Patent Publication Number: US-2022218422-A1

Title: Surgical Systems And Methods For Guiding Robotic Manipulators

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The subject application is a Bypass Continuation of International Patent App. No. PCT/US2020/053803, filed Oct. 1, 2020, which claims priority to and all the benefits of U.S. Provisional Patent App. No. 62/908,915, filed Oct. 1, 2019, the contents of each of the aforementioned applications being hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     Robotic manipulators are frequently used to assist medical professionals in carrying out various conventional surgical procedures. To this end, a surgeon may use a surgical robot or another type of manipulator to guide, position, move, actuate, or otherwise manipulate various tools, components, prostheses, and the like during surgery. 
     Surgical robots can be used to assist surgeons in performing a number of different types of surgical procedures, and are commonly used in procedures involving the correction, resection, or replacement of degenerated joints to help improve patient mobility and reduce pain. By way of illustrative example, in hip replacement procedures, the surgeon replaces portions of the patient&#39;s hip joint with artificial prosthetic components. To this end, in total hip arthroplasty, the surgeon typically removes portions of the patient&#39;s femur to accommodate a prosthetic femoral component comprising a head, and resurfaces the acetabulum of the pelvis with a reamer to facilitate installing a prosthetic cup shaped to receive the head of the prosthetic femoral component. 
     Depending on the specific procedure being performed, the surgical robot may be used to help the surgeon approach the surgical site, remove portions of joints and/or bone, install prosthetic components, and the like. For example, in order to install the prosthetic cup into the acetabulum of the pelvis, the surgeon connects the cup to an impactor to implant the cup into the prepared acetabulum by striking the impactor to apply force (e.g., such as with a mallet). In order to facilitate installing the cup, the surgical robot helps keep the impactor aligned relative to the acetabulum, and the surgeon closely monitors the trajectory and depth of the cup during impaction to ensure proper alignment of the cup. Here, reaming or resecting the acetabulum generally defines the intended position of the cup which, in turn, defines the trajectory of impaction, which may be monitored via a tracker secured to the pelvis that is tracked via a navigation system. 
     Depending on the configuration of the prosthetic components, the impaction tools, and the surgical robot, maintaining a set trajectory can be difficult with certain approaches and surgical techniques, whereby misalignment of the cup or other prosthetic components frequently results from improper alignment and/or application of impact force. Furthermore, as the cup is being implanted into the reamed acetabulum, the patient&#39;s body effectively becomes physically-attached to the impactor and surgical robot in one or more degrees of freedom. Here, because the surgical robot typically restricts movement of the impactor relative to the trajectory based on the tracker secured to the pelvis, misalignment that may occur during impaction between the cup and the trajectory can sometimes lead to a “runaway” condition where the impactor and the pelvis are moved concurrently by the surgical robot attempting to bring the impactor tool back into alignment with the trajectory. Because of the physical connection between the surgical robot and the pelvis, this type of “runaway” condition may result in undesirable movement of the patient and/or unseating of an implanted or partially-implanted cup. 
     Similar “runaway” conditions may occur during other surgical procedures which employ different types of tools that are guided by surgical robots. By way of non-limiting example, a tool which comprises a powered surgical device may be used to drive an energy applicator configured to remove tissue at the surgical site. Here, under certain operating conditions, the energy applicator may engage tissue in such a way that effectively creates a lockup condition between the energy applicator to the tissue. For example, a rotary instrument driving a drill bit, or a bur could become misaligned and lodged in bone while forming a pilot hole in a pedicle of a vertebra in the spine. Here too, a “runaway” condition may result in undesirable movement of the patient and/or energy applicator engaged against tissue such as bone. 
     Accordingly, there remains a need in the art for addressing one or more of these deficiencies. 
     SUMMARY 
     This Summary introduces a selection of concepts in a simplified form that are further described below in the Detailed Description below. This Summary is not intended to limit the scope of the claimed subject matter and does not necessarily identify each and every key or essential feature of the claimed subject matter. 
     According to a first aspect, a surgical system is provided comprising: a tool for engaging a target site; a manipulator configured to support the tool; a sensing system configured to detect one or more system conditions associated with one or more of the tool, the manipulator, the target site, or combinations thereof; and a controller coupled to the manipulator and to the sensing system, the controller being configured to operate the manipulator between: a first mode to maintain alignment of the tool with respect to the target site according to a first constraint criteria, and a second mode to maintain alignment of the tool with respect to the target site according to a second constraint criteria different from the first constraint criteria; and wherein the controller is further configured to change operation of the manipulator from the first mode to the second mode in response to determining that at least one of the one or more system conditions satisfies a predetermined condition. 
     According to a second aspect, a method of operating the surgical system of the first aspect is provided. 
     According to a third aspect, a surgical system is provided comprising: a tool for engaging a target site along a trajectory; a manipulator configured to support the tool; at least one sensor configured to obtain measurements indicative of a force occurring between the target site and the manipulator; and a controller coupled to the manipulator and to the at least one sensor, the controller being configured to operate the manipulator between: a first mode to maintain alignment of the tool with respect to the trajectory according to a first constraint criteria, and a second mode to maintain alignment of the tool with respect to the trajectory according to a second constraint criteria different from the first constraint criteria; and wherein the controller is further configured to change operation of the manipulator from the first mode to the second mode in response to determining that the force satisfies a predetermined condition. 
     According to a fourth aspect, a method of operating the surgical system of the third aspect is provided. 
     According to a fifth aspect, a surgical system is provided comprising: a tool for engaging a target site; a manipulator configured to support the tool relative to the target site; a patient tracker adapted for attachment relative to the target site; a navigation system configured to track states of the patient tracker; and a controller coupled to the manipulator and to the navigation system, the controller being configured to operate the manipulator between: a first mode to maintain alignment of the tool with respect to the target site according to a first constraint criteria, and a second mode to maintain alignment of the tool with respect to the target site according to a second constraint criteria different from the first constraint criteria; wherein the controller is further configured to compare tracked movement of the tool against movement of the patient tracker based on tracked states received from the navigation system; and wherein the controller is further configured to change operation of the manipulator from the first mode to the second mode in response to determining that tracked movement of the tool corresponds to movement of the patient tracker. 
     According to a sixth aspect, a method of operating the surgical system of the fifth aspect is provided. 
     According to a seventh aspect, a method of operating a surgical system is provided comprising an impactor assembly having an interface for releasably securing a prosthesis, a guide having a channel formed to receive the impactor assembly, a manipulator configured to support the guide relative to a target site along a trajectory, at least one sensor, and a controller coupled to the manipulator and to the at least one sensor and being configured to perform the steps of: operating the manipulator in a first mode to maintain alignment of the guide with respect to the trajectory according to a first constraint criteria; operating the manipulator in a second mode to maintain alignment of the guide with respect to the trajectory according to a second constraint criteria different from the first constraint criteria; detecting a force occurring between the target site and the manipulator based on measurements from the at least one sensor; and determining that the force satisfies a predetermined condition and changing operation of the manipulator from the first mode to the second mode in response 
     According to a seventh aspect, a surgical system is provided comprising: a tool for engaging a target site; a manipulator configured to support the tool; a sensing system configured to detect one or more system conditions associated with one or more of the tool, the manipulator, the target site, or combinations thereof; and a controller coupled to the manipulator and to the sensing system, the controller being configured to: operate the manipulator to maintain alignment of the tool with respect to the target site according to a first constraint criteria; and in response to detecting the one or more system conditions, operate the manipulator to maintain alignment of the tool with respect to the target site according to a second constraint criteria that is different from the first constraint criteria. 
     According to an eighth aspect, a method of operating the surgical system of the seventh aspect is provided. 
     According to a ninth aspect, a surgical system is provided comprising: a tool for engaging a target site along a trajectory; a manipulator configured to support the tool; at least one sensor configured to obtain measurements indicative of a force occurring between the target site and the manipulator; and a controller coupled to the manipulator and to the at least one sensor, the controller being configured to: operate the manipulator to maintain alignment of the tool with respect to the trajectory according to a first constraint criteria; evaluate the obtained measurements indicative of the force; and in response to the evaluation, operate the manipulator to maintain alignment of the tool with respect to the trajectory according to a second constraint criteria that is different from the first constraint criteria. 
     According to a tenth aspect, a method of operating the surgical system of the ninth aspect is provided. 
     According to an eleventh aspect, a surgical system is provided comprising: a tool for engaging a target site; a manipulator configured to support the tool relative to the target site; a patient tracker adapted for attachment relative to the target site; a navigation system configured to track states of the patient tracker; and a controller coupled to the manipulator and to the navigation system, the controller being configured to: operate the manipulator to maintain alignment of the tool with respect to the target site according to a first constraint criteria; evaluate tracked movement of the tool relative to movement of the patient tracker based on tracked states of the patient tracker received from the navigation system; and in response to the evaluation, operate the manipulator to maintain alignment of the tool with respect to the target site according to a second constraint criteria that is different from the first constraint criteria. 
     According to a twelfth aspect, a method of operating the surgical system of the eleventh aspect is provided. 
     According to an thirteenth aspect, a surgical system is provided comprising: a tool for engaging a target site; a manipulator configured to support the tool relative to the target site; a patient tracker adapted for attachment relative to the target site; a navigation system configured to track states of the patient tracker; and a controller coupled to the manipulator and to the navigation system, the controller being configured to: operate the manipulator to constrain movement of the tool with respect to a virtual boundary associated with the target site according to a first constraint criteria; evaluate tracked movement of the tool relative to movement of the patient tracker based on tracked states of the patient tracker received from the navigation system; and in response to the comparison, operate the manipulator to constrain movement of the tool with respect to the virtual boundary according to a second constraint criteria different from the first constraint criteria. 
     According to a fourteenth aspect, a method of operating the surgical system of the thirteenth aspect is provided. 
     Any of the aspects above can be combined in part, or in whole. Furthermore, any of the aspects above can be implemented with any of the following implementations: 
     In one implementation, the first constraint criteria comprises a first number of degrees of freedom in which movement of the tool is restricted relative to the target site. In one implementation, the second constraint criteria comprises a second number of degrees of freedom in which movement of the tool is restricted relative to the target site. In one implementation, the second number of degrees of freedom being different from the first number of degrees of freedom. In one implementation, the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the target site based on the first number of degrees of freedom; and in the second mode to maintain alignment of the tool with respect to the target site based on the second number of degrees of freedom. 
     In one implementation, the second number of degrees of freedom is smaller than the first number of degrees of freedom such that the controller permits movement of the tool relative to the target site in at least one more degree of freedom in the second mode than in the first mode. In one implementation, the first constraint criteria comprises at least one positional degree of freedom and at least one orientational degree of freedom. In one implementation, the first constraint criteria and the second constraint criteria each comprise at least one orientational degree of freedom. In one implementation, the first constraint criteria comprises at least one more positional degree of freedom than the second constraint criteria. In one implementation, the first constraint criteria and the second constraint criteria comprise at least one common degree of freedom. 
     In one implementation, the first constraint criteria comprises a first resilience parameter, and the second constraint criteria comprise a second resilience parameter different from the first resilience parameter. In one implementation, the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the target site based on the first resilience parameter; and in the second mode to maintain alignment of the tool with respect to the target site based on the second resilience parameter. In one implementation, the controller permits more resilient movement of the tool relative to the target site in the second mode than in the first mode. In one implementation, the first resilience parameter and the second resilience parameter are each associated with resilient movement of the tool relative to the target site in a common degree of freedom. 
     In one implementation, the tool defines a tool center point. In one implementation, the controller is configured to operate the manipulator in the first mode to restrict movement of the tool center point away from the target site according to the first constraint criteria. 
     In one implementation, the controller is configured to operate the manipulator in the second mode to permit movement of the tool center point away from the target site according to the second constraint criteria. 
     In one implementation, a mode indicator is coupled to the controller. In one implementation, the controller is configured to activate the mode indicator in response to determining that at least one of the one or more system conditions satisfies the predetermined condition to communicate to a user the change in operation of the manipulator from the first mode to the second mode. 
     In one implementation, the controller is configured to operate the manipulator in the first mode to permit movement of the tool relative to the target site in at least one degree of freedom according to the first constraint criteria. 
     In one implementation, the controller is configured to operate the manipulator in the second mode to permit movement of the tool relative to the target site in at least one degree of freedom according to the second constraint criteria. 
     In one implementation, the controller is further configured to operate the manipulator in a third mode to maintain alignment of the tool with respect to the target site according to a third constraint criteria different from both the first constraint criteria and the second constraint criteria. In one implementation, the predetermined condition is further defined as a first predetermined condition. In one implementation, the controller is further configured to change operation of the manipulator from the second mode to the third mode in response to determining that at least one of the one or more system conditions satisfies a second predetermined condition different from the first predetermined condition. 
     In one implementation, the first constraint criteria comprises a first number of degrees of freedom in which movement of the tool is restricted relative to the target site. In one implementation, the second constraint criteria comprises a second number of degrees of freedom in which movement of the tool is restricted relative to the target site. In one implementation, the third constraint criteria comprises a third number of degrees of freedom in which movement of the tool is restricted relative to the target site. In one implementation, the third number of degrees of freedom is different from one or more of the first number of degrees of freedom and the second number of degrees of freedom; and wherein the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the target site based on the first number of degrees of freedom; in the second mode to maintain alignment of the tool with respect to the target site based on the second number of degrees of freedom; and in the third mode to maintain alignment of the tool with respect to the target site based on the third number of degrees of freedom. 
     In one implementation, the first constraint criteria further comprises a first resilience parameter. In one implementation, the second constraint criteria further comprises a second resilience parameter. In one implementation, the third constraint criteria further comprises a third resilience parameter different from one or more of the first resilient parameter and the second resilience parameter. In one implementation, the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the target site based on the first number of degrees of freedom and also based on the first resilience parameter; in the second mode to maintain alignment of the tool with respect to the target site based on the second number of degrees of freedom and also based on the second resilience parameter; and in the third mode to maintain alignment of the tool with respect to the target site based on the third number of degrees of freedom and also based on the third resilience parameter. 
     In one implementation, the third number of degrees of freedom is smaller than the first number of degrees of freedom such that the controller permits movement of the tool relative to the target site in at least one more degree of freedom in the third mode than in the first mode. In one implementation, the third number of degrees of freedom is smaller than the second number of degrees of freedom such that the controller permits movement of the tool relative to the target site in at least one more degree of freedom in the third mode than in the second mode. In one implementation, the first constraint criteria and the second constraint criteria each comprise at least one positional degree of freedom and at least one orientational degree of freedom. In one implementation, the first constraint criteria, the second constraint criteria, and the third constraint criteria each comprise at least one orientational degree of freedom. In one implementation, the first constraint criteria comprises at least one more positional degree of freedom than the third constraint criteria. In one implementation, the second constraint criteria comprises at least one more positional degree of freedom than the third constraint criteria. In one implementation, the controller permits more resilient movement of the tool relative to the target site in the second mode than in the first mode. In one implementation, the controller permits more resilient movement of the tool relative to the target site in the second mode than in the third mode. 
     In one implementation, the first constraint criteria comprises a first resilience parameter, the second constraint criteria comprises a second resilience parameter, and the third constraint criteria comprises a third resilience parameter different from one or more of the first resilient parameter and the second resilience parameter; and wherein the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the target site based on the first resilience parameter; in the second mode to maintain alignment of the tool with respect to the target site based on the second resilience parameter; and in the third mode to maintain alignment of the tool with respect to the target site based on the third resilience parameter. 
     In one implementation, the sensing system comprises at least one sensor configured to obtain measurements indicative of a force occurring between the target site and the manipulator; and wherein the measurements indicative of the force obtained by the at least one sensor define at least one of the one or more system conditions such that the controller is configured to change operation of the manipulator: from the first mode to the second mode in response to determining that the force detected by the at least one sensor satisfies the first predetermined condition, and from the second mode to the third mode in response to determining that the force detected by the at least one sensor satisfies the second predetermined condition. In one implementation the first predetermined condition is defined by a first force detected by the at least one sensor, the second predetermined condition is defined by a second force detected by the at least one sensor, and the second force is larger than the first force 
     In one implementation, a patient tracker is adapted for attachment relative to the target site. In one implementation, the sensing system comprises a navigation system configured to track states of the patient tracker. In one implementation, tracked states of the patient tracker define at least one of the one or more system conditions such that the controller is configured to change operation of the manipulator from the first mode to the second mode in response to determining that tracked states of the patient tracker satisfy the predetermined condition. In one implementation, the controller is further configured to compare tracked movement of the tool against movement of the patient tracker based on tracked states received from the navigation system. In one implementation, tracked movement of the tool defines at least one of the one or more system conditions. In one implementation, the predetermined condition is defined based on tracked movement of the tool corresponding to tracked states of the patient tracker. 
     In one implementation, the sensing system comprises at least one sensor configured to obtain measurements indicative of a force occurring between the target site and the manipulator. In one implementation, measurements indicative of the force obtained by the at least one sensor define at least one of the one or more system conditions such that the controller is configured to change operation of the manipulator from the first mode to the second mode in response to determining that the force detected by the at least one sensor satisfies the predetermined condition. 
     In one implementation, the controller is further configured to operate the manipulator in the first mode to resist movement of the tool relative to the target site with increasing resilience as the measurements indicative of the force obtained by the at least one sensor increases toward the predetermined condition. In one implementation, the tool comprises a guide with a channel formed to receive an impactor assembly and permit limited movement of the impactor assembly relative to the guide, the impactor assembly having an interface for releasably securing a prosthesis. In one implementation, the manipulator is configured to support the guide along a trajectory relative to the target site while the impactor assembly is received in the channel of the guide and while the prosthesis is secured to the impactor assembly. In one implementation, the target site is further defined as an acetabular cup. In one implementation, the at least one sensor is configured to detect the force occurring as a result of a force applied on the impactor assembly to install the prosthesis in the acetabular cup. In one implementation, the controller is further configured to deduce a torque being applied to the acetabular cup based on the detected force. In one implementation, the controller is further configured to change operation of the manipulator from the first mode to the second mode in response to determining that the deduced torque applied to the acetabular cup satisfies the predetermined condition. 
     In one implementation, the at least sensor is further defined as one or more of a: force torque transducer; joint actuator current sensor; joint force sensor; joint torque sensor; and joint encoder 
     In one implementation, the first constraint criteria comprises a first number of degrees of freedom in which movement of the tool is restricted relative to the trajectory. In one implementation, the second constraint criteria comprises a second number of degrees of freedom in which movement of the tool is restricted relative to the trajectory. In one implementation, the second number of degrees of freedom being different from the first number of degrees of freedom. In one implementation, the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the trajectory based on the first number of degrees of freedom; and in the second mode to maintain alignment of the tool with respect to the trajectory based on the second number of degrees of freedom. 
     In one implementation, the second number of degrees of freedom is smaller than the first number of degrees of freedom such that the controller permits movement of the tool relative to the trajectory in at least one more degree of freedom in the second mode than in the first mode. In one implementation, the first constraint criteria comprises at least one positional degree of freedom and at least one orientational degree of freedom. In one implementation, the first constraint criteria and the second constraint criteria each comprise at least one orientational degree of freedom. In one implementation, the first constraint criteria comprises at least one more positional degree of freedom than the second constraint criteria. In one implementation, the first constraint criteria and the second constraint criteria comprise at least one common degree of freedom. 
