Patent Publication Number: US-9417621-B2

Title: Control of medical robotic system manipulator about kinematic singularities

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 12/494,695 (filed Jun. 30, 2009), now U.S. Pat. No. 8,768,516 B2, which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention generally relates to medical robotic systems and in particular, to the control of a medical robotic system manipulator about kinematic singularities. 
     BACKGROUND OF THE INVENTION 
     Medical robotic systems such as teleoperative systems used in performing minimally invasive surgical procedures offer many benefits over traditional open surgery techniques, including less pain, shorter hospital stays, quicker return to normal activities, minimal scarring, reduced recovery time, and less injury to tissue. Consequently, demand for such medical robotic systems is strong and growing. 
     One example of such a medical robotic system is the da Vinci® Surgical System from Intuitive Surgical, Inc., of Sunnyvale, Calif., which is a minimally invasive robotic surgical system. The da Vinci® Surgical System has a number of robotic arms that move attached medical devices, such as an image capturing device and Intuitive Surgical&#39;s proprietary EndoWrist® articulating surgical instruments, in response to movement of input devices by a surgeon viewing images captured by the image capturing device of a surgical site. Each of the medical devices is inserted through its own minimally invasive incision into the patient and positioned to perform a medical procedure at the surgical site. The incisions are placed about the patient&#39;s body so that the surgical instruments may be used to cooperatively perform the medical procedure and the image capturing device may view it without their robotic arms colliding during the procedure. 
     To perform certain medical procedures, it may be advantageous to use a single entry aperture, such as a minimally invasive incision or a natural body orifice, to enter a patient to perform a medical procedure. For example, an entry guide may first be inserted, positioned, and held in place in the entry aperture. Instruments such as an articulatable camera and a plurality of articulatable surgical tools, which are used to perform the medical procedure, may then be inserted into a proximal end of the entry guide so as to extend out of its distal end. Thus, the entry guide provides a single entry aperture for multiple instruments while keeping the instruments bundled together as it guides them toward the work site. 
     To properly guide the instruments to and maneuver them about a work site within a patient, an entry guide manipulator commandable through operator interaction with one or more input devices is desirable to move the entry guide through and about a pivot point at the entry aperture. In doing so, however, it is important to maintain good control of the entry guide manipulator when encountering singularities in its operation. In particular, it is desirable to avoid control problems encountered when axes for two rotational degrees of freedom of an entry guide manipulator coincide during its operation. Conventional systems employ either a control system that avoids operating at a singularity using a so-called “no-fly zone”, which limits the workspace of the manipulator, or redundant degrees-of-freedom, which allow the manipulator to reach the desired tip position and orientation without approaching the singularity. 
     OBJECTS AND SUMMARY OF THE INVENTION 
     Accordingly, one object of one or more aspects of the present invention is a medical robotic system and method implemented therein for positioning and/or orienting a medical device using a manipulator without losing good control of the manipulator when encountering a singularity in its operation. 
     Another object of one or more aspects of the present invention is a medical robotic system and method implemented therein for positioning and/or orienting a medical device using a manipulator without avoiding operation at a singularity of the manipulator. 
     Another object of one or more aspects of the present invention is a medical robotic system and method implemented therein that retains intuitive tele-operation of a non-redundant manipulator while it operates around and at a singularity of the manipulator. 
     Another object of one or more aspects of the present invention is a medical robotic system and method incorporated therein for positioning and/or orienting a medical device having a camera extending out of its distal end without unintentionally changing the orientation of an image captured by the camera while operating at or near a singularity of a manipulator used for such positioning and/or orienting. 
     These and additional objects are accomplished by the various aspects of the present invention, wherein briefly stated, one aspect is a medical robotic system comprising: a medical device, a manipulator, and a controller. The manipulator is capable of manipulating the medical device in at least first, second and third rotational degrees of freedom in which the medical device is respectively rotatable about first, second and third axes at a pivot point. The first axis is fixed in space, and the second and third axes are fixed relative to the medical device and orthogonal to each other so as to move in space as the medical device moves. The controller is configured to command the manipulator to manipulate the medical device to the commanded state while resolving any control ambiguity caused by the first and the third axes coinciding. 
     Another aspect is a method for controlling a manipulator for manipulating a medical device in at least first, second and third rotational degrees of freedom in which the medical device is respectively rotatable about first, second and third axes at a pivot point, the first axis fixed in space, and the second and third axes fixed relative to the medical device and orthogonal to each other so as to move in space as the medical device moves. The method comprising: commanding the manipulator to manipulate the medical device to a commanded state while resolving any control ambiguity caused by the first and third axes coinciding. 
