. This may be practiced with link assemblies different than the described link assemblies. 
     The desired joint angles generated by the inverse kinematic module are applied to a command dynamics module  544 , also a motion control module. Command dynamics module differentiates the sequence of joint angles for each joint. These differentiations are performed to, for each joint, generate data indicating its angular velocity and acceleration. Command dynamics module also has a data describing the mass and inertia properties of each of the links. 
     Based on the above data, command dynamics module  544  performs an inverse dynamics calculation for the motion of the links and joints. This inverse dynamics calculation produces, for each active joint, the torque that should be applied to the joint to cause motion of the joint to the commanded joint angle. This torque is referred to as the feed forward torque. In some versions, this torque is calculated based on the iterative Newton-Euler method. Alternatively, these torques can be calculated using the Lagrangian method. 
     While not shown in  FIG.  13 D , the signals representative of the forces and torques detected by sensor  108  are sometimes applied to command dynamics module  544 . By employing these signals as additional input variables in the dynamics calculation, module  544  produces more accurate calculations of the feed forward torque. 
     There are periods in which the manipulator  50  holds the instrument  160  in a static pose. During these periods, the velocities and accelerations of the joints fall to zero. Even during these time periods, command dynamic module  544  outputs data indicating that the joint motors should still produce non-zero torques. This is because the joint motors need to output at least some torque to prevent the arm links from slipping from their static positions. This is because, even when the arm links are not exposed to direct mechanical forces, the arms are still subjected to the force of gravity. 
     Each joint motor controller  126  receives three inputs. One input is the commanded joint angle for the associated joint from the inverse kinematics module. The second input is the feed forward torque for the joint from the commanded dynamics module  544 . The third input is the input signal from the rotary encoder  112 ,  114  or  116  associated with the joint. Each motor controller  126  also stores as a constant, the gear ratio of the reduction gears  105  of the actuator  92 ,  94  or  96  with which the controller is associated. Based on these rotor angle data and the gear ratio data, the controller  126  generates data that represents the actual joint angle of the joint. This is known as the measured joint angle. 
     Based on the above inputs, the joint motor controller  126  determines the energization signals that should be applied to the associated motor  101  that cause the motor to drive the joint towards the commanded joint angle. It should be understood that the measured joint angle is used as the representation of the actual joint angle. The feed forward torque from the command dynamics module is the feed forward torque signal added to the input of the current control loop of the controller  126 . Prior to adding this indication of feed forward torque to the current control loop, controller  124  adjusts the torque from joint torque to motor torque based on the gear ratio. The torque is then adjusted from motor torque to motor current based on a stored torque constant of the motor. 
     As a consequence of the application of the energization signals applied to the motors  101 , the active joints are driven towards their commanded joint angles. The resultant displacement of the shoulders and links results in the passive joints being driven towards their desired joint angles. 
     The measured joint angles of the six active joints generated by the joint motor controllers  126  are forwarded to a forward kinematics module  562 . Also applied to the forward kinematics module  562  are the signals from encoders  117  and  118 . These signals are the measured joint angles for the passive joints integral with these encoders. Based on the measured joint angles and preloaded data, the forward kinematics module  562  determines a representation of the actual pose of the end effector  110 , coordinate system EFCT, relative to coordinate system MNPL. The preloaded data are data that define the geometry of the links and joints. In some versions, these data are in the form Denavit-Hartenberg parameters. 
     Forward kinematics module  562  also calculates joint angles for the passive joints to which encoders are not attached. These calculated joint angles function as representations of the actual joint angles for the passive joints to which encoders are not attached. The forward kinematics module  562  calculates these joint angles as part of the process of determining the actual pose of the end effector  110 . 
     Based on the measured pose of the end effector, forward kinematics module  562  produces data describing the measured pose of coordinate system CMVB and coordinate system EAPP both relative to coordinate system MNPL. This is because coordinate systems EFCT, CMVB and EAPP have fixed poses relative to each other. 
     The measured pose of coordinate system CMVB is applied to a Jacobian calculator  564 . Jacobian calculator  564 , based on this measured pose, calculates Jacobian matrices relating motion within individual coordinate spaces to motion of the origin of coordinate system CMVB expressed in coordinate system CMVB. One such coordinate space is joint space. Joint space is a vector consisting of all the joint angles of the manipulator. One of the calculated matrices is the Jacobian matrix between joint space and coordinate system CMVB, Jacobian J JNT . A second coordinate space is interference space. Interference space is a vector that includes minimum distances between the below-discussed potentially colliding pairs of links. In some cases, these minimum distances are distances along the common normals between the potentially colliding pairs of links. A second calculated matrix is the Jacobian matrix between interference space and coordinate system CMVB, Jacobian J INF . Coordinate system EAPP is a third coordinate space. Calculator  564  calculates the Jacobian matrix between the origin of coordinate system EAPP, expressed in coordinate system MNPL, to the origin of coordinate system CMVB, Jacobian J WSB . 
     Often calculator  564  initially calculates the inverse Jacobian of the desired Jacobian using numerical methods. Once the inverse Jacobian is calculated, calculator  564  determines the desired Jacobian by computing an inverse of the inverse Jacobian. In the case of a non-square Jacobian matrix, the pseudoinverse must be used to compute this inverse. 
     The measured joint angles from encoders  112 - 118  and the calculated joint angles from forward kinematics module  562  are applied to a joint limit comparator  582 . Joint limit comparator  582  and the associated modules generate signals that prevent each joint, active and passive, from moving beyond a specific range of motion. A minimum and maximum joint limit angle is defined for each joint. For proper operation of the manipulator, each joint angle should be between the associated joint limit angles. Joint limit comparator  582  employs the measured or calculated joint angle for each joint as the representation of the actual joint angle for the joint. 
     Associated with each joint limit angle is a joint boundary angle. The joint boundary angle is an angle within the range of motion of the joint that is relatively close to the joint limit angle. For example, if the minimum joint limit angle associated with a joint is 10° the minimum boundary angle may be between 12 and 20°. If the maximum joint angle of a joint is 115°, the maximum boundary angle may be between 105° and 113°. Joint limit comparator  582  determines the differences between the representation of actual joint angle to the minimum and maximum boundary joint angles, step  591  of  FIG.  24   . This difference is known as a boundary exceeded angle, angle ANGLE B_E . 
     If the representation of actual joint angle is greater than the minimum boundary joint angle and less than the maximum joint boundary angle, the joint is considered acceptably spaced away from the joint limit angles for the joint. There is no need to apply forces and torques to the virtual rigid body that would prevent movement of the joint towards the closest joint limit. Accordingly, in a step  591  if the above conditions tests true, joint limit comparator outputs a boundary exceeded angle of 0° (step not shown). If the above condition tests false, joint limit comparator  582  outputs a boundary exceeded angle that is the signed difference of the representation of actual joint angle and the crossed boundary angle (step not shown). Typically, the sign is negative if the minimum joint boundary angle is crossed and positive if the maximum joint boundary angle is crossed. 
     Step  592  represents the evaluation of the boundary exceeded angle. If this angle is equal to zero for a particular joint angle, manipulator controller  124  interprets this information as indicating that manipulator  50  can continue to freely move the joint towards the closest boundary joint angle. In  FIG.  24    this is represented by, step  594 , the motion control software&#39;s not outputting a joint limit torque. 
     If the boundary exceeded angle is non-zero, the angle is applied to a joint limit torque generator  584 , step not shown. Generator  584 , based on the input series of boundary exceeded angles, computes a time derivative of these angles. This time derivative is angular velocity V B_E . Joint limit torque generator  584  outputs a torque that would be applied to the joint to prevent the manipulator from being moved in such a way that joint will move further beyond the boundary angle towards the adjacent joint limit angle, step  596 . This torque, torque T J_L , is determined according to the following formula:
 
 T   J_L   =f (ANGLE B_E )+ f ( V   B_E )  (13)
 
In some cases:
 
 f (ANGLE B_E )= K   B_E ANGLE B-E   (13A)
 
 f ( V   B_E )= D   B_E   V   B_E   (13B)
 
Coefficient K B_E  is a spring coefficient. This coefficient may be variable. This is because as the joint angle approaches the adjacent joint limit angle there would be a need to appreciably increase the torque that limits joint movement towards this angle. Consequently, there is often greater than first order relationship between the magnitude of this torque and the absolute difference between the crossed boundary angle and the representation of actual joint angle.
 
     Coefficient D B_E  is a damping coefficient. The damping coefficient may be variable. In some versions, this coefficient is a function of the boundary exceed angle ANGLE B-E  and/or velocity V B_E . Varying coefficient D B_E  may be desirable to enhance the stability of the movement of the instrument. 
     In practice, joint limit torque generator  584  does not actually execute Equation (13) to determine the joint limit torque. Instead, the generator  584  maintains look up tables of limiting torques (tables not illustrated). The inputs to determine the appropriate limiting torques are representations of boundary exceeded angle ANGLE B-E  and angular velocity V B_E . If the boundary exceeded angle is 0°, torque T J_L  is inherently a zero torque. 
     Joint limit torque generator  584  applies the plurality of torques T J_L , one for each joint, to CMVB force converter  586 , step not shown. A second input into force converter  586  is the previously generated Jacobian J JNT  from Jacobian calculator  564 . The force converter  584  places the individual torques T J_L  into a column vector, {right arrow over (T)} J_L . Force converter converts these torques {right arrow over (T)} J_L  into the equivalent forces and torques, force F J_L , that should be applied to the virtual rigid body at the origin of coordinate system CMVB, step  597 . This conversion is performed according to the following formula:
 
 F   J_L   =J   JNT   −T   {right arrow over (T)}   J_L   (14)
 
Force F J_L  is expressed in coordinate system CMVB. Force F J_L  is one of the inputs applied to force summer  379 , (step not shown).
 
     Another software module to which the measured and calculated joint angles are applied is the interference limit comparator  622 . Comparator  622  employs these angles as representations of the actual joint angles. In brief, the joint limit comparator  622  and associated modules outputs data describing forces that should be applied to the virtual rigid body if the movement of the arms could potentially result in link collisions. Here a “link” is more than just the links  72 ,  74 ,  76  and  80 , that form each arm  68  and  70 . A “link,” for the purpose of the processing performed by comparator  622 , is any structural member, moving or rigid, that, as a result of the movement of one of the joints could collide with another component of the manipulator. For example, if the manipulator  50  is constructed so that one of the arm links could potentially collide with an outer surface of the cart  52 , comparator  622  would consider the cart surface to be a link. The shells in which the actuators are disposed if they could potentially collide with a link, are also considered to be links. 
     One reason to prevent these collisions is to prevent the movement of the links relative to each other that could result in pinch points forming between the links. Preventing these collisions also avoids the damage caused by such collisions. 
     It should be understood that each link of the manipulator may not potentially be capable of a collision with every other link of the manipulator. For example, the four-bar link  78  and driven link  80  of each arm  68  and  70  cannot, due to the inherent construction of the manipulator  50 , collide with each other. Nevertheless, the driven link  80  of arm  68  can collide with the driven link  80  of arm  70 . Most pairs of potentially colliding links consists of a link integral with arm  68  and a link integral with the other arm, arm  70 . 
     Based on the representations of the actual joint angles, interference limit comparator  622  determines a minimum distance between each pair of potentially colliding links, step  632  in  FIG.  25   . In some embodiments, this minimum distance is the distance along the common normal between the links. To make this determination, comparator  622 , using data and processes similar to that employed by forward kinematics module  562 , determines the pose of each joint. Based on the pose data, module  622  models each link as one or more line segments between each joint. Based on the line segment models, module  622  determines the common normal distance, the minimum distance, between each pair of potentially colliding links. 
     In step  634 , the interference limit comparator  622  calculates a difference between the minimum distance for each pair of potentially colliding links and a boundary distance for the pair of links. This boundary distance is the distance below which movement of the links towards each other is undesirable. It should be appreciated that this movement includes movement in which only one link moves towards the other link. This boundary distance is greater than what could be considered a collision avoided distance. Here, the collision avoided distance is a distance which is a minimal clearance distance between the links. The collision avoided distance is a distance for the pair of potentially colliding pair of links that is greater than the smallest distance between the links that would be considered to form a pinch point between the links. 
     The boundary distance is determined for each pair of potentially colliding links is typically determined prior to the start of the procedure. The boundary distance can be determined by modeling each link including a longitudinal axis that is surrounded by a three dimensions volume. This volume may have a cylindrical or capsule like shape. Alternatively, the shape may be in the form of parallel pipette. This volume may have a more complex shape. The outer surface of this volume is typically located at least 3 cm beyond the actual outer surface of the modeled link. In some versions this volume has an outer diameter of at least 5 cm or at least 10 cm beyond the actual surface of the link. If the volume is capsule-like or cylindrical, the boundary distance for each pair of potentially colliding links comprises the sum of the radii for each of link encasing capsules or cylinders. 
     The difference between the minimum distance and a boundary distance for a pair of potentially colliding links is the interference boundary exceeded distance, distance DIST I_B_E . 
     If the minimum distance for a pair of links is greater than the associated boundary distance, the manipulator  50  is considered in a condition in which the links are spaced sufficiently far apart from each other that movement of the links towards each other would not result in formation of a pinch point or collision. For each pair of potentially colliding links in this condition, comparator returns an interference boundary exceeded distance of zero (step not shown). 
     If the minimum distance for a pair of links is less than the associated boundary distance, interference limit comparator  622  outputs the absolute value of the difference as distance DIST I_B_E , step not shown. 
     In a step  635 , for the pairs of potentially colliding links, the interference boundary exceeded distance, distance DIST I_B_E  is evaluated. If this distance is zero, the motion control processes do not output a force that would prevent the links from continuing to move together, step  636 . 
     If the interference boundary exceeded distance, distance DIST I_B_E  is non-zero, the distance is applied to an interference limit force generator  624 , step not shown. Generator  624 , based on the input series of interference boundary exceeded distances, computes a time derivative of these distances, step  637 . This time derivative is a linear velocity V I_B_E . Interference limit force generator  624  outputs a force that would be applied along the line of minimum distance between the links to prevent the manipulator from being moved in such a way that will result in the further closing of the distance between the potentially colliding links, step  638 . For some constructions, this line is along the common normal between the links. This force, force F I_B_E , is determined according to the following formula:
 
 F   I_B_E   =f (DIST I_B_E )+ f ( V   I_B_E )  (15)
 
In some cases:
 
 f (DIST I_B_E )= K   C_A DIST I_B_E   (15A)
 
 f ( V   I_B_E )= D   C_A   V   I_B_E   (15B)
 
Coefficient K C_A  is a spring coefficient. This coefficient may be variable. This is because as the minimum distance approaches the collision stopped distance, there is a need to appreciably increase the force that limits the movement of the links towards each other. Consequently, there is often greater than first order relationship between the magnitude of this force and the interference boundary exceeded distance.
 
     Coefficient D C_A  is a damping coefficient. The damping coefficient may be variable. In some versions, this coefficient is a function of distance DIST I_B_E  and/or velocity V I_B_E . Varying coefficient D C_A  may be desirable to enhance the stability of the movement of the instrument. 
     In practice, interference limit force generator  624  does not actually execute Equation (15) to determine the collision preventing force. Instead, the generator  624  maintains look up tables of collision preventing forces (tables not illustrated). The inputs to determine collision preventing forces are representations of the interference boundary exceeded distance DIST I_B_E  and velocity V I_B_E . If the interference boundary exceeded distance is zero, force F I_B_E  is inherently a zero force. Interference limit force generator  624  generates a plurality of forces F I_B_E  one for each potentially colliding pair of links. 
     The plural forces F I_B_E  generated by generator  624  are applied to a CMVB force converter  626 , step not shown. A second input into force converter  626  is the previously generated Jacobian J INF  from Jacobian calculator  564 . Force converter  626  places the individual forces F I_B_E  into a column vector, F I_B_E . Force converter converts forces F I_B_E  into the equivalent forces and torques, force F INF , which should be applied to the origin of coordinate system CMVB of the virtual rigid body, step  639 . This conversion is performed according to the following formula:
 
 F   INF   =J   INF   −T   {right arrow over (F)}   I_B_E   (16)
 
Force F INF  is expressed in coordinate system CMVB. Force F INF  is one of the inputs applied to force summer  379 , step not shown.
 