     In one implementation, the first constraint criteria comprises a first resilience parameter, and the second constraint criteria comprise a second resilience parameter different from the first resilience parameter. In one implementation, the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the trajectory based on the first resilience parameter; and in the second mode to maintain alignment of the tool with respect to the trajectory based on the second resilience parameter. 
     In one implementation, the controller permits more resilient movement of the tool relative to the trajectory in the second mode than in the first mode. In one implementation, the first resilience parameter and the second resilience parameter are each associated with resilient movement of the tool relative to the trajectory in a common degree of freedom. 
     In one implementation, the controller is further configured to operate the manipulator in the first mode to resist movement of the tool relative to the trajectory with increasing resilience as the measurements indicative of the force obtained by the at least sensor increases toward the predetermined condition. 
     In one implementation, the tool defines a tool center point and the controller is configured to operate the manipulator in the first mode to restrict movement of the tool center point away from the trajectory according to the first constraint criteria. In one implementation, the controller is configured to operate the manipulator in the second mode to permit movement of the tool center point away from the trajectory according to the second constraint criteria. 
     In one implementation, a mode indicator is coupled to the controller and the controller is configured to activate the mode indicator in response to determining that the measurements indicative of the force obtained by the at least sensor satisfies the predetermined condition to communicate to a user the change in operation of the manipulator from the first mode to the second mode. 
     In one implementation, the controller is configured to operate the manipulator in the first mode to permit movement of the tool relative to the trajectory in at least one degree of freedom according to the first constraint criteria. 
     In one implementation, the controller is configured to operate the manipulator in the second mode to permit movement of the tool relative to the trajectory in at least one degree of freedom according to the second constraint criteria. 
     In one implementation, the controller is further configured to operate the manipulator in a third mode to maintain alignment of the tool with respect to the trajectory according to a third constraint criteria different from both the first constraint criteria and the second constraint criteria. In one implementation, the predetermined condition is further defined as a first predetermined condition. In one implementation, the controller is further configured to change operation of the manipulator from the second mode to the third mode in response to determining that measurements indicative of force obtained by the at least one sensor satisfies a second predetermined condition different from the first predetermined condition. In one implementation, the first predetermined condition is defined by a first force detected by measurements obtained from the at least one sensor, the second predetermined condition is defined by a second force detected by measurements obtained from the at least one sensor, and the second force is larger than the first force. In one implementation, the first constraint criteria comprises a first number of degrees of freedom in which movement of the tool is restricted relative to the trajectory, the second constraint criteria comprises a second number of degrees of freedom in which movement of the tool is restricted relative to the trajectory, and the third constraint criteria comprises a third number of degrees of freedom in which movement of the tool is restricted relative to the trajectory, the third number of degrees of freedom being different from one or more of the first number of degrees of freedom and the second number of degrees of freedom; and wherein the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the trajectory based on the first number of degrees of freedom; in the second mode to maintain alignment of the tool with respect to the trajectory based on the second number of degrees of freedom; and in the third mode to maintain alignment of the tool with respect to the trajectory based on the third number of degrees of freedom. 
     In one implementation, the first constraint criteria further comprises a first resilience parameter, the second constraint criteria further comprises a second resilience parameter, and the third constraint criteria further comprises a third resilience parameter different from one or more of the first resilient parameter and the second resilience parameter; and wherein the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the trajectory based on the first number of degrees of freedom and also based on the first resilience parameter; in the second mode to maintain alignment of the tool with respect to the trajectory based on the second number of degrees of freedom and also based on the second resilience parameter; and in the third mode to maintain alignment of the tool with respect to the trajectory based on the third number of degrees of freedom and also based on the third resilience parameter. 
     In one implementation, the third number of degrees of freedom is smaller than the first number of degrees of freedom such that the controller permits movement of the tool relative to the trajectory in at least one more degree of freedom in the third mode than in the first mode. In one implementation, the third number of degrees of freedom is smaller than the second number of degrees of freedom such that the controller permits movement of the tool relative to the trajectory in at least one more degree of freedom in the third mode than in the second mode. 
     In one implementation, the first constraint criteria and the second constraint criteria each comprise at least one positional degree of freedom and at least one orientational degree of freedom. In one implementation, the first constraint criteria, the second constraint criteria, and the third constraint criteria each comprise at least one orientational degree of freedom. In one implementation, the first constraint criteria comprises at least one more positional degree of freedom than the third constraint criteria. In one implementation, the second constraint criteria comprises at least one more positional degree of freedom than the third constraint criteria. In one implementation, the controller permits more resilient movement of the tool relative to the trajectory in the second mode than in the first mode. In one implementation, the controller permits more resilient movement of the tool relative to the trajectory in the second mode than in the third mode. 
     In one implementation, the first constraint criteria comprises a first resilience parameter, the second constraint criteria comprises a second resilience parameter, and the third constraint criteria comprises a third resilience parameter different from one or more of the first resilient parameter and the second resilience parameter. In one implementation, the controller is further configured to operate the manipulator: in the first mode to maintain alignment of the tool with respect to the trajectory based on the first resilience parameter; in the second mode to maintain alignment of the tool with respect to the trajectory based on the second resilience parameter; and in the third mode to maintain alignment of the tool with respect to the trajectory based on the third resilience parameter. 
     In one implementation, a patient tracker is adapted for attachment relative to the target site and a navigation system configured to track states of the patient tracker; and wherein the controller is coupled to the navigation system and is further configured to define the trajectory based on the tracked states of the patient tracker received from the navigation system. 
     In one implementation, the tool comprises a guide with a channel formed to receive an impactor assembly and permit limited movement of the impactor assembly relative to the guide, the impactor assembly having an interface for releasably securing a prosthesis. In one implementation, the manipulator is configured to support the guide relative to the target site. 
     In one implementation, the manipulator is configured to support the guide relative to the target site while the impactor assembly is received in the channel of the guide and while the prosthesis is secured to the impactor assembly and wherein the target site is further defined as an acetabular cup. In one implementation, the at least one sensor is configured to obtain measurements indicative of the force occurring as a result of a force applied on the impactor assembly to install the prosthesis in the acetabular cup. In one implementation, the controller is further configured to deduce a torque being applied to the acetabular cup based on the detected force. In one implementation, the controller is further configured to change operation of the manipulator from the first mode to the second mode in response to determining that the deduced torque applied to the acetabular cup satisfies the predetermined condition. 
     In one implementation, the controller is configured to determine parameters of the second constraint criteria based on the detected system condition from the sensing system. 
     In one implementation, the controller is configured to determine parameters of the second constraint criteria based on the obtained measurements indicative of the force. 
     In one implementation, the controller is configured to determine parameters of the second constraint criteria based on the evaluated tracked movement. 
     Any of the above implementations can be utilized for any of the aspects described above. Any of the above implementations can be combined in whole, or in part, for any one or more aspects described above. 
     Other features and advantages of the present disclosure will be readily appreciated, as the same becomes better understood, after reading the subsequent description taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a surgical system comprising a manipulator, a navigation system, and tools for engaging a target site, with one of the tools shown having a powered surgical device for driving an energy applicator, and with another of the tools shown having an impactor assembly coupled to a prosthesis and supported along a trajectory by a guide attached to the manipulator. 
         FIG. 2  is a block diagram of a control system for controlling the surgical system of  FIG. 1 . 
         FIG. 3  is a functional block diagram of a software program of the control system of  FIG. 2 . 
         FIG. 4  is an illustrative view of a target site realized as an acetabulum depicting an output of a boundary generator of the software program of  FIG. 3 . 
         FIG. 5  is an illustrative view of the target site of  FIG. 4  depicting an output of a path generator of the software program of  FIG. 3 . 
         FIG. 6  is an illustrative view of a target site and one of the tools of  FIG. 1 , depicting virtual constraints of the surgical system. 
         FIG. 7  is a block diagram of modules operable by the control system of  FIG. 2 . 
         FIG. 8  depicts a sample constraint equation of the control system of  FIG. 2 . 
         FIG. 9  depicts a sample forward dynamics algorithm for carrying out a virtual simulation with the control system of  FIG. 2 . 
         FIG. 10  depicts an exemplary set of steps for implementing the forward dynamics algorithm of  FIG. 9 . 
         FIG. 11  depicts an exemplary set of steps carried out by the control system of  FIG. 2  to solve constraints, perform forward dynamics, and determine a commanded pose. 
         FIG. 12  is an illustrative schematic view of the tool of  FIG. 1  shown supporting the energy applicator along an axis aligned with the trajectory of the target site, and shown with the energy applicator spaced from the target site. 
         FIG. 13A  is another illustrative schematic view of the tool, the energy applicator, and the target site of  FIG. 12 , shown with the energy applicator engaging the target site along the trajectory. 
         FIG. 13B  is another illustrative schematic view of the tool, the energy applicator, and the target site of  FIG. 13A , shown with the energy applicator advanced along the trajectory and engaging deeper into the target site. 
         FIG. 14A  is another illustrative schematic view of the tool, the energy applicator, and the target site of  FIG. 13B , shown with the energy applicator encountering resistance to rotation about the axis while in engagement with the target site. 
         FIG. 14B  is another illustrative schematic view of the tool, the energy applicator, and the target site of  FIG. 14A , shown with the energy applicator engaging the target site misaligned relative to the trajectory in response to the resistance to rotation illustrated in FIG.  14 A, with the tool and the energy applicator arranged in an exaggerated misalignment relative to the trajectory to illustrate a runaway condition. 
         FIG. 14C  is another illustrative schematic view of the tool, the energy applicator, and the target site of  FIG. 14B , shown with the tool moved together with the energy applicator and the target site away from a support surface to illustrate the runaway condition as the manipulator of  FIG. 1  attempts to bring the tool into alignment with the trajectory defined by the target site. 
         FIG. 14D  is another illustrative schematic view of the tool, the energy applicator, and the target site of  FIG. 14C , shown with the tool moved further together with the energy applicator and the target site away from a support surface to illustrate the runaway condition as the manipulator of  FIG. 1  continues to attempt to bring the tool into alignment with the trajectory defined by the target site. 
         FIG. 15  is a partial perspective view of portions of the surgical system of  FIG. 1 , depicting the tool comprising guide and the impactor assembly supporting the prosthesis spaced from the trajectory defined by a target site monitored by the navigation system via a tracker. 
         FIG. 16A  is a perspective view of the impactor assembly of  FIG. 15  shown having an interface spaced from the prosthesis with a shaft extending between the interface and a flange arranged adjacent to a handle extending between the flange and a head. 
         FIG. 16B  is an exploded perspective view of the impactor assembly of  FIG. 16A . 
         FIG. 17A  is a perspective view of the guide of  FIG. 15 . 
         FIG. 17B  is a partially-exploded perspective view of the guide of  FIG. 17A , shown comprising a body defining a channel. 
         FIG. 18  is an illustrative schematic view of the prosthesis and tool of  FIGS. 15-17B , shown with the guide defining a guide axis aligned with the trajectory of the target site, and shown with the impactor assembly attached to the prosthesis and spaced from both the target site and the guide. 
         FIG. 19A  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 18 , shown with the prosthesis and the impactor assembly positioned adjacent to the target site, with the flange of the impactor assembly supported in the channel of the guide, and with an applied force acting on the guide. 
         FIG. 19B  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 19A , shown with the tool and the prosthesis moved relative to the trajectory and the target site in response to the applied force illustrated in  FIG. 19A . 
         FIG. 20A  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 18 , shown with the prosthesis and the impactor assembly positioned adjacent to the target site, with the flange of the impactor assembly supported in the channel of the guide, and with an applied force acting on the head of the impactor assembly substantially along the trajectory. 
         FIG. 20B  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 20A , shown with the prosthesis implanted at the target site along the trajectory in response to the applied force illustrated in  FIG. 20A . 
         FIG. 21A  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 18 , shown with the prosthesis and the impactor assembly positioned adjacent to the target site, with the flange of the impactor assembly supported in the channel of the guide, and with an applied force acting on the head of the impactor assembly transverse to the trajectory. 
         FIG. 21B  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 21A , shown with the prosthesis implanted at the target site misaligned relative to the trajectory in response to the applied force illustrated in  FIG. 20A , with the tool and the prosthesis arranged in an exaggerated misalignment relative to the trajectory to illustrate a runaway condition. 
         FIG. 21C  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 21B , shown with the tool moved together with the implanted prosthesis and the target site away from a support surface to illustrate the runaway condition as the manipulator of  FIG. 1  attempts to bring the guide into alignment with the trajectory defined by the target site. 
         FIG. 21D  is another illustrative schematic view of the tool, the prosthesis, and the target site of  FIG. 21C , shown with the tool further moved together with the implanted prosthesis and the target site away from the support surface to illustrate the runaway condition as the manipulator of  FIG. 1  continues to attempt to bring the guide into alignment with the trajectory defined by the target site. 
         FIG. 22A  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIGS. 15-17B , shown with the prosthesis arranged at the target site and spaced from the guide coupled to the manipulator. 
         FIG. 22B  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIG. 22A , shown with the guide coupled to the manipulator having moved toward the trajectory with the shaft of the impactor assembly arranged within the channel of the guide. 
         FIG. 22C  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIG. 22B , shown with the guide coupled to the manipulator having moved along the trajectory to bring the flange of the impactor assembly into engagement with the channel of the guide. 
         FIG. 23  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIG. 22C , shown with the guide coupled to the manipulator having moved about the trajectory in one rotational degree of freedom from a previous arrangement depicted in phantom. 
         FIG. 24A  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIG. 22B , shown with the guide coupled to the manipulator arranged along the trajectory with the flange of the impactor assembly disposed in engagement with the channel of the guide, and with an applied force acting on the head of the impactor assembly transverse to the trajectory. 
         FIG. 24B  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIG. 24A , shown with the prosthesis partially implanted at the target site and misaligned relative to the trajectory in response to the applied force illustrated in  FIG. 24A , and with the tool and the prosthesis arranged in exaggerated misalignment relative to the trajectory and relative to a previous arrangement depicted in phantom. 
         FIG. 24C  is another partial perspective view of the guide, the impactor assembly supporting the prosthesis, and the target site of  FIG. 24B , shown with the prosthesis partially implanted at the target site and further misaligned relative to the trajectory in response to the applied force illustrated in  FIG. 24A , and with the tool and the prosthesis arranged in further exaggerated misalignment relative to the trajectory. 
         FIG. 25  is a block diagram depicting interaction between a sensing system, a controller, and the manipulator of  FIG. 1  according to embodiments of the present disclosure. 
         FIG. 26  illustrates a runaway condition occurring as a result of a bur being trapped between a virtual boundary and a target site bone. 
     
    
    
     Any one or more of the embodiments depicted throughout the drawings may have certain components, structural features, and/or assemblies removed, depicted schematically, and/or shown in phantom for illustrative purposes. 
     DETAILED DESCRIPTION 
     Referring now to  FIG. 1 , a surgical system  100  comprising a robotic manipulator  102  supporting a tool  104  is shown. The surgical system  100  is useful for treating an anatomical volume or target site TS of a patient&#39;s P body B, such as bone or soft tissue. To this end, the manipulator  102  generally comprises a base  106 , a robotic arm  108 , and a coupling  110 . The robotic arm  108  is supported by the base  106  and is configured to move, maintain, or otherwise control the position and/or orientation of the coupling  110  relative to the base  106  during use. The coupling  110  is adapted to releasably secure one or more types of tools  104  which, in turn, generally support or otherwise include an instrument  112  utilized in connection with various types of surgical procedures. In some embodiments, the instrument  112  may be configured to support, drive, rotate, oscillate, vibrate, and/or otherwise direct energy to an energy applicator  114  (e.g., drill bits, taps, burs, blades, saws, reamers, and the like) used to effect treatment at or adjacent to the target site TS. In some embodiments, the instrument  112  may be configured to support, position, align, and/or guide implantable components  116  (e.g., cups, stems, screws, pins, rods, wires, anchors, prostheses, and the like) at or with respect to the target site TS, such as along a trajectory T maintained by the manipulator  102 . 
     In  FIG. 1 , the patient P is undergoing an illustrative surgical procedure where the target site TS includes or is otherwise defined by portions of the patient&#39;s hip and femur. However, that various types of surgical procedures are contemplated by the present disclosure, including without limitation surgical procedures involving partial or total knee or hip replacement surgery, shoulder replacement surgery, spine surgery, ankle surgery, and the like. The surgical procedure may involve tissue removal or other forms of treatment (e.g., cutting, drilling, reaming, coagulating, lesioning, other in-situ tissue treatments, and the like). In some embodiments, the surgical system  100  may be designed to facilitate cutting away material to be replaced by implantable components  116  (also referred to as “implants”), such as hip and knee implants, including unicompartmental, bicompartmental, multicompartmental, or total knee implants. Some types of implantable components  116  are shown in U.S. Pat. No. 9,381,085, entitled “Prosthetic Implant and Method of Implantation,” the disclosure of which is hereby incorporated by reference in its entirety. However, and as will be appreciated from the subsequent description below, other configurations are contemplated, and the surgical system  100  could be utilized in connection with a number of different surgical procedures and may employ various types, styles, and configurations of manipulators  102 , tools  104 , instruments  112 , energy applicators  114 , and/or implantable components  116  without departing from the scope of the present disclosure. Furthermore, the surgical system  100  and techniques disclosed herein may be used to perform other procedures, surgical or non-surgical, or may be used in industrial applications or other applications where robotic systems are utilized. 
     The manipulator  102  (also referred to as a “surgical robot”) moves the tool  104  relative to the target site TS and relative to the base  106  via the robotic arm  108  to, among other things, assist medical professionals in carrying out various types of surgical procedures with precise control over movement and positioning of the tool  104 , the instrument  112 , the energy applicator  114 , and/or the implantable component  116 . As noted above, the manipulator  102  generally comprises the base  106 , the robotic arm  108 , and the coupling  110 . The base  106  is fixed to a manipulator cart  118  and supports the robotic arm  108  which, in turn, is configured to move, maintain, or otherwise control the position and/or orientation of the coupling  110  relative to the base  106  during use. To this end, the robotic arm  108  illustrated in  FIG. 1  comprises a plurality of links  120  and joints J arranged in a serial arm configuration. However, the manipulator  102  could employ a different configuration without departing from the scope of the present disclosure. By way of non-limiting example, the manipulator  102  may have a parallel arm configuration, or any other suitable configuration. In some embodiments, more than one manipulator  102  may be utilized in a multiple arm configuration. One exemplary arrangement of the robotic arm  108  is described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” the disclosure of which is hereby incorporated by reference in its entirety. The robotic arm  108  and other portions of the manipulator  102  may be arranged in a number of different configurations without departing from the scope of the present disclosure. 
     In the example shown in  FIG. 1 , the manipulator  102  comprises a plurality of joint encoders  122  located at the joints J for determining position data of the joints J. For simplicity, only one joint encoder  122  is labeled in  FIG. 1 , although other joint encoders  122  may be similarly illustrated. In the representative embodiment illustrated herein, the robotic arm  108  has six joints J 1 , J 2 , J 3 , J 4 , J 5 , J 6  implementing at least six degrees of freedom (DOF) for the manipulator  102 . However, the manipulator  102  may have any suitable number of degrees of freedom, may have any suitable number of joints J, and may have redundant joints J. The manipulator  102  need not require joint encoders  122  but may alternatively, or additionally, utilize motor encoders present on motors at each joint J. Furthermore, the manipulator  102  need not require rotary joints, but may alternatively, or additionally, utilize one or more prismatic joints. Any suitable combination of joint types are contemplated. 