     Additional objects, features and advantages of the various aspects of the present invention will become apparent from the following description of its preferred embodiment, which description should be taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a top view of an operating room employing a medical robotic system utilizing aspects of the present invention. 
         FIG. 2  illustrates a block diagram of components for controlling and selectively associating device manipulators to input devices in a medical robotic system utilizing aspects of the present invention. 
         FIG. 3  illustrates a perspective view of a distal end of an entry guide with a plurality of articulatable instruments extending out of it in a medical robotic system utilizing aspects of the present invention. 
         FIG. 4  illustrates a cross-sectional view of an entry guide as used in a medical robotic system utilizing aspects of the present invention. 
         FIG. 5  illustrates a perspective view of an entry guide along with four degrees-of-freedom movement as used in a medical robotic system utilizing aspects of the present invention. 
         FIG. 6  illustrates a block diagram of an entry guide controller used to control an entry guide manipulator in a medical robotic system utilizing aspects of the present invention. 
         FIG. 7  illustrates a side view of an entry guide with various reference frames and a pitch angle indicated thereon as used in a medical robotic system utilizing aspects of the present invention. 
         FIG. 8  illustrates a perspective view of an entry guide at a yaw/roll singularity position in a medical robotic system utilizing aspects of the present invention. 
         FIG. 9  illustrates a flow diagram of a method for controlling an entry guide manipulator near a singularity in a medical robotic system utilizing aspects of the present invention. 
         FIG. 10  illustrates a plot of 1/cos q OP  vs. q OP  as an entry guide approaches a yaw/roll singularity in a prior art medical robotic system. 
         FIG. 11  illustrates a plot of 1/cos q OP  vs. q OP  as an entry guide approaches a yaw/roll singularity in a medical robotic system utilizing aspects of the present invention. 
         FIG. 12  illustrates an x 0 -z 0  plane view as an allowed direction of the entry guide is changed at a yaw/roll singularity in a medical robotic system utilizing aspects of the present invention. 
         FIG. 13  illustrates a perspective view of an entry guide as its allowed direction is changed at a yaw/roll singularity in a medical robotic system utilizing aspects of the present invention. 
         FIG. 14  illustrates a perspective view of an entry guide as it moves to a commanded state in its allowed direction in a medical robotic system utilizing aspects of the present invention. 
         FIGS. 15-17  illustrate sequential views of an entry guide tip as it changes its allowed direction and compensates for unintended changes to its orientation at a yaw/roll singularity, utilizing aspects of the present invention. 
         FIGS. 18-19  illustrate sequential views of an entry guide tip during a roll rotation of the tip about its axis at a yaw/roll singularity, utilizing aspects of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIG. 1  illustrates, as an example, a top view of an operating room in which a medical robotic system  100  is being utilized by a Surgeon  20  for performing a medical procedure on a Patient  40  who is lying face up on an operating table  50 . One or more Assistants  30  may be positioned near the Patient  40  to assist in the procedure while the Surgeon  20  performs the procedure teleoperatively by manipulating input devices  108 ,  109  on a surgeon console  10 . 
     In the present example, an entry guide (EG)  200  is inserted through a single entry aperture  150  into the Patient  40 . Although the entry aperture  150  is a minimally invasive incision in the present example, in the performance of other medical procedures, it may instead be a natural body orifice. The entry guide  200  is held and manipulated by a robotic arm assembly  130 . 
     As with other parts of the medical robotic system  100 , the illustration of the robotic arm assembly  130  is simplified in  FIG. 1 . In one example of the medical robotic system  100 , the robotic arm assembly  130  includes a setup arm and an entry guide manipulator. The setup arm is used to position the entry guide  200  at the entry aperture  150  so that it properly enters the entry aperture  150 . The entry guide manipulator is then used to robotically insert and retract the entry guide  200  into and out of the entry aperture  150 . It may also be used to robotically pivot the entry guide  200  in pitch, roll and yaw about a pivot point located at the entry aperture  150 . An example of such an entry guide manipulator is the entry guide manipulator  202  of  FIG. 2  and an example of the four degrees-of-freedom movement that it manipulates the entry guide  200  with is shown in  FIG. 5 . 
     The console  10  includes a 3-D monitor  104  for displaying a 3-D image of a surgical site to the Surgeon, left and right hand-manipulatable input devices  108 ,  109 , and a processor (also referred to herein as a “controller”)  102 . The input devices  108 ,  109  may include any one or more of a variety of input devices such as joysticks, gloves, trigger-guns, hand-operated controllers, or the like. Other input devices that are provided to allow the Surgeon to interact with the medical robotic system  100  include a foot pedal  105 , a conventional voice recognition system  160  and a Graphical User Interface (GUI)  170 . 