     Another module that is part of the motion control processes performed by the manipulator controller  124  is a workspace limit comparator  652 . Workspace limit comparator  652  determines if the energy applicator  184  is reaching the boundary of a defined workspace. The limit of this workspace is spaced from the origin of the coordinate system MNPL and is defined by reference to this coordinate system. The workspace is within the volume in which energy applicator  184  can move if shoulders  67  and  69  and links  72  and  74  are allowed to move to the full extensions of their ranges of motion. This workspace, sometimes referred to as the “dexterous workspace,” is less than the volume of the space within the full range of motion of the manipulator  50 . This is because, as the energy applicator  184  moves towards the limit of its inherent boundary, the ability to adjust the orientation of the instrument and energy applicator  184  is reduced. By way of example, at an extreme, in order to position the energy applicator  184  at the location where it is spaced a maximum distance from the origin of manipulator reference frame, the arms can only be in one position, a fully extended position. Since the arms can only be in a single position, by extension the instrument and energy applicator  184  can only be aligned in one orientation. To ensure that the practitioner has at least some ability to so reorient the energy applicator  184 , the manipulator  50  does not allow the energy applicator  184  to advance outside of this workspace. 
     It should be appreciated that, owing to the physical construction of the manipulator  50 , this workspace is typically not in the form of a simple geometric structure such as a sphere or a cube. The workspace is often defined by a set of contiguous volumes each of which has a different shape and or size. Thus, while the distance to the ceiling of the workspace above and distal to the origin of the manipulator may be a distance of 1.5 m from the origin of the manipulator coordinate system, the distance to the base of the workspace below the origin of the manipulator coordinate system may be 0.2 m. In these and other versions, the proximal end of the workspace may be located distal to origin of the coordinate system MNPL. Thus, in some versions the arms may be able to move the instrument within a workspace that may extend from a location 0.5 m distal from the origin of the coordinate system MNPL to a location 2.0 m distal from the same point. 
     The virtual surfaces around the manipulator defining the workspace are collectively referred to as the workspace limit. Within the workspace limit there is a workspace boundary. The workspace boundary is located typically 1 to 5 cm inwardly from the workspace limit. Like the workspace limit, the workspace boundary is defined in coordinate system MNPL. 
     The workspace limit comparator  652  receives as an input a representation of the actual position of the energy applicator  184 , the origin of coordinate system EAPP. In one version, this representation of the actual position of the origin of coordinate system EAPP on the position is calculated by the forward kinematics module  562 . Based on the representation of energy applicator  184  position, comparator  652  determines the location of the energy applicator  184 , the origin of coordinate system EAPP, relative to the workspace boundary, step  639   a . Step  640  represents the evaluation that occurs after this initial determination is made. If the energy applicator  184  is within the workspace boundary, the motion control processes do not apply forces to ensure the energy applicator  184  remains within the workspace limit. This is represented by the branching to step  661 . 
     If the evaluation of step  661  tests false, comparator  652  calculates a positive workspace boundary exceeded distance, distance DIST W_B_E , step  663 . This distance is the distance along a line from the origin of coordinate system EAPP back to a point on the workspace boundary such that the line is normal to the surface of the boundary. This distance is typically the shortest distance from the origin of coordinate system EAPP back to the workspace boundary. As part of step  663 , a unit direction vector, vector D W_B_E , along this line from the origin of coordinate system EAPP towards the workspace boundary is determined. Vector D W_B_E  is expressed in coordinate system MNPL. 
     The workspace boundary exceeded distance is applied to a workspace limit force generator  654 , step not shown. Generator  654 , based on the input series of workspace boundary exceeded distances, computes a time derivative of these distances, step  664 . This time derivative is a linear velocity V W_B_E . 
     In a step  665  workspace boundary exceeded force generator  654  outputs a force that would be applied along the normal line from the origin of coordinate system EAPP back to the workspace that would prevent the energy applicator  184  from being moved further away from the workspace boundary towards the workspace limit. The magnitude of this force, force F W_B_E , is determined according to the following formula:
 
 F   W_B_E   =f (DIST W_B_E )+ f ( V   W_B_E )  (17)
 
In some cases:
 
 f (DIST W_B_E ) K   WS_E DIST W_B_E   (17A)
 
 f ( V   W_B_E )= D   WS_E   V   W_B_E   (17B)
 
Coefficient K WS_E  is a spring coefficient. This coefficient may be variable. This is because as the energy applicator  184  moves outwardly from the workspace boundary towards the workspace limit, there is a need to appreciably increase the force that prevents the continued movement of the energy applicator  184  towards the workspace limit. Consequently, there is often greater than first order relationship between the magnitude of this force and the workspace boundary exceeded distance.
 
     Coefficient D WS_E  is a damping coefficient. The damping coefficient may be variable. In some versions, this coefficient is a function of distance DIST W_B_E  and/or velocity V W_B_E . Varying coefficient D WS_E  may be desirable to enhance the stability of the movement of the instrument. 
     In practice, workspace boundary force generator  654  does not actually execute Equation (17) to determine the workspace boundary exceeded force. Instead, the generator  654  maintains look up tables of these forces (tables not illustrated). The inputs to determine collision preventing forces are representations of the workspace boundary exceeded distance DIST I_B_E  and velocity V I_B_E . If the workspace boundary exceeded distance is zero, force F W_B_E  is inherently a zero force. 
     Scalar force F W_B_E  is converted into a vector force, F W_B_E  according to the following equation:
 
 {right arrow over (F)}   W_B_E   =F   W_B_E   D   W_B_E   (17C)
 
Force {right arrow over (F)} W_B_E  is expressed in coordinate system MNPL.
 
     Force {right arrow over (F)} W_B_E  is applied to a CMVB force converter  655 , step not shown. A second input into force converter  655  is Jacobian J WSB  from Jacobian calculator  564 . The force converter converts force F W_B_E  into the equivalent forces and torques, force F WSB , that should be applied to the origin of coordinate system CMVB of the virtual rigid body, step  666 . This conversion is performed according to the following formula:
 
 F   WSB   =J   WSB   −T   {right arrow over (F)}   W_B_E   (18)
 
Force F WSB  is expressed in coordinate system CMVB. Force F WSB  is one of the forces applied to force summer  379 , step not shown.
 
     The behavior controller also includes modules that provide data about external forces and torques that are applied to the manipulator  50 , the instrument  160  and energy applicator  184 . These external forces and torques include the resistance of the tissue to instrument advancement and practitioner applied forces and torques. 
     One method of determining external forces and torques is to determine the magnitude of backdrive torques output by the joint motors  101 . Backdrive torques are output by joint motors  101  in response to external forces and torques placed on the manipulator, instrument and energy applicator  184 . The backdrive torques are the torques output by the joint motors  101  beyond the torques needed to overcome inertia and the force of gravity. 
     Backdrive torques function as representations of external forces and torques because each joint motor  101  and associated joint motor controller  126  form a position control loop. The joint motor controller  126  regulates the joint angle of the joint with which the controller is associated. Each controller  126  continually adjusts the torque the associated motor  101  outputs to, as closely as possible, ensure that the motor drives the associated joint to the commanded joint angle. When the instrument is subjected to external forces and torques, these forces and torques momentarily disrupt the advancement of the instrument to the commanded pose. This, in turn, momentarily disrupts the advancement of one or more of the joints to their commanded joint angles. The control loops typically operate at a much higher bandwidth than the behavior and motion control processes. The control loops therefore, essentially simultaneously with the application of the external forces and torques, adjust the torques output by the joint motors  101  to compensate for these forces and torques. Thus, the torques output by the joint motors represent a sum of torques. These torques are the torques needed to overcome inertia and gravity and the torques needed to overcome the external forces and torques, the back drive torques. 
     To calculate the backdrive torques, the manipulator controller  124  determines the torques that joint motors  101  should output if external forces and torques are not present. These torques are determined by an expected dynamics module, module  690 . The inputs into expected dynamics module  690  are the measured joint angles from encoders  112 ,  114 ,  116 ,  117  and  118  and the calculated joint angles from forward kinematics module  562 . Using the methods employed by command dynamics module  544 , expected dynamics module  690  calculates, for the active joints, estimates of torques consistent with the observed movement of the joints. These torques are estimates of the torques that would be applied in the absence of external forces and torques applied to the manipulator, the instrument or the energy applicator  184 . These torques are referred to as the expected torques. 
     The second set of variables upon which the backdrive torques are determined is the actual torques that the joint motors apply to the arms  68  and  70  to advance the instrument  160  towards the commanded pose. Manipulator  50  employs two methods for obtaining representations of the actual torques. One method is the measuring of the torques output by the joint motors  101 , more accurately, the reduction gears  105 . In practice, signals representative of the currents applied to the joint motors  101  from the joint motor controllers  126  are often employed as signals representative of the joint motor/reduction gear torques. This is because there is a linear relationship between the current applied to a motor  101  and the torque output by the motor. 
     The second method of determining representations of actual torques is to monitor the torques the joint motors  101  output as measured by torque sensors  89 . 
     A backdrive torque summer  691  receives as inputs the currents applied to the joint motors  101  and the signals output by torque sensors  89 . Torque summer  691  blends these inputs to produce a single stream of output data representative of the actual joint torque. In some versions, backdrive torque summer  691  produces a weighted average of these two representations of actual torques. These average torque values reflect the strengths in accuracies in torque measurements that are inherent but different in the two separate methods of determining actual joint torque. Torque sensors  89  may produce signals that are incrementally more sensitive to changes in torque output. The torque measurements based on the applied current in some cases are more representative of the output torque over a broader range of torques. 
     The representation of actual joint torques produced by torque summer  691  is applied to a backdrive torque calculator  693 . The second input into calculator  693  is the set of expected joint torques. Calculator  693  computes the difference between these two sets of torques. This difference is an estimate of the backdrive torques, torque T BDR , Outputted to compensate for the external forces and torques. Torque T BDR  is a column vector that includes estimates of the backdrive torques applied to the active joints. The components of torque T BDR  for the passive joints are set to zero. 
     If external forces and torques are not present, the representations of actual joint torques should be equal to the expected joint torques. If this condition exists, the output from the backdrive torque calculator  693 , torque T BDR , is essentially the zero vector. 
     Torque T BDR  is applied to a CMVB force converter  694 . A second input into force converter  694  is Jacobian J JNT  from the Jacobian calculator  564 . Force converter  694  converts torque T BDR  into the equivalent forces and torques, force F BDR , which should be applied to the origin of coordinate system CMVB of the virtual rigid body. This conversion is performed according to the following formula:
 
 F   BDR   =J   JNT   −T   T   BDR   (19)
 
Force F BDR  is expressed in coordinate system CMVB. Force F BDR  is in the same direction as the direction of the external forces and torques applied to the manipulator  50 , the instrument  160  and energy applicator  184 .
 
     Backdrive force F BDR  are applied to a deadband filter  695 . Deadband filter  695  only passes through for subsequent processing backdrive forces with absolute values above certain defined threshold values stored in the filter  695 . In some versions there is a threshold for each component of force F BDR . Alternatively, the thresholds are based on the magnitude of the force component and the magnitude of the torque component of force F BDR . 
     The outputs of filter  695  are based on the differences between the components of backdrive forces F BDR  and the threshold values. Components of force F BDR  with absolute values below the threshold values are set to zero. This filtering offsets the inherent limitations in modeling the structure of the manipulator  50 . These limitations are due in part to the difficulty in accounting for extra loads, such as the existence of cables that may be attached to the manipulator arms  68  and  70 . These limitations also compensate for the difficulty in modeling friction and the dynamics of the manipulator. 
     Force/torque sensor  108  provides manipulator controller  124  a second indicia of the external forces and torques applied to the manipulator  50 , the instrument  160  and energy applicator  184 . The output signals from sensor  108  are applied to a gravity compensator  689 , depicted in  FIG.  13 E . Gravity compensator  689  outputs signals representative of the applied forces and torques from which the effect of gravity on the sensor  108 , the instrument  160  and energy applicator  184  have been substantially eliminated. 
     These compensations are typically subtracted from the signals representative of the sensed forces and torques. The compensation is often performed by reference to values stored in look up tables integral with the compensator  689 . These values may be positive or negative. The specific compensation value subtracted from any individual signal representative of measured force and torque is generally a function of the orientation of the instrument. A second input into compensator  689  is therefore data representative of the actual orientation of the instrument. The orientation component of the measured pose from the forward kinematics module  562  can function as this representation of actual instrument orientation. 
     The data for compensation value tables maintained by compensator  689  can be defined each time the manipulator  50  is initially activated. To obtain these data, the arms  68  and  70 , position the instrument  160  and attached energy applicator  184  in a number of predefined orientations. Compensator  689 , based on the output from sensor  108  when the instrument is in each of these orientations, generates the data for the look up tables. Alternatively, the data for the tables are calculated using predefined data regarding the sensor  108  and data defining the mass properties of the components attached to the distally directed portion of the sensor. These data may include data stored in a memory integral to the instrument. 
     As a result of this compensation the practitioner, when holding the instrument, is neither exposed to the actual force of gravity working against the instrument nor an emulated version of this force. This reduces the physical fatigue to which the practitioner may otherwise be exposed when holding the instrument for extended periods. 
     Compensator  689  also compensates for inherent errors in the signals output by the sensor. These errors include offsets due to temperature drift. Compensator  689  compensates for these errors by adding or subtracting offset values that are specific for the sensor. These offset values may also be a function of sensor orientation. These offset values are often stored in look up tables integral with the compensator  689 . These look up tables are separate from the tables in which the gravity-compensating offset values are stored. 
     The gravity compensated signals from sensor  108  are applied to a CMVB force converter  696 . Converter  696  converts these forces and torques from a coordinate system specific to sensor  108  into the equivalent forces and torques applied to coordinate system CMVB. The Jacobian employed by CMVB force converter  696  is a Jacobian with constant coefficients that is defined at the start of the procedure in which the manipulator is employed. This Jacobian is based on the relative pose between the coordinate system of sensor  108  and coordinate system CMVB. Converter  696  thus outputs representations of the forces and torques measured by sensor  108  that are expressed in coordinate system CMVB. 
     The output of converter  696  is applied to an attenuator  697  internal to manipulator controller  124 . Attenuator  697  selectively attenuates the signals from zero values to their unattenuated levels. In some versions of this invention, the ramping is performed using finite impulse response digital filters. The extent to which attenuator  697  attenuates these signals is a function of the depressed/released state of switch  176 . When switch  176  is depressed, attenuator  697  ramps the signals down to their fully attenuated, zero values. Upon the release of switch  176 , the signals are ramped to their unattenuated levels. The ramping down/ramping up is typically performed over a period of between 10 to 500 milliseconds. The actual time periods of these two ramping processes need not be equal. In some versions of this invention, the ramping is performed using finite impulse response digital filters. The output from attenuator  697  are force F FTS . Force F FTS  is expressed in coordinate system CMVB. 
     This signal ramping reduces the extent to which large impulse forces are applied to the instrument when switch  176  is initially depressed or released. 
     Force F BDR  from CMVB force converter  694  and force F FTS  are applied to an external forces summer  698 . Summer  698  produces a weighted sum of these two representations of the external forces and torques, force F EXT . Force F EXT  includes a force vector component, F EXT  and a torque vector component, T EXT . External forces force summer  698  outputs the force vector component according to the following equation:
 
 {right arrow over (F)}   EXT   =A   BDR   {right arrow over (F)}   BDR   +A   FTS   {right arrow over (F)}   FTS   (20A)
 
Here, {right arrow over (F)} BDR  is the force vector component of F BDR . Vector {right arrow over (F)} FTS  is the force vector component of F FTS . The torque vector component of external forces F EXT  is calculated using a similar equation:
 
 {right arrow over (T)}   EXT   =B   BDR   {right arrow over (T)}   BDR   +B   FTS   {right arrow over (T)}   FTS   (20B)
 
Here, {right arrow over (T)} BDR  is the torque vector component of F BDR . Vector {right arrow over (T)} FTS  is the torque vector component of F FTS .
 