     The surgical system  100  is able to monitor, track, and/or determine changes in the relative position and/or orientation of one or more parts of the manipulator  102 , the robotic arm  108 , the tool  104 , the instrument  112 , the energy applicator  114 , and/or the implantable component  116 , as well as various parts of the patient&#39;s body B, within a common coordinate system by utilizing various types of trackers (e.g., multiple degree-of-freedom optical, inertial, and/or ultrasonic sensing devices), navigation systems (e.g., machine vision systems, charge coupled device cameras, tracker sensors, surface scanners, and/or range finders), anatomical computer models (e.g., magnetic resonance imaging scans of the patient&#39;s P anatomy), data from previous surgical procedures and/or previously-performed surgical techniques (e.g., data recorded during prior steps of the surgical procedure), and the like. To these ends, and as is depicted schematically in  FIG. 1 , the surgical system  100  employs a control system  124  (also referred to as a “controller”  124 ) which may comprise or otherwise communicate with one or more of a robotic control system  126 , a navigation system  128 , and a tool control system  130  which cooperate to facilitate positioning, moving, and/or driving the tool  104  relative to the target site TS and other parts of the surgical system  100  via the manipulator  102 , as described in greater detail below. Exemplary control methodologies are described in U.S. Pat. No. 10,327,849, entitled “Robotic System and Method for Backdriving the Same,” the disclosure of which is hereby incorporated by reference in its entirety. 
     The base  106 , or another portion of the manipulator  102 , generally provides a fixed reference coordinate system for other components of the manipulator  102  and/or other components of the surgical system  100 . Generally, the origin of a manipulator coordinate system MNPL is defined at the fixed reference of the base  106 . The base  106  may be defined with respect to any suitable portion of the manipulator  102 , such as one or more of the links  120 . Alternatively, or additionally, the base  106  may be defined with respect to the manipulator cart  118 , such as where the manipulator  102  is physically attached to the cart  118 . In some embodiments, the base  106  is defined at an intersection of the axis of joint J 1  and the axis of joint J 2 . Thus, although joint J 1  and joint J 2  are moving components in reality, the intersection of the axes of joint J 1  and joint J 2  is nevertheless a virtual fixed reference pose, which provides both a fixed position and orientation reference and which does not move relative to the manipulator  102  and/or the manipulator cart  118 . In some embodiments, the manipulator  102  could be hand-held such that the base  106  would be defined by a base portion of a tool (e.g., a portion held free-hand by the user) with a tool tip (e.g., an end effector) movable relative to the base portion. In this embodiment, the base portion has a reference coordinate system that is tracked, and the tool tip has a tool tip coordinate system that is computed relative to the reference coordinate system (e.g., via motor and/or joint encoders and forward kinematic calculations). Movement of the tool tip can be controlled to follow a path since its pose relative to the path can be determined. One example of this type of hand-held manipulator  102  is shown in U.S. Pat. No. 9,707,043, 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,” the disclosure of which is hereby incorporated by reference in its entirety. The forgoing is a non-limiting, illustrative example, and other configurations are contemplated by the present disclosure. 
     As is depicted schematically in  FIG. 1 , the robotic control system  126  comprises a manipulator controller  132 , the navigation system  128  comprises a navigation controller  134 , and the tool control system  130  comprises a tool controller  136 . In the illustrated embodiment, the manipulator controller  132 , the navigation controller  134 , and the tool controller  136  are generally disposed in communication with each other (e.g., directly or indirectly), and/or with other components of the surgical system  100 , such as via physical electrical connections (e.g., a tethered wire harness) and/or via one or more types of wireless communication (e.g., with a WiFi™ network, Bluetooth®, a radio network, and the like). The manipulator controller  132 , the navigation controller  134 , and/or the tool controller  136  may be realized as or with various arrangements of computers, processors, control units, and the like, and may comprise discrete components or may be integrated (e.g., sharing hardware, software, inputs, outputs, and the like). Other configurations are contemplated. 
     The manipulator controller  132 , the navigation controller  134 , and/or the tool controller  136  may each be realized as a computer with a processor  138  (e.g., a central processing unit) and/or other processors, memory  140 , and/or storage (not shown), and are generally loaded with software as described in greater detail below. The processors  138  could include one or more processors to control operation of the manipulator  102 , the navigation system  128 , or the tool  104 . The processors  138  could be any type of microprocessor, multi-processor, and/or multi-core processing system. The manipulator controller  132 , the navigation controller  134 , and/or the tool controller  136  may additionally or alternatively comprise one or more microcontrollers, field programmable gate arrays, systems on a chip, discrete circuitry, and/or other suitable hardware, software, and/or firmware capable of carrying out the functions described herein. The term “processor” is not intended to limit any embodiment to a single processor. The robotic control system  126 , the navigation system  128 , and/or the tool control system  130  may also comprise, define, or otherwise employ a user interface  142  with one or more output devices  144  (e.g., screens, displays, status indicators, and the like) and/or input devices  146  (e.g., push button, keyboard, mouse, microphone, voice-activation devices, gesture control devices, touchscreens, foot pedals, pendants, and the like). Other configurations are contemplated. 
     As noted above, one or more tools  104  (sometimes referred to as “end effectors”) releasably attach to the coupling  110  of the manipulator  102  and are movable relative to the base  106  to interact with the anatomy of the patient P (e.g., the target site TS) in certain modes. The tool  104  may be grasped by the user (e.g., a surgeon). The tool  104  generally includes a mount  148  that is adapted to releasably attach to the coupling  110  of the manipulator  102 . The mount  148  may support or otherwise be defined by the instrument  112  which, in some embodiments, may be configured as a powered surgical device  150  which employs a power generation assembly  152  (e.g., a motor, an actuator, gear trains, and the like) used to drive the energy applicator  114  attached thereto (e.g., via a chuck, a coupling, and the like). One exemplary arrangement of this type of manipulator  102 , tool  104 , and instrument  112  is described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. The manipulator  102 , the tool  104 , and/or the instrument  112  may be arranged in alternative configurations. In some embodiments, the tool  104  and/or the instrument  112  may be like that shown in U.S. Pat. No. 9,566,121, entitled “End Effector of a Surgical Robotic Manipulator,” the disclosure of which is hereby incorporated by reference in its entirety. In some embodiments, the tool  104  and/or the instrument  112  may be like that shown in U.S. Patent Application Publication No. US 2019/0231447 A1, entitled “End Effectors And Methods For Driving Tools Guided By Surgical Robotic Systems,” the disclosure of which is hereby incorporated by reference in its entirety. Other configurations are contemplated. In some embodiments, and as is described in greater detail below, the instrument  112  may not be configured as a powered surgical device  150 . 
     In some embodiments, the energy applicator  114  is designed to contact and remove the tissue of the patient P at the target site TS. To this end, the energy applicator  114  may comprise a bur  154  in some embodiments. The bur  154  may be substantially spherical and comprise a spherical center, a radius, and a diameter. Alternatively, the energy applicator  114  may be a drill bit, a saw blade, an ultrasonic vibrating tip, and the like. The tool  104 , the instrument  112 , and/or the energy applicator  114  may comprise any geometric feature, including without limitation a perimeter, a circumference, a radius, a diameter, a width, a length, a volume an area, a surface/plane, a range of motion envelope (along any one or more axes), and the like. The geometric feature may be considered to determine how to locate the tool  104  relative to the tissue at the target site TS to perform the desired treatment. In some of the embodiments described herein, a spherical bur  154  having or otherwise defining tool center point (TCP) will be described for convenience and ease of illustration, but is not intended to limit the tool  104 , the instrument  112 , and/or the energy applicator  114  to any particular form. In some of the embodiments described herein, the tool center point TCP is defined by a portion of the instrument  112  or the tool  104  rather than the energy applicator  114 . Other configurations are contemplated. 
     In some embodiments, such as where the instrument  112  is realized as a powered surgical device  150 , the tool  104  may employ the tool controller  136  to facilitate operation of the tool  104 , such as to control power to the power generation assembly  152  (e.g., a rotary motor), control movement of the tool  104 , control irrigation/aspiration of the tool  104 , and the like. The tool controller  136  may be in communication with the manipulator controller  132  and/or other components of the surgical system  100 . In some embodiments, the manipulator controller  132  and/or the tool controller  136  may be housed in the manipulator  102  and/or the manipulator cart  118 . In some embodiments, parts of the tool controller  136  may be housed in the tool  104 . Other configurations are contemplated. The tool control system  130  may also comprise the user interface  142 , with one or more output devices  144  and/or input devices  146 , which may formed as a part of the tool  104  and/or may be realized by other parts of the surgical system  100  and/or the control system  124  (e.g., the robotic control system  126  and/or the navigation system  128 ). Other configurations are contemplated. 
     The manipulator controller  132  controls a state (position and/or orientation) of the tool  104  (e.g., the tool center point TCP) with respect to a coordinate system, such as the manipulator coordinate system MNPL. The manipulator controller  132  can control (linear or angular) velocity, acceleration, or other derivatives of motion of the tool  104 . The tool center point TCP, in one example, is a predetermined reference point defined at the energy applicator  114 . However, as noted above, other components of the tool  104  and/or instrument  112  could define the tool center point TCP in some embodiments. In any event, the tool center point TCP has a known pose relative to other coordinate systems. The pose of the tool center point TCP may be static or may be calculated. In some embodiments, the geometry of the energy applicator  114  is known in or defined relative to a tool center point TCP coordinate system. The tool center point TCP may be located at the spherical center of the bur  154  of the energy applicator  114  supported or defined by the instrument  112  of the tool  104  such that only one point is tracked. The tool center point TCP may be defined in various ways depending on the configuration of the energy applicator  114 , the instrument  112 , the tool  104 , and the like. 
     The manipulator  102  could employ the joint encoders  122  (and/or motor encoders, as noted above), or any other non-encoder position sensing method, to enable a pose of the tool center point TCP to be determined. The manipulator  102  may use joint J measurements to determine the tool center point TCP pose, and/or could employ various techniques to measure the tool center point TCP pose directly. The control of the tool  104  is not limited to a center point. For example, any suitable primitives, meshes, and the like can be used to represent the tool  104 . Other configurations are contemplated. 
     With continued reference to  FIG. 1 , as noted above, the surgical system  100  also includes the navigation system  128  which, among other things, is configured to track, monitor, detect, or otherwise sense movement of various objects, such as the tool  104 , a pointer  156  used for registering objects (e.g., portions of the anatomy, trackers, and the like), and parts of the patient&#39;s body B (e.g., bones or other anatomy at or adjacent to the target site TS). To this end, the navigation system  128  employs a localizer  158  configured to sense the position and/or orientation of trackers  160  within a localizer coordinate system LCLZ. The navigation controller  134  is disposed in communication with the localizer  158  and gathers position and/or orientation data for each tracker  160  sensed within a field of view of the localizer  158  in the localizer coordinate system LCLZ. 
     The localizer  158  can sense the position and/or orientation of a plurality of trackers  160  to track a corresponding plurality of objects within the localizer coordinate system LCLZ. By way of example, and as is depicted in  FIG. 1 , trackers  160  may comprise a pointer tracker  160 P coupled to the pointer  156 , a manipulator tracker  160 M coupled to the base  106  of the manipulator  102 , one or more tool trackers  160 G,  160 I coupled to portions of the tool  104 , a first patient tracker  160 A coupled to one portion of the anatomy of the patient P, and a second patient tracker  160 B coupled to another portion of the anatomy of the patient P, as well as additional patient trackers, trackers for additional medical and/or surgical tools, instruments, and the like. 
     In some embodiments, and as is shown in  FIG. 1 , the one or more tool trackers  160 G,  160 I may each be firmly affixed to different portions of the tool  104 , such as those that may be configured to move relative to each other and/or to the manipulator tracker  160 M, which is firmly affixed to the base  106  of the manipulator  102 . By way of non-limiting example, and as is described in greater detail below, a first tool tracker  160 G could be coupled to the mount  148  (or to another part of the tool  104 ) for concurrent movement with the coupling  110  via the manipulator  102 , and a second tool tracker  160 I could be coupled to a different portion of the tool  104  which moves relative to the mount  148  and/or the coupling  110  in one or more degrees of freedom. While the first tool tracker  160 G and the second tool tracker  160 I depicted in  FIG. 1  can be used by the navigation system  128  to readily determine the relative positions and/or orientations of different parts of the tool  104  via the localizer  158 , certain embodiments of the present disclosure may be configured to facilitate this determination in other ways (e.g., such as with one or more sensors). Here, other configurations are contemplated by the present disclosure, and various combinations of trackers  160 , sensors, predetermined geometric relationships, and the like can be utilized in order to track certain objects or otherwise relate those objects to a tracked object. 
     With continued reference to  FIG. 1 , the first patient tracker  160 A is firmly affixed to one bone of the patient&#39;s body B at or adjacent to the target site TS (e.g., to the pelvis near the acetabulum), and the second patient tracker  160 B is firmly affixed to a different bone (e.g., to a portion of the femur). While not shown in detail, the patient trackers  160 A,  160 B can be coupled to a number of different bones in the patient&#39;s body B in various ways, such as by threaded engagement, clamping, or by other techniques. Similarly, the first tool tracker  160 G and/or the second tool tracker  160 I could be fixed to portions of the tool  104  in various ways, such as by integration during manufacture or by releasable attachment ahead of or during a surgical procedure. Various trackers  160  may be firmly affixed to different types of tracked objects (e.g., discrete bones, tools, pointers, and the like) in a number of different ways. For example, trackers  160  may be rigidly fixed, flexibly connected (optical fiber), or not physically connected at all (ultrasound), as long as there is a suitable (e.g., supplemental) way to determine the relationship (e.g., measurement) of that respective tracker  160  to the object or anatomy that it is associated with. 
     The position and/or orientation of the trackers  160  relative to the objects or anatomy to which they are attached can be determined by utilizing known registration techniques. For example, determining the pose of the patient trackers  160 A,  160 B relative to the portions of the patient&#39;s body B to which they are attached can be accomplished with various forms of point-based registration, such as where a distal tip of the pointer  156  is used to engage against specific anatomical landmarks (e.g., touching specific portions of bone) or is used to engage several parts of a bone for surface-based registration as the localizer  158  monitors the position and orientation of the pointer tracker  160 P. Conventional registration techniques can then be employed to correlate the pose of the patient trackers  160 A,  160 B to the patient&#39;s anatomy (e.g., to each of the femur and the acetabulum). 
     Other types of registration are also possible, such as by using patient trackers  160 A,  160 B with mechanical clamps that attach to bone and have tactile sensors (not shown) to determine a shape of the bone to which the clamp is attached. The shape of the bone can then be matched to a three-dimensional model of bone for registration. A known relationship between the tactile sensors and markers  162  on the patient tracker  160 A,  160 B may be entered into or otherwise known by the navigation controller  134  (e.g., stored in memory  140 ). Based on this known relationship, the positions of the markers  162  relative to the patient&#39;s anatomy can be determined. Position and/or orientation data may be gathered, determined, or otherwise handled by the navigation controller  134  using a number of different registration/navigation techniques to determine coordinates of each tracker  160  within the localizer coordinate system LCLZ or another suitable coordinate system. These coordinates are communicated to other parts of the control system  124 , such as to the robotic control system  126  to facilitate articulation of the manipulator  102  and/or to otherwise assist the surgeon in performing the surgical procedure, as described in greater detail below. 
     In the representative embodiment illustrated herein, the manipulator controller  132  and the tool controller  136  are operatively attached to the base  106  of the manipulator  102 , and the navigation controller  134  and the localizer  158  are supported on a mobile cart  164  which is movable relative to the base  106  of the manipulator  102 . The mobile cart  164  may also support the user interface  142  to facilitate operation of the surgical system  100  by displaying information to, and/or by receiving information from, the surgeon or another user. While shown as a part of the navigation system  128  in the representative embodiment illustrated in  FIG. 1 , the user interface  142  could form part of, or otherwise communicate with, other parts of the control system  124  such as the robotic control system  126  and/or the tool control system  130 . To this end, the user interface  142  may be disposed in communication with navigation controller  134 , the manipulator controller  132 , and/or the tool controller  136 , and may likewise comprise one or more output devices  144  (e.g., monitors, indicators, display screens, and the like) to present information to the surgeon or other users (e.g., images, video, data, graphics, navigable menus, and the like), and one or more input devices  146  (e.g., physical or virtual input controls, buttons, touch screens, keyboards, mice, gesture or voice-based input devices, and the like). One type of mobile cart  164  and user interface  142  utilized in this type of navigation system  128  is described in U.S. Pat. No. 7,725,162, entitled “Surgery System,” the disclosure of which is hereby incorporated by reference in its entirety. 
     Because the mobile cart  164  and the base  106  of the manipulator  102  can be positioned relative to each other and also relative to the patient&#39;s body B, one or more portions of the surgical system  100  are generally configured to transform the coordinates of each tracker  160  sensed via the localizer  158  from the localizer coordinate system LCLZ into the manipulator coordinate system MNPL (or to other coordinate systems), or vice versa, so that articulation of the manipulator  102  can be performed based at least partially on the relative positions and/or orientations of certain trackers  160  within a common coordinate system (e.g., the manipulator coordinate system MNPL, the localizer coordinate system LCLZ, or another common coordinate system). Coordinates within the localizer coordinate system LCLZ can be transformed into coordinates within the manipulator coordinate system MNPL (or other coordinate systems), and vice versa, using a number of different transformation techniques. One example of the translation or transformation of data between coordinate systems is described in U.S. Pat. No. 8,675,939, entitled “Registration of Anatomical Data Sets”, the disclosure of which is hereby incorporated by reference in its entirety. 
     In the illustrated embodiment, the localizer  158  is an optical localizer and includes a camera unit  166  with one or more optical sensors  168  and, in some embodiments, a video camera  170 . The localizer  158  may also comprise a localizer controller (not shown) which communicates with the navigation controller  134  or otherwise forms part of the navigation system  128 . The navigation system  128  employs the optical sensors  168  of the camera unit  166  to sense the position and/or orientation of the trackers  160  within the localizer coordinate system LCLZ. In the representative embodiment illustrated herein, the trackers  160  each employ a plurality of markers  162  (see  FIG. 2 ) which can be sensed by the optical sensors  168  of the camera unit  166 . One example of a navigation system  128  of this type is described in U.S. Pat. No. 9,008,757, entitled “Navigation System Including Optical and Non-Optical Sensors,” the disclosure of which is hereby incorporated by reference in its entirety. In some embodiments, the markers  162  are active markers (e.g., light emitting diodes “LEDs”) which emit light that can be sensed by the localizer  158 . In some embodiments, the trackers  160  may employ passive markers (e.g., reflectors) which reflect light emitted from the localizer  158  or another light source. Although one embodiment of the navigation system  128  is illustrated throughout the drawings, the navigation system  128  could have any suitable configuration for monitoring trackers  160  which, as will be appreciated from the subsequent description below, may be of various types and configurations. For example, the navigation system  128  may comprise multiple localizers  158  and/or trackers  160  of the same or different type. 