     The console  10  is usually located in the same room as the Patient so that the Surgeon may directly monitor the procedure, is physically available if necessary, and is able to speak to the Assistant(s) directly rather than over the telephone or other communication medium. However, it will be understood that the Surgeon can also be located in a different room, a completely different building, or other remote location from the Patient allowing for remote surgical procedures. 
     As shown in  FIG. 3 , the entry guide  200  has articulatable instruments such as articulatable surgical tools  231 ,  241  and an articulatable stereo camera  211  extending out of its distal end. The camera has a stereo pair of image capturing devices  311 ,  312  and a fiber optic cable  313  (coupled at its proximal end to a light source) housed in its tip. The surgical tools  231 ,  241  have end effectors  331 ,  341 . Although only two tools  231 ,  241  are shown, the entry guide  200  may guide additional tools as required for performing a medical procedure at a work site in the Patient. For example, as shown in  FIG. 4 , a passage  351  is available for extending another articulatable surgical tool through the entry guide  200  and out through its distal end. Each of the surgical tools  231 ,  241  is associated with one of the input devices  108 ,  109  in a tool following mode. The Surgeon performs a medical procedure by manipulating the input devices  108 ,  109  so that the controller  102  causes corresponding movement of their respectively associated surgical tools  231 ,  241  while the Surgeon views the work site in 3-D on the console monitor  104  as images of the work site are being captured by the articulatable camera  211 . 
     Preferably, input devices  108 ,  109  will be provided with at least the same degrees of freedom as their associated tools  231 ,  241  to provide the Surgeon with telepresence, or the perception that the input devices  108 ,  109  are integral with the tools  231 ,  241  so that the Surgeon has a strong sense of directly controlling the tools  231 ,  241 . To this end, the monitor  104  is also positioned near the Surgeon&#39;s hands so that it will display a projected image that is oriented so that the Surgeon feels that he or she is actually looking directly down onto the work site and images of the tools  231 ,  241  appear to be located substantially where the Surgeon&#39;s hands are located. 
     In addition, the real-time image on the monitor  104  is preferably projected into a perspective image such that the Surgeon can manipulate the end effectors  331 ,  341  of the tools  231 ,  241  through their corresponding input devices  108 ,  109  as if viewing the work site in substantially true presence. By true presence, it is meant that the presentation of an image is a true perspective image simulating the viewpoint of an operator that is physically manipulating the end effectors  331 ,  341 . Thus, the processor  102  transforms the coordinates of the end effectors  331 ,  341  to a perceived position so that the perspective image being shown on the monitor  104  is the image that the Surgeon would see if the Surgeon was located directly behind the end effectors  331 ,  341 . 
     The processor  102  performs various functions in the system  100 . One important function that it performs is to translate and transfer the mechanical motion of input devices  108 ,  109  through control signals over bus  110  so that the Surgeon can effectively manipulate devices, such as the tools  231 ,  241 , camera  211 , and entry guide  200 , that are selectively associated with the input devices  108 ,  109  at the time. Another function is to perform various methods and implement various controllers described herein. 
     Although described as a processor, it is to be appreciated that the processor  102  may be implemented in practice by any combination of hardware, software and firmware. Also, its functions as described herein may be performed by one unit or divided up among different components, each of which may be implemented in turn by any combination of hardware, software and firmware. Further, although being shown as part of or being physically adjacent to the console  10 , the processor  102  may also comprise a number of subunits distributed throughout the system. 
     For additional details on the construction and operation of various aspects of a medical robotic system such as described herein, see, e.g., U.S. Pat. No. 6,493,608 “Aspects of a Control System of a Minimally Invasive Surgical Apparatus,” and U.S. Pat. No. 6,671,581 “Camera Referenced Control in a Minimally Invasive Surgical Apparatus,” which are incorporated herein by reference. 
       FIG. 2  illustrates, as an example, a block diagram of components for controlling and selectively associating device manipulators to the input devices  108 ,  109 . Various surgical tools such as graspers, cutters, and needles may be used to perform a medical procedure at a work site within the Patient. In this example, two surgical tools  231 ,  241  are used to robotically perform the procedure and the camera  211  is used to view the procedure. The instruments  231 ,  241 ,  211  are inserted through passages in the entry guide  200 . As described in reference to  FIG. 1 , the entry guide  200  is inserted into the Patient through entry aperture  150  using the setup portion of the robotic arm assembly  130  and maneuvered by the entry guide manipulator (EGM)  202  of the robotic arm assembly  130  towards the work site where the medical procedure is to be performed. 