     In Equations (20A) and (20B) A BDR , A FTS , B BDR  and B FTS  are the weighting factor coefficients for the individual force and torque variables. These weighting factors may not be constant for the full range of external forces and torques applied to the manipulator, the instrument or energy applicator  184 . These weighting factors may be varied to compensate for characteristics associated with the sources of the representations of the external forces and torques. For example, when relatively low external forces and torques are applied to the instrument, the sensor  108  may provide the more accurate representation of these forces and torques. Accordingly, when the manipulator is in this state, weighting factors A FTS  and B FTS  are relatively high and weighting factors A BDR  and B BDR  and are relatively low. 
     When the external forces and torques are relatively large, the output signals from the same sensor  108  may be saturated. For this construction of manipulator  50 , the backdrive torques are representative of the external forces and torques over a wider dynamic range. Accordingly, when the external forces and torques are relatively large, weighting factors A BDR  and B BDR  are relatively high and weighting factors A FTS  and B FTS  and are relatively low. 
     The weighting factors typically range from 0.0 to 1.0. As a result of empirical testing, in some versions, the maximum values of weighting factors A BDR  and B BDR  are set to values above unity. The factors A xxx  and B xxx  for each pair typically add to unity. In some versions, this sum may be less than or greater than unity. 
     Force F EXT  is expressed in coordinate system CMVB. External forces summer applies force F EXT  to force summer  379 . 
     Damping forces and torques are also components of the forces F TTL  and torques T TTL  output by force summer  380 . Collectively, the damping forces and torques are identified as force F DMP . Damping force F DMP  is generated to provide a resistance to movement of the instrument that emulates the natural motion of the instrument. 
     Damping force F DMP  is generated by damping force calculator  734  seen in  FIG.  13 B . A representation of the actual velocity of coordinate system CMVB functions as the input data from which calculator  734  determines damping force F DMP . In the depicted version, the commanded velocity output by the cut guide  390  is employed as the representation of this velocity. 
     There are a number of different means by which damping force calculator  734  could generate forces in opposition to the advancement of the instrument  160 . Calculator  734  may use an algorithm to generate these forces wherein the input variable is the velocity vector. This algorithm is typically in the form of:
 
 F   DMP   =f ( V   CMND )  (21)
 
In some cases:
 
 f ( V   CMND )= D   DMP   V   CMND   (21A)
 
Velocity V CMND  is the vector comprising the linear and rotational components of commanded velocity, expressed in coordinate system CMVB. Coefficient D DMP  is a matrix including the damping coefficients. In many constructions, this matrix is a diagonal matrix in which the linear and rotational coefficients are not equal. Often the linear coefficients are identical and the rotational coefficients are identical. The coefficients of this algorithm may change as a function of the specific range of velocities of the velocity supplied to the calculator. These coefficients are typically stored in a look-up table associated with calculator  734 .
 