     In some embodiments, the navigation system  128  and/or the localizer  158  are radio frequency (RF) based. For example, the navigation system  128  may comprise an RF transceiver coupled to the navigation controller  134  and/or to another computing device, controller, and the like. Here, the trackers  160  may comprise RF emitters or transponders, which may be passive or may be actively energized. The RF transceiver transmits an RF tracking signal, and the RF emitters respond with RF signals such that tracked states are communicated to (or interpreted by) the navigation controller  134 . The RF signals may be of any suitable frequency. The RF transceiver may be positioned at any suitable location to track the objects using RF signals effectively. Furthermore, embodiments of RF-based navigation systems may have structural configurations that are different than the active marker-based navigation system  128  illustrated herein. 
     In some embodiments, the navigation system  128  and/or localizer  158  are electromagnetically (EM) based. For example, the navigation system  128  may comprise an EM transceiver coupled to the navigation controller  134  and/or to another computing device, controller, and the like. Here, the trackers  160  may comprise EM components attached thereto (e.g., various types of magnetic trackers, electromagnetic trackers, inductive trackers, and the like), which may be passive or may be actively energized. The EM transceiver generates an EM field, and the EM components respond with EM signals such that tracked states are communicated to (or interpreted by) the navigation controller  134 . The navigation controller  134  may analyze the received EM signals to associate relative states thereto. Here too, embodiments of EM-based navigation systems may have structural configurations that are different than the active marker-based navigation system  128  illustrated herein. 
     In some embodiments, the navigation system  128  and/or the localizer  158  could be based on one or more types of imaging systems that do not necessarily require trackers  160  to be fixed to objects in order to determine location data associated therewith. For example, an ultrasound-based imaging system could be provided to facilitate acquiring ultrasound images (e.g., of specific known structural features of tracked objects, of markers or stickers secured to tracked objects, and the like) such that tracked states (e.g., position, orientation, and the like) are communicated to (or interpreted by) the navigation controller  134  based on the ultrasound images. The ultrasound images may be three-dimensional, two-dimensional, or a combination thereof. The navigation controller  134  may process ultrasound images in near real-time to determine the tracked states. The ultrasound imaging device may have any suitable configuration and may be different than the camera unit  166  as shown in  FIG. 1 . By way of further example, a fluoroscopy-based imaging system could be provided to facilitate acquiring X-ray images of radio-opaque markers (e.g., stickers, tags, and the like with known structural features that are attached to tracked objects) such that tracked states are communicated to (or interpreted by) the navigation controller  134  based on the X-ray images. The navigation controller  134  may process X-ray images in near real-time to determine the tracked states. Similarly, other types of optical-based imaging systems could be provided to facilitate acquiring digital images, video, and the like (e.g., via a charge-coupled device “CCD” sensor such as the video camera  170 ) of specific known objects (e.g., based on a comparison to a virtual representation of the tracked object or a structural component or feature thereof) and/or markers (e.g., stickers, tags, and the like that are attached to tracked objects) such that tracked states are communicated to (or interpreted by) the navigation controller  134  based on the digital images. The navigation controller  134  may process digital images in near real-time to determine the tracked states. 
     Accordingly, various types of imaging systems, including multiple imaging systems of the same or different type, may form a part of the navigation system  128  without departing from the scope of the present disclosure. The navigation system  128  and/or localizer  158  may have other suitable components or structure not specifically recited herein. For example, the navigation system  128  may utilize solely inertial tracking or any combination of tracking techniques, and may additionally or alternatively comprise fiber optic-based tracking, machine-vision tracking, and the like. Furthermore, any of the techniques, methods, and/or components associated with the navigation system  128  illustrated in  FIG. 1  may be implemented in a number of different ways, and other configurations are contemplated by the present disclosure. 
     In some embodiments, the surgical system  100  is capable of displaying a virtual representation of the relative positions and orientations of tracked objects to the surgeon or other users of the surgical system  100 , such as with images and/or graphical representations of the anatomy of the patient&#39;s body B, the tool  104 , the instrument  112 , the energy applicator  114 , and the like presented on one or more output devices  144  (e.g., a display screen). The manipulator controller  132  and/or the navigation controller  134  may also utilize the user interface  142  to display instructions or request information such that the surgeon or other users may interact with the robotic control system  126  (e.g., using a graphical user interface GUI) to facilitate articulation of the manipulator  102 . Other configurations are contemplated. 
     As noted above, the localizer  158  tracks the trackers  160  to determine a state of each of the trackers  160  which corresponds, respectively, to the state of the object respectively attached thereto. The localizer  158  may perform known triangulation techniques to determine the states of the trackers  160  and associated objects. The localizer  158  provides the state of the trackers  160  to the navigation controller  134 . In some embodiments, the navigation controller  134  determines and communicates the state of the trackers  160  to the manipulator controller  132 . As used herein, the state of an object includes, but is not limited to, data that defines the position and/or orientation of the tracked object, or equivalents/derivatives of the position and/or orientation. For example, the state may be a pose of the object, and may include linear velocity data, and/or angular velocity data, and the like. Other configurations are contemplated. 
     Referring to  FIG. 2 , the surgical system  100  generally comprises the control system  124  which, among other components, may include or otherwise be defined as the manipulator controller  132 , the navigation controller  134 , the tool controller  136 , and/or various components of the robotic control system  126 , the navigation system  128 , and/or the tool control system  130  as noted above. The control system  124  may also include one or more software modules shown in  FIG. 3 . The software modules may be part of one or more programs that operate on the manipulator controller  132 , the navigation controller  134 , the tool controller  136 , or any combination thereof, to process data used to facilitate or otherwise assist with control of the surgical system  100 . The software programs and/or modules include computer readable instructions stored in non-transitory memory  140  on the manipulator controller  132 , the navigation controller  134 , the tool controller  136 , or a combination thereof, to be executed by one or more processors  138  of one or more of the controllers  136 ,  132 ,  134 . 
     The memory  140  may be of any suitable configuration, such as random-access memory (RAM), non-volatile memory, and the like, and may be implemented locally or from a remote location (e.g., a database, a server, and the like). Additionally, software modules for prompting and/or communicating with the user may form part of the modules or programs, and may include instructions stored in memory  140  on the manipulator controller  132 , the navigation controller  134 , the tool controller  136 , or any combination thereof. The user may interact with any of the input devices  146  and/or output devices  144  of any of the user interfaces  142  (e.g., the user interface  142  of the navigation system  128  shown in  FIG. 1 ) to communicate with the software modules and/or programs. The control system  124  may also comprise user interfaces  142  (e.g., a graphical user interface GUI) or other software or modules that could run on a separate device from the manipulator controller  132 , the navigation controller  134 , and/or the tool controller  136  (e.g., a portable electronic device such as a tablet computer). Other configurations are contemplated. 
     The control system  124  may comprise any suitable arrangement and/or configuration of input, output, and processing devices suitable for carrying out the functions and methods described herein. The surgical system  100  may comprise the manipulator controller  132 , the navigation controller  134 , or the tool controller  136 , or any combination thereof, or may comprise only some of these controllers, or additional controllers, any of which could form part of the control system  124  as noted above. The controllers  132 ,  134 ,  136  may communicate via a wired bus or communication network as shown in  FIG. 2 , via wireless communication, or otherwise. The control system  124  may also be referred to as a controller, and may likewise comprise one or more microcontrollers, field programmable gate arrays, systems on a chip, discrete circuitry, sensors, displays, user interfaces, indicators, and/or other suitable hardware, software, or firmware that is capable of carrying out the functions described herein. Other configurations are contemplated. 
     Referring to  FIG. 3 , in some embodiments, the software employed by the control system  124  may include a boundary generator  172 . As shown in  FIG. 4 , the boundary generator  172  is a software program or module that generates a virtual boundary  174  for constraining movement and/or operation of the tool  104 . The virtual boundary  174  may be one-dimensional, two-dimensional, or three-dimensional, and may comprise a point, line, axis, trajectory, plane, or other shapes, including complex geometric shapes. In some embodiments, the virtual boundary  174  is a surface defined by a triangle mesh. Such virtual boundaries  174  may also be referred to as virtual objects. The virtual boundaries  174  may be defined with respect to an anatomical model AM, such as a three-dimensional bone model. The anatomical model Am is associated with the real anatomy of the patient P by virtue of the anatomical model AM being mapped to the anatomy of the patient P via registration or other processes. In the example of  FIG. 4 , the virtual boundaries  174  comprises a generally spherical mesh substantially surrounding an acetabulum with an entry portion (e.g., an opening) that provides access to the acetabulum. The entry portion has a funnel or conical shape. In this representative embodiment, the virtual boundary  174  is associated with a three-dimensional model of the acetabulum of the pelvis. 
     The anatomical model AM and associated virtual boundaries  174  are registered to one or more patient trackers  160 A,  160 B. Thus, the anatomical model AM (and the associated real anatomy of the patient P) and the virtual boundaries  174  fixed to the anatomical model AM can be tracked by the patient trackers  160 A,  160 B. The virtual boundaries  174  may be implant-specific (e.g., defined based on a size, shape, volume, and the like of an implantable component  116 ) and/or patient-specific (e.g., defined based on the anatomy of the patient P). The virtual boundaries  174  may be boundaries that are created pre-operatively, intra-operatively, or combinations thereof. In other words, the virtual boundaries  174  may be defined before the surgical procedure begins, during the surgical procedure (including during tissue removal), or combinations thereof. In any event, the control system  124  obtains the virtual boundaries  174  by storing/retrieving the virtual boundaries  174  in/from memory  140 , obtaining the virtual boundaries  174  from memory  140 , creating the virtual boundaries  174  pre-operatively, creating the virtual boundaries  174  intra-operatively, and the like. 
     The manipulator controller  132  and/or the navigation controller  134  may track the state of the tool  104  relative to the virtual boundaries  174 . In some embodiments, the state of the tool center point TCP is measured relative to the virtual boundaries  174  for purposes of determining haptic forces to be applied to a virtual rigid body VRB model via a virtual simulation VS so that the tool  104  remains in a desired positional relationship to the virtual boundaries  174  (e.g., not moved beyond them). The results of the virtual simulation VS are commanded to the manipulator  102 . The control system  124  (e.g., the manipulator controller  132  of the robotic control system  126 ) controls/positions the manipulator  102  in a manner that emulates the way a physical handpiece would respond in the presence of physical boundaries/barriers. The boundary generator  172  may be implemented on the manipulator controller  132 . Alternatively, the boundary generator  172  may be implemented on other components, such as the navigation controller  134 , or other portions of the control system  124 . Other configurations are contemplated. 
     Referring to  FIG. 3  and  FIG. 5 , a path generator  176  is another software program or module that may be run by the control system  124 . In some embodiments, the path generator  176  is run by the manipulator controller  132 . The path generator  176  generates a tool path TP for the tool  104  to traverse, such as for removing sections of the anatomy of the patient P at the target site TS to receive an implantable component  116 . The tool path TP may comprise a plurality of path segments PS, or may comprise a single path segment PS. The path segments PS may be straight segments, curved segments, combinations thereof, and the like. The tool path TP may also be defined with respect to the anatomical model AM. The tool path TP may be implant-specific (e.g., defined based on a size, shape, volume, and the like of an implantable component  116 ) and/or patient-specific (e.g., defined based on the anatomy of the patient P). Other configurations are contemplated. 
     In some embodiments described herein, the tool path TP is defined as a tissue removal path adjacent to the target site TS. However, in some embodiments, the tool path TP may be used for treatment other than tissue removal. One example of the tissue removal path described herein comprises a milling path MP. It should be understood that the term “milling path” generally refers to the path of the tool  104  in the vicinity of the target site TS for milling the anatomy, and is not intended to require that the tool  104  be operably milling the anatomy throughout the entire duration of the path. For instance, the milling path MP may comprise sections or segments where the tool  104  transitions from one location to another without milling. Additionally, other forms of tissue removal along the milling path MP may be employed, such as tissue ablation, and the like. The milling path MP may be a predefined path that is created pre-operatively, intra-operatively, or combinations thereof. In other words, the milling path MP may be defined before the surgical procedure begins, during the surgical procedure (including during tissue removal), or combinations thereof. In any event, the control system  124  obtains the milling path MP by storing/retrieving the milling path MP in/from memory  140 , obtaining the milling path MP from memory  140 , creating the milling path MP pre-operatively, creating the milling path MP intra-operatively, and the like. The milling path MP may have any suitable shape, or combinations of shapes, such as circular, helical/corkscrew, linear, curvilinear, combinations thereof, and the like. Other configurations are contemplated. 
     One example of a system and method for generating the virtual boundaries  174  and/or the milling path MP is described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. Further examples are described in U.S. Pat. No. 8,010,180, entitled “Haptic Guidance System and Method;” and U.S. Pat. No. 7,831,292, entitled “Guidance System and Method for Surgical Procedures with Improved Feedback,” the disclosures of which are each hereby incorporated by reference in their entirety. In some embodiments, the virtual boundaries  174  and/or the milling paths MP may be generated offline rather than on the manipulator controller  132 , navigation controller  134 , or another component of the surgical system  100 . Thereafter, the virtual boundaries  174  and/or milling paths MP may be utilized at runtime by the manipulator controller  132 . 
     Referring back to  FIG. 3 , another software program or module which may be run on the manipulator controller  132  and/or the navigation controller  134  is shown for performing behavior control  178 . Behavior control  178  is the process of computing data that indicates the next commanded position and/or orientation (e.g., pose) for the tool  104 . In some cases, only the position or orientation of the tool center point TCP is output from the behavior control  178 , while in other cases, the position and the orientation of the tool center point TCP is output from the behavior control  178 . In some embodiments, output from the boundary generator  172 , the path generator  176 , and a sensor  180  (e.g., a six degree of freedom DOF force/torque transducer) may feed as inputs into the behavior control  178  to determine the next commanded position and/or orientation for the tool  104 . The behavior control  178  may process these inputs, along with one or more virtual constraints VC as described in greater detail below, to determine a commanded pose CP. 
     With continued reference to  FIG. 3 , another software program or module which may be run on the manipulator controller  132  and/or the navigation controller  134  is shown for performing motion control  182 . One aspect of motion control  182  is the control of the manipulator  102 . The motion control  182  receives data defining the next commanded pose CP from the behavior control  178 . Based on these data, the motion control  182  determines the next position of the joint angles of the joints J of the robotic arm  108  of the manipulator  102  (e.g., via inverse kinematics and Jacobian calculators) so that the manipulator  102  is able to position the tool  104  as commanded by the behavior control  178  (e.g., at the commanded pose CP). In other words, the motion control  182  processes the commanded pose CP, which may be defined in Cartesian space, into joint angles of the manipulator  102 , so that the manipulator controller  132  can command the joint motors accordingly in order to move the joints J of the manipulator  102  to commanded joint angles corresponding to the commanded pose CP of the tool  104 . In some embodiments, the motion control  182  regulates the joint angle of each joint J of the robotic arm  108  and continually adjusts the torque that each joint motor outputs in order to, as closely as possible, ensure that the joint motor drives the associated joint J to the commanded joint angle. 
     The boundary generator  172 , the path generator  176 , the behavior control  178 , and the motion control  182  may be sub-sets (e.g., modules) of a software program  184 . Alternatively, each may be a software program that operates separately and/or independently, or any combination thereof. The term “software program” is used herein to describe the computer-executable instructions that are configured to carry out the various capabilities of the technical solutions described. For simplicity, the term “software program” is intended to encompass, at least, any one or more of the boundary generator  172 , the path generator  176 , the behavior control  178 , and/or the motion control  182 . The software program  184  can be implemented on the manipulator controller  132 , navigation controller  134 , or any combination thereof, or may be implemented in any suitable manner by the control system  124 . 
     In some embodiments, a clinical application  186  may be provided to facilitate user interaction and coordinate the surgical workflow, including pre-operative planning, implant placement, registration, bone preparation visualization, post-operative evaluation of implant fit, and the like. The clinical application  186  may be configured to output data to the output devices  144  (e.g., displays, screens, monitors, and the like), to receive input data from the input devices  146 , or to otherwise interact with the user interfaces  142 , and may include or form part of a graphical user interface GUI. The clinical application  186  may run on its own separate processor or may run alongside the navigation controller  134 , the manipulator controller  132 , and/or the tool controller  136 , or any other suitable portion of the control system  124 . 
     In some embodiments, the clinical application  186  interfaces with the boundary generator  172  and/or path generator  176  after implant placement is set by the user, and then sends the virtual boundary  174  and/or the tool path TP returned by the boundary generator  172  and/or the path generator  176  to the manipulator controller  132  for execution. Here, the manipulator controller  132  executes the tool path TP as described herein. The manipulator controller  132  may additionally create certain segments (e.g., lead-in segments) when starting or resuming machining to smoothly get back to the generated tool path TP. The manipulator controller  132  may also process the virtual boundaries  174  to generate corresponding virtual constraints VC as described in greater detail below. 
     The surgical system  100  may operate in a manual mode, such as described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. Here, the user manually directs, and the manipulator  102  executes movement of the tool  104  and its energy applicator  114  at the surgical site. The user (e.g., the surgeon) physically contacts the tool  104  to cause movement of the tool  104  in the manual mode. In some embodiments, the manipulator  102  monitors forces and torques placed on the tool  104  by the user in order to position the tool  104 . To this end, the surgical system  100  may employ the sensor  180  (e.g., a multiple degree of freedom DOF force/torque transducer) that detects and measures the forces and torques applied by the user to the tool  104  and generates corresponding input used by the control system  124  (e.g., one or more corresponding input/output signals). The forces and torques applied by the user at least partially define an external force F ext  that is used to determine how to move the tool  104  in the manual mode (or other modes). The external force F ext  may comprise other forces and torques, aside from those applied by the user, such as gravity-compensating forces, backdrive forces, and the like, as described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. Thus, the forces and torques applied by the user at least partially define the external force F ext , and in some cases may fully define the external force F ext  that influences overall movement of the tool  104  in the manual mode and/or in other modes as described in greater detail below. 
     The sensor  180  may comprise a six degree of freedom DOF force/torque transducer arranged to detect forces and/or torque occurring between the manipulator  102  and the target site TS (e.g., forces applied to the tool  104  by the user). For illustrative purposes, the sensor  180  is generically-depicted adjacent to or otherwise as a part of the coupling  110  of the manipulator  102  (e.g., coupled to joint J 6  of the robotic arm  108 ). However, other configurations and arrangements are contemplated. The manipulator controller  132 , the navigation controller  134 , the tool controller  136 , and/or other components of the surgical system  100  may receive signals (e.g., as inputs) from the sensor  180 . In response to the user-applied forces and torques, the manipulator  102  moves the tool  104  in a manner that emulates the movement that would have occurred based on the forces and torques applied by the user. Movement of the tool  104  in the manual mode may also be constrained in relation to the virtual boundaries  174  generated by the boundary generator  172 . In some embodiments, measurements taken by the sensor  180  are transformed from a sensor coordinate system SN of the sensor  180  to another coordinate system, such as a virtual mass coordinate system VM, in which a virtual simulation VS is carried out on a virtual rigid body VRB model of the tool  104  so that the forces and torques can be virtually applied to the virtual rigid body VRB in the virtual simulation VS to ultimately determine how those forces and torques (among other inputs) would affect movement of the virtual rigid body VRB, as described below. 