     Each of the devices  231 ,  241 ,  211 ,  200  is manipulated by its own manipulator. In particular, the camera  211  is manipulated by a camera manipulator (ECM)  212 , the first surgical tool  231  is manipulated by a first tool manipulator (PSM1)  232 , the second surgical tool  241  is manipulated by a second tool manipulator (PSM2)  242 , and the entry guide  200  is manipulated by an entry guide manipulator (EGM)  202 . So as to not overly encumber the figure, the devices  231 ,  241 ,  211 ,  200  are not shown, only their respective manipulators  232 ,  242 ,  212 ,  202  are shown in the figure. 
     Each of the instrument manipulators  232 ,  242 ,  212  is a mechanical assembly that carries actuators and provides a mechanical, sterile interface to transmit motion to its respective articulatable instrument. Each instrument  231 ,  241 ,  211  is a mechanical assembly that receives the motion from its manipulator and, by means of a cable transmission, propagates it to the distal articulations (e.g., joints). Such joints may be prismatic (e.g., linear motion) or rotational (e.g., they pivot about a mechanical axis). Furthermore, the instrument may have internal mechanical constraints (e.g., cables, gearing, cams and belts, etc.) that force multiple joints to move together in a pre-determined fashion. Each set of mechanically constrained joints implements a specific axis of motion, and constraints may be devised to pair rotational joints (e.g., joggle joints). Note also that in this way the instrument may have more joints than the available actuators. In contrast, the entry guide manipulator  202  has a different construction and operation, as will be described below in reference to  FIG. 5 . 
     In this example, each of the input devices  108 ,  109  may be selectively associated with one of the devices  211 ,  231 ,  241 ,  200  so that the associated device may be controlled by the input device through its controller and manipulator. For example, by placing switches  258 ,  259  in their respective tool following modes “T2” and “T1”, the left and right input devices  108 ,  109  may be respectively associated with the first and second surgical tools  231 ,  241 , which are telerobotically controlled through their respective controllers  233 ,  243  (preferably implemented in the processor  102 ) and manipulators  232 ,  242  so that the Surgeon may perform a medical procedure on the Patient while the entry guide  200  is locked in place. 
     When the camera  211  or the entry guide  200  is to be repositioned by the Surgeon, either one or both of the left and right input devices  108 ,  109  may be associated with the camera  211  or entry guide  200  so that the Surgeon may move the camera  211  or entry guide  200  through its respective controller ( 213  or  203 ) and manipulator ( 212  or  202 ). In this case, the disassociated one(s) of the surgical tools  231 ,  241  is locked in place relative to the entry guide  200  by its controller. For example, by placing switches  258 ,  259  respectively in camera positioning modes “C2” and “C1”, the left and right input devices  108 ,  109  may be associated with the camera  211 , which is telerobotically controlled through its controller  213  (preferably implemented in the processor  102 ) and manipulator  212  so that the Surgeon may position the camera  211  while the surgical tools  231 ,  241  and entry guide  200  are locked in place by their respective controllers  233 ,  243 ,  203 . If only one input device is to be used for positioning the camera, then only one of the switches  258 ,  259  is placed in its camera positioning mode while the other one of the switches  258 ,  259  remains in its tool following mode so that its respective input device may continue to control its associated surgical tool. 
     On the other hand, by placing switches  258 ,  259  respectively in entry guide positioning modes “G2” and “G1”, the left and right input devices  108 ,  109  may be associated with the entry guide  200 , which is telerobotically controlled through its controller  203  (preferably implemented in the processor  102 ) and manipulator  202  so that the Surgeon may position the entry guide  200  while the surgical tools  231 ,  241  and camera  211  are locked in place relative to the entry guide  200  by their respective controllers  233 ,  243 ,  213 . As with the camera positioning mode, if only one input device is to be used for positioning the entry guide, then only one of the switches  258 ,  259  is placed in its entry guide positioning mode while the other one of the switches  258 ,  259  remains in its current mode. 
     The selective association of the input devices  108 ,  109  to other devices in this example may be performed by the Surgeon using the GUI  170  or the voice recognition system  160  in a conventional manner. Alternatively, the association of the input devices  108 ,  109  may be changed by the Surgeon depressing a button on one of the input devices  108 ,  109  or depressing the foot pedal  105 , or using any other well known mode switching technique. 
     As shown in a perspective view of the entry guide  200  in  FIG. 5 , the entry guide  200  is generally cylindrical in shape and has a longitudinal axis X′ running centrally along its length. The pivot point, which is also referred to as a remote center “RC”, serves as an origin for both a fixed reference frame having x 0 , y 0  and z 0  axes as shown and an entry guide reference frame having X′, y 0  and Z′ axes as shown. When the system  100  is in the entry guide positioning mode, the entry guide manipulator  202  is capable of pivoting the entry guide  200  in response to movement of one or more associated input devices about the y 0  axis (which remains fixed in space) at the remote center “RC” in yaw (OY). In addition, the entry guide manipulator  202  is capable of pivoting the entry guide  200  in response to movement of the one or more input devices about the Z′ axis (which is orthogonal to and moves accordingly with the longitudinal axis X′ of the entry guide  200 ) in pitch (OP), capable of rotating the entry guide  200  about its longitudinal axis X′ in roll (RO), and linearly moving the entry guide  200  along its longitudinal axis X′ in insertion/retraction or in/out “I/O” (or IO) directions in response to movement of the one or more associated input devices. Note that unlike the y 0  axis which is fixed in space, the X′ and Z′ axes move with the entry guide  200 . Since the yaw, pitch and roll are respectively performed about the y 0 , Z′ and X′ axes, these axes are also referred to herein as the OY, OP and RO axes. 