     Alternatively, damping calculator  734 , based on the velocity vector, refers to a look-up table in which a number of different values for damping force F DMP  are stored. Based on the specific velocity supplied to the calculator  734 , the calculator retrieves data that collectively describe an appropriate force F DMP . 
     Often manipulator  50  is provided with plural sets of damping coefficients D DMP  or multiple sets of look up tables in which values for force F DMP  are stored. Depending on the mode of operation of the manipulator  50 , a particular set of coefficients or look up table is used as the reference data upon which force F DMP  is generated. This is because it is often desirable to set the damping force as a function of the mode of operation of the manipulator. For example, in comparison to when being operated in the manual mode, when the manipulator is operated in the semi-autonomous mode it is often desirable to provide a higher magnitude damping force. This increase in damping force has been found to minimize the reaction of the instrument to the forces (the resistance) to which the instrument and energy applicator  184  are exposed. This can improve the precision with which the manipulator  50  advances the energy applicator  184  along the path segment. 
     Another means by which damping force calculator  734  could generate forces in opposition to the advancement of the instrument  160  is by using an algorithm to generate forces due to “sliding friction.” The magnitude of sliding friction is a constant value and is independent of surface area, displacement or position, and velocity. This type of damping is of the first order and is referred to as Coulomb damping. Coulomb damping and the above-described viscous damping may be adjusted independently to maintain the stability of the instrument and to control how the instrument feels to the practitioner. 
     Also, it is often desirable to output a decreased magnitude damping force F DMP  when the practitioner depresses switch  176  to manually set the position of the instrument  176 . As soon as switch  176  is released, it is typically desirable to employ coefficients D DMP  or reference look up tables that result in the outputting of a damping force F DMP  of increased magnitude. This higher magnitude force F DMP  is output to rapidly stop the movement of the instrument. 
     Damping force calculator  734  outputs damping force F DMP  as a force to be applied to the center of mass of the virtual rigid body, expressed in coordinate system CMVB. Damping force F DMP  is applied to force summer  379 . 
     Force summer  379 , the environmental force summer, receives the following inputs: the joint limit force F J_L ; the interference limit force F INF ; the workspace boundary force F WSB ; the external force F EXT ; and the damping force F DMP . These forces are summed together. The output of force summer  379  is the environmental force, force F ENV . 
     Environmental force summer  379  may output force F ENV  as a weighted sum. Coefficients are applied to the individual inputs to perform this weighting. The weighting may be performed to appropriately balance the relative contribution of each input force. This balancing is performed to increase the extent to which, when the manipulator  50  advances the instrument in the manual mode, the impression the practitioner perceives is the same as that which would be perceived if he/she was directly applying force to advance the instrument. The coefficients may change as a function of the transition of the manipulator between operating modes. During these transitions, the coefficients are typically ramped up or down over a time interval following the transition. Typically, this interval is between 10 and 100 milliseconds. 
     Environmental force F ENV  is applied to the energy applicator force calculator  358  of the tool path force calculator  278 . Energy applicator force calculator  358  uses force F ENV  as the above described input into its solving of Equation (5). Environmental force F ENV  is also applied to total force summer  380 . 
     Total force summer  380  receives as inputs the environmental force F ENV , the semi-autonomous instrument advancement force F INST  and the force required to maintain the orientation of the instrument, F ORNT . Based on these three inputs, total force summer  380  produces the above-discussed outputs: forces F TTL ; and torques T TTL . Forces F TTL  and torques T TTL  may be weighted sums of the inputs for the same reasons environmental force F ENV  may be a weighted sum. 
     Another module internal to manipulator controller  124  is an instrument manager  702 , seen in  FIG.  27   . Instrument manager  702  controls the on/off state of instrument  160 . Inputs into manager  702  include signals indicating the depressed/released states of pendant trigger  194 , instrument buttons  164  and  174  and instrument control switch  176 . Force overrider  375  provides a signal if it is necessary to deactivate the instrument power generating unit  163 . Tool path generator  234  selectively asserts a signal to the instrument manager  702  at the start of semi-autonomous advancement of the instrument. This signal is asserted if the instrument is within the below discussed target region. The cut guide  390  provides a signal to the instrument manager  702  indicating that the boundaries have been defined. The localization engine  270  provides data indicating that the engine is able to generate data describing the relative pose of the instrument and the bone. Inferentially these latter data are data indicating that the signals transmitted by the tracker  212  and  214  are being received by the localizer  216 . Based on the above data, the instrument manager  702  selectively asserts signals to activate and deactivate the instrument power generating unit  163 . These signals are forwarded to the tool controller  132 . 
     Instrument manager  702  asserts the signals that result in the turning on of the tool power generating unit  163  in response to a number of conditions being meet. One of these conditions is that the cut guide  390  has indicated that the boundaries have been defined. Another condition that should be met is that localization engine  270  is able to track the relative pose of the instrument to the bone. 
     Instrument manager  702  actuates the instrument  160  when the practitioner takes positive action to intentionally actuate the instrument. When the manipulator is operated in the manual mode, this action is the continued depression of switch  176  in combination with the toggling of one of buttons  164  or  174 . When the manipulator is operated in the semi-autonomous mode, instrument manager  702  only sends the signals to the tool controller  132  indicating that the power generating unit  163  should be energized if the manager receives an indication that pendant trigger  194  is depressed. 
     IV. Operation 
     A. Manual Mode 
     Manipulator  50  is prepared for use by attaching the energy applicator  184  to the instrument  160 . Instrument  160  is, by way of coupling assembly  111 , mounted to end effector  110 . Using calibration techniques, the pose of coordinate system EAPP, the pose of coordinate system CMVB, the pose of coordinate system EFCT and the pose of coordinate system TLTR relative to each other are determined. Data describing these relative poses are supplied to the manipulator controller  124 , specifically coordinate system transformer  272 . 
     Upon initial actuation of the manipulator  50 , the boundaries upon which the cut guide limits the advancement of the instrument have not yet been defined. Instrument manager  702  therefore does not assert signals to the tool controller  132  that can result in the actuation of the instrument power generating unit  163 . 
     Once the bone tracker  212  is fixed to the bone, the bone is registered relative to coordinate system BTRK. Surgical personnel, using navigation interface  220  adjust and confirm the positioning of the boundaries relative to the bone. Once this step is performed, boundary generator  232  employs these data to calculate the pose of the coordinate system associated with the boundaries relative to coordinate system BTRK. This relationship is fixed. These relationship data are applied to the coordinate system transformer  272 . Data defining the positions of the boundary-defining tiles are loaded into the cut guide  390 . 
     Once the tile-defining data are loaded into cut guide  390 , the cut guide  390  asserts a signal to the instrument manager  702  indicating the boundaries have been defined. Receipt of this signal is recognized by the instrument manager  702  that the practitioner can now actuate the instrument  160 . 
     Also as part of the initial configuration of the instrument, the tool controller  132  is set to output the energization signals needed to cause the instrument to, when actuated, output the energy designated by the practitioner. For example, if the instrument  160  includes a motor, the tool controller  132  is set to cause the instrument motor to operate at the practitioner desired motor speed. If the instrument  160  is an electrosurgical tool, tool controller  132  is set to cause the instrument to source the appropriate current and/or cause an appropriate voltage to develop across two electrodes. If the instrument emits photonic energy, instrument controller  132  is set to cause the instrument  160  to output photonic energy of the appropriate wattage. These setting are performed by entry of commands through user interface  130 . 
     Manipulator  50  is enabled for operation by depressing a button presented on user interface  130  (button not illustrated). In response to the depression of this button, manipulator controller reads the signals from the encoders  112 ,  114 ,  116 ,  117  and  118  as the measured joint angles. Based on these data, the forward kinematics module  562  determines an initial set of calculated joint angles. Forward kinematic module  562  also outputs an initial pose of coordinate system CMVB relative to the origin of manipulator coordinate system MNPL. 
     Based on the measured joint angles, the calculated joint angles and the initial pose of coordinate system CMVB initial comparisons are performed by comparators  582 ,  622  and  652 . These comparisons are performed to determine if in the initial state, the manipulator is violating any one of the joint limits, the interference limits or workspace limits, (steps not shown). If any of these limits are violated, an error message is displayed on user interface  130 . Further operation of the manipulator is blocked until the violation is resolved. 
     The forward kinematics-derived initial pose of coordinate system CMVB is also employed as the initial commanded pose of this coordinate system. The commanded velocity is initially set to zero. 
     Integrator  386  therefore has as the first frame initial conditions data representative of the actual pose of coordinate system CMVB and an initial commanded velocity of zero. This commanded pose is initially forwarded to the inverse kinematics module  542 . 
     As with any commanded pose data, the inverse kinematics module uses this commanded pose to determine the commanded joint angles that are applied to the joint motor controllers  126 . In this initial frame, the measured joint angles are essentially already at the commanded joint angles. 
     When the joint motor controllers  126  are initially activated, the brakes are holding the active joints static. After the joint motor controllers  126  are activated, the brakes are released. In response to the release of the brakes, gravity starts to act on the links. As the active joints start to depart from the commanded joint angles, controllers  126  cause the motors  101  to output torques that counteract the force of gravity. Joint motor controllers  126  therefore cause torques to be output that essentially holds the arms static. Once brakes  103  have been released, the manipulator  50  is able to position the instrument  160 . 
     During periods in which switch  176  is not depressed, sensor signal attenuator  697  completely attenuates, blocks, the passing of the signals from the force torque sensor  108  to the external force summer  698 . Blocking these signals prevents unintended movement of the manipulator that could result from the drift of and random variations of the signals from sensor  108 . If these drifting and varying sensor signals are forwarded beyond attenuator  697 , they would be interpreted as an indication that the practitioner has applied forces and/or torques to the instrument. This would result in the other modules internal to the manipulator controller  124  generating commands that would cause the unintended movement of the manipulator. 
     Even if the practitioner does not attempt to move the instrument, manipulator controller  124  will reposition the instrument  160  if the backdrive force F BDR  indicates that one of the arms  68  or  70  or attached components is subjected to an external force. This prevents damage to structural components of the manipulator and instrument  160  if either of these devices is somehow inadvertently bumped. It should be appreciated that these unintended forces must be greater than the minimum forces passed by deadband filter  695 . 
     Manipulator  50  is, by default, initialized in the manual mode. When the manipulator is in the manual mode, instrument  160  is not semi-autonomously advanced. Tool path force calculator  278  does not output signals of forces and torques to total force summer  380  that would facilitate semi-autonomous advancement of the instrument. 
     For the practitioner to position the instrument, the practitioner depresses switch  176 . Simultaneously, the practitioner places forces and torques on the instrument. These forces and torques are similar in magnitude to those that would be placed on an instrument held in the hand to control instrument pose. In response to sensing the state transition of switch  176 , sensor signal attenuator  697  ramps up the signals from sensor  108  to their unattenuated levels. This signal ramping ensures that the joint motors  101 , when initially applying torques to the arms, do not suddenly apply large amounts of torque to the manipulator  50 . 
     In response to the practitioner placing the forces and torques on the instrument, sensor  108  outputs signals representative of these forces and torques. These signals are passed through the sensor signal attenuator  697  to the external forces summer  698 . The external forces summer blends these signals as appropriate with the signals representative of external forces as represented by backdrive force F BDR . External forces summer  698 , in turn, outputs these signals through environmental force summer  379  to total force summer  380 . These practitioner applied forces are consequently components of the forces F TTL  and torque T TTL  output by total force summer  380 . 
     Consequently, when integrator  386  generates pose and velocity data, it does so based, in part, on the representation of practitioner applied forces and torques. Cut guide  390 , based on the integrator-generated pose and velocity, outputs the commanded pose and commanded velocity for coordinate system CMVB. Based on the commanded pose, inverse kinematics module  542  and command dynamics module  544  generate signals indicating, respectively, commanded joint angles and feed forward torques for the active joints. Joint motor controllers  126 , based on the commanded joint angles and feed forward torques, apply the necessary currents to joint motors  101 . These are the currents that result in the motors  101  outputting torques that result in advancement of the active joints towards their commanded joint angles. This results in motion of the instrument that emulates the motion of the instrument  160  if the forces and torques that the practitioner applied were applied to the center of mass of an instrument held in the hand. 
     To actuate the instrument  160 , either one of buttons  164  or  174  is toggled while switch  176  is depressed. When this condition exists, instrument manager  702  asserts a command signal to the tool controller  132 . This is the command signal instructing the controller  132  that it is to now actuate the instrument. Based upon receipt of this command signal, tool controller  132  applies the appropriate energization signals to the instrument  160  to actuate the instrument. In the situation where the instrument  160  includes a motor and the energy applicator  184  is a bur or other cutting accessory, the application of the energization signals result in the rotation of the energy applicator  184 . 
     As the instrument  160  and energy applicator  184  are advanced, the localization engine  270  continually generates data indicating the poses of both the bone tracker  212  and tool tracker  214  relative to the localizer  216 . These data are forwarded to the coordinate system transformer  272 . Coordinate system transformer  272  receives data from the forward kinematics module  562  that indicates the pose of the end effector  110  relative to the manipulator coordinate system MNPL. Coordinate system transformer  272  generates data indicating the pose of the boundary coordinate system relative to coordinate system MNPL based on the following data: the fixed pose of the boundary coordinate system relative to bone tracker coordinate system BTRK; the moving pose of the bone tracker coordinate system BTRK relative to the localizer coordinate system LCLZ; the moving pose of the localizer coordinate system LCLZ relative to tool tracker coordinate system TLTR; the fixed pose of tool tracker coordinate system TLTR relative to end effector coordinate system EFCT; and, based on the forward kinematics module; the pose of the end effector coordinate system EFCT relative to manipulator coordinate system MNPL. 
     Based on the fixed pose of energy applicator  184 , coordinate system EAPP relative to coordinate system EFCT and the moving pose of the end effector coordinate system EFCT relative to coordinate system MNPL, coordinate system transformer  272  generates data indicating the pose of the coordinate system EAPP relative to coordinate system MNPL. 
     The coordinate system transformer  272  thus provides the cut guide  390  with data that indicate poses of both coordinate system EAPP and the boundary coordinate system relative to manipulator coordinate system MNPL. 
     In addition to the above data, cut guide  390  contains the previously stored data defining the poses of the boundary-forming tiles relative to the origin of the boundary coordinate system. Based on these data, the cut guide  390  performs the process steps described above with respect to  FIGS.  21 A- 21 C  to determine if the practitioner&#39;s intended advancement of the instrument  160  would result in the energy applicator  184  crossing a boundary defining tile. If this evaluation tests negative, cut guide  390  outputs the integrator-generated pose and velocity as the commanded pose and velocity. 
     Alternatively, if it appears that the integrator generated position is beyond a boundary-defining tile, the cut guide  390  generates data determining the impulse or impulses that need to be applied to the virtual rigid body to avoid this motion. The commanded pose output by the cut guide  390  is based on this impulse (or impulses). Manipulator  50  therefore does not advance the arms in a manner that would result in the energy applicator  184  crossing the tile. Instead, the manipulator advances the arms in a manner that maintains the energy applicator  184  within the volume defined by boundary. If the energy applicator  184  is being used to remove tissue, this method of advancement of the energy applicator  184  results in the manipulator only allowing the energy application to remove the tissue the practitioner requires removed. This results in the remaining tissue having the defined shape, surface  242 , desired by the practitioner. 
     As mentioned above, the gear assemblies that transmit torque from the joint motors to the shoulders and links are essentially zero backlash gear assemblies. This feature means that, during the actual rotation of the gears, there is essentially no slippage, looseness, in the movement of the shoulder or link/links being actuated. The minimization of this slippage results in very stable movement of the components. Moreover, this minimization results in the precise positioning of the attached arm and shoulders. Collectively, these features make it possible for the joint motors to rapidly reposition the shoulders and links and to perform such repositioning with a high degree of accuracy. This includes the repositioning that occurs as a result of the reversal of rotational directions of the joint motors and gear assemblies. 
     During manual mode advancement of the energy applicator  184 , the joint limit comparator  582 , the interference limit comparator  622  and the workspace limit comparator  652  perform their above described analyses. If a respective one of the boundaries is crossed, an appropriate constraining force is supplied to environmental forces summer  379 . The constraining force, which is applied to the virtual rigid body, essentially prevents the manipulator from advancing the arms in such a manner that would cause a joint to exceed a joint limit, a pair of arms to move beyond their interference limit or the energy applicator  184  to exceed the workspace limit. 
     While not depicted in the flow charts, the joint limit comparator  582  evaluates if any joint has exceeded one of its joint limits; the interference limit comparator  622  evaluates if any pair of arms are at distance less than their interference limit; and the workspace boundary comparator  652  evaluates if the energy applicator  184  has moved beyond its workspace boundary limit. Typically, one of these conditions only occurs if the manipulator is damaged, malfunctioning or being subjected to extremely high external forces. If any of these conditions test true, manipulator controller  124  stops the advancement of the arms and engages the brakes, and the instrument power generating unit  163  is deactivated, connections not shown. An error message is displayed to the user. The manipulator is considered to have entered a disabled state. The manipulator remains in this state until the error is resolved. 
     As described above, during the advancement of the instrument, the removed material logger  275  generates and stores data. These data identify the volumes of tissue to which the energy applicator  184  was applied. 
     At any time during the manual mode advancement of the instrument the practitioner can deactivate the instrument by a second toggling of one of buttons  164  or  174 . In response to this second toggling of a button  164  or  174 , instrument manager  702  asserts a signal to the tool controller  132  that results in the controller deactivating the instrument power generating unit  163 . An additional toggling of the button  164  or  174  results in the instrument manager  702  and tool controller  132  reactivating the instrument power generating unit  163 . 
     Once the practitioner completes a particular application of the energy applicator  184  to the tissue, the practitioner releases pressure on switch  176 . In response to the release of switch  176 , instrument manager  702  asserts the signal to the tool controller  132  that results in the controller deactivating the instrument power generating unit  163 . This prevents activation of the instrument when the practitioner has removed his/her hand from the instrument. 
     Sensor signal attenuator  697  also responds to the release of switch  176 . When this event occurs, attenuator  697  ramps down the application of the signals from force/torque sensor  108  to the external forces summer  698 . This results in ramping down of the external forces component applied to environmental forces summer  379 . The ramping down of this component results in a like ramping down of the extent to which the forces and torques output by total force summer  380  include components based on the practitioner desired instrument positioning. 
     Integrator  386  also receives data indicating that the switch  176  has been released. In response to receipt of this data, integrator  386  rapidly ramps down the magnitude of the velocity signals output by the integrator. These velocities are ramped down to zero over a time period that is typically 250 milliseconds or less. This velocity ramp down can alternatively be accomplished by momentarily increasing the damping force applied to environmental force summer  379 . 
     Assuming no other forces are applied to environmental force summer  379 , the velocity ramp down results in the stopping of the advancement of the instrument  160 . Joint motor controllers  126  continue to apply currents to the joint motors  101 . These currents cause the joint motors  101  to output torques that hold the shoulder and arms in their last positions based on the last commanded pose output by cut guide  390 . The manipulator at least momentarily holds the instrument in the last pose prior to release of switch  176 . 
     At the time switch  176  is released, cut guide  390  may be in the process of applying a force to the virtual rigid body to prevent the energy applicator  184  from crossing a tile. If this condition exists, then the release of switch  176  does not result in the rapid cessation of the instrument advancement. The cut guide  390  continues to output forces that need to be applied to the virtual rigid body. The outputting of these forces therefore results in manipulator continuing to position the instrument in a manner such that the energy applicator  184  remains within the boundaries. 
     As described above, the release of switch  176  typically results in the cessation of the advancement of the instrument  160  by the manipulator  50 . Conditions may exist that foster further movement of the instrument. As was mentioned above, one such condition is the determination by the cut guide  390  that it appears that the energy applicator  184  will cross a tile. In some circumstances, cut guide  390  makes this determination after the release of switch  176 . This determination can occur because, even after switch  176  is released, the software modules remain active. The cut guide  390  continues to selectively generate forces that are applied to the virtual rigid body to prevent the energy applicator  184  from crossing a boundary. This event can occur if, when the instrument  160  is stationary, movement of the patient relative to the instrument results in the energy applicator  184  apparently crossing a boundary. If the cut guide  390  determines that this crossing is occurring, the cut guide applies forces to the virtual rigid body that effectively move the energy applicator  184  such that the applicator does not cross the boundary. Stated another way, as a consequence of the movement of the bone, the manipulator  50  may continue to reposition the instrument. 
     Other conditions may exist that result in some movement of the instrument  160  by the manipulator  184  when switch  176  is in the released state. Specifically, if the joint motors  101  are subject to backdriving forces or one of the behavior control modules outputs a constraining force, non-zero addends are still applied to the environmental forces summer  379 . Total force summer  380  in turn, outputs a non-zero total force and total torque to the acceleration calculator  384 . If these outputs from total force summer  380  are non zero, integrator  386 , after initially ramping down the velocity, ramps up the velocity to the velocity based on the total force and total torque. Thus, if the backdriving or constraining forces are present, the manipulator  50 , after initially stopping the advancement of the instrument, continues to reposition the instrument. This advancement occurs until the integrations of these accelerations over time due to these forces fall to zero. 
     Once the integrations of these accelerations over time fall to zero and the cut guide  390  no longer applies forces to the virtual rigid body, the manipulator  50  holds instrument  160  in a static pose. Manipulator  50  remains in this state until repositioned by the practitioner. 
     Upon completion of a procedure, the manipulator may be deactivated by depressing a button presented on the user interface  130 , button not shown. Upon depression of this button, the brakes  103  are reengaged. Once a sufficient time has elapsed to ensure that the brakes  103  are engaged, manipulator controller  124  sends commands to the joint motor controllers  126 . In response to these commands, the joint motor controllers terminate the applied currents to the joint motors  101 . 
     B. Semi-Autonomous Mode 
     The initialization steps performed to operate the manipulator in the manual mode are performed to prepare the manipulator for semi-autonomous operation. The instrument  160  and energy applicator  184  are connected together and to the end effector  110 . The appropriate calibrations, navigation registrations and boundary positioning are performed. The boundaries are loaded into the cut guide  390 . 
     In some versions, manipulator  50 , once enabled for manual mode operation, is ready to semi-autonomously advance the instrument  160 . By reference to  FIG.  28 A , it is observed that an initial step in the semi-autonomous operation of the instrument is the generation of the tool path along which the energy applicator  184  should advance, step  760 . In step  760 , tool path generator  234  generates data defining tool path  248  ( FIG.  15 C ). This tool path, again a set of path segments  256 ,  262  and  266 , defines the locations along the tissue to which the energy applicator  184  should be applied. As part of step  760 , tool path generator  234  references the data retrieved from the removed material logger  275 . When step  760  is executed at the start of the procedure, these data indicate that there has been no application of the energy applicator  184  to the tissue. If this condition exists, the starting point, point  258 , of the tool path against the tissue, is the originally calculated path starting point. 
     Alternatively, the data from removed material logger  275  may indicate the energy applicator  184  was previously applied to one or more volumes of the tissue. Often this is due to previous removal of tissue by the manual mode advancement of the instrument. If this condition exists, tool path generator  234  generates a revised tool path  248 . This revised tool path  248  is a collection of path segments along the remaining tissue, the tissue to which the energy applicator  184  was not applied, over which the energy applicator  184  should now traverse. The generation of the revised tool path  248  avoids having the energy applicator  184  move in free space to attempt to remove tissue that was previously removed. As a consequence of the generation of this revised tool path, the tool path generator may generate a new location for point  258 , the starting point for the tool path along the tissue against which the energy applicator  184  is to be applied. 
     It should be appreciated that even though the tool path generator  234  defines a set of path segments that extend over the tissue to be removed, not all path segments may extend over tissue. Some path segments may extend in free space between path segments that do extend over tissue. 
     Prior to the start of semi-autonomous advancement of the instrument, the practitioner, by engaging in manual mode operation of the manipulator  50 , positions the instrument so that origin of coordinate system EAPP is in what is referred to as a target region, step  762 . This target region is a space in close proximity to the starting point of the on-tissue tool path, point  258 . In some versions, this target region is the volume above the bone within 2 cm of path start point  258 . In other versions, this target region is the volume within 1 cm above the path start point  258 . Based in part on the tracking of the instrument and bone by the localization engine, the coordinate system transformer  272  generates data indicating the proximity of the origin of energy applicator  184  coordinate system EAPP to the start point  258 . The coordinate system transformer  272  provides data to the navigation processor  218 . Based on these data, navigation processor  218  presents images on interface  220  indicating the position of the energy applicator  184  relative to the tool path start point  258 . The practitioner references this display in order to so position the instrument. 
     Once the practitioner completes coarse positioning of the instrument, manipulator controller  124  continues to hold the instrument in the last commanded pose. This assumes that neither the arms nor instrument are subjected to constraining or backdriving forces. 
     Once it is believed that the instrument is in the target region, and the practitioner wants to initiate semi-autonomous operation, the practitioner depresses the pendant trigger switch  194 , step not illustrated. User interface  130  continually monitors pendant  190  to determine whether or not the trigger switch is depressed, step  764 . The depressing of trigger  194  places the manipulator in the semi-autonomous mode. Throughout the time period the practitioner wants to advance the instrument semi-autonomously, pendant trigger  194  must remain depressed. As discussed in more detail below, the release of pendant trigger  194  returns manipulator  50  to the manual mode. 
     One immediate effect of the placement of the instrument in the semi-autonomous mode is that the tool path generator  234  generates a path segment that extends through free space, step  766 . The free space path segment is the portion of the tool path along which the energy applicator  184  should advance to reach point  258 . 