     The surgical system  100  may also operate in a semi-autonomous mode in which the manipulator  102  moves the tool  104  in an automated manner along the milling path MP, such as by operating active joints J of the manipulator  102  to move the tool  104  without requiring force/torque on the tool  104  from the user. Examples of operation in the semi-autonomous mode are also described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. In some embodiments, when the manipulator  102  operates in the semi-autonomous mode, the manipulator  102  is capable of moving the tool  104  free of user assistance. Here, “free of user assistance” may mean that the user does not physically contact the tool  104  or the robotic arm  108  to move the tool  104 . Instead, the user may use some form of remote control (e.g., a pendant; not shown) to control starting and stopping of movement. For example, the user may hold down a button of the remote control to start movement of the tool  104  and release the button to stop movement of the tool  104 . Examples of this type of remote control embodied in user pendant are described in U.S. Pat. No. 10,117,713, entitled “Robotic Systems and Methods for Controlling a Tool Removing Material from Workpiece,” the disclosure of which is hereby incorporated herein by reference in its entirety. Other configurations are contemplated. 
     In the manual mode, it may be challenging for the user to move the tool  104  from a current state SC to a target state ST (e.g., to a target position PT, a target orientation OT, or a target pose). It may be desirable for the tool  104  to be moved to a particular target state ST for any number of reasons, such as to place the tool  104  in a desired proximity to the milling path MP, to place the tool  104  at an orientation suitable for preparing tissue to receive an implantable component  116 , for aligning the tool  104  with a particular trajectory/plane, and the like. However, it may be difficult for the user to place the tool  104  with sufficient precision. This can be especially difficult when the anatomy of the patient P is partially obstructed from the user&#39;s view by soft tissue, fluids, and the like. Here, the surgical system  100  may be switched from the manual mode to the semi-autonomous mode, such as in the manner described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. Accordingly, to place the tool  104  at the target state ST, the manipulator  102  may autonomously move the tool  104  from the current state SC to the target state ST. 
     Should the user wish to maintain manual contact with the tool  104  to effect control of the tool  104  during movement toward the target state ST, the surgical system  100  may also operate in a guided-haptic mode. The guided-haptic mode may be used to help guide the user into placing the tool  104  at or otherwise in the target state ST (attractive) or to guide the user away from the target state (repulsive). In the guided-haptic mode, aspects of control used in both the manual mode and the semi-autonomous mode are utilized. For example, forces and torques applied by the user are still detected by the sensor  180  to determine the external force F ext  that is fed into the virtual simulation VS to at least partially influence overall movement of the tool  104 . Additionally, in the guided-haptic mode, the surgical system  100  generates virtual attractive (or repulsive) forces VF (or torques) embodied in a virtual constraint VC force F c  that is fed, along with the external force F ext , into the virtual simulation VS. The guided-haptic mode may be used to keep the tool  104  from the target state ST (repulsive haptics), and/or to attract the tool  104  toward the target state ST (attractive haptics). 
     The virtual attractive force VF comprises forces and/or torques that can be virtually applied to the virtual rigid body VRB in the virtual simulation VS and that are adapted to attract or otherwise urge the tool  104  toward the target state ST. The virtual attractive force VF influences overall movement of the tool  104  in a way that provides the user with haptic feedback to indicate to the user how the tool  104  should be moved to reach the target state ST. More specifically, in the virtual simulation VS, the forces and/or torques associated with the virtual attractive force VF may counteract the effects of the forces and/or torques of the external force F ext  (and/or other forces and/or torques) such that the tool  104  is ultimately moved in a way that provides the user with haptic interaction effects which indicate the direction/rotation in which the tool  104  needs to be moved in order to reach the target state ST. Thus, the guided-haptic mode relies on manual manipulation to move the tool  104 , but such movement, instead of merely emulating the movement that would have occurred based on the forces and torques applied by the user, is actively controlled so as to guide the user toward the target state ST. Therefore, the guided-haptic mode allows direct user engagement with the tool  104  while affording the benefits associated with autonomous (or semi-autonomous) movement of the tool  104 . 
     In the guided-haptic mode, the tool  104  is effectively attracted toward the target state ST to provide haptic interaction effects to the user. These effects may be generated in one or more degrees of freedom DOF to attract the tool  104  toward the target state ST. Thus, the target state ST may be defined such that the tool  104  is being attracted in only one degree of freedom DOF, or may be defined such that the tool  104  is being attracted in more than one degree of freedom DOF. Accordingly, the target state ST may comprise a target position PT, target orientation OT, or both (e.g., a target pose TP), defined in a target coordinate system TF. The target position PT may comprise one or more position components with respect to x, y, and/or z axes of the target coordinate system TF (e.g., an x position XP, a y position YP, and/or a z position ZP). In some cases, the target position PT can be represented as the origin of the target coordinate system TF. Similarly, the target orientation OT may comprise one or more orientation components with respect to the x, y, and/or z axes of the target coordinate system TF (e.g., an x orientation XO, a y orientation YO, and/or a z orientation ZO). The x position XP, the y position YP, the z position ZP, the x orientation XO, the y orientation YO, and the z orientation ZO each represent a respective degree of freedom DOF (e.g., of a coordinate system). In some cases, the target orientation OT can be represented as the orientation of the x, y, and z axes of the target coordinate system TF. The term “target pose” TP means a combination of the one or more position components XP, YP, ZP and the one or more orientation components XO, YO, ZO. In some cases, the target pose TP may comprise a target position PT and target orientation OT in all six degrees of freedom DOF of the target coordinate system TF. In some cases, the target position PT and/or the target orientation OT may also be referred to as starting position and/or starting orientation. 
     The target coordinate system TF can be any coordinate system in which the target state ST is defined, and the target state ST can be transformed to any other coordinate system desired for monitoring the current state SC of the tool  104  relative to the target state ST of the tool  104 . The target state ST can be tracked in a tracker coordinate system, the localizer coordinate system LCLZ, the manipulator coordinate system MNPL, the virtual mass coordinate system VM, the tool center point TCP coordinate system, and the like. The target state ST may be defined with respect to the anatomical model AM for the patient P and may be fixed with respect to the anatomy of the patient P in an anatomical model coordinate system, an anatomy tracker coordinate system (e.g., tracked by one or more patient trackers  160 A,  160 B), and the like. The current state SC of the tool  104  may be defined with respect to a guided coordinate system GF. The guided coordinate system GF may be tied to another coordinate system, or the current state SC may be transformed to any the guided coordinate system GF to enable tracking of the current state SC relative to the target state ST. For example, the current state SC can be tracked in a tracker coordinate system, the localizer coordinate system LCLZ, the manipulator coordinate system MNPL, the virtual mass coordinate system VM, the tool center point TCP coordinate system, and the like. In some of the embodiments, the current state SC of the tool  104  may initially be defined by to the tool center point TCP coordinate system (e.g., where the TCP coordinate system and the guided coordinate system GF are shown as being the same for illustrative purposes) and the target state ST may initially be defined with respect to an anatomical model coordinate system, but both the guided coordinate system GF and the target coordinate system TF can be transformed to a common coordinate system for tracking purposes. The target state ST may be defined pre-operatively, intraoperatively, or both. Various aspects of intraoperative planning, anatomical models, and the like are described in U.S. Patent Application Publication No. US 2018/0333207 A1, entitled “Surgical Systems and Methods for Facilitating Ad-hoc Intraoperative Planning of Surgical Procedures,” the disclosure of which is hereby incorporated by reference in its entirety. Other configurations are contemplated. 
     The control system  124  employs virtual constraints VC that are defined to yield the virtual attractive forces VF (e.g., forces and/or torques) employed in the virtual simulation VS that attract the tool  104  to the target state ST. These virtual constraints VC are referred to herein as guide constraints GC. The guide constraints GC are defined to ultimately influence movement of the tool  104  toward the target state ST so that the user is provided with one or more of the haptic interaction effects described above. Generally, virtual constraints VC are restrictions on the motion of rigid bodies that are considered by the control system  124 , along with other motion-related information, to determine how to command the manipulator  102  to move the tool  104 . The guide constraints GC, as described further below, have configurable spring parameters PS and damping parameters PD so that the guide constraints GC are not infinitely stiff. More specifically, in some versions, the guide constraints GC are defined as “soft constraints” such that they do not prevent motion that violates them, such as motion resulting from forces and torques applied by the user in opposite directions to the target state ST. Thus, in the guided-haptic mode or other modes, the user may still be able to influence motion of the tool  104  into a direction opposing the target state ST, in violation of the guide constraints GC, yet the guide constraints GC still act to generate attractive forces and torques opposing the user that the user feels (e.g., haptic interaction effects) so that the user knows which direction the tool  104  should be moved to reach the target state ST. For example, the user may feel these haptic interaction effects by virtue of the ease in which the tool  104  may be moved toward the target state ST, as compared to moving away from the target state ST (e.g., the user may feel as though more work is needed to move the tool  104  away from the target state ST as compared to moving toward the target state ST). In other words, it may feel to the user as though a physical spring interconnects the guided coordinate system GF of the tool  104  with the target coordinate system TF (see illustration of spring and damper in  FIG. 6 ). 
     One or more guide constraints GC may be used by the control system  124  to guide the user, including up to three guide constraints GC associated with the target position PT and up to three guide constraints GC associated with the target orientation OT. As described in greater detail below, the control system  124  operates to calculate the constraint force F c  that satisfies the guide constraints GC (and other virtual constraints VC, if used). The constraint force F c  incorporates the virtual attractive forces VF (e.g., forces and/or torques) therein to attract the tool  104  to the target state ST. Each of the guide constraints GC are considered one-dimensional, virtual constraints VC. In some embodiments, the guide constraints GC are velocity impulse constraints. In some embodiments, the constraints are similar to those used in the impulse modeling described in U.S. Pat. No. 9,119,655, entitled “Surgical Manipulator Capable of Controlling a Surgical Instrument in Multiple Modes,” previously referenced. In some embodiments, these virtual constraints VC are defined exclusively in the guided-haptic mode, and not in the manual mode or the semi-autonomous mode. In some embodiments, virtual constraints VC are used in all modes. Other configurations are contemplated. 
     In  FIG. 6 , three guide constraints GC associated with a target position PT are illustratively represented as being defined in the target coordinate system TF. The constraint force F c  that is ultimately calculated as a result of these three guide constraints GC is illustrated as comprising an attractive force that incorporates spring parameters PS and damping parameters PD that guides the tool center point TCP of the tool  104  to the target position PT (e.g., to the origin of the target coordinate system TF). This is merely one example. The constraint force F c  may comprise components of force and torque to also align the tool  104  with a target orientation. 
     The guide constraints GC (and other virtual constraints VC, if used) are defined primarily by three runtime parameters: a constraint Jacobian Jp, a desired velocity V des  (or Vp2), and a constraint distance Δd. The Jacobian Jp maps each one-dimensional, guide constraint GC to a coordinate system employed for the virtual simulation VS (e.g., the virtual mass coordinate system VM). The desired velocity V des  (or Vp2) is a scalar velocity of the guide constraint GC in the target coordinate system TF. Here, the desired velocity V des  may be zero when the patient P is immobile and the associated target state ST defined relative to the patient P is not moving, but may not be zero when the patient P moves since the target state ST may be tied to the patient P. The constraint distance Δd refers to how close the guided coordinate system GF is to the constraint and dictates whether the constraint is being violated. In some cases, Δd refers to a distance/angle of the current state SC from the target state ST, and a guide constraint GC is violated any time the current state SC does not match the target state ST for the associated degree of freedom. 
     The guide constraints GC are not perfectly rigid, but instead each of the guide constraints GC has tuning parameters TPA to adjust the stiffness of the virtual constraints VC (e.g., by incorporating spring parameters PS and/or damping parameters PD). Such tuning parameters TPA may include a constraint force mixing parameter C and an error reduction parameter E. The spring parameters PS and damping parameters PD may be adjusted during operation in the guided-haptic mode, or during other modes as described in greater detail below. In some embodiments, values for the tuning parameters TPA may change based on a relationship between the current state SC and the target state ST. For example, the tuning parameters TPA may be configured to increase in stiffness the closer the tool  104  gets to the target state ST, or the tuning parameters TPA may decrease in stiffness as the tool  104  approaches the target state ST. The tuning parameters TPA may be different for different guide constraints GC. For example, the guide constraints GC may comprise a first virtual constraint VC that has a first value for a tuning parameter TP 1  and a second virtual constraint VC that has a second value for the tuning parameter TPA, the first value being greater than the second value so that the resulting virtual attractive force VF (e.g., forces and/or torques) embodied in the constraint force F c  is adapted to attract the tool  104  more strongly as a result of the first virtual constraint VC as compared the second virtual constraint VC. The values of the tuning parameters TPA may be greater (e.g., stiffer) for position constraints than for orientation constraints, or vice versa. Other configurations are contemplated. 
     The tuning parameters TPA may also be set to: remain constant regardless of the distance/angle from the current state SC to the target state ST; rise/fall exponentially with distance between the current state SC to the target state ST; vary linearly with distance between the current state SC and the target state ST; vary with constraint direction; take gravitational effects into account; and the like. A tuning parameter TPA for one virtual constraint VC associated with one degree of freedom DOF may be set based on a relationship associated with another degree of freedom DOF (e.g., the stiffness of an x-axis constraint may change based on the distance along the y-axis between the current state SC and the target state ST). The tuning parameters TPA may also vary depending on the direction in which the tool  104  needs to move in order to reach the target state ST (e.g., more stiff when moving in one direction along the x-axis when compared to the opposite direction along the x-axis). The tuning parameters TPA can also be scaled depending on the constraint force F c  that is ultimately computed based on the guide constraints GC, such as by increasing/decreasing the stiffness depending on the magnitude of the constraint force F c , or any components thereof. Fixed values for one or more virtual attractive forces VF could also be added into the virtual simulation VS in some cases. 
     The tuning parameters TPA for the guide constraints GC may be set so that the user can easily cause the tool  104  to move away from the target position PT and/or target orientation OT. In other words, the tuning parameters TPA may be set so that, in the virtual simulation VS, the influence of the forces and torques applied by the user may outweigh the influence of the virtual attractive forces VF (e.g., forces and torques). Thus, the control system  124  may be configured to enable the user to reposition and/or reorient the tool  104  away from the target position PT and/or the target orientation OT even when the guide constraints GC are enabled. The tuning parameters TPA for the guide constraints GC may be set preoperatively or intraoperatively, may be updated intraoperatively, or combinations thereof. The tuning parameters TPA and their values, their correlation to a particular relationship, and the manner in which they may be scaled, could be stored in one or more look-up tables in any suitable memory  140  of the control system  124  for later retrieval. 
     Each guide constraint GC also has configuration parameters CPA. The configuration parameters CPA may comprise: information regarding the tuning parameters TPA such as the constraint force mixing parameter C and the error reduction parameter E; upper force limits FLU and/or lower force limits FLL; and/or upper constraint distance offsets DOU and/or lower constraint distance offsets DOL. The upper and lower force limits FLU, FLO refer to limits on the forces computed for each guide constraint GC that are ultimately solved by the constraint solver  192  to produce the constraint force F c , as described further below. The guide constraints GC are two-sided constraints (e.g., the forces computed to satisfy the constraints can be positive or negative), the force limits FLU, FLO can be set high in positive and negative directions (e.g., −100,000/+100,000 Newtons) or at any desired limit. The upper and lower constraint distance offsets DOU, DOL dictate when the constraint is active. With respect to the guide constraints GC, the upper and lower constraint distance offsets DOU, DOL can be set so that the constraint is active any time the current state SC is different than the target state ST. 
       FIG. 7  illustrates processes carried out to execute the guided-haptic mode in some embodiments. Here, the behavior control  178  comprises a path handler  188 , a guide handler  190 , a constraint solver  192 , and a virtual simulator  194 . The behavior control  178  further comprises a boundary handler  196  to generate virtual boundary constraints BC based on the one or more virtual boundaries  174  generated by the boundary generator  172 . The path handler  188 , guide handler  190 , constraint solver  192 , virtual simulator  194 , and boundary handler  196  each comprise executable software stored in a non-transitory memory  140  of any one or more of the aforementioned controllers  132 ,  134 ,  136  and implemented by the control system  124 . Each of the portions of the behavior control  178  introduced above will be described in greater detail below. 
     The guide handler  190  obtains the target state ST for the tool  104  and generates one or more guide constraints GC based on the target state ST and the current state SC of the tool  104 . As shown in  FIG. 7 , two inputs into the guide handler  190  comprise the current state SC and the target state ST. The current state SC may be defined with respect to the last commanded pose CP, since the last commanded pose CP correlates to the current pose of the tool  104 . The target state ST may be defined in the anatomical coordinate system, anatomy tracker coordinate system, and the like, and transformed to a common coordinate system with the current state SC. Other inputs into the guide handler  190  comprise the configuration parameters CPA and tuning parameters TPA for the guide constraints GC. The guide handler  190  defines the one or more guide constraints GC based on the relationship between the currents state SC and the target state ST, and the configuration parameters CPA and the tuning parameters TPA. The guide constraints GC are output from the guide handler  190  into the constraint solver  192 . 
     Various virtual constraints VC may be fed into the constraint solver  192 , including guide constraints GC, path constraints PC, boundary constraints BC, and other constraints. These virtual constraints VC may be turned on/off by the control system  124 . For example, in some cases, there may be no path constraints PC, no boundary constraints BC, and no other constraints being generated. Similarly, there may be no guide constraints GC being generated in some instances, and in certain modes of operation. All of the virtual constraints VC employed in the behavior control  178  may affect movement of the tool  104 . For purposes of illustration, only the guide constraints GC will be described in detail. 
     The constraint solver  192  calculates the constraint force F c  to be virtually applied to the tool  104  in the virtual simulator  194  based on the virtual constraints VC fed into the constraint solver  192 . In the guided-haptic mode, the constraint force F c  comprises components of force and/or torque adapted to attract the tool  104  toward the target state ST from the current state SC based on the one or more guide constraints GC. In cases where only the guide constraints GC are input into the constraint solver  192 , the constraint force F c  can be considered to be the virtual attractive force VF described above. However, when other virtual constraints VC are employed, the constraint solver  192  is ultimately tasked with providing a solution for the constraint force Fc that satisfies all of the virtual constraints VC, and thus other virtual constraints VC may also influence the magnitude/direction of the constraint force F c . In those cases, the virtual attractive forces VF (e.g., forces and/or torques) are considered those force and torque components of the constraint force F c  that are directed toward the target state ST as a result of the guide constraints GC. 
     Referring to the constraint equation CEQ shown in  FIG. 8 , the constraint solver  192  places the constraint data for each virtual constraint VC into a corresponding row of a constraint equation CEQ, in matrix form, to solve for F p . Here, F p  is a force vector in the target coordinate system TF, whereby each component of F p  is a scalar constraint force acting in the corresponding constraint direction. In order to solve for F p , as described in greater detail below, the equation shown in  FIG. 8  is converted into a matrix equation where each row represents a single, one-dimensional virtual constraint VC. The constraint data are placed in the constraint equation CEQ, along with other information known by the constraint solver  192  such as the external force F cgext , a damping force F damping , an inertial force F inertial , a virtual mass matrix M, a virtual mass velocity V cg1 , and the time step Δt (e.g., 125 microseconds). 