       FIG. 6  illustrates, as an example, a block diagram of a controller  600  (which is one version of the controller  203 ) for controlling movement of the entry guide  200  in response to movement of the input devices  108 ,  109  when the input devices  108 ,  109  are selectively associated with the entry guide  200  in their respective entry guide positioning modes “G2” and “G1”. In this example, both input devices  108 ,  109  are used to move the entry guide  200  according to an image referenced control scheme as the Surgeon views images captured by the camera  211 . Alternatively, only one of the input devices  108 ,  109  may be used, and in lieu of the image referenced control described herein, a tip referenced control scheme such as conventionally used to control individual surgical instruments may be used to move the entry guide  200 . In any such alternative, however, the articulatable camera  211 , which extends out of the distal end of the entry guide  200 , is preferably “soft” locked (through its controller  213 ) at its current position relative to the entry guide  200  during the entry guide positioning mode. 
     In an image referenced control, the controller  600  controls movement of the entry guide  200  while the Surgeon is given the impression that he or she is moving the image captured by the camera  211 . In particular, the Surgeon is provided with the sensation that he or she is grasping the image being displayed on the monitor  104  with his or her left and right hands and moving the image about the work site to a desired viewing point. Note that under this type of control, the image on the monitor  104  appears to move in opposite directions in response to movement of the input devices  108 ,  109 . For example, the image moves to the right when the input devices  108 ,  109  are moved to the left (and vice versa) and the image moves up when the input devices  108 ,  109  are moved down (and vice versa). 
     The input devices  108 ,  109  include a number of links connected by joints so as to facilitate multiple degrees-of-freedom movement. For example, as the Surgeon moves the input devices  108 ,  109  from one position to another, sensors associated with the joints of the input devices  108 ,  109  sense such movement at sampling intervals (appropriate for the processing speed of the controller  102  and entry guide control purposes) and provide digital information indicating such sampled movement in joint space to input processing blocks  610 ,  620 . 
     Input processing blocks  610 ,  620  process the information received from the joint sensors of the input devices  108 ,  109  to transform the information into corresponding desired positions and velocities for the image being displayed on the monitor  104  in a Cartesian space relative to a reference frame associated with the Surgeon&#39;s eyes (the “eye reference frame”) by computing, for example, joint velocities from the joint position information (or, alternatively, using velocity sensors) and performing the transformation using a Jacobian matrix and eye related information using well-known transformation techniques. 
     Scale and offset processing blocks  601 ,  602  receive the processed information  611 ,  613  from the input processing blocks  610 ,  620 , convert the desired positions and velocities to camera tip positions and velocities in the reference frame of the entry guide  200 , and apply scale and offset adjustments to the information so that the resulting movement of the camera  211  and consequently, the image being viewed on the monitor  104  appears natural and as expected by the operator of the input devices  108 ,  109 . The scale adjustment is useful where small movements of the camera  211  are desired relative to larger movement of the input devices  108 ,  109  in order to allow more precise movement of the camera  211  as it views the work site. To implement the shared control for moving the camera  211  by the input devices  108 ,  109 , lateral offsets are applied to shift the control point to the left for the input device  108  which is being operated by the left hand of the operator and to the right for the input device  109  which is being operated by the right hand of the operator so that each of the input devices  108 ,  109  appears to control a corresponding view of the stereoscopic image being displayed on the monitor  104 . In addition, offset adjustments are applied for aligning the input devices  108 ,  109  with respect to the Surgeon&#39;s eyes as he or she manipulates the input devices  108 ,  109  to command movement of the camera  211  and consequently, its captured image that is being displayed at the time on the monitor  104 . 
     The outputs  621 ,  622  of the scale and offset blocks  601 ,  602  are provided to a set-point generation block  703  so that a single set of position and velocity commands for the camera tip  311  in the reference frame of the entry guide  200  is provided for the entry guide manipulator  202 . Therefore, as the operator moves the input devices  108 ,  109 , he or she forces a motion on the mid-point of what feels like to the operator to be a “virtual handlebar”. This motion is then “transferred” to subsequent blocks of the controller  600  as a set-point for Cartesian motions. 