     Prior to the depression of trigger  194 , user interface  130  sets the user adjustment input to feed rate calculator  284  to zero, step not shown. Consequently, when trigger  194  is initially depressed, the feed rate calculator  284  outputs a default instrument feed rate of zero. These output signals therefore cause the tool path force calculator  278  to initially generate a set of forces and torques to the total force summer  380  that essentially hold the energy applicator  184  in the position in which it is located at the time trigger  194  is depressed. Often the forces and torques output by the tool path force calculator  278  at this stage in the semi-autonomous advancement of the instrument are close to zero. 
     Upon initial depression of pendant trigger  194 , manipulator controller  124  also verifies that the origin of the energy applicator  184  coordinate system EAPP is within the target region. If the energy applicator  184  is outside of the target region, the likelihood increases that the free space path segment may cross one of the boundary defining tiles or a section of tissue that is not to be cut. Accordingly, manipulator  50  only allows semi-autonomous instrument advancement to begin when energy applicator  184  is in the target region. 
     In  FIG.  28 A , steps  768  and  770  represent the process by which the manipulator  50  evaluates the proximity of the origin of the energy applicator  184  coordinate system EAPP to tool path point  258 . Step  768  is the determination by the tool path generator  234  of the distance from the energy applicator  184  to point  258 . Step  770  is the evaluation of whether or not this distance indicates that the energy applicator  184  is within the target region. If the instrument is not within the target region, a message is presented on interface  220 , step  772 . The practitioner must then reposition the instrument. To so reposition the instrument, the practitioner must first release trigger  194 , step not shown. In the described version, as a consequence of the release of trigger  194 , manipulator automatically cycles back to step  760 . 
     When it is determined that the origin of coordinate system EAPP is in the target region, the tool path generator  234  sends data regarding this fact to the instrument manager  702 , step not shown. The instrument manager  702 , in turn, sends a command to the tool controller  132 . This command instructs the tool controller to apply energization signals to the instrument that result in the actuation of the instrument power generating unit  163 . Collectively the above steps are represented in  FIG.  28 A  as step  774 . To adjust the operational settings used for driving the instrument  160 , commands are entered through buttons presented on manipulator display (buttons not illustrated). Based on the depression of these buttons, the user interface  130  sends commands to the tool controller  132  that adjust the operation of the tool power generating unit  163 , step not shown. 
     Should the evaluation of step  770  test positive, the tool orientation regulator  368  defines the reference surface  369 , aperture  370  and centering point  371 , step  776 . These geometric landmarks are defined based on a representation of actual pose of the instrument  160  relative to the bone. The commanded pose, transformed into coordinate system BONE, is employed as the representation of the actual pose. 
     Once the practitioner is ready to begin semi-autonomous advancement of the instrument  160 , the practitioner depresses button  195 , step not illustrated. In some versions, user interface  130 , based on the depression of buttons  193  and  195 , outputs a coefficient representative of the user adjustment of the feed rate. In some versions, the coefficient is 0.0, 0.25, 0.40, 0.70 or 1.0. This is the coefficient that is applied to feed rate calculator  284  as the USER ADJUST input. Each depression of pendant button  193  results in the user interface readjusting the feed rate coefficient down a level. Each depression of pendant button  195  results in the user interface readjusting the feed rate coefficient up to the next higher level. User interface  130  continually monitors the pendant  190  to determine whether or not either of buttons  193  or  195  is depressed, step  778 . For the purposes of understanding the invention it should be understood that a necessary command to start instrument advancement is a command to reset the USER ADJUST coefficient to above 0. 
     The initial depression or depressions of button  195  causes user interface  130  to upwardly adjust the level of the USER ADJUST coefficient applied to the feed rate calculator  284 . The level to which this coefficient is set is a function of the number of times button  195  is pulsed. The feed rate calculator  284 , in response to receipt of this non-zero coefficient, outputs a non-zero instrument feed rate, step not shown. This assumes that none of the other coefficients applied to feed rate calculator  284  are zero. Based on this indication that the instrument is to advance at a non-zero speed, the downline modules of the tool path force generator  234  cooperate to output the sequence of forces and torques needed to be applied to the virtual rigid body to cause the advancement of the energy applicator  184  along the tool path. These forces and torques are applied to the total force summer  380 . In turn, the modules down line from the total force summer  380  cooperate to result in the desired advancement of instrument  160  and energy applicator  184 , step  782 . While the advancement of the instrument is depicted as a distinct step, it is appreciated that the below described steps occur while the instrument is advancing semi-autonomously. 
     Initially in this advancement of the energy applicator  184 , the energy applicator  184  moves along the free space path segment; the path segment that leads to point  258 . From point  258  the energy applicator  184  advances along an on-tissue path segment. In the described version, wherein the energy applicator  184  is a bur, this means that, as a result of this advancement of the energy applicator  184  beyond point  258 , the rotating bur head is pressed against tissue. Owing to the geometry of the bur head, the rotation of the bur head by the instrument power generating unit (motor  163 ), and the force applied to the bur head by the manipulator  50 , the bur head removes the tissue against which it is applied, step not identified. 
     In the  FIGS.  28 A- 28 G  the steps are depicted as occurring sequentially. It should be appreciated that many of the steps occur both continually and essentially simultaneously throughout the time in which the instrument is semi-autonomously advanced. In some cases the functions represented by the process steps are implemented as independent continuous functions.  FIGS.  28 A- 28 G  do not represent the order in which process steps are executed by the modules or the decisions made by the modules. The Figures represent the aggregate effect perceived by the practitioner of the above-described processes performed by the modules. 
     As the energy applicator  184  advances against the tissue, the removed material logger  275  generates and stores data indicating the portions of the tissue to which the energy applicator  184  was applied, step  784 . These data are used to update the previously acquired data identifying the portions of the tissue to which the energy applicator  184  was applied. In subsequent executions of step  760 , tool path generator  234  employs these updated data to generate the revised tool paths. 
     During operation of manipulator  50  in the semi-autonomous mode, the force overrider  375  performs its previously described monitoring of the manipulator and the instrument. The determination of the power output by the energy applicator  184  is represented by step  786 . A determination that the power output is in excess of the pre-defined lower limit value for the designated time period, is interpreted by the manipulator  50  that the system of this invention may be operating in an undesired state. Accordingly, as part of step  786  the indicia of the power output by the energy applicator  184  is compared to the lower limit value for this indicia. If this evaluation tests true, the force overrider  375  sends a command to the instrument manager  702 . In response to this command, instrument manager  702  instructs controller  132  to deactivate the instrument power generating unit  163 . Tool controller  132  consequently deactivates the instrument. The above steps collectively form an execution of step  794 . Force overrider  375  instructs the feed rate calculator  284  to ramp the instrument feed rate to zero. This results in the manipulator stopping the advancement of the energy applicator  184 . This is represented if  FIG.  28 B  as an execution of step  796 . 
     Force overrider  375  also causes the user interface  130  to present a message identifying the reason semi-autonomous advancement of the instrument was terminated, step  798 . This gives the surgeon the opportunity to investigate why the instrument is outputting more torque than expected so as to determine if an undesirable condition exists at the site to which the energy applicator  184  is applied. 
     The stopping of the advancement of the instrument by manipulator  50  in step  796  does not stop the manipulator from continuing to regulate the extent to which the joint motors  101  output torques. The forces and torques output by tool path force calculator  278  are the forces and torques that need to be applied to the virtual rigid body to maintain the energy applicator  184  in its last target position. Total force summer  380  and the downline modules cause the joint motors  101  to output torques that result in the arms  68  and  70  holding the energy applicator  184  in the last target position, step not shown. 
     While manipulator  50  is still in the semi-autonomous mode, the manipulator, after step  798 , is not advancing the energy applicator  184 . This provides the practitioner the opportunity to attend to the condition that resulted in the halting of applicator advancement. Manipulator controller  124  allows the practitioner to restart the semi-autonomous advancement of the energy applicator  184  after the warning has been acknowledged. Step  799  represents the force overrider  375  waiting for this acknowledgement. The practitioner makes this acknowledgment by depressing a button. When the manipulator  50  is in this state, instrument button  172  may function as the button that is depressed for the practitioner to acknowledge the warning of step  798 . 
     Once the warning is acknowledged, the force overrider  375  places the manipulator in a state in which it can continue the current semi-autonomous tool advancement. This is represented by the transition from step  799  back to step  774 . The instrument manager  702  again asserts commands that result in the actuation of the instrument power generating unit  163 . The instrument orientation landmarks are reset in the reexecution of step  776 . Then, based on practitioner resetting the USER ADJUST coefficient above 0.0, the reexecution of step  778 , the energy applicator  184  is again advanced, step  782  is executed. 
     Still another component of step  786  is the comparison of the indicia of power output by the energy applicator  184  to the higher limit level of this indicia for the designated time period. The testing true of this evaluation is interpreted by the force overrider  375  that there is a greater likelihood that the manipulator is in an undesirable state. Accordingly, should this evaluation test true, the manipulator controller takes the steps necessary to transition to the manual mode and deactivate the operation of the energy applicator  184 . This is represented as the branching from step  786  to the below described steps  864  and  866 . 
     Step  788  represents the monitoring by the force overrider of force F INST  output by force calculator  358 . In step  788 , force overrider  375  compares force F INST  to its associated lower limit and upper limit values as described above. If the evaluation indicates that force F INST  has exceeded its lower limit value for the designated time period is interpreted as indicating that there is an obstruction  828  in the vicinity of the surgical site that is inhibiting the advancement of the energy applicator  184 . Accordingly, should this evaluation of step  788  test true, the force overrider  375  causes the previously described steps  794 ,  796 ,  798  and  799  to be executed. 
     This provides the surgeon the opportunity to determine why the advancement of the energy applicator  184  is being inhibited. The surgeon can, if appropriate, take steps to attend to the condition causing the energy applicator force calculator  358  to indicate that large magnitude forces/torques need to be applied to the virtual rigid body. 
     In step  788 , force overrider  375  may determine that force F INST  has exceeded its higher limit value for the designated time period. The testing true of this evaluation is interpreted as an indication that there is a greater likelihood that the manipulator is in an undesirable state. Accordingly, manipulator controller branches to steps  864  and  866  to return to manual mode and deactivate the energy applicator  184 . 
     Force overrider  375  also monitors the signals representative of the forces and torques sensed by sensor  108 , step  804 . This monitoring is performed to determine if excessive external forces are being applied to the instrument  160  or energy applicator  184 . As a result of the normal resistance of the tissue to which the energy applicator  184  is applied, there is some resistance to the advancement of the instrument  160 . During semi-autonomous advancement of the instrument, the force/torque sensor  108 , in response to the application of the tissue resistance, outputs signals indicating that the sensor is being exposed to a minimal level of forces and torques. 
     The evaluation may indicate that the forces and torques sensed by sensor  108  exceeded the lower limit values for more than the designated time period. This event could occur if an obstruction  828  imposes some sort of resistive force that inhibits advancement of the energy applicator  184 . If this condition tests true, the force overrider  375  branches to steps  794 ,  796 ,  798  and  799  to temporarily stop the semi-autonomous advancement of the energy applicator  184 . 
     Further, during semi-autonomous advancement of the instrument, a condition may occur that causes the surgeon to suddenly attempt to reposition the instrument. When taking this action, the practitioner may inadvertently not release the pendant trigger  194 . Should this event occur, in response to the practitioner&#39;s efforts to displace the instrument away from the tool path, the force/torque sensor  108  is exposed to relatively high forces and torques. These forces and torques are above the high limit force/torque limits maintained by the force overrider  375 . Accordingly, in step  804 , force overrider also evaluates the output of sensor  108  to determine if these forces/torques have exceeded their higher limit values for a time greater than the designated time period. 
     If the above evaluation tests true, force overrider  375  asserts commands that result in the deactivation of the instrument power generating unit, step  808 . The force overrider  375  also asserts commands that result in the stopping of the semi-autonomous advancement of the instrument, step  810 . The same software and hardware components that execute steps  794  and  796  perform, respectively, steps  808  and  810 . 
     The force overrider  375  also ramps the force F INST  output by the energy applicator force calculator to zero. This takes the manipulator out of the semi-autonomous mode and returns the manipulator to manual mode operation, represented by step  811 . Owing to the magnitude of the forces and torques that are applied by the practitioner, the backdrive forces are greater than the threshold values stored in the deadband filter  695 . External forces summer  698 , based on the practitioner applied forces, outputs a force to the environmental force summer  379 . Consequently, even though switch  176  may not be depressed, the manipulator  50 , as represented by step  812 , repositions the instrument in response to the forces and torques the practitioner applies to force the energy applicator off the tool path. 
     Once the instrument is so repositioned, the manipulator returns to step  760 . Semi-autonomous advancement of the instrument is reactivated by the depression of the pendant trigger, step  764 . 
     During the advancement of the energy applicator  184 , the tool orientation regulator  368  monitors the orientation of the instrument  160 . In  FIG.  28 C  this is shown as a separate step  814 . It should be understood that this monitoring occurs simultaneously with the advancement of the energy applicator  184 . It should be understood that during this process, the location of reference surface  369 , aperture  370  and centering point  371  are defined relative to coordinate system BONE. 
     The changes in orientation of the instrument during semi-autonomous advancement are explained by initial reference to  FIGS.  29 A and  29 B . These Figures depict the initial orientation of the instrument and energy applicator  184 . Here, the instrument longitudinal axis extends through the centering point  371  in aperture  370 . The instrument longitudinal axis is perpendicular to reference surface  369 . 
     During semi-autonomous advancement of the instrument, the objective is to advance the energy applicator  184  along the tool path. From above, it should be appreciated that this is the movement that results from the application of forces and torques that are applied to the virtual rigid body based on the calculations performed by the energy applicator force calculator  358 . 
     As discussed above, the tool orientation regulator  368  generates another set of forces and torques that are applied to the virtual rigid body. This is to ensure that, at a minimum, the manipulator orients the instrument so that the instrument axis remains in the reference surface aperture  370 . Ideally, the manipulator is able to orient the instrument so the instrument axis intersects the aperture centering point  371 . 
       FIGS.  30 A and  30 B , depict when the origin of the energy applicator coordinate system EAPP is spaced a relatively short distance away from a line extending normal to reference plane  369  through centering point  371 . As the energy applicator  184  advances from the position of  FIG.  29 B  to the position of  FIG.  30 B , forces F ORNT  are output by the tool orientation regulator  368  for application to the virtual rigid body. These are force F ORNT  that results in the manipulator pivoting the instrument so the common axis continues to extend through centering point  371 . 
     As depicted in  FIG.  31   , during semi-autonomous advancement of the instrument, the manipulator may position the energy applicator  184  so the applicator is advanced along a portion of the tool path  248  located outside of the area subtended by aperture  370 . This area is depicted by dashed enclosure. Even when the energy applicator  184  is so positioned, tool orientation regulator  368  applies a force F ORNT  that results in the manipulator orienting the instrument so the common axis essentially intersects centering point  371 . In some constructions, when the tool orientation regulator  368  defines an aperture  370  having a radius of 3 cm in a reference surface  369  located approximately 15 cm above the surface of the tissue, the manipulator  50  is able to position the energy applicator  184  so it can be located 20 cm or more from the normal line through the centering point  371 . Even when the energy applicator  184  is located at the perimeter of this area, the force F ORNT  applied to the virtual rigid body will result in the manipulator orienting the instrument so the common axis essentially intersects the centering point  371 . 
     Manipulator  50  is further configured so that minor obstructions  828  that may present themselves above the tool path  248  do not block the advancement of the energy applicator  184  along the tool path. These obstructions  828  include tissue that projects outward above tool path. Instruments, such as suction applicators and retractors may also project above the tool path. In  FIG.  28 C , whether or not an obstruction is present is depicted as the condition test of step  818 . Assuming an obstruction is not present, the condition of step  818  is negative, this semi-autonomous advancement of the instrument continues as represented by the progression to step  836 . 
     If an obstruction is present, the condition of step  818  is positive, the obstruction resists the ability of tool orientation regulator  368  to output a sufficient force F ORNT  that results in the manipulator maintaining the common axis through the centering point  371 , step not illustrated. In response to this event occurring, manipulator  50  advances the instrument such that the common axis moves toward the perimeter of aperture  370 , step not illustrated. The displacement of the common axis away from the centering point  371  can be said to result from the resistive forces of the obstruction being out of equilibrium with, greater than, the force F ORNT  applied to the virtual rigid body. In response to this displacement, tool orientation regulator adjusts force F ORNT  to ensure that the manipulator  50  orients the instrument so that the common axis remains within the aperture, step  824 . Typically, this force F ORNT  is greater in magnitude than the previously output force F ORNT . 
     In response to the newly applied force F ORNT  the manipulator may position the instrument so that the common axis intersects the aperture through a point in aperture  370  spaced from centering point  371 .  FIGS.  32 A,  32 B and  32 C  depict the instrument in this position. This new location of the common axis is the location where force F ORNT  applied to the virtual rigid body and the resistive force of the obstruction  828  is in equilibrium. 
     The obstruction  828  may yield to the instrument, step  826 . This may occur if the obstruction  828  is yieldable material, such as soft tissue. Alternatively, this event may occur if the obstruction  828 , though rigid, is fixed to yieldable tissue. 
     If the obstruction  828  yields, the manipulator continues to advance the instrument. As the obstruction  828  yields, force F ORNT  applied to the virtual rigid body becomes greater than the resistive force of the obstruction  828 . This results in the manipulator restoring the instrument to an orientation in which the common axis essentially intersects centering point  371 , step not shown. In  FIG.  28 F , the yielding of the obstruction is identified as a branching to step  836 . 
     Even if the obstruction does not yield, the condition of step  826  is negative, the common axis may remain within the reference surface aperture  370 , the condition evaluation of step  830 . If this condition exists, the manipulator  50  continues the semi-autonomous advancement of the instrument, branching to step  836 . 
     Alternatively, the result of the condition test of step  830  may be negative. In this event, tool orientation force regulator  368  outputs a high magnitude force F ORNT . This force F ORNT  is based on the table values between inflection point  377  and peak point  378  of  FIG.  19   . The outputting of this force F ORNT  is represented by step  832 . 
     In a step  834  the magnitude of force F ORNT  is compared to the low and high limit values associated with this force. This evaluation is performed by the force overrider  375 . If both evaluations test negative, the manipulator, in response to the application of the new force F ORNT  to the virtual rigid body, reorients the manipulator. This is depicted as the branching back to step  824 . 
     Alternatively, as a result of the evaluation of step  834 , force overrider  375  may determine that the force F ORNT  is above the lower limit value for this force for the designated time period. If the force overrider  375  makes this determination, the force overrider interprets the manipulator in being in a state in which semi-autonomous advancement should at least be temporarily stopped. This is depicted as the branching to previously described steps  794 ,  796 ,  798  and  799 . 
     In some situations, the force F ORNT  output by the tool orientation regulator  368  may exceed the high limit value associated with this force for more than the designated time period. This event could occur if an obstruction collides with the instrument  160  or energy applicator  184 . Accordingly, force overrider  375  interprets this second evaluation of step  834  testing true as an indication that manipulator is in an undesirable state. Manipulator controller  124  therefore branches to steps  864  and  866  to transition the manipulator back to the manual mode and deactivate the instrument. 
     During the semi-autonomous advancement of the instrument  160  the practitioner may decide to reset the orientation of the instrument while the energy applicator  184  is advanced along the tool path  252 . It may be desirable to so reorient the instrument to avoid having the instrument contact tissue or another instrument that may be in the vicinity of the tool path. 
     Step  836  represents the decision associated with the practitioner deciding to reorient the instrument. If the practitioner wants to so reorient the instrument, he/she depresses instrument button  172 , step not shown. User interface  130  monitors the state of this button. As long as the evaluation of step  836  tests negative, tool orientation regulator  368  continues to output force F ORNT  that results in the manipulator orienting the instrument so the common axis, as closely as possible, intersects the previously defined centering point  371 . In  FIG.  28 C , this is represented as a progression to step  850 . 
     If the evaluation of step  836  tests positive, tool orientation regulator  368  redefines the reference surface  369 , the tool aperture  370  and centering point  371 , step  840 . These redefinitions of these geometric reference features are based on the current actual pose of the instrument, represented by the commanded pose. 
     Consequently, in the subsequent reexecutions of step  814 , the input variables into the orientation regulator  368  indicate that the instrument is essentially centered on the centering point  371 . Given that the instrument is in this state, the tool orientation regulator determines that there is no need to apply an appreciable orienting force, F ORNT =0, to the virtual rigid body, step  842 . 
     During instrument reorientation, the practitioner applies forces and torques to the instrument to reorient the instrument. These forces and torques are typically the largest component of the external force F EXT  applied to the environmental forces summer  379 . Since F ORNT  is zero, tool orientation regulator  368  does not apply forces to the virtual rigid body that oppose the practitioner applied external force F EXT . Thus, in response to this external force F EXT , manipulator  50  orients the instrument so the instrument orientation is based on the practitioner desired orientation, step  844 . 
     While in this process, F ORNT  is zero, energy applicator force calculator  358  and force transformer  362  continue to output a non-zero force F INST . This is the force F INST  applied to the virtual rigid body that causes the manipulator to advance the energy applicator  184  along the tool path  248 . Accordingly, manipulator  50 , simultaneously with emulating the reorienting of the instrument desired by the practitioner, continues to position the instrument so the energy applicator  184  advances along the tool path  248 , step  782  continues to be executed. 
     Manipulator continues to reorient the instrument according to the above process steps as long as button  172 , remains depressed. This is represented in  FIG.  28 G  as the loop back from decision step  846  to step  840 . 
     Once the instrument is in the orientation desired by the practitioner, the practitioner releases button  172 , step not shown. In response to this event occurring, tool orientation regulator  368  no longer continually updates the orientation landmarks based on the commanded pose of the instrument. The landmarks stored when button  172  is released are the landmarks upon which the subsequent calculations to determine force F ORNT  are based, step  848 . Manipulator continuous with the semi-autonomous regulation of instrument orientation based on these landmarks, step  849 . Manipulator  50  can then be considered to advance to step  850 . 
     In some constructions of manipulator  50 , the release of button  172  is recognized as indication that the practitioner has performed the step  799  process of clearing the warning presented in step  798 . This is because a number of the conditions that may have caused manipulator  50  to temporarily stop semi-autonomous advancement of the instrument  160  are remedied by the reorienting of the instrument. 
     When manipulator  50  operates in the semi-autonomous mode, user interface  130  continually monitors pendant  190  to determine if either buttons  193  or  195  are depressed. This is represented in  FIG.  28 C  as the manipulator monitoring whether or not surgeon has elected to adjust the feed rate of the advancement of the energy applicator  184  along the tool path, step  850 . In response to either of buttons  193  or  195  being depressed, the processes described with respect to step  778  are employed to result in a new USER ADJUST coefficient being applied the feed rate calculator  284 , step not shown. This results in controller  124  adjusting the rate at which the manipulator advances the energy applicator  184  along tool path  248 , step  858 . 
     If in step  858  the instrument feed rate is set to the zero speed, the tool path force calculator  278  still outputs a force F INST . This is the force F INST  applied to the virtual rigid body that results in manipulator  50  holding the energy applicator  184  at the last determined target position on the tool path, step not illustrated. 
     In some versions, when the instrument feed rate is set to zero speed, the instrument manager  702  also asserts commands that result in deactivation of the tool power generating unit  163 , step not illustrated. In these versions, when button  195  is again depressed to again cause the semi-autonomous advancement of the instrument, instrument manager  702  causes the instrument power generating unit to be reactivated. User interface  130  applies the non-zero USER ADJUST coefficient to feed rate calculator  284 , step not illustrated. 
     Also, in some versions, upon the resetting of the instrument feed rate to a speed greater than zero, the energy applicator force calculator  358  initially outputs a force F INST  that is essentially opposite in direction of the force F INST  that results in the forward advancement of the energy applicator  184  along the tool path. As a consequence of this initial force F INST  being momentarily applied the virtual rigid body, the manipulator initially moves the energy applicator  184  in a reverse direction along the tool path  248 . This movement is typically 2 mm or less. Once the energy applicator  184  engages in this back movement, the instrument power generating unit  163  is reactivated. Once the instrument power generating is reactivated, the energy applicator force calculator  358  outputs a force F INST  that results in the manipulator forward advancing the energy applicator  184  along the tool path  248 . 
     The above process steps avoid the condition of reactuating the energy applicator  184  while the applicator is pressed against tissue. This reduces the likelihood that the applicator  184 , upon reactuation, binds against the tissue. 
     During the semi-autonomous advancement of the instrument  160 , the cut guide  390  monitors the position of the energy applicator  184  relative to the boundary tiles as if the manipulator is operating in the manual mode, step  860 . The method of operation of the cut guide  390  when the manipulator is in the semi-autonomous mode is the same as when the manipulator is operated in the manual mode. Since the manipulator  50  positions the energy applicator  184  along the tool path  248 , very rarely does the cut guide  390  determine that the positions cross one of the boundary defining tiles. 
     However, there is a possibility that the occurrence of an extraneous event will cause the rapid transition of the manipulator from the semi-autonomous mode back into the manual mode. One example of such an event is the above-discussed act of the practitioner applying a force on the instrument to redirect the instrument while the manipulator is performing the semi-autonomous advancement, see step  788 . A second example of such event is the below-discussed event of the practitioner depressing instrument switch  176  to position the instrument when the energy applicator  184  is in close proximity to one of the boundary defining tiles. 
     Thus, even when the manipulator  50  engages in semi-autonomous energy applicator advancement, cut guide  390  still verifies that the commanded position of the energy applicator  184  is within the defined boundary. If the cut guide  390  determines that the energy applicator  184  will cross the boundary, the cut guide applies an impulse or impulses to the virtual rigid body. The application of this force can be considered part of step  860 . The application of the impulse (or impulses) causes the manipulator  50  to avoid this motion. Thus, the cut guide  390 , even when the manipulator advances the energy applicator  184  semi-autonomously, substantially eliminates the possibility that the energy applicator  184  will move beyond the boundary. 