     The virtual mass matrix M combines 3×3 mass and inertia matrices. The damping and inertial forces F damping  and F inertial  are calculated or otherwise known by the virtual simulator  194  and are based on the virtual mass velocity V cg1  (e.g., the velocity of the virtual mass coordinate system VM) output by the virtual simulator  194  in a prior time step. The virtual mass velocity V cg1  is a six degree of freedom DOF velocity vector comprising linear and angular velocity components. The damping force F damping  is a six degree of freedom DOF force/torque vector computed as a function of the virtual mass velocity V cg1  and a damping coefficient matrix (linear and rotational coefficients may not be equal). Damping is applied to the virtual mass to improve its stability. The inertial force F inertial  is also a six degree of freedom DOF force/torque vector computed as a function of the virtual mass velocity V cg1  and the virtual mass matrix M. The damping and inertial forces, F damping  and F inertial , can be determined in the manner described in U.S. Pat. No. 9,566,122, entitled “Robotic System and Method for Transitioning Between Operating Modes,” the disclosure of which is hereby incorporated herein by reference in its entirety. 
     The constraint solver  192  may be configured with any suitable algorithmic instructions (e.g., an iterative constraint solver, a Projected Gauss-Seidel solver, and the like) to solve the system of constraint equations CEQ in order to provide a solution which best satisfies the system of equations (e.g., best satisfying the various virtual constraints VC). In some cases, all virtual constraints VC may not simultaneously be met. For example, in the case where motion is over-constrained by the various virtual constraints VC, the constraint solver  192  will essentially find a “best fit” solution given the relative stiffness/damping of the various virtual constraints VC. The constraint solver  192  solves the system of equations and ultimately outputs the constraint force F c . 
     When a Projected Gauss-Seidel solver is employed, the constraint solver  192  constructs A and b matrices based on the virtual constraints VC, and uses Projected Gauss-Seidel to solve the system of equations to determine the resulting force vector F p . The constraint solver  192  then takes the output of Projected Gauss-Seidel and transforms it from the target coordinate system TF (e.g., the constraint coordinate system) to the virtual mass coordinate system VM. For example, using the equation F c =J p   T  F p , wherein F c  is the constraint force, each resulting force vector F p  is converted to a force/torque vector applied to the virtual mass coordinate system VM. 
     Methods of using Project Gauss-Seidel to solve a system of equations for multiple constraints is shown, for example, in “Constraint based physics solver” by Marijn Tamis and Giuseppe Maggiore, dated Jun. 15, 2015 (v1.02), which can be found at http://www.mft-spirit.nl/files/MTamis_ConstraintBasedPhysicsSolver.pdf; or in “Comparison between Projected Gauss-Seidel and Sequential Impulse Solvers for Real-Time Physics Simulations,” by Marijn Tamis, dated Jul. 1, 2015 (v1.01), which can be found at http://www.mft-spirit.nl/files/MTamis_PGS_SI_Comparison.pdf; both of which are hereby incorporated herein by reference in their entirety. 
     The Projected Gauss-Seidel method addresses Linear Complementarity Problems LCP. Inequality associated with LCP arises since some constraint types (e.g., one-sided virtual constraints VC such as the boundary constraints BC) can only push or “apply force” in one direction (e.g., positive constraint force). If the calculated force for such a virtual constraint VC is negative (or, more broadly, is outside of its allowed range) for a given iteration of the constraint solver  192 , which is invalid, the given virtual constraint VC must be pruned (or alternately limited/capped at its upper or lower allowed value FLU, FLO) and the remaining virtual constraints VC solved until a suitable result (e.g., convergence) is found. In this manner, the constraint solver  192  determines the active set of virtual constraints VC for a given time step, and then solves for their values. Other virtual constraint VC types can apply forces in both positive and negative directions (e.g., two-sided virtual constraints VC). Such virtual constraints VC include the guide constraints GC used to guide the user into moving the tool  104  toward the target state ST. Such two-sided virtual constraints VC, when enabled, are usually active and not pruned/limited during the constraint solver  192  iterations. 
     The constraint force F c  calculated by the constraint solver  192  comprises three components of force along x, y, z axes and three components of torque about the x, y, z axes. The virtual simulator  194  utilizes the constraint force F c , along with the external force F cgext , the damping force F damping , and the inertial force F inertial  (all of which may comprise six components of force/torque), in its virtual simulation VS. In some cases, these components of force/torque are first transformed into a common coordinate system (e.g., the virtual mass coordinate system VM) and are then summed to define a total force F T . The resulting six degree of freedom DOF force (e.g., force and torque) is applied to the virtual rigid body VRB and the resulting motion is calculated by the virtual simulator  194 . The virtual simulator  194  thus acts to effectively simulate, among other things, how the various virtual constraints VC affect motion of the virtual rigid body VRB. The virtual simulator  194  performs forward dynamics to calculate the resulting six degree of freedom DOF pose and velocity of the virtual rigid body VRB based on the given total force F T  being applied to the virtual rigid body VRB. In some embodiments, the virtual simulator  194  comprises a physics engine realized as executable software stored in a non-transitory memory  140  of any one or more of the aforementioned controllers  132 ,  134 ,  136  and implemented by the control system  124 . 
     For the virtual simulation VS, the virtual simulator  194  models the tool  104  as the virtual rigid body VRB in the virtual mass coordinate system VM, with the origin of the virtual mass coordinate system VM being located at the center of mass of the virtual rigid body VRB, and with the coordinate axes being aligned with the principal axes of the virtual rigid body VRB. The virtual rigid body VRB is a dynamic object and a rigid body representation of the tool  104  for purposes of the virtual simulation VS. The virtual rigid body VRB is free to move according to six degrees of freedom DOF in Cartesian space according to the virtual simulation VS. The virtual simulation VS may be processed computationally without visual or graphical representations. Thus, it is not required that the virtual simulation VS display dynamics of the virtual rigid body VRB. In other words, the virtual rigid body VRB need not be modeled within a graphics application executed on a processing unit. The virtual rigid body VRB may exist only for the virtual simulation VS. However, other configurations are contemplated. 
     The virtual rigid body VRB and its properties (e.g., mass, inertia matrix, center of mass, principal axes, and the like) define how the tool  104  will move in response to applied forces and torques (e.g., from the total force F T , which incorporates forces and torques applied by the user and virtual attractive forces VF and/or torques). The virtual rigid body VRB governs whether the tool  104  will feel heavy or light and how it will move (e.g., accelerate in translation and/or rotation) in response to applied forces and torques. By adjusting the properties of the virtual rigid body VRB, the control system  124  can adjust how the tool  104  feels to the user. It may be desirable to have the properties of the virtual rigid body VRB modeled so as to be reasonably close to the actual properties of the tool  104 , such as to afford motion/feel that is as realistic as possible, but that is not required. For control stability reasons (e.g., given the finite acceleration of the manipulator, control latencies, and the like), the virtual mass and inertia may be modeled to be somewhat higher than that of the physical tool  104 . 
     The virtual rigid body VRB may correspond to components which may be on or within the tool  104 . Additionally, or alternatively, the virtual rigid body VRB may extend, in part, beyond the physical tool  104 . The virtual rigid body VRB may consider the tool  104  with the energy applicator  114 , or may consider the tool  104  without the energy applicator  114 . Furthermore, the virtual rigid body VRB may be based on the tool center point TCP. In one example, the center of mass of the virtual rigid body VRB is understood to be the point around which the virtual rigid body VRB would rotate if a virtual force were applied to another point of the virtual rigid body VRB and the virtual rigid body VRB were otherwise unconstrained (e.g., not constrained by the manipulator  102 ). The center of mass of the virtual rigid body VRB may be close to, but need not be the same as, the actual center of mass of the tool  104 . The center of mass of the virtual rigid body VRB can be determined empirically. Once the tool  104  is attached to the manipulator  102 , the position of the center of mass can be reset to accommodate the preferences of the individual users. 
     The virtual simulator  194  effectively simulates rigid body dynamics of the tool  104  by virtually applying forces and/or torques on the virtual rigid body VRB in the virtual simulation VS, such as by virtually applying the components of force and torque from the total force F T  on the center of mass of the virtual rigid body VRB in the virtual mass coordinate system VM. Thus, the forces/torques virtually applied to the virtual rigid body VRB may comprise forces/torques associated with the external force F cgext  (e.g., based on input from one or more sensors  180 ), the damping force F damping , the inertial force F inertial , and the forces/torques from the constraint force F c  associated with the various virtual constraints VC (by virtue of being embodied in the constraint force F c ). 
     Rigid body Jacobians can be used to transform velocities and forces from one coordinate system (or “reference frame”) to another on the same virtual rigid body VRB, and may be employed here to transform the forces and torques of the external force F ext  to the virtual mass coordinate system VM (e.g., to yield the external force F cgext  used in the constraint equation CEQ). The virtual simulator  194  then internally calculates the damping force F damping  and the inertial force F inertial  to determine the total force F T , and also to output the damping force F damping  and the inertial force F inertial  for use by the constraint solver  192  in its system of equations in the next time step. 
     A virtual forward dynamics algorithm VFA, as shown in  FIGS. 9 and 10 , may be employed in the virtual simulation VS to simulate the motion of the virtual rigid body VRB as it would move upon application of the total force F T . Effectively, the virtual forward dynamics algorithm VFA solves the equation F=ma (or a=F/M) in six degrees of freedom DOF and integrates the acceleration to yield velocity, which is then used to determine a new pose, as shown in  FIG. 10 . The control system  124  inputs the virtual forces and/or torques (e.g., the total force F T ) into the virtual simulator  194  and these virtual forces and/or torques are applied to the virtual rigid body VRB at the center of mass (e.g., the CG) in the virtual simulation VS when the virtual rigid body VRB is in the initial pose with the initial velocity. The virtual rigid body VRB is moved to a final pose having a different state (e.g., position and/or orientation) and with a final velocity within Cartesian space in response to the control system  124  satisfying the inputted virtual forces and/or torques. The next commanded pose CP to be sent to the motion control  182  is based on the final pose calculated by the virtual simulator  194 . Thus, the virtual simulator  194  operates to determine the next commanded pose CP by simulating the effects of applying the total force F T  on the virtual rigid body VRB using virtual forward dynamics as shown in  FIG. 10 . 
     Velocity limits VL may be imposed on the virtual rigid body VRB in the virtual simulation VS. In some cases, the velocity limits VL may be set high so that they generally don&#39;t affect the virtual simulation VS, or they may be set at any desired value. The virtual rigid body VRB is in an initial pose (e.g., an initial state) and has an initial velocity at commencement of each iteration of the virtual simulation VS (e.g., at each time step/interval dt). The initial pose and the initial velocity may be defined as the final pose and the final velocity output by the virtual simulator  194  in the previous time step. 
     Ultimately, the virtual simulator  194  calculates and outputs the next commanded pose CP based on its virtual simulation VS. The control system  124  is configured to command the manipulator  102  to move the tool  104  based on the commanded pose CP, which ideally causes movement of the tool  104  in a manner that guides the user into placing the tool  104  at the target state ST by providing haptic feedback to the user that guides the user toward placing the tool  104  at the target state ST. Thus, the user is able to manually manipulate the tool  104 , while the control system  124  assists in guiding the tool movement, by utilizing the guide constraints GC. The forces and torques applied to the tool  104  by the user (e.g., detected by the sensor  180 ) may still influence the overall movement of the tool  104  because the external force F ext  is combined with the constraint force F c  before running the virtual simulation VS to determine the commanded pose CP. In some instances (e.g., time steps), the total force F T  includes components of force and torque form the external force F ext  with magnitude and direction sufficient to overcome the forces and torques of the constraint force F c  such that the tool  104  is movable away from the target state ST. However, as noted above, the guide constraints GC have configurable stiffness and damping (e.g., based on the spring parameters PS and the damping parameters PD) that can be tuned such that the external force F ext  has less influence in certain situations. 
       FIG. 11  summarizes various steps carried out by the behavior control  178 . These include steps performed by the constraint solver  192  and the virtual simulator  194  as described above. In step  1100 , the external force F ext  is calculated based on readings taken from the sensor  180 . In step  1102 , the constraints data associated with the various virtual constraints VC are fed into the constraint solver  192  from the path handler  188 , from the guide handler  190 , from the boundary handler  196 , and/or from other constraint sources. 
     In steps  1104 - 1108 , rigid body calculations are carried out by the virtual simulator  194  to determine the inverse mass matrix M −1 , the inertial force F inertial , and the damping force F damping  of the virtual rigid body VRB. In steps  1110 - 1114 , the constraint solver  192  utilizes the output from the rigid body calculations performed in steps  1104 - 1108  and the constraints data provided in step  1102  to perform the constraint force calculations previously described to ultimately yield the constraint force F e . In step  1116 , the constraint force F c  is summed with the external force F ext  transformed to the virtual mass coordinate system VM (F cgext ), the damping force F damping , and the inertial force F inertial  to yield the total force F T . In step  1118 , the total force F T  is applied to the virtual rigid body VRB in the virtual simulation VS conducted by the virtual simulator  194  to determine a new pose and velocity of the virtual rigid body VRB in step  1120 , and ultimately to transform the new pose and velocity to the tool center point TCP in step  1122 . The new commanded pose CP (TTCP) and velocity (V TCP ) are output by the virtual simulator  194  in step  1124 . 
     Referring now to  FIG. 12 , portions of the surgical system  100 , including one of the tools  104  of  FIG. 1 , and a generically-depicted target site TS are shown schematically, with the target site TS shown supported on a work surface WS such as a surgical table (not shown in detail). Here, the target site TS represents a portion of the anatomy of the patient P, such as a bone or another type of tissue, that is to be treated during a surgical procedure. To this end, the tool  104  is shown spaced from the target site TS along the trajectory T which, as noted above, is monitored or otherwise known by the navigation system  128  from tracked states of the first patient tracker  160 A secured to the target site TS. For illustrative purposes, the first tool tracker  160 G is shown firmly fixed to the tool  104 . However, while the navigation system  128  can track states of multiple trackers  160  within a common coordinate system as noted above, the pose of a tracked object (e.g., the tool  104 ) can be determined in other ways (e.g., based on known geometric relationships) and transformed between coordinate systems (e.g., between the manipulator coordinate system MNPL and the localizer coordinate system LCLZ). Put differently, the surgical system  100  can determine changes in the pose of the tool  104  relative to the first patient tracker  160 A without necessarily utilizing the illustrated first tool tracker  160 G because, among other things, the geometry of the tool  104  and the energy applicator  114  are known. 
     In this representative example, the tool  104  similarly comprises the mount  148  (depicted in phantom) to facilitate releasable attachment to the coupling  110  of the manipulator  102 , and the instrument  112  is realized as a powered surgical device  150  with a power generation assembly  152  (depicted in phantom) that is driven by the tool controller  136  or another part of the control system  124 . Here, the power generation assembly  152  is realized as an electric motor configured to selectively generate rotational torque about a drive axis AD to drive one or more types of energy applicators  114 . To this end, the powered surgical device  150  comprises a chuck assembly  198  (see  FIG. 12 ; depicted in phantom) disposed in rotational communication with the power generation assembly  152  to facilitate releasable attachment of the energy applicator  114  which, in this illustrative embodiment, is realized by the bur  154  (attachment not shown in detail). However, the tool  104 , the instrument  112 , and/or the energy applicator  114  could be of a number of different configurations without departing from the scope of the present disclosure. Here, the tool  104  comprises a handling region  200  arranged to be grasped by the user, with a trigger that may serve as an input device  146  (e.g., to start and stop rotation of the energy applicator  114 ). In some embodiments, tool  104  and/or the powered surgical device  150  may be like that shown in U.S. Pat. No. 9,566,121, entitled “End Effector of a Surgical Robotic Manipulator,” previously referenced. In some embodiments, the tool  104  and/or the powered surgical device  150  may be like that shown in U.S. Patent Application Publication No. US 2018/0110572 A1, entitled “Systems and Tools for Use With Surgical Robotic Manipulators,” the disclosure of which is hereby incorporated by reference in its entirety. Other configurations are contemplated. 
     With continued reference to  FIG. 12 , the power generation assembly  152  of the powered surgical device  150  is operatively attached to the mount  148  by a frame  202  (generically depicted in phantom), such as by one or more fasteners (not shown). While the frame  202  is formed separately from the mount  148  in the illustrated embodiment, other configurations are contemplated, and the mount  148  could be formed from or otherwise realized by any suitable number of components sufficient to facilitate coupling to the manipulator  102 . Similarly, the frame  202  could similarly be defined by a number of different components which cooperate to support the power generation assembly  152  and other parts of the tool  104 . In some embodiments, one or more covers  204  may be employed by tool  104  to conceal, protect, or otherwise shield certain components (e.g., the mount  148 ) from the outside environment. The covers  204  may also conceal electrical components (e.g., wires, electrical connectors, printed circuit boards, and the like), and may be shaped and arranged to permit access to a sterile interface system (not shown, but generally known in the related art) arranged between the mount  148  and the coupling  110  of the manipulator  102  to facilitate removably attaching the tool  104  to the manipulator  102 . Here, releasable attachment of the coupling  110  to the mount  148  could be achieved in a number of different ways sufficient to secure the tool  104  to the manipulator  102 . 
     In  FIG. 12 , a portion of the target site TS is shown in phantom to depict the intended volume of tissue (e.g., bone) to be removed by the bur  154  along the trajectory T which, for illustrative purposes, serves as the milling path MP in this representative example. Here too, the intended “depth” of tissue removal at the target site TS is represented by a target reference point TRP which, like the tool center point TCP, could be defined as a coordinate system. Here, both the tool center point TCP and the target reference point TRP are shown arranged along the trajectory T. 
     Continuing to  FIG. 13A  from  FIG. 12 , the tool  104  has been advanced along the trajectory T into engagement with the target site TS, such as by operating the manipulator  102  in one or more of the various modes described herein, with the bur  154  of the energy applicator  114  disposed along the trajectory T maintained by the manipulator  102 . More specifically, the tool center point TCP of the energy applicator  114  defined by the bur  154  is disposed along the trajectory T, with the energy applicator  114  rotating about the drive axis AD, which is likewise aligned with the trajectory T. Here, the tool center point TCP is spaced from the target reference point TRP to illustrate the remaining volume of tissue (e.g., bone) to be removed by the bur  154  as the tool  104  is advanced along the trajectory T. This is depicted in  FIG. 13B , which shows the tool center point TCP arranged closer to the target reference point TRP (compare  FIG. 13B  with  FIG. 13A ). 
       FIGS. 14A-14D  sequentially illustrate a hypothetical “runaway” condition of the surgical system  100  which may occur under certain use cases which result in the energy applicator  114  or another part of the tool  104  becoming effectively “attached” to the manipulator  102  such that the target site TS and tool  104  move together in one or more degrees of freedom DOF, either momentarily or for an extended duration. Here, by way of illustrative example, the energy applicator  114  could potentially encounter changes in tissue types or properties, irregularities, or other types of increased resistance caused such as by friction and/or heat, reduced cutting performance, the accumulation of tissue fragments (e.g., “swarf”), and the like, which may be significant enough to interrupt tissue removal and result in the energy applicator  114  becoming “locked” to the tissue at the target site TS, either momentarily or for an extended period. In some cases, the resistance described above can result in the energy applicator  114  being “locked” to tissue at the target site TS off of the trajectory T. 