     Up to this point, the controller  600  has treated the operator movement of the input devices  108 ,  109  as commanding a corresponding movement of the camera  211  using image referenced control. Ultimately, however, it is the entry guide manipulator  202 , not the camera manipulator  213  that is to be moved in response to the operator commands. Therefore, an inverse “entry guide-to-camera” transform ( EG X CAM ) −1  block  651  converts the desired movement of the tip of the camera  211  into a desired movement of the tip of the entry guide  202  while still in the reference frame of the entry guide. In particular, as shown in  FIG. 8 , a camera reference frame &lt;CAM&gt; represents what the Surgeon is seeing at the time on the monitor  104 , an entry guide tip reference frame &lt;EG&gt; represents what the controller  600  controls in entry guide positioning mode “G”, and a remote center reference frame &lt;REF&gt; represents a fixed reference frame. 
     A simulated entry guide manipulator block  604  receives the output  624  of the inverse “entry guide-to-camera” transform ( EG X CAM ) −1  block  651  and transforms the commanded position and velocity for the distal end of the entry guide  200  from its Cartesian space to corresponding desired joint positions and velocities for the entry guide manipulator (EGM)  202  (e.g., EGM joint space) using the known inverse kinematics of the entry guide manipulator  202  and characteristics of the entry guide  200 . In doing so, the simulated entry guide manipulator block  604  manages operation of the entry guide manipulator  202  through singularities and limits its commanded joint positions and velocities to avoid physical or other limitations. 
     The output  625  of the simulated entry guide manipulator block  604  is then provided to an EGM joint controller block  605  and a forward kinematics block  606 . The joint controller block  605  includes a joint control system for each controlled joint (i.e., each mechanical element controlling one of the four degrees-of-freedom described in reference to  FIG. 5 ) of the entry guide manipulator  202 , and the output  625  of the simulated entry guide manipulator block  604  provides, as its inputs, the commanded value for each joint of the entry guide manipulator  202 . For feedback control purposes, sensors associated with each of the controlled joints of the entry guide manipulator  202  provide sensor data  632  back to the joint controller block  605  indicating the current position and/or velocity of each joint of the entry guide manipulator  202 . The sensors may sense this joint information either directly (e.g., from the joint on the entry guide manipulator  202 ) or indirectly (e.g., from the actuator in the entry guide manipulator  202  driving the joint). Each joint control system in the joint controller  605  then generates torque or other appropriate commands for its respective actuator (e.g., motor) in the entry guide manipulator  202  so as to drive the difference between the commanded and sensed joint values to zero in a conventional feedback control system manner. 
     The forward kinematics block  606  transforms the output  625  of the simulated entry guide manipulator block  604  from joint space back to the Cartesian space of the entry guide manipulator  202  using the forward kinematics of the entry guide manipulator  202 . The output of the forward kinematics block  606  is then translated in an “entry guide-to-camera” transformation ( EG X CAM ) block  652  so that the controller  600  operates once again in camera referenced control mode. 
     The scale and offset blocks  601 ,  602  perform an inverse scale and offset functions on the output  642  of the “entry guide-to-camera” transformation ( EG X CAM ) block  652  (as well as performing a reversal of the set-point generation) before passing their respective outputs  612 ,  614  to the input processing blocks  610 ,  620  where error values are calculated between their respective outputs  611 ,  613  and inputs  612 ,  614 . If no limitation or other constraint had been imposed on the input  624  to the simulated entry guide manipulator block  604 , then the calculated error values would be zero. On the other hand, if a limitation or constraint had been imposed, then the error value is not zero and it is converted to a torque command that drives actuators in the input devices  108 ,  109  to provide force feedback felt by the hands of their operator. Thus, the operator becomes aware that a limitation or constraint is being imposed by the force that he or she feels resisting his movement of the input devices  108 ,  109  in that direction. In addition to this force feedback, forces coming from other sensors or algorithms may be superimposed on the force feedback. 
     An output  641  of the forward kinematics block  606  may also be provided to the simulated entry guide manipulator block  604  for control purposes. For example, the simulated position output may be fed back and compared with the commanded position. 
     One singularity that the entry guide manipulator  202  may encounter during its operation is a yaw/roll singularity. As illustrated in  FIG. 8 , this singularity occurs when the pitch angle q OP  of the entry guide  200  is at either +90 degrees or −90 degrees (i.e., in a vertical position) so that the yaw (OY) axis (which is fixed) and roll (RO) axis (which moves with the entry guide  200 ) coincide. Note that the entry guide manipulator  202  loses the capability of actuating motion of the entry guide  200  in any arbitrary direction in the (x 0 , z 0 ) plane at this singularity. In particular, only motion perpendicular to the OP axis can be freely actuated in the (x 0 , z 0 ) plane. 
     One problem with the yaw/roll singularity is the control ambiguity that it causes. The simulated entry guide manipulator block  604  uses the inverse Jacobian to transform a commanded position and velocity for the distal end of the entry guide  200  from its Cartesian space to the joint space of the entry guide manipulator  202  according to the following equation:
 