     During semi-autonomous advancement of the instrument, the user interface also monitors the state of instrument switch  176 , step  862 . If switch  176  is depressed, the user interface transitions the manipulator back to manual mode operation, step  864 . This process involves the zeroing out of the forces F INST  and F ORNT  that the tool path force calculator  278  outputs to total force summer  380 . Sensor signal attenuator  697  ramps up the extent to which the forces and torques measured by sensor  108  function as components of force F EXT . Collectively, these actions transition the manipulator from the state in which it performs semi-autonomous advancement to one in which it performs instrument positioning that emulates the positioning that would have occurred based on the practitioner applied forces and torques. 
     During this transition between operating modes, instrument manager  702  generates a command to the tool controller to deactuate the instrument, step not shown. Upon receipt of the command, tool controller  132  negates the application of energization signals to the instrument power generating unit, step  866 . 
     Manipulator controller then generates a new on tissue tool path; step  760  is reexecuted. 
     User interface  130  continually monitors the pendant  190  to determine the state of trigger  194 , step  868 . If trigger  194  remains depressed, manipulator  50  continues to advance the instrument in the semi-autonomous mode. In  FIGS.  28 B and  28 D , this is depicted as the loop back from step  868  to step  782 . 
     Once trigger  194  is released, the manipulator returns to the manual mode operation and deactuates the energy applicator  184 . This is represented by branching from step  868  to steps  864  and  866 . It should be understood that in this version of the execution of step  864 , the practitioner may not be applying forces and torques to the instrument. Consequently, in addition to forces F INST  and F ORNT  being zeroed out, force F EXT  is also essentially zero. Accordingly, the forces F TTL  and torques T TTL  output by total force summer  380  are the forces and torques that, applied to the virtual rigid body, result in the manipulator  50  holding the instrument in a static pose. This is the pose in which the energy applicator  184  is in the last target position along the tool path  248 . 
     As described above, once step  866  is executed, a new on tissue tool path is generated, step  760  is re-executed. 
     Once semi-autonomous advancement of the instrument has been terminated, the surgeon can position the instrument and actuate the instrument through manual mode operation. 
     Semi-autonomous advancement of the instrument  160  can be restarted by the surgeon again depressing pendant trigger  194 . This will again result in the evaluation of step  764  testing positive. 
     V. Alternative Embodiments 
     It should be appreciated that the manipulator of this invention is not limited to the described configuration wherein there is a manipulator controller and a navigation processor. In some versions, a single processor or a multi-core processor, multiple multi-core processors or GPUs, plural DSPs or a set of parallel processors may perform the data processing performed by these processors. Likewise, some versions may have more processors than what has been described. For example, a first processor may perform some of the navigation data processes, a second processor may perform the behavior control functions and a third processor may perform the motion control processes. Likewise, in some versions many of the navigation and behavior control functions may be performed by a processor dedicated to these tasks. 
     Likewise, the various software modules that have been described should be understood to be illustrative and not limiting. Other software modules may perform the processing steps that result in the joint motors  101  outputting torques necessary to: emulate the advancement of the instrument if the practitioner&#39;s forces and torques were applied to the instrument; semi-autonomously advance the instrument; and allow the practitioner to adjust instrument orientation during semi-autonomous advancement. 
     Also, in some versions, by pressing buttons presented on one of the interfaces  130  or  220 , it is possible to change the characteristics of the mass and inertia properties of the virtual rigid body. For example, it is possible to decrease or increase the magnitude of the virtual mass. Decreasing the virtual mass causes the manipulator to respond as if the instrument and energy applicator  184  were, in comparison to their actual mass, lower in mass. Consequently, when the practitioner applies forces and torques to the instrument, the emulated movement of the instrument by the manipulator would cause the instrument to feel both lower in mass in the hand of the practitioner and more responsive to the applied forces and torques. The inertia properties that can be reset include the inertia tensor or matrix. 
     Another inertia property that can be changed is the location of the center of mass of the virtual rigid body. The movement of the center of mass of the virtual rigid body is performed by redefining the location of this point relative to the origin of end effector coordinate system EFCT. This movement of the center of mass of the virtual rigid body results in the manipulator positioning the instrument in a manner that provides the practitioner the impression that the center of mass of the instrument is shifted. It should be understood that it may even be possible to position the center of mass so it is not located within the instrument  160 . It is further possible to redefine the orientation of the coordinate system CMVB relative to coordinate system EFCT or other static coordinate system associated with the instrument  160  or energy applicator  184 . 
     Similarly, there is no requirement that the Z-axis of energy applicator coordinate system EAPP be oriented so to extend in a direction opposite the corresponding axis of coordinate system CMVB. In some implementations, these axes may be oriented in the same direction. Further in some versions, these Z axes may be angled relative to each other. Further, these axes may even be parallel to each other. 
     Moreover, while the various Z-axes of the different coordinate systems are generally shown being vertical, this should not be interpreted as limiting. In alternative constructions, for one or more coordinate system the X axis or Y axis may be the axis that is most closely perpendicular to the horizontal base plane of the cart  52 . 
     Likewise, the specific processing steps may be different from what has been described and variations in the algorithms and models are possible. For instance, there is no requirement that the forces F EAPP  and F BNDR  calculated by, respectively, the energy applicator force calculator  358  and the cut guide  390 , be calculated for application to the origin of coordinate system EAPP. In alternative versions of this invention, these forces are calculated for application to other points that are typically spaced away from the origin of coordinate system CMVB. The exact location to which these forces are applied is often a function of the geometry of the energy applicator  184 . Likewise, there is no requirement that both the energy applicator  358  and cut guide  390  apply the forces they respectively generate to the same point. With regard to the cut guide, the point to which force F BNDR  is applied may be recalculated each frame. The point of application of force F BNDR  may be a function of a boundary crossing analysis step in which the cut guide  390  determines which point on or section of the energy applicator  184  first would cross a boundary-defining tile. The same alternatives are possible with regard to the calculation of force F EAPP_SPR . As described below, in some version, energy applicator calculator  358  may calculate this force F EAPP_SPR . 
     For example, there is no requirement that the interference limit calculator comparator  622  always include models of the links that are cylindrical or capsule-shaped. The links could be modeled as rectilinear, conical or triangular structures. In some versions, each link may be modeled as a collection of one or more structures wherein the individual structures are of different sizes and/or shapes. 
     Similarly, there is no requirement that in all versions that running average filters be employed to generate the target positions along the tool path  248 . Alternative smoothing techniques including: using splines; finite impulse response filtering; infinite impulse response filtering; Chebychev filtering; Butterworth filtering; and blending linear segments with parabolic blends. 
     Likewise, there is no requirement that the signal ramping, such as the signal ramping performed by attenuator  697 , always be performed using finite impulse filters. Other processes such as infinite impulse response filtering, Chebychev filtering, Butterworth filtering or adaptive filtering may alternatively be employed to perform this signal ramping. 
     There is no requirement that in all versions the feed rate calculator  284  always calculate the instrument feed rate based on the instantaneous values of the variables. In some versions, these input variables may be filtered. Likewise, there may be reasons to vary the coefficients that are used as the multipliers to establish the extent any variable effects feed rate. The application of a particular variable may be delayed. The varying of the coefficient may be filtered or ramped to blend in/out the effect of the change in the magnitude of the coefficient. This filtering or blending results in a smoothing out of the advancement of the instrument  160 . This smoothing out of the advancing of the instrument may reduce the likelihood that, owing to rapid changes in the positioning of the instrument, the manipulator may become unstable or overshoot the target position. The effect of any variable may be selectively disregarded. For example, it may be desirable to only generate the instrument feed rate based on either the smallest or largest coefficient. The other coefficients are disregarded. 
     In some versions, two or more variables into feed rate calculator  284  may be combined. This combining may be by summing, multiplying, averaging or dividing. The calculated coefficients may likewise be summed, multiplied, averaged or divided to provide a final coefficient used to, based on the defined feed rate, establish the instrument feed rate. Likewise, there is no requirement that the coefficients may be determined solely on the basis of a variable-to-coefficient feed rate table. Other means to determine these coefficients are based on using the variables as input variables into an equation the result of which is the coefficient used to establish the instrument feed rate. The equations may be polynomial equations or non-linear equations. 
     Likewise, data other than instrument current draw may be used as the data by the feed rate calculator  284  that serves as the indicia of instrument power. These data include, the voltage or duty cycle required to be applied to the instrument to maintain a constant output. This output may be speed or temperature. In the case of a closed loop energy output device, the measurement of the output can serve as the indicia of instrument power. More specifically, a drop of the output can serve as the indicia of a change in instrument power. For example, if the sensed parameter is motor speed, a drop in speed indicates there was an increase in the power demand of the instrument. Based on this inferential indication that power demand has changed, the INST POWER coefficient applied to the feed rate calculator  284  is adjusted. 
     Alternative representations of the torques output by the joint motors  101  may be employed to facilitate the determination of the backdrive torques that are output by these motors. For example, it may not always be necessary to employ signals representative of the actual current applied to joint motors  101  as indicia of the torque output by these motors. In alternative configurations of this invention, signals representative of the commanded currents or feed forward torques input into the current control loops of the joint motor controllers  126  are employed as the signals representative of the torques output by the motors. 
     Data representative of the actual joint torques may also be supplied by sensors attached to the joint motors  101  or other components integral with the active joints. Also, in some versions, there is no backdrive force summer  691 . In these versions, a single one of the representations of actual torque is applied to the back drive torque calculator  693 . 
     Alternative methods to determine the backdrive forces and torques may also be employed. For example, in one alternative method of this invention, a first difference between the expected torques and the torques produced by the joint motors  101  is calculated. This set of torque difference values is then converted into coordinate system CMVB as the first set of backdrive forces and torques. A second difference is calculated between the expected torques and the torques sensed by sensors  89 . This set of torque difference values is then converted into coordinate system CMVB as the second set of backdrive forces and torques. These two sets of instrument backdrive forces and torques are summed together to produce data representing the backdrive forces and torques. The inputs into this sum may be weighted. 
     It should be understood that the physical construction of the links forming the manipulator may vary from what has been described. For example, in some manipulators with parallel four bar linkages the linkages may be designed so that the wrists connecting the coupler to the links may rotate around axes that are laterally offset from the axes of the driven links. Likewise, the wrists may not even rotate around axes that are exactly parallel or perpendicular to the drive links. Similarly, there is no requirement that in all versions, the manipulator have plural four bar linkage assemblies. The invention may be constructed out of plural links that collectively form a single-arm serial linkage. In versions that include parallel links that are coupled together, the coupler between the links may not be rigid. 
     Motors other than permanent magnet synchronous motors may be employed as actuators. For example, brushless DC motors, brush-type DC motors, stepper motors and induction motors. Likewise, there is no requirement that the actuators be electrically driven motors. In some versions the actuators may be hydraulic or pneumatic actuators. 
     The structure of the joint motor controllers should be understood to be a function of the nature of the motors internal to the actuators. Variations in motor control processes are also possible. For example, it may be possible to omit the speed control loop when regulating motor operation. 
     In some versions, it may be desirable to provide at least one of the active joints plural encoders. A first encoder monitors the angular position of the shaft integral with the joint motor  101 . Data from this encoder is used by the joint motor controller to regulate the actuation of the joint actuator. If the joint actuator is an electric motor, these data are often used to regulate commutation of the motor windings. A second encoder monitors the joint angle. Data from this second encoder is employed by modules such as the forward kinematics module  562  as the representation of actual joint angle. This more direct measurement of the joint angle is not affected by the inherent tolerances of the gear train. Accordingly, employing this more direct measurement of joint angle as the actual representation of joint angle may improve the accuracy with which the manipulator sets the pose of the instrument  160 . 
     In constructions that include plural encoders for at least one of the active joints, the position data from the plural encoders can be used by the joint motor controller to regulate actuation of the joint actuator. For example, in some constructions, the data from one encoder, often the encoder associated with the joint actuator, is used as the primary feedback variable into the position control loop. The data from the second encoder, often the encoder that generates data representative of actual joint angle, is employed as an input to determine the damping component of the output signal. In still other constructions of the manipulator of this invention, the primary feedback variable into the position control loop is a representation of joint angle based on a weighted average of data representative of joint angle from the plural encoders. Further, the damping component may be based on a difference between the representations of the joint angles from the plural encoders. Employing these plural representations of joint angle as input variables into the joint angle position control loop can improve the stability of this control process. 
     Similarly, other methods may be used to map the tissue to which the instrument is to be applied. In one of these methods the practitioner uses a pointer, the positions of which are tracked by the surgical navigation system  210 . At the start of the procedure, the practitioner uses the pointer to identify specific landmarks on the body of the patient. Based on the locations of these landmarks, data are generated that define the boundary of the space to which the energy applicator  184  should be applied. 
     In alternative versions, the cut guide uses other methods to determine the point on the boundary the energy applicator  184  will cross. In regard to this analysis, there is no requirement that it is always assumed that the velocity of coordinate system CMVB is constant when determining where the energy applicator  184  will cross the boundary. The velocity of coordinate system BONE may also vary during a frame. There is no requirement that the plural energy applicator  184  against boundary contacts during a single frame be handled sequentially. These contacts may be aggregated to produce a single effective contact. This single effective contact is mitigated by a single boundary constraining force. 
     Likewise, cut guide  390  may not rely on impulses to prevent the energy applicator  184  from crossing a boundary. For example, in an alternative construction of manipulator  50 , each boundary tile may be modeled as a compliant surface, such as a spring/damper system. When it is determined that the energy applicator  184  will move to a position beyond a tile, the spring defining the tile is considered to be compressed. The force the spring would apply to oppose this compression is calculated. 
     Similarly, the manipulator of this invention is not designed solely for use with tool path generators that generate tool paths that include parallel path segments. The manipulator of this invention can be used with tool path generators that generate tool paths that include segments that, when connected together form either a two-dimensional or three-dimensional spiral. 
     In the described version, the tool path is described as being a set of points along the tissue against which the energy applicator  184  is applied. This is only exemplary, not limiting. Depending on the type of instrument, the tool path may be one that is generated to position the instrument so that the energy applicator  184  is both a select distance from the target tissue and in a defined orientation relative to the target tissue. This type of tool path may be generated if, for example, the instrument emits photonic energy. This type of instrument may be designed so that, to perform the desired procedure, the distal end tip of the energy applicator  184  needs to be spaced a given distance, for example 0.1 to 2.0 cm from the tissue to which the energy is to be applied. 
     Similarly, in some versions, it is further possible to adjust the spacing of the aperture  370  relative to the surface of the tissue to which the energy applicator  184  is to be applied. Generally, as the distance between aperture  370  and the underlying tissue surface increases, the volume of the space in which the instrument can pivot decreases. Controls to perform this adjustment may be presented as buttons on one of the interfaces  128  or  220 . This allows the practitioner to perform this adjustment. 
     In some versions, the tool orientation regulator  368  may not be configured to, in the general condition, always generate a force F ORNT  that results in the manipulator  50  positioning the instrument so that the common axis intersects a fixed centering point. In these versions, even when an obstruction  828  is not present, the tool orientation regulator  368  output forces F ORNT  applied to the virtual rigid body that do not always result in the manipulator positioning the instrument so the common axis intersects the fixed centering point. Instead, these forces F ORNT  only result in the manipulator positioning the instrument so the common axis intersects the reference surface aperture.  FIGS.  33 A and  33 B  illustrate how the instrument is so positioned. 
     A benefit of this version is that it increases the area of surface of the tissue below the reference plane to which the energy applicator  184  can be applied. An additional benefit of this feature is that it makes it possible to, once a single reference surface and aperture have been defined, position the instrument over a wide area and use the instrument to form shapes that are in appreciably different planes. 
     Still another benefit of this version is that it makes it possible to, when advancing the energy applicator  184  along the tool path, maintain the instrument in orientations in which the minor angle between the common axis and the reference surface  390  does not appreciably vary from the normal. This benefit of this version is depicted diagrammatically in  FIG.  33 C . Here, the distal end tip of the energy applicator  184  is seen in various positions as the applicator advances along the tool path  248 . When the applicator  184  is in each of these positions, the force F ORNT  output by the regulator  368  for application to the virtual rigid body only results in manipulator holding the instrument so the common axis extends through aperture  370 . Since the manipulator is not constrained to pivot the instrument so the common axis extends through the center of the aperture  370 , the instrument is able to be maintained in orientations that often vary less than 450 from the normal. 
     This method of operating the instrument can be achieved by having the tool orientation regulator  368  dynamically change the position of the location of the centering point as the energy applicator  184  is advanced semi-autonomously. Each new position of the centering point is based on variables such as the representation of the actual angle of the common axis relative to the reference surface  369 , applicator target positions and the commanded pose and commanded velocity of the instrument. Each new position of the centering point it is understood is within the reference surface aperture  370 . Distance DIST INST-CP  is calculated based on the distance between the dynamically defined centering point and the intersection of the common axis with the reference surface aperture  370 . 
     Likewise, there is no obligation that orientation regulator  368  always calculate forces and torques applied to the virtual rigid body to maintain instrument orientation based on spring/damper modeling. Tool orientation regulator  368  could calculate these forces and torques based on other models that generate the forces and torques applied to the virtual rigid body to maintain the common axis at least in close proximity to the centering point. 
     Impulse force modeling, the modeling employed to determine forces and torques applied to the virtual rigid body to perform semi-autonomous advancement of the instrument, can be used to define these forces and torques. An equation similar to Equation (5) is employed to determine force F ORNT . In this use of Equation (5) the variables upon which direction D xyz  is based are the location of the centering point and the intersection of the longitudinal axis of the instrument with the reference plane. Distance Δd is the negative of the magnitude of the distance between the centering point and the intersection of the longitudinal axis of the instrument with the reference plane. Velocity V 0  is the velocity of coordinate system CMVB expressed in coordinate system CMVB. Velocity V 1  is the velocity of the centering point expressed in coordinate system CMVB. The Jacobian used is the Jacobian matrix from the origin of coordinate system CMVB to the centering point along the direction D xyz . The remaining terms are the same as are employed for the impulse modeling of semi-autonomous advancement of the energy applicator  184 . 
     The computed forces and torques applied to the virtual rigid body to prevent the joints from exceeding their limits, the links from colliding or the manipulator from extending beyond the workspace boundary may also be calculated using modeling other than spring/damper modeling. Each one of these sets of forces and torques could, for example, be computed using impulse modeling. 
     When impulse modeling is employed to determine the forces and torques that prevent the joints from moving beyond their minimum and maximum joint limit angles, an equation similar to Equation (5) is employed to determine force F J_L . This equation is employed for each joint when the corresponding boundary exceeded angle for the joint is non-zero. In this use of Equation (5), the angular components of direction D xyz  are the components of the unit vector defining the axis of rotation for the joint. The linear components of direction D xyz  are set to zero. In many cases as a convention, the z-axis is chosen to define the axis of rotation. In this case direction D xyz  is set to [0, 0, 0, 0, 0, 1]. Distance Δd is the negative of the boundary exceeded angle. Velocity V 0  is the velocity of coordinate system CMVB expressed in coordinate system CMVB. Velocity V 1  represents the desired velocity of the joint defined as a vector having components consistent with the definition of direction D xyz . For this case it is desired to inhibit advancement of the joint beyond the boundary. This is accomplished by setting the component of velocity V 1  corresponding to rotation about the axis to zero. If the above convention is employed, velocity V 1  is the null vector. The Jacobian used is the Jacobian matrix from the origin of coordinate system CMVB expressed in coordinate system CMVB to the joint space defined by direction D xyz . Using this version of Equation (5), force F ENV  is the previously defined force F ENV  with the previously defined force F J_L  component removed. The remaining terms are the same as are employed for the impulse modeling of semi-autonomous advancement of the energy applicator  184 . 
     When impulse modeling is employed to determine the forces and torques that prevent the links from colliding, an equation similar to Equation (5) is employed to determine force F INF . This equation is employed for each pair of potentially colliding links when the corresponding interference boundary exceeded distance for the pair of links is non-zero. In this use of Equation (5), the linear components of direction D xyz  are the components of the unit vector defining the line of minimum distance between the links. In many cases this is the common normal between the links. The angular components of direction D xyz  are set to zero. In many cases as a convention, the z-axis is chosen to be along the line of minimum distance. In this case direction D xyz  is set to [0, 0, 1, 0, 0, 0]. Distance Δd is the negative of the boundary exceeded distance. Velocity V 0  is the velocity of coordinate system CMVB expressed in coordinate system CMVB. Velocity V 1  represents the desired velocity between the links along the line of minimum distance, defined as a vector having components consistent with the definition of direction D xyz . For this case it is desired to inhibit advancement of the links towards each other along this line. This is accomplished by setting the component of velocity V 1  corresponding to direction of minimum distance to zero. If the above convention is employed, velocity V 1  is the null vector. The Jacobian used is the Jacobian matrix from the origin of coordinate system CMVB expressed in coordinate system CMVB to the interference space defined by direction D xyz . Using this version of Equation (5), force F ENV  is the previously defined force F ENV  with the previously defined force F INF  component removed. The remaining terms are the same as are employed for the impulse modeling of semi-autonomous advancement of the energy applicator  184 . 
     When impulse modeling is employed to determine the forces and torques that prevent the manipulator from exceeding the workspace boundary, an equation similar to Equation (5) is employed to determine force F WSB . This equation is employed when workspace boundary exceeded distance DIST W_B_E  is non zero. In this use of Equation (5), the linear portion of direction D y , is the previously defined unit direction vector D W_B_E . The angular components of direction D xyz  are set to zero. Distance Δd is the negative of the distance DIST W_B_E . Velocity V 0  is the velocity of coordinate system CMVB expressed in coordinate system CMVB. Velocity V 1  represents the desired velocity of coordinate system EAPP away from the workspace boundary defined as a vector having components consistent with the definition of direction D y z. For this case it is desired to inhibit advancement of coordinate system EAPP beyond the workspace boundary. This is accomplished by setting the component of velocity V 1  corresponding to the velocity of the movement beyond the boundary to zero. This results in the product of distance DIST W_B_E  and velocity V 1  being the null vector. The Jacobian used is the Jacobian matrix from the origin of coordinate system CMVB expressed in coordinate system CMVB to the point where the line of minimum distance back to the boundary intersects the boundary along direction D xyz . This intersection point is expressed in coordinate system MNPL. Using this version of Equation (5), force F ENV  is the previously defined force F ENV  with the previously defined force F WSB  component removed. The remaining terms are the same as are employed for the impulse modeling of semi-autonomous advancement of the energy applicator  184 . 
     If impulse modeling is used to determine plural forces applied to the virtual rigid body, the plural versions of Equation (5) are solved together as a system of equations. The unknowns determined as a result of the solving of these equations are individual corresponding forces. Each of these forces are scalar forces along their respective D xyz  directions. Each force is converted to equivalent forces and torques acting at the origin of coordinate system CMVB. These conversions are performed using versions of Equation (6). In each case the respective Jacobian is employed. 
     If the set of forces that are being solved include any one of forces F J_L , F INF  or F WSB , the equations are solved as a linear complementarity problem. This is because each one of the forces F J_L , F INF  or F WSB  has the characteristic that it may not be present if the corresponding boundary is not exceeded. This problem is of the form in which, for each force and velocity pair, the force must be equal to or greater than zero and the velocity also be equal to or greater than zero. 
     If any one of forces F J_L , F INF  or F WSB  are solved for as part of the impulse modeling of forces and torques applied to the virtual rigid body, each of the solved forces is applied directly to the total force summer  380 . These impulse modeled forces are not applied to the environmental force summer  379 . 
     In a process used to generate the workspace boundary force F WSB  there is no need to generate this force based only on the pose of coordinate system EAPP. For example, it may be desirable to perform this modeling based on one of the coordinate systems the pose of which is fixed relative to coordinate system EAPP. These coordinate systems include coordinate system EFCT and coordinate system CMVB. This modeling control could also be based on the evaluating the position/positions of one or more moveable points on the arms  68  and  70 . It may be desirable to model force F WSB  based on the pose of plural coordinate systems. This type of modeling might be performed if it is desirable to avoid having any one of or more than one of plural points on different components attached to the manipulator move beyond the workspace boundary. 
     In some versions, the evaluation of step  770  to determine whether or not the energy applicator  184  is within the target region at the start of the semi-autonomous operation is performed by evaluating the length of the free space tool path segment generated in step  766 . If the length of this path segment is below a maximum length, manipulator controller  124  considers the origin of energy applicator coordinate system EAPP to be close enough to the start of the on-tissue path segments, point  258 , the semi-autonomous advancement of the instrument can proceed. 
     When manipulator  50  is operated in the semi-autonomous mode processes other than impulse based calculations may be used to determine the force needed to advance the energy applicator  184  to the target position. For example, the forces may be modeled as spring/damping forces. Generally, these spring/damping forces are modeled according to the following formula:
 