     The hypothetical scenario described above may be illustrated by comparing  FIGS. 14A-14B . Here, in  FIG. 14A , the energy applicator  114  is engaging the target site TS and encounters a significant resistance to rotation about the drive axis AD which brings the tool center point TCP off of the trajectory T maintained by the manipulator  102  and results in the energy applicator  114  becoming “locked” to the target site TS, as is depicted by the exaggerated misalignment between the trajectory T and the drive axis AD illustrated in  FIG. 14B . While the target state ST of the tool  104  could be defined in a number of different ways, for illustrative purposes in this representative example, the target state ST includes coincident alignment between the drive axis AD and the trajectory T. However, because the current state SC of the tool  104  shown in  FIG. 14B  includes misalignment between the drive axis AD and the trajectory T with the energy applicator  114  “locked” to the target site TS, a “runaway” condition may occur as the manipulator  102  attempts to move from the current state SC to the target state ST. The “runaway” condition may also occur as a result of the patient tracker  160  becoming loose from the target site TS thereby causing a loss of tracking accuracy. 
     In this illustrative example, and as is shown by successively comparing  FIGS. 14B-14D , movement of the tool  104  toward the target state ST also results in corresponding movement of the target site TS which, as noted above, defines the trajectory T (and, thus, the target state ST) based on the tracked states of the first patient tracker  160 A monitored by the navigation system  128 . Put differently, as the manipulator  102  attempts to move the tool  104  from the current state SC to the target state ST (e.g., such that the drive axis AD comes back into coincident alignment with the trajectory T), the target site TS moves together with the tool  104  and the target state ST is not reached (e.g., coincident alignment does not occur). As is depicted in  FIGS. 14C-14D , this may ultimately result in the target site TS being “lifted off” of the work surface WS. 
     Various techniques for detecting and/or responding to “runaway” conditions as they occur are disclosed herein. To this end, and as is described in greater detail below, in some embodiments, the surgical system  100  employs the tool  104  for engaging the target site TS, with the manipulator  102  configured to support the tool  104  relative to the target site TS (e.g., in a target state ST where the tool center point TCP is positioned along the trajectory T). As is described in greater detail below, a sensing system  206  (see  FIGS. 1-2 ) is configured to detect one or more system conditions SYC associated with one or more of the tool  104 , the manipulator  102 , the target site TS, or combinations thereof. The controller  124  (e.g., the manipulator controller  132 , the tool controller  136 , or another suitable controller of the surgical system  100 ; see  FIG. 25 ) coupled to the manipulator  102  and the sensing system  206  is configured to operate the manipulator  102  between: a first mode M 1  to maintain alignment of the tool  104  with respect to the target site TS according to a first constraint criteria C 1 ; and a second mode M 2  to maintain alignment of the tool  104  with respect to the target site TS according to a second constraint criteria C 2  different from the first constraint criteria C 1 . The controller  124  is further configured to change operation of the manipulator  102  from the first mode M 1  to the second mode M 2  in response to determining that at least one of the one or more system conditions SYC satisfies a predetermined condition PR. While the sensing system  206 , the system conditions SYC, the first and second modes M 1 , M 2 , the first and second constraint criteria C 1 , C 2 , and the predetermined condition PR are each described in greater detail below, the techniques described herein can be utilized both in connection with tools  104  which engage the target site TS via energy applicators  114 , as well as in connection with tools  104  which engage the target site TS via implantable components  116 , such as is depicted in  FIG. 15 . However, other configurations are contemplated, and additional techniques are described in greater detail below. 
     In some implementations, the first mode M 1  and second mode M 2  are separate and discrete operating modes of the manipulator  102  that can be activated and deactivated and such as wherein the user can be directly informed of the mode change or wherein there is a pause between mode changes. Alternatively, however, in another implementation, the first and second modes M 1  and M 2  can be understood as different manners of controlling the manipulator  102  according to a feedback control scheme. For example, the constraint criteria C 1 , C 2  can be changed in real-time or near real-time without activating or deactivating any particular mode, without directly informing the user, or without pausing between mode changes. In other words, the constraint criteria C 1 , C 2  can be changed in a seamless transition with or without the user even being aware or initiating any of the modes M 1 , M 2 . Any combination of these implementations is contemplated and the terms “first mode” and “second mode” should understood to include either of these implementations without limitation. 
     In one implementation, the first and second constraint criteria C 1 , C 2 , and values of any parameters associated therewith, are preoperatively determined or predetermined based on information such as clinical data, experimental data, surgeon preferences, or system default settings. In another implementation, the first and second constraint criteria C 1 , C 2 , and values of any parameters associated therewith, can be dynamically and intraoperatively determined and/or adjusted by the controller based on measurements from the sensing system, sensor, navigation system or the like, detecting the system conditions SYC or force occurring between the target site and the manipulator. In other implementations, one of the first and second constraint criteria C 1 , C 2  are preoperatively determined or predetermined and the other one of the first and second constraint criteria C 1 , C 2  are intraoperatively determined. 
     Referring now to  FIG. 15 , portions of the surgical system  100 , including one of the tools  104  of  FIG. 1 , is shown adjacent to a generically-depicted target site TS. In this embodiment, the tool  104  is configured to facilitate impacting an implantable component  116  (e.g., a prosthetic acetabular cup) at the target site TS (e.g., a reamed acetabulum) along the trajectory T maintained by the manipulator  102 . To this end, the instrument  112  of the tool  104  is realized as a guide  208  which, among other things, is configured to attach to the coupling  110  of the robotic arm  108  and supports an impactor assembly  210  for relative movement in one or more degrees of freedom, as described in greater detail below. The impactor assembly  210  comprises, among other things, an interface  212  to releasably secure the implantable component  116 , and a head  214  arranged to receive impact force FI (e.g., applied such as by striking the head  214  with a mallet). 
     In the representative embodiments illustrated herein, the implantable component  116  is a generally hemispherical-shaped cup which forms part of an artificial hip joint adapted for impaction into the patient&#39;s P acetabulum. Prior to impaction, the patient&#39;s P acetabulum is reamed or otherwise prepared so as to define the target site TS. The reaming, preparing, and impaction processes are described in detail in U.S. Pat. No. 8,979,859 entitled “Depth of Impaction;” and U.S. Pat. No. 8,753,346 entitled “Tool, Kit-of-Parts for Multi-Functional Tool, and Robotic System for Same,” the disclosures of which are each hereby incorporated by reference in their entirety. While the present disclosure describes various orthopedic procedures involving hip joints, the subject matter described herein may be applicable to other joints in the patient&#39;s P body B, such as for example, shoulders, elbows, wrists, spines, knees, ankles, and the like. Furthermore, the surgical system  100  of the present disclosure may be utilized in connection with a number of different types of orthopedic procedures, and the implantable component  116  could be of a number of different types, styles, configurations, and the like (e.g., cups, stems, screws, pins, rods, wires, anchors, prostheses, and the like). Accordingly, various tools  104  are contemplated, and various styles, types, and/or configurations of guides  208 , impactor assemblies  210 , and/or implantable components  116  could be utilized without departing from the scope of the present disclosure. 
     Referring now to  FIGS. 15-17B , the representative embodiment of the guide  208  is configured to facilitate advantageous positioning of the implantable component  116  together with the impactor assembly  210  before movement of the impactor assembly  210  and the implantable component  116  is limited by support from the guide  208  (and, thus, the manipulator  102 ). Put differently, the user (e.g., a surgeon) can approach the target site TS with the implantable component  116  manually and without initially having to support the impactor assembly  210  with the guide  208 . After the approach has been completed manually and the implantable component  116  has been disposed at the target site TS, the surgeon can subsequently articulate the implantable component  116  and the impactor assembly  210  into engagement with the guide  208  in a quick, efficient, and reliable manner to facilitate aligning the implantable component  116  with the trajectory T maintained by the manipulator  102 . With proper alignment maintained, the surgeon can apply impact force FI to the head  214  of the impactor assembly  210  to install the implantable component  116  into the target site TS. To this end, and as is described in greater detail below, the guide  208  is configured to permit movement of the impactor assembly  210  in one or more degrees of freedom relative to the guide  208  under certain operating conditions of the surgical system  100 . 
     Referring now to  FIGS. 16A-16B , the impactor assembly  210  generally comprises the interface  212  to releasably secure the implantable component  116 , and the head  214  arranged to receive impact force FI, as noted above. The impactor assembly  210  also comprises a flange  216  defining a first engagement surface  218  which, as described in greater detail below, abuts the guide  208  to limit movement of the impactor assembly  210  during use. The impactor assembly  210  generally extends along a first axis A 1  between a distal end  220  adjacent to the interface  212 , and a proximal end  222  adjacent to the head  214 . The flange  216  is arranged between the interface  212  and the head  214 , has a spherical profile defining the first engagement surface  218 , and defines a flange reference point FRP along the first axis A 1  that is arranged in the center of the flange  216  (e.g., at the geometric center of the spherical profile which defines the first engagement surface  218 ). Similarly, the implantable component  116  defines a implant reference point IRP along the first axis A 1  of the impactor assembly  210  to which the prosthesis is releasably attached (see  FIG. 15 ), and the target site TS defines a target reference point TRP along the trajectory T (see  FIG. 15 ). A shaft  224  extends along the first axis A 1  from the distal end  220  to the flange  216 , and a handle  226  with a grip  228  extends between the flange  216  and the head  214 . Each of the components of the impactor assembly  210  introduced above will be described in greater detail below. 
     In the representative embodiment illustrated herein, the head  214 , the flange  216 , and the shaft  224  are defined by an impactor body, generally indicated at  230 , and the interface  212  is defined by a carrier shaft  232  which is accommodated within the impactor body  230 . More specifically, the impactor body  230  defines a hollow region  234  which extends along the first axis A 1  from the distal end  220 , through the shaft  224  and the handle  226  towards the head  214 . The carrier shaft  232  generally extends along the first axis A 1  between a distal shaft end  236  and a proximal shaft end  238 , with one or more bearing regions  240  provided therebetween to facilitate rotation and force distribution. The interface  212  is arranged at the distal shaft end  236 , and releasably engages the implantable component  116  such that the impactor assembly  210  and the implantable component  116  move together when attached. To this end, the interface  212  and the implantable component  116  are each provided with a respective threaded engagement, generally indicated at  242  (e.g., internal and external threads; see  FIG. 16A ), which allows the implantable component  116  to be releasably attached to the impactor assembly  210 . 
     Adjacent to the threaded engagement  242  of the carrier shaft  232 , the impactor body  230  is provided with key portion  244  formed at the distal end  220  of the shaft  224 . The key portion  244  has a generally rectangular profile shaped to engage a correspondingly-shaped notch portion  246  formed in the implantable component  116  (see  FIG. 15A ; depicted in phantom). This configuration permits the implantable component  116  to be indexed relative to the shaft  224  (and, thus, the handle  226 ), which may be advantageous for applications where the implantable component  116  has certain features that need to be aligned relative to the target site TS. Furthermore, this configuration also helps facilitate releasable attachment between the implantable component  116  and the impactor assembly  210  in that rotation and translation of the carrier shaft  232  relative to the shaft  224  can be used to disengage the threaded engagement  242  without also rotating the shaft  224  about the first axis A 1 . To this end, the handle  226  is also provided with a cage  248  disposed between the head  214  and the grip  228  shaped to accommodate and facilitate access to a knob  250  which, in turn, is operatively attached to the proximal shaft end  238  of the carrier shaft  232 . In the illustrated embodiment, the knob  250  comprises an axial knob aperture  252  formed along the first axis A 1 , and a transverse knob aperture  254  formed transverse to the first axis A 1  and disposed in communication with the axial knob aperture  252 . The axial knob aperture  252  is shaped to receive the proximal shaft end  238  of the carrier shaft  232 , and the transverse knob aperture  254  is shaped to receive a transverse pin  256  which is also received within a transverse shaft aperture  258  formed in the carrier shaft  232  (see  FIG. 16B ). In addition to ensuring retention of the carrier shaft  232 , this configuration also permits the knob  250  and the carrier shaft  232  rotate and translate concurrently about the first axis A 1 . Here, the cage  248  of the handle  226  has a generally U-shaped profile and is configured to permit limited translation of the knob  250  along the first axis A 1  while also providing the surgeon with access to the knob  250 . 
     Referring now to  FIGS. 15 and 17A-17B , as noted above, the illustrated embodiment of the tool  104  comprises the guide  208  to releasably secure the impactor assembly  210  in order to, among other things, facilitate maintaining alignment of the first axis A 1  with the trajectory T via the robotic arm  108  of the manipulator  102 . To this end, the guide  208  generally comprises a mount  148  (see  FIG. 15 ; generically depicted in phantom) adapted to attach to the manipulator  102 , and a body  260  operatively attached to the mount  148  and having a channel  262  that extends along a second axis A 2 . In the representative embodiment illustrated herein, the body  260  of the guide  208  is provided with one or more threaded holes  264  and recessed regions  266  (see  FIGS. 17A-17B ) which are shaped and arranged to secure to the mount  148  (see  FIG. 15 ; depicted generically) such as via fasteners (not shown). While the mount  148  depicted in  FIG. 15  is formed separately from the body  260  in the illustrated embodiment, other configurations are contemplated, and the guide  208  could be formed from or otherwise realized by any suitable number of components sufficient to facilitate coupling to the manipulator  102 . Here too, in some embodiments, one or more covers  204  may be employed by the guide  208  of the tool  104  to conceal, protect, or otherwise shield certain components (e.g., the mount  148 ) from the outside environment. The covers  204  may also conceal electrical components (e.g., wires, electrical connectors, printed circuit boards, and the like), and may be shaped and arranged to permit access to a sterile interface system (not shown, but generally known in the related art) arranged between the mount  148  and the coupling  110  of the robotic arm  108  to facilitate removably attaching the tool  104  to the manipulator  102 . Here too, releasable attachment of the coupling  110  to the mount  148  could be achieved in a number of different ways sufficient to secure the tool  104  to the manipulator  102 . 
     As shown in  FIGS. 17A-17B , the channel  262  formed in the body  260  of the guide  208  defines an opening  268  arranged to receive a portion of the shaft  224  of the impactor assembly  210  therethrough. The guide  208  also comprises a second engagement surface, generally indicated at  270  (see also  FIG. 15 ), and a limiter  272 . The second engagement surface  270  is shaped to abut the first engagement surface  218 , and the limiter  272  is configured to maintain abutment between the engagement surfaces  218 ,  270  and to facilitate coaxial alignment of the axes A 1 , A 2  with the trajectory T maintained by the manipulator  102 . The opening  268  of the guide  208  is arranged to permit the shaft  224  of the impactor assembly  210  to pass therethrough when the guide  208  is disposed between the flange  216  and the interface  212  of the impactor assembly  210  so as to facilitate bringing the first axis A 1  into alignment with the second axis A 2 . As is depicted with phantom lines in  FIG. 16A , the shaft  224  of the impactor assembly  210  has a first perimeter  274 , and the flange  216  of the impactor assembly  210  has a second perimeter  276  which is larger than the first perimeter  274 . Put differently, the flange  216  is larger than the shaft  224  and cannot pass through the opening  268  of the guide  208 , but the shaft  224  is sized so as to be able to pass through the opening  268 . 
     With continued reference to  FIGS. 17A-17B , as noted above, the limiter  272  of the guide  208  is configured to maintain abutment between the first engagement surface  218  and the second engagement surface  270  during impaction, and helps facilitate achieving coaxial alignment of the axes A 1 , A 2  with the trajectory T maintained by the manipulator  102 . To this end, the limiter  272  of the illustrated embodiment comprises a pair of fingers, generally indicated at  278 , disposed adjacent to the channel  262 . The fingers  278  extend from the body  260  of the guide  208  to respective finger ends  280  spaced from each other so as to define the opening  268  therebetween (see  FIG. 15 ). The fingers  278  also each define a respective arc-shaped surface, generally indicated at  282 . The arc-shaped surfaces  282  are arranged to contact the flange  216  of the impactor assembly  210  when the second engagement surface  270  abuts the first engagement surface  218 , which maintains abutment of the first engagement surface  218  with the second engagement surface  270  and limits movement of the impactor assembly  210  relative to the guide  208  as described below. The arc-shaped surfaces  282  of the limiter  272  are substantially continuous with the second engagement surface  270  of the guide  208 , and both the second engagement surface  270  and the arc-shaped surfaces  282  are at least partially defined by the channel  262 . More specifically, and as is best depicted in  FIG. 17A , the arc-shaped surfaces  282  of the limiter  272  and the second engagement surface  270  of the guide  208  are each spaced from the second axis A 2  at a common radius  284  such that the channel  262  has a substantially continuous and generally cylindrical, C-shaped profile, and defines both the second engagement surface  270  and the arc-shaped surfaces  282 . 
     The implantable component  116  and the impactor assembly  210  necessarily translate along the trajectory T as impact force FI is applied to the head  214  of the impactor assembly  210 . Thus, the guide  208  and the impactor assembly  210  are configured so as to ensure that abutment between the first engagement surface  218  and the second engagement surface  270  is maintained as the flange  216  moves within the channel  262  (e.g., as the surgeon successively strikes the head  214  of the impactor assembly  210  with a mallet). To this end, the channel  262  of the guide  208  extends between first and second axial channel ends  262 A,  262 B which are spaced from each other along the second axis A 2  at a depth that is greater than a thickness of the flange  216  (not shown in detail). Here, the guide  208  defines the tool center point TCP in this embodiment, which is arranged along the second axis A 2  in the center of the channel  262  (e.g., spaced equidistantly between the first and second axial channel ends  262 A,  262 B). However, the tool center point TCP could be defined in other ways without departing from the scope of the present disclosure. 
     Because the flange  216  has a generally spherical profile as noted above, only a portion of the flange  216  which defines the first engagement surface  218  actually engages the cylindrical channel  262  when the second engagement surface  270  abuts the first engagement surface  218 . Thus, the channel  262  is advantageously configured so as to be deep enough to ensure that the flange  216  can be readily positioned within and remain in abutment with the channel  262  during impaction. However, maintaining abutment between the second engagement surface  270  and the first engagement surface  218  can be achieved in other ways, such as by advancing the guide  208  along the trajectory T and toward the target site TS with the manipulator  102  during impaction (e.g., to position the tool center point TCP at the flange reference point FRP). Other configurations are contemplated. 
     As is best shown in  FIG. 17B , the body  260  of the guide  208  also comprises a pocket  286  which accommodates a sensor subassembly  288 , a follower subassembly  290 , and an input module  292 , each of which are described in greater detail below. The pocket  286  extends into communication with the channel  262  to facilitate attachment of the follower subassembly  290  which sits in the pocket  286  adjacent to the channel  262 . Here, a portion of the follower subassembly  290  also defines part of the second engagement surface  270  (see  FIG. 17A ). 