 {right arrow over ({dot over (q)})}=J   −1 ( {right arrow over (q)} ) 0   {right arrow over ({dot over (x)})}   DES   (1)
 
where “{right arrow over ({dot over (q)})}” and “{right arrow over (q)}” are the joint velocity and position vectors, “J −1 ” is the inverse Jacobian, and “ O {right arrow over ({dot over (x)})} DES ” is the commanded (or desired) state in terms of a Cartesian velocity vector for the distal tip of the entry guide  200  with respect to the remote center reference frame &lt;REF&gt;.
 
     The inverse of the rotation part of the Jacobian may be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               q 
                               . 
                             
                             OY 
                           
                         
                       
                       
                         
                           
                             
                               q 
                               . 
                             
                             OP 
                           
                         
                       
                       
                         
                           
                             
                               q 
                               . 
                             
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                     ] 
                   
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                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
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                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     As the entry guide pitch angle q OP  approaches the entry guide manipulator&#39;s yaw-roll singularity, the term “cos q OP ” approaches zero and the term “1/cos q OP ” approaches infinity as shown in  FIG. 10 , and as a consequence, the roll and yaw joint velocities, {dot over (q)} RO  and {dot over (q)} OY , become very large until they become saturated by programmed limits in the simulated entry guide manipulator block  604 . Stated differently, the {dot over (q)} RO  and {dot over (q)} OY  joint velocities tend to become very large because there is no unique solution to the following equation:
 
 0 ω y,DES   =−{dot over (q)}   OY   +{dot over (q)}   RO   (3)
 
Any combination of ({dot over (q)} RO , {dot over (q)} OY ) such that their difference corresponds to the desired angular velocity about the fixed OY axis satisfies the inverse kinematics, but the individual {dot over (q)} RO  and {dot over (q)} OY  joint velocities can be very large.
 
       FIG. 9  illustrates, as an example, a flow diagram of a method  900  which is implemented in the entry guide controller  203  for commanding the entry guide manipulator  202  to manipulate the entry guide  200 . In  901 , an entry guide manipulator command, which indicates a commanded state (e.g., position and orientation) of the entry guide  200 , is received from at least one of the input devices  108 ,  109 . In  902 - 905 , the method then resolves any control ambiguity caused by a yaw/roll singularity. Although shown as sequential tasks in a particular order, the tasks performed in  902 - 905  may be concurrently and/or in any order. 
     In  902 , the method applies modified inverse kinematics to the commanded state to determine joint state commands for driving joint actuators in the entry guide manipulator  203  in a smooth and controllable manner. As an example of such application of modified inverse kinematics, a modified inverse Jacobian is applied in the simulated entry guide manipulator block  604  by modifying the previously described inverse Jacobian to avoid commanding excessive {dot over (q)} RO  and {dot over (q)} OY  joint velocities near and at the singularity, wherein the term “1/cos q OP ” is replaced with the following function “γ(q OP )” in equation (2): 
                     γ   ⁡     (     q   OP     )       =     {           function   ⁢           ⁢   1102   ⁢           ⁢   for   ⁢           ⁢     q   OP     ⁢           ⁢   outside   ⁢           ⁢   1101               function   ⁢           ⁢   1103   ⁢           ⁢   for   ⁢           ⁢     q   OP     ⁢           ⁢   inside   ⁢           ⁢   and   ⁢           ⁢   at   ⁢           ⁢   the   ⁢           ⁢   limits   ⁢           ⁢   of   ⁢           ⁢   1101                     (   4   )               
where, as shown in  FIG. 11 , the threshold distance as indicated by the range  1101  is preferably ±0.3 radians about −π/2 radians and ±0.3 radians about π/2 radians (to avoid commanding the high joint velocities); the function  1102  is “1/cos q OP ”; and the function  1103  is a preferably smooth function that is zero at the singularity (i.e., −π/2 radians and π/2 radians).
 
     Equation (2) is thus modified as follows to define a modified version of the inverse Jacobian:
 
 {dot over (q)}   OP =−cos  q   OY   0 ω x −sin  q   OY   0 ω z   (5)
 
 {dot over (q)}   RO =γ( q   OP )[sin  q   OY   0 ω x −cos  q   OY   0 ω z ]  (6)
 
 {dot over (q)}   OY =−sin  q   OP γ( q   OP )[sin  q   OY   0 ω x −cos  q   OY   0 ω z ]− 0 ω y   (7)
 
     By implementing equations (5)-(7) in the simulated entry guide manipulator block  604 , the roll joint velocity {dot over (q)} RO  approaches zero and the yaw joint velocity {dot over (q)} OY  actuates the commanded  0 ω y  from the operator of the input devices  108 ,  109  as the entry guide  200  approaches the yaw/roll singularity of the entry guide manipulator  202 . Thus, the excessive joint velocity problem caused by the entry guide manipulator&#39;s yaw and roll axes coinciding at the singularity is avoided. 
     It is to be appreciated that other techniques, such as dynamic low pass filtering, which are position dependent and result in smooth behavior may be used instead of the “γ(q OP )” function in  902 , to compute an appropriate modified inverse Jacobian when the manipulator is close to the singularity, while leaving it essentially unchanged away from the singularity. 
     In  903 , the method determines whether the commanded state of the entry guide  200  is in an allowed direction, which is the direction in which force feedback on the input devices  108 ,  109  is such that entry guide motion along a plane including the RO and OY axes has little to no resistance while motion away from that plane is more heavily resisted. Stated in another way, the “allowed direction” is one in which a point in space may be reached using only a pitch rotation about the OP axis and I/O translation as necessary along the RO axis. Conversely, a “forbidden direction” is any direction parallel to the OP axis and perpendicular to the “allowed direction”. It is to be appreciated that a generic desired Cartesian velocity vector {dot over (X)} des  can always be split into its components along the “allowed direction” and along the “forbidden direction”. 
     It can be shown that the allowed direction “ 0 {circumflex over (l)}” in the (x 0 , z 0 ) plane is represented by the unit vector: 
     