 F   EAPP_SPR   =K   EAPP *DIST TRGT-CMND   −D   EAPP_REL   *V   TRGT-CMND   −D   EAPP_MNPL   *V   TRGT   (22)
 
Here, F EAPP_SPR , is the spring/damping force that would need to be applied to the virtual rigid body at the origin of coordinate system EAPP to pull the energy applicator  184  along the path segment towards the target position. Constant K EAPP , is a spring constant; D EAPP_REL  is a damping coefficient for the relative velocity; and D EAPP_MNPL  is a damping coefficient for the velocity in manipulator coordinate system MNPL. Distance DIST TRGT-CMND  is a position vector defining the location of the target position relative to the command position. Velocity V TRGT-CMND  is a vector that provides the relative velocity of the target position to the commanded position. Velocity V TRGT  is a vector that provides the velocity of the target position in manipulator coordinate system MNPL. It may not be necessary to employ the velocity V TRGT  as an input variable for determining the force that needs to be applied to the virtual rigid body.
 
     Once F EAPP_SPR  is determined, this force is converted to an equivalent set of forces and torques that would need to be applied to the virtual rigid body at the origin of coordinate system CMVB. This conversion may be performed according to the following formula:
 
 F   INST_SPR   =J   T   F   EAPP_SPR   (23)
 
Force F INST_SPR  are the forces and torques applied to the virtual rigid body. This particular Jacobian J is defined from coordinate system CMVB to the coordinate system EAPP. Force/torque vector F INST_SPR  is substituted as an input variable for where force/torque variable F INST  is otherwise employed.
 
     If none of forces applied to the virtual rigid body to produce forces F TTL  and torques T TTL  are determined based on impulse modeling, the forces can all be applied directly to the total force summer  380 . This eliminates the need to provide the environmental forces summer  379 . 
     There is no requirement that a specific integration technique be used by either the integrator or cut guide to determine either velocity or pose of a coordinate system. For example, the semi-implicit Euler method, Verlet, rectangular, trapezoidal, Taylor series expansion or Riemann numerical integration techniques may be employed. Likewise, in some versions, the period of the frame or period of the integration may be variable. 
     In both manual mode and semi-autonomous positioning of the instrument, there is no requirement that the commanded pose/position be the variable representative of actual instrument pose/position employed in the force and torque calculations. In some versions, the measured pose/position of the instrument/energy applicator is employed as the representation of actual position. This “measured” pose/position includes but is not limited to the position determined as a result of: the forward kinematics calculation; and the determination made by monitoring the position and orientation of the tool tracker. Measurements of the joints by direct means, such as with joint angle sensors, or indirect means, such as separate external monitoring unit can also be used to produce data used to determined measured pose/position. A goniometer is one such external monitoring unit. 
     This measured pose/position data, in addition to being used in the force/torque calculations, may be used as an alternative to the commanded pose/position data in other calculations. These calculations include: the joint limit calculations; the interference limit calculations; and the workspace limit calculations. It should likewise be understood that this substitution need not be absolute. There may be some processes where it is desirable to employ the commanded pose/position as this variable and still others wherein the measured pose/position is employed. Here it is understood that this substitution applies not just to the substitution of measured pose/position data for commanded pose/position data, but also to the substitution of measured joint angles for commanded joint angles. 
     Similarly, in cases where a representation of actual velocity is needed, either commanded or measured velocity may be employed. This includes representation of actual angular velocity of the joints as well as representations of actual velocity, linear and angular, of the instrument  160  and the coordinate systems that move with the instrument. 
     Likewise, there may be instances wherein the most appropriate variable that is descriptive of actual instrument pose/position, and or manipulator joint angle is a variable that is derived from a combination of the commanded pose/position/joint angle and the measured pose/position/joint angle. This derived value may be: an unweighted average; a weighted average; a minimum value; and/or a maximum value. 
     Further, in some versions, one or more of the forces and torques that are supplied to either of the force summers  379  or  380  may be multiplied by a coefficient. The product of this multiplication is then used by the force summer as one of the addend variables upon which the forces F ENV  and F TTL  and torques T TTL  are based. In some versions, depending on the state of the manipulator, one or more of the coefficients may change over time. As with the external forces summer, this blending is performed to smooth the movement of the instrument. 
     For example, when the practitioner depresses either button  172  to reset the orientation of the instrument  160  or switch  176  when the manipulator is in the manually operated mode, the forces and torques output by the external forces summer  698  may be subjected to a blending process. In this process the forces and torques output by summer  698  are multiplied by coefficients. The products of these multiplications are then employed as the addends representative of the surgeon desired movement of the instrument. Initially, these coefficients may be appreciably below unity, 0.2 or less. Then over a period of time that is typically less than a second and more often less than 0.5 seconds, these coefficients rise to 1.0. Thus, if the surgeon, when depressing button  172  or switch  176  is already placing significant forces and torques on the instrument, these forces are and torques are not immediately applied to the force summer  380  as addends. This reduces the extent to which the combining of these forces and torques into the forces F TTL  and torques T TTL  results in manipulator rapidly resetting the position of the instrument. 
     Likewise, it should further be appreciated that the tool orientation regulator  368  may not always keep the position of the reference surface and aperture defined within the reference surface constant. Either as a result of preprogrammed instructions or commands entered through the user interface the position and geometries of both these geometric landmarks may be reset. 
       FIGS.  34 A,  34 B, and  34 C  illustrate one situation in which the position and reorientation of the reference surface and aperture are reset. In  FIG.  34 A  a reference surface  910  is shown in relatively close proximity to the surface of the tissue, bone  902 , to which the energy applicator  184  is to be applied. The aperture  912  defined in the reference surface is, at least in the depicted plane, shown to have a narrow length. Aperture  912  is thus well suited to define the area through which the axis of the energy applicator  184  should intersect when the energy applicator  184  is applied to a section of tissue that is relatively small in area. This is the section of the tissue which is removed so as to form the initial bore  904  in the bone as depicted in  FIG.  34 B . 
     Once bore  904  is formed, the tool orientation regulator defines a new reference surface, surface  918 , with aperture  920 , as depicted in  FIG.  34 C . Reference surface  918  is spaced further from the surface of bone  902  than reference surface  910 . Aperture  920  is greater in width than aperture  912 . The change in position of the reference surface and increase in size in the aperture increases the area in which the origin of the energy applicator coordinate system EAPP can be applied relative to the initial state. This means the energy applicator  184  could then be used, as depicted in  FIG.  34 C , to form an undercut  906  in the bone  902 . This undercut  906 , it is observed, has, at least in the depicted plane, a width greater than the diameter across bore  904 . 
       FIGS.  35 A,  35 B, and  35 C  depict another situation in which the position and orientation of the reference surface and aperture are reset.  FIG.  35 A  depicts when the reference surface  938  is initially defined so as to be in a plane generally parallel to the surface of the bone  902  that appears generally horizontal in the Figure. Aperture  940  is defined in surface  938 . Aperture  940  is an aperture from which the tool orientation regulator  368  regulates the orientation of the energy applicator  184  when the energy applicator  184  is used to define surfaces  930  and  932  in bone, seen in  FIG.  35 B . 
     After surfaces  930  and  932  are defined, the procedure may call for the forming of a surface that is tapered away from surface  932 . This is why in  FIG.  35 B , a new reference surface  944  is shown. Tool orientation regulator defines reference surface  944  so that it is angled, not parallel to, the top horizontal surface of bone  902 . An aperture  946  is defined in reference surface  944 . Given the specifics of the area to which the energy applicator  184  is to be applied, aperture  946  has a width, in the plane of the Figures, less than that of aperture  940 . 
     Once reference surface  944  and aperture  946  are defined, the manipulator may apply the energy applicator  184 . Specifically, the energy applicator  184  may be used to remove bone so as to define surface  936  in  FIG.  35 C . During this process, the tool orientation regulator  368  maintains the orientation of the energy applicator  184  based on the position of aperture  946 . 
     While not illustrated it should further be understood that either the computer generated or manually defined reference surface and, by extension aperture, need not always be planar. The reference surface and aperture may lie in one or more intersecting planes that are angled to each other. All or a portion of the reference surface and associated aperture may even be a curved surface. Likewise, there is no requirement that the aperture used to establish the limits of the orientation of the energy applicator  184  be circular in shape. 
     It should further be appreciated that, for some procedures, the tool orientation regulator may not even define an aperture. Tool orientation regulator  368  may only define a centering point. In these versions, tool orientation regulator  368  outputs a force F ORNT  of such magnitude that the manipulator  50  always orients the instrument so that the common axis, with only minimal variance, intersects the centering point. When operating the manipulator  50  in this mode, the presence of many obstructions  828  may cause the force F ORNT  to exceed either the associated lower limit level or higher limit level associated with this force. Force overrider  375  responds as appropriate for the limit level that is exceeded. 
     Tool orientation regulator  368  may be designed such that the manipulator  50  holds the instrument  160  in a predetermined orientation relative to the surface of the tissue against which the energy applicator  184  is applied. A predetermined orientation may be advantageous when the energy applicator  184  is a milling cutter, which does not cut well on its axis of rotation. For example, when the energy applicator  184  is a ball cutter, the tooth speed approaches zero along this axis and material removal rates and surface finish suffer if cuts are made with the portion of the ball rotating along the axis of rotation presented into the material to be removed. Cutting in this orientation will also increase the required force to push the cutter into the material to be removed and will often generate heat at the surface interface. Thus, a pose is selected that presents the cutting teeth in an orientation that provides the most effective material removal and optimizes the surface finish. 
     Tool orientation regulator  368  may further be designed to output a force F ORNT  that results in the manipulator  50  holding the instrument in a fixed orientation relative to the surface of the tissue against which the energy applicator  184  is applied. One means of performing this orientation regulation is to have the orientation regulator output a force F ORNT  that results in the manipulator holding the instrument so the common axis intersects the reference surface at a fixed angle. Often but not always, this angle is a right angle. This type of orientation regulation is employed if the instrument attached to the manipulator is a drill used to form a bore at a precise angle. The fixed angle or the location of the centering point through which common axis intersects can be updated by the tool path generator as the energy applicator  184  is advanced. 
     In versions in which the surgeon manually sets the extent to which regulator  368  regulates instrument orientation, by entering commands through the user interface  130  the surgeon is able to change the position and orientation of the reference surface as well as the shape and size of the aperture. This allows the surgeon to, in real time, change the extent to which the manipulator  50  regulates the orientation of the instrument  160 . 
     Likewise, there is no requirement that the centering point defined by the orientation regulator be in the center of the aperture defined by the regulator. Using the user interface, the surgeon may be able to define the centering point so that it is spaced from the center of this aperture. Likewise, the surgeon may be able to define this centering point by the selective depression of an instrument switch such as button  172 . In this implementation, the aperture itself would still be fixed in shape and location relative to the origin of the coordinate system in which the aperture is defined. 
     Some manipulators  50  of this invention are further configured to allow the adjustment in essentially real time of the boundaries of the areas to which the instrument energy applicator  184  can be applied. An understanding of the establishment of these boundary settings is understood by reference to  FIGS.  36 A,  36 B, and  36 C .  FIG.  36 A  is a top view depicting the bone  952  for which manipulator  50  is used to assist in the performance of the procedure. Dashed rectangle  954  represents the boundary of the surface of the bone to which the energy applicator  184  is to be applied. Also seen is the retracted soft tissue  950  that was initially pulled away to expose the surface of bone  952 . The surface of the skin of the patient is called out with identification number  948 . 
     Retractors  956 , seen in  FIG.  36 B , retain the pulled back tissue away from the exposed bone. The retractors  956  extend into the space above area to which the energy applicator  184  is to be applied. Once the retractors  956  are set, a navigation pointer (not illustrated) is pressed against the retractors. The navigation system, by monitoring the position of the pointer, then generates data indicating the positions of the retractors  956  relative to the bone. Based on these data, boundary generator  232 , generates a revised boundary represented by dashed line  960 . Boundary  960  while similar to boundary  954  has two notches  962 . Notches  962  define the sections of the boundary around and spaced from retractors  956 . Consequently, during operation of the instrument in either manual or semi-autonomous mode, the behavior control modules now cooperate to prevent the energy applicator  184  from attempting to move against the tissue covered by the retractors  956 . This substantially reduces the likelihood that the instrument or energy applicator  184  will collide with the retractors. 
     Once the energy applicator  184  has been applied to one section of the bone  952 , it may be necessary to, as seen in  FIG.  36 C , reset the positions of the retractors  956  to hold another section of soft tissue  950  away from the bone. Once the retractors are reset, their positions are again, through the navigation system, forwarded to the boundary generator  232 . This results in the generator of a new boundary, represented by dashed line  964 , defining the area to which the instrument should be applied. This new boundary defines notches  966 . Notches  966  define the out-of-boundary spaces in which the retractors  956  are positioned. This ensures that, even though the retractors  956  have been repositioned, the manipulator will not reposition the instrument in such manner that the energy applicator  184  collides with the retractors  956 . 
     The boundaries of the aperture upon which the orientation regulator  368  determines whether or not the resultant orientation of the instrument is within an acceptable range may likewise be defined using a pointer. In still other versions, the location of markers attached to the patient may be used to define the perimeters of the aperture defined by the orientation regulator  368 . The positions of these markers may be monitored by the navigation system  210  or by a separate tracking system. When either pointers or markers are employed to establish the boundary of the aperture defined by the regulator  368 , it should be understood that the regulator dynamically changes the shape of this aperture. 
     Likewise, the physical constructions of some of the control members may change. Manipulator  50  may be provided with a set of foot switches. One of these foot switches may perform one or more of the functions of switch  176 . In these versions, in order to have the manipulator emulate manual movement of the instrument and/or actuate the instrument, the practitioner must depress the footswitch. 
     Similarly, in other versions, the switch that should be depressed in order to cause the semi-autonomous advancement of the instrument may be on the instrument  160 . For example, in some versions, the instrument is provided with an additional button or lever. The surgeon depresses this button on order to cause the semi-autonomous advancement of the instrument. When the manipulator is operated in this state, buttons  164  and  174  no longer function as the buttons that regulate the on/off state of the instrument power generating unit  163 . Instead, buttons  164  and  170  perform the functions of pendant buttons  193  and  195 , respectively. Button  164  is depressed to decrease the semi-autonomous defined feed rate. Button  174  is depressed to increase the semi-autonomous feed rate. Thus, when the manipulator is operated in this configuration, the surgeon, using the hand used to hold the instrument  160 , is able to: cause the manual positioning of the instrument; take the instrument in/out of the semi-autonomous mode; and control the semi-autonomous feed rate. 
     Further, there is no requirement that in all versions, the practitioner must continually depress pendant trigger  194  to cause tool path force calculator  278  to output non-zero forces F INST  and F ORNT . In some versions, the forces applied to the virtual rigid body that result in the energy applicator  184  advancing along the tool path  248 , are output in response to a single pulse to pendant trigger  194 . Manipulator  50  advances the instrument until the practitioner applies a second pulse, a stop pulse, to trigger  194 . 
     The navigation system used with this manipulator is not limited to the disclosed system. For example, the manipulator may be used with an electromagnetic navigation system. Also, there may be wired connections between the localizer and the navigation trackers. 
     Removed tissue logger  275  can provide data that indicates the percent of the volume of tissue marked for removal that was removed. This provides the practitioner with an indication of the extent to which the procedure has been completed. Logger  275  performs this function when the manipulator is operated in either the manual mode or the semi-autonomous mode. 
     Therefore, it is an object of the appended claims to cover all such modifications and variations that come within the true spirit and scope of this invention.