       
         
           
             
               
                 
                   
                     
                         
                       0 
                     
                     ⁢ 
                     
                       l 
                       ^ 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
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                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     If the determination in  903  is YES, i.e., the commanded state is in the allowed direction, then in  906 , the entry guide controller  203  commands the entry guide manipulator  202  to move the entry guide  200  to the commanded state by using only a pitch rotation about the OP axis and I/O translation as necessary along the RO axis. 
     On the other hand, if the determination in  903  is NO, i.e., the commanded state is not in the allowed direction, then in  904 , the entry guide controller  203  commands the entry guide manipulator  202  to manipulate the entry guide  200  so as to change the allowed direction to one where the commanded state may be reached with little to no resistance to the operator on the input devices  108 ,  109 . As indicated in equation (8), since the allowed direction only depends on the yaw joint angle q OY , the allowed direction may be relocated in space simply by commanding rotation of the yaw joint of the entry guide manipulator  202 . 
     A graphical representation of repositioning the allowed direction is shown in  FIG. 12 , wherein the allowed direction may be repositioned from  0 {circumflex over (l)} 1  to  0 {circumflex over (l)} 2  by rotating the yaw joint q OY , and a corresponding perspective view of the entry guide is shown in  FIG. 13 , wherein the pitch axis has moved from Z′ to Z″ by rotating the yaw joint q OY . 
     By rotating the entry guide  200  about its yaw axis to change the allowed direction, each of the articulated instruments  211 ,  231 ,  241  extending out of its distal end also rotates at the yaw/roll singularity about the central longitudinal axis X′ of the entry guide  200  accordingly. However, if the operator of the input devices  108 ,  109  does not intend such a rotation, then it is necessary to rotate the instruments back to their original positions without using a yaw rotation q OY  so that the allowed direction remains where it has been repositioned. This is especially important for maintaining the orientation of images captured by the camera  211  that are being displayed at the time on the display screen of the monitor  104 . 
     In  905 , the roll rotational degree of freedom of the entry guide manipulator  202  is used to provide the necessary compensating rotation after or concurrently with  904 . As an example,  FIGS. 15-17  illustrate sequential views of an entry guide tip as its allowed direction  1502  is repositioned and its orientation realigned at the yaw/roll singularity. In  FIG. 15 , the desired direction (as indicated by the velocity vector {dot over (X)} des ) of the entry guide tip is in a different direction than the current allowable direction “ 0 {circumflex over (l)}”  1502  of the entry guide  200 . So, as shown in  FIG. 16 , the yaw joint of the entry guide manipulator  202  is actuated (as indicated by its velocity {dot over (q)} OY ) to rotate the entry guide tip  1501  (and the allowable direction  1502 ) so as to include the desired direction {dot over (X)} des . Finally, as shown in  FIG. 17 , the roll joint of the entry guide manipulator  202  is actuated (as indicated by the velocity {dot over (q)} RO ) to compensate for the orientation change caused by the yaw movement. 
     In the process described in reference to  FIGS. 15-17 , the operator of the input devices  108 ,  109  perceives through force feedback a vanishing resistance in the direction of the motion on the input devices  108 ,  109 , which represents the finite velocity with which the entry guide manipulator  202  of the robotic arm  130  is repositioning its joints to accommodate the command. As a consequence, only “slow” motions are generally performable using the control strategy described herein. 
     Note that since the entry guide manipulator&#39;s yaw and roll joints have finite ranges of motion, one of the two joints might hit a limit before the other, thus “destroying” the illusion created by the described orientation control scheme. To prevent this, the simulated entry guide controller  203  preferably saturates the movements of the yaw and roll joints in a “coupled” manner so that if one is limited, the other is limited too. 
     Also, note that although the roll joint is used for orientation compensation in  905 , its use is still disengaged from user control according to  902  when the entry guide  200  is at the yaw/roll singularity. Therefore, if the user desires to rotate the entry guide tip at the yaw/roll singularity, the yaw joint must be used instead.  FIGS. 18-19  illustrate, as an example, sequential views of the entry guide tip  1501  during such a pure rotation of the tip about the entry guide&#39;s yaw axis at the yaw/roll singularity. 
     After changing the allowed direction and compensating for the orientation shift, in  906 , the entry guide controller  203  commands the entry guide manipulator  202  to move the entry guide  200  to the commanded state by using only a pitch rotation about the OP axis and I/O translation as necessary along the RO axis, such as shown for example in  FIG. 14  which follows the repositioning of the allowed direction in  FIG. 13 . 
     Although the various aspects of the present invention have been described with respect to a preferred embodiment, it will be understood that the invention is entitled to full protection within the full scope of the appended claims. For example, although the method is described in reference to a yaw/roll singularity of the entry guide manipulator  203 , it is to be appreciated that the general teaching of the method described in reference to  FIG. 11  may be generally applied to the control of medical robotic system manipulators about their kinematic singularities.