     The sensor subassembly  288  generally comprises a sensor housing  294  which is secured to the body  260  of the guide  208  via fasteners (not shown in detail) and supports a first trigger sensor  296 , a second trigger sensor  298 , and an input sensor  300 , each of which may be disposed in communication (e.g., wired or wireless electrical communication) with the controller  124  (e.g., the manipulator controller  132 , the tool controller  136 , or another suitable) or other components of the surgical system  100 . The input sensor  300  is arranged so as to be engaged by or otherwise disposed in communication with the input module  292 , and the first and second trigger sensors  296 ,  298  are arranged so as to be engaged by or otherwise disposed in communication with the follower subassembly  290 . As will be appreciated from the subsequent description below, each of the sensors of the sensor subassembly  288  could be of a number of different types, styles, configurations, and the like, and other configurations besides those specifically illustrated herein are contemplated by the present disclosure. 
     The input module  292  is configured for selective actuation by the surgeon and generally comprises an input frame  302  and an input button  304 . The input frame  302  is secured to the body  260  of the guide  208  via one or more fasteners (not shown in detail), and supports the input button  304  for movement relative thereto. The input button  304  comprises a protrusion  306  arranged to engage the input sensor  300  in response to actuation by the surgeon (e.g., by pressing on the input button  304 ). In some embodiments, the input button  304  could be resiliently biased away from the input frame, such as by a spring (not shown). However, other configurations are contemplated. The input module  292  may be configured to facilitate operating the manipulator  102  in different ways during a surgical procedure, and may serve as an input device  146 . 
     The follower subassembly  290 , like the sensor subassembly  288 , is accommodated within the pocket  286  formed in the body  260  of the guide  208  and is secured to the body  260  with fasteners (not shown in detail). The follower subassembly  290  generally comprises a follower housing  308  which supports first and second triggers  310 ,  312  which are shaped and arranged to engage against the flange  216  of the impactor assembly  210  in the illustrated embodiment. To this end, the first and second triggers  310 ,  312  extend into the channel  262  and are supported by the follower housing  308  so as to deflect towards the sensor subassembly  288  in response to engagement with the flange  216 , and independently actuate respective pushrods (not shown) supported within the follower housing  308  which respectively engage the first and second trigger sensors  296 ,  298 . Here, the follower subassembly  290  and the sensor subassembly  288  facilitate the ability to determine one or more of the presence of the flange  216  within the channel  262  and/or the relative position of the flange  216  between the first and second axial channel ends  262 A,  262 B such as to facilitate “tracking” movement of the implantable component  116  along the trajectory T during impaction at the target site TS based on corresponding to changes in the axial position of the flange  216  along the channel  262 . 
     As noted above, the manipulator  102  is configured to position the tool  104  with respect to the target site TS and to maintain the trajectory T which, in embodiments directed toward impacting the implantable component  116 , is generally linear and is aligned with the axes A 1 , A 2 . Here, external impact force FI applied to the head  214  of the impactor assembly  210  translates through the impactor assembly  210  and to the implantable component  116  which, in turn, causes the implantable component  116  to advance along the trajectory T toward the target site TS. While the process of impacting the implantable component  116  is described in greater detail below, maintaining the trajectory T may involve the manipulator  102  restricting all or certain types of movement of the guide  208  relative to the target site TS in certain conditions, and/or may involve limiting or directing movement of the guide  208  into translation along the trajectory T relative to the target site TS in some embodiments. The manipulator  102  may permit the surgeon to translate the guide  208  along the trajectory T to, among other things, facilitate passing the shaft  224  of the impactor assembly  210  through the opening  268  of the guide  208 , as noted above. Certain steps of surgical procedures may involve controlling the manipulator  102  in different ways. Furthermore, various configurations of tools  104  are contemplated by the present disclosure and, in some embodiments, one or more portions of the surgical system  100 , the tool  104 , the instrument  112 , and/or the implantable component  116  may be similar to as is described in U.S. Patent Application Publication No. US 2019/0231446 A1 entitled “End Effectors, Systems, And Methods For Impacting Prosthetics Guided By Surgical Robots,” the disclosure of which is hereby incorporated by reference in its entirety. Other configurations are contemplated. 
     Referring now to  FIGS. 18-21D , portions of the surgical system  100  and a generically-depicted target site TS are shown schematically, with the target site TS shown supported on the work surface WS (e.g., a surgical table; not shown in detail). Here, the target site TS represents intended position of the implantable component  116  when impacted into the acetabular cup (intended position shown in phantom in  FIG. 18 ). The acetabulum, here, has been reamed or otherwise prepared to define the trajectory T and has the first patient tracker  160 A firmly fixed thereto. As noted above, tracked states (e.g., positional and/or orientational data, or data based thereon) of first patient tracker  160 A monitored by the navigation system  128  are used to facilitate maintaining the target state SA to ensure alignment of the manipulator  102  with the target site TS, such as by controlling the robotic arm  108  of the manipulator  102  to keep the second axis A 2  defined by the guide  208  in coincident alignment with the trajectory T defined by the target site TS. 
     In  FIG. 18 , the mount  148  (represented by the covers  204  for illustrative purposes; see also  FIG. 15 ) and the guide  208  of the tool  104  are positioned adjacent to the target site TS supported by the manipulator  102  (partially depicted and shown in phantom), with the second axis A 2  aligned to the trajectory T (and, thus, with the tool center point TCP arranged along the trajectory T). The impactor assembly  210  is shown spaced from both the target site TS and the guide  208 , with the implantable component  116  secured to the interface  212  and arranged along the first axis A 1 . For illustrative purposes, the first tool tracker  160 G is shown firmly fixed to the guide  208 , and the second tool tracker  160 I is shown firmly fixed to the impactor assembly  210 . However, while the navigation system  128  can track states of multiple trackers  160  within a common coordinate system as noted above, the pose of a tracked object (e.g., the tool  104 ) can be determined in other ways (e.g., based on known geometric relationships) and transformed between coordinate systems (e.g., between the manipulator coordinate system MNPL and the localizer coordinate system LCLZ). Put differently, the surgical system  100  can determine changes in the pose of the tool  104  relative to the first patient tracker  160 A without necessarily utilizing the illustrated first tool tracker  160 G and/or second tool tracker  160 I because, among other things, the geometry of the guide  208 , the impactor assembly  210 , and the implantable component  116  are known and the arrangement of the flange reference point FRP relative to the tool center point TCP can be determined when the flange  216  is disposed within the channel  262  (e.g., via the sensor subassembly  288 ). 
     Referring now to  FIG. 19A , the impactor assembly  210  has been moved together with the implantable component  116  into an initial position adjacent to the target site TS (here, the reamed acetabulum), with the first axis A 1  defined by the impactor assembly  210  in coaxial alignment with both the second axis A 2  defined by the guide  208  and with the trajectory T defined by the target site TS. Here, the flange  216  of the impactor assembly  210  is disposed within the channel  262  of the guide  208 , with the flange reference point FRP disposed in alignment with the tool center point TCP. The implant reference point IRP defined by the implantable component  116  is spaced from the target reference point TRP defined by the target site TS. 
     As noted above, when operating in the guided-haptic mode, or other modes, the surgical system  100  may be configured to interpret force detected by the sensor  180  an input that is used to drive the robotic arm  108  of the manipulator  102  which, among other things, may allow the surgeon to touch or otherwise engage against different parts of the robotic arm  108  and/or the tool  104  to move them in certain directions during certain operational conditions. To illustrate this concept,  FIG. 19A  depicts an applied force FA acting on the guide  208 , such as from the surgeon pushing and/or pulling on the guide  208  or the impactor assembly  210  with their hand (not shown in detail). For illustrative purposes, if the manipulator  102  were not configured to maintain alignment with the trajectory T as depicted here (e.g., where the target state ST is defined so as to result in coincident alignment between the second axis A 2  and the trajectory T), the applied force FA depicted in  FIG. 19A  could result in movement of the tool  104  (via the robotic arm  108 ) to the arrangement depicted in  FIG. 19B , bringing the axes A 1 , A 2  out of coincident alignment with the trajectory T (e.g., as depicted in  FIG. 19A ). In this hypothetical, illustrative example, the surgeon could be operating the robotic arm  108  in the manual mode or another mode (e.g., activated via the input button  304 ) to refine or finalize their approach and initial positioning of the implantable component  116  in engagement with the target site TS prior to impaction, before subsequently bringing the axes A 1 , A 2  into coincident alignment with the trajectory T defined by the target site TS and maintaining the coincident alignment with the manipulator  102  as illustrated in  FIG. 20A . 
     In the illustrative example depicted in  FIG. 20A , manipulator  102  is being operated so as to maintain alignment of the second axis A 2  (defined by the guide  208 ) with the target site TS (e.g., via coincidence with the trajectory T), which is also aligned with the first axis A 1  (defined by the impactor assembly  210 ). Here, the target state ST could be defined by the tool center point TCP being disposed along the trajectory T. With the alignment maintained by the manipulator  102  as illustrated here, the surgeon can apply impact force FI to the head  214  of the impactor assembly  210 , such as by successively striking the head  214  with a mallet (not shown) in order to install the implantable component  116  into the target site TS. As illustrated by  FIG. 20B , in response to the proper application of impact force FI to the head  214 , the impactor assembly  210  and the implantable component  116  move together along the trajectory T to bring the implant reference point IRP (defined by the implantable component  116 ) into alignment with the target reference point TRP (defined by the target site TS). 
     Here, the manipulator  102  could be configured to advance the guide  208  along the trajectory T toward the target site TS between mallet strikes during impaction in order to bring the tool center point TCP (defined by the channel  262  of the guide  208 ) back into alignment with the flange reference point FRP (defined by the flange  216  of the impactor assembly  210 ) which, as noted above, may be determined via the follower subassembly  290  and/or the sensor subassembly  288 , and or via the navigation system  128  based on tracked states of the second tool tracker  160 I and the first tool tracker  160 G. The manipulator  102  may not necessarily advance the guide  208  along the trajectory T if, for example, the axial channel ends  262 A,  262 B are spaced from each other at a distance large enough to ensure that the flange  216  will remain in engagement with the channel  262  during impaction, which may be advantageous in embodiments where the surgical system  100  is able to determine the relative position of the flange  216  along the channel  262  with a high degree of accuracy, such by using a linear variable differential transformer (LVDT) coil arrangement coupled to the tool  104 . Embodiments of this type of LVDT coil arrangement are described in U.S. Patent Application Publication No. US 2019/0231446 A1 entitled “End Effectors, Systems, And Methods For Impacting Prosthetics Guided By Surgical Robots,” previously referenced. Other configurations are contemplated. 
     As noted above, the illustrated embodiments of the tool  104  are generally configured to permit translation of the impactor assembly  210  relative to the guide  208  to facilitate bringing the implantable component  116  into engagement with the target site TS. Furthermore, the embodiments of the tool  104  are also generally configured to permit rotation of the impactor assembly  210  relative to the guide  208 , and/or vice-versa, in one or more degrees of freedom. This relative rotation is achieved by bearing-type contact (e.g., sliding contact) occurring between the first engagement surface  218  and the second engagement surface  270 . Here, the ability of the impactor assembly  210  to rotate and translate relative to the guide  208  helps prevent significant amounts of force and/or torque from translating from the impactor assembly  210  to the guide  208  (and, thus, to the manipulator  102 ) such as, for example, during the application of impact force FI. However, a certain amount of force and/or torque are necessarily translated to the manipulator  102  in one or more degrees of freedom DOF due to the physical contact occurring between the guide  208  and the impactor assembly  210 . 
     In  FIG. 21A , the impactor assembly  210 , the guide  208 , the implantable component  116 , and the manipulator  102  are generally arranged in the same way as is depicted in  FIG. 20A , with the second axis A 2  (defined by the guide  208 ) aligned with the target site TS (e.g., via coincidence with the trajectory T), which is also aligned with the first axis A 1  (defined by the impactor assembly  210 ), and with the implantable component  116  arranged in engagement with the target site TS prior to impaction. However, in  FIG. 21A , the impaction force FI is shown as being improperly applied to the head  214  of the impactor assembly  210  (e.g., transverse to the trajectory T). Here, the improper application of impact force FI (e.g., relatively high in magnitude and/or misaligned with the trajectory T) may result in the implantable component  116  becoming seated (e.g., partially seated) into the target site TS in a way that is misaligned with the trajectory T (e.g., where the first axis A 1  and the second axis A 2  are not coincident with the trajectory T). Such a hypothetical scenario is depicted in  FIG. 21B , which shows exaggerated misalignment between the axes A 1 , A 2  and the trajectory T for illustrative purposes. 
     In  FIG. 21B , like the scenario described above in connection with  FIGS. 14A-14D , a hypothetical “runaway” condition of the surgical system  100  may occur as a result of the misalignment with the trajectory T. Here, the improper application of impact force FI has seated the implantable component  116  into the target site TS in a way that causes misalignment of the first and second axes A 1 , A 2  with the trajectory T. While the target state ST of the tool  104  could be defined in a number of different ways, for illustrative purposes in this representative example, the target state ST includes (or otherwise results in) coincident alignment between the second axis A 2  and the trajectory T (e.g., with the tool center point TCP disposed along the trajectory T). However, because the current state SC of the tool  104  shown in  FIG. 21B  includes misalignment between the second axis A 2  and the trajectory T with the implantable component  116  “locked” to the target site TS, a “runaway” condition may similarly occur as the manipulator  102  attempts to move from the current state to the target state ST. The “runaway” condition may also occur as a result of the patient tracker  160  becoming loose from the target site TS thereby causing a loss of tracking accuracy. 
     In this illustrative example, and as is shown by successively comparing  FIGS. 21B-21D , movement of the tool  104  (e.g., the guide  208 ) toward the target state ST (e.g., to bring the tool center point TCP back onto the trajectory T) also results in corresponding movement of the target site TS which, as noted above, defines the trajectory T (and, thus, the target state ST) based on the tracked states of the first patient tracker  160 A monitored by the navigation system  128 . Put differently, as the manipulator  102  attempts to move the tool  104  (e.g., the guide  208 ) from the current state SC to the target state ST (e.g., such that the first and second axes A 1 , A 2  come back into coincident alignment with the trajectory T), the target site TS moves together with the tool  104  and the target state ST is not reached (e.g., coincident alignment does not occur). Here too, as depicted in  FIGS. 21C-21D , this may ultimately result in the target site TS being “lifted off” of the work surface WS. 
     As noted above, various techniques for detecting and/or responding to “runaway” conditions as they occur are contemplated by the present disclosure, including for surgical systems  100  which utilize tools  104  with instruments  112  such as the guide  208  to support the impactor assembly  210  to facilitate engagement of the implantable component  116  with the target site TS (e.g., as described above in connection with  FIGS. 18-21D ), as well as for surgical systems  100  which utilize tools  104  with instruments  112  such as the powered surgical device  150  to facilitate engagement of the energy applicator  114  with the target site TS (e.g., as described above in connection with  FIGS. 12-14D ). To this end, the controller  124  may detect a “runaway” condition by monitoring one or more system conditions SYC (e.g., as detected via the sensing system  206 ) against one or more predetermined conditions PR (e.g., a first predetermined condition PR 1 , a second predetermined condition PR 2 , and the like), as noted above and as is described in greater detail below. 
     The sensing system  206  is configured to detect one or more system conditions SYC associated with one or more of the tool  104 , the manipulator  102 , the target site TS, or combinations thereof, as noted above (see  FIG. 25 ). Put differently, the sensing system  206  may detect one or more system conditions SYC associated with the tool  104 , one or more system conditions SYC associated with the manipulator  102 , and/or one or more system conditions SYC associated with the target site TS. To this end, in some embodiments, the sensing system  206  may comprise the sensor  180  to detect force FD occurring between the target site TS and the manipulator  102 . Here, for example, forces FD (e.g., force and/or torque in one or more degrees of freedom DOF) detected by the sensor  180  could define system conditions SYC used by the controller  124  to facilitate changing operation of the manipulator  102  between the first and second modes M 1 , M 2 , as described in greater detail below. In some embodiments, the sensing system  206  may comprise one or more components of the navigation system  128  (e.g., the localizer  158 ) and/or one or more trackers  160 . Here, for example, tracked states of trackers  160  monitored by the localizer  158  could define systems conditions SYC used by the controller  124  to facilitate changing operation of the manipulator  102  between the first and second modes M 1 , M 2 , as described in greater detail below. Here too, as noted above, one or more components of the surgical system  100  are able to determine (either directly or indirectly) the arrangement of the tool  104  within one or more coordinate systems (e.g., the pose of the tool center point TCP within the localizer coordinate system LCLZ). Here, arrangement of the tool  104 , as well as changes in arrangement of the tool  104  (e.g., movement relative to one or more trackers  160 ), could define system conditions SYC used by the controller to facilitate changing operation of the manipulator  102  between the first and second modes M 1 , M 2 , as described in greater detail below. In some implementations, the sensing system  206  or sensors  180  may additionally or alternatively comprise sensors  180  configured to detect electrical current from any one or more of the actuators of the joints J, sensors to detect torque or torques applied to any one or more of the joints J or joint actuators, or sensors to detect any other external (e.g., backdrive) force or torques applied to any one or more of the joints J. One example of a method for computing backdrive forces on the joints can be like that described in U.S. Pat. No. 10,327,849, entitled “Robotic System and Method for Backdriving The Same” which is incorporated by reference herein. Current measurements obtained by the sensors  180  at any one or more of the actuators of the joints J can be converted into force or torque measurements, which can be projected onto the target site TS where the tool  104  is interacting. In some examples, these force torque measurements obtained from the joints can be compared with the measurements from the six degree of freedom DOF force/torque transducer arranged to detect forces and/or torque occurring between the manipulator  102  and the target site TS or compared with state data regarding the patient or tool obtained by the navigation system. The sensing system  206  may comprise (or otherwise communicate with) various components of the surgical system  100  including, by way of non-limiting example, one or more instruments  112 , joint encoders  122 , controllers  124 ,  132 ,  134 ,  136 , input devices  146 , output devices  144 , user interfaces  142 , power generation assemblies  152 , pointers  156 , localizers  158 , trackers  160 , video cameras  170 , and the like. Other configurations are contemplated. 
     The system conditions SYC could be defined in a number of different ways, including based on relationships between different components of the surgical system  100  and/or the target site TS. For example, the pose of the first patient tracker  160 A (e.g., tracked within the localizer coordinate system LCLZ) and the pose of the tool center point TCP of the tool  104  (e.g., transformed into or tracked within the localizer coordinate system LCLZ) could each define respective system conditions SYC, and concurrent movement of the pose of the first patient tracker  160 A together with the pose of the tool center point TCP could define a different system condition SYC. Accordingly, a number of different system conditions SYC are contemplated by the present disclosure, which could be defined in various ways based on changes occurring at and/or between one or more of the tool  104 , the manipulator  102 , and/or the target site TS. 
     Referring now to  FIG. 22A , as noted above, the controller  124  is configured to operate the manipulator  102  in the first mode M 1  to maintain alignment of the tool  104  with respect to the target site TS based on the first constraint criteria C 1 , and to operate the manipulator  102  in the second mode M 2  to maintain alignment of the tool  104  with respect to the target site TS based on the second constraint criteria C 2 , which is different from the first constraint criteria C 1 . To this end, in some embodiments, the difference between the first constraint criteria C 1  and the second constraint criteria C 2  may be based on the degrees of freedom DOF in which movement of the tool  104  relative to the target site TS is restricted (or permitted), as well as how movement in one or more degrees of freedom DOF could be effected (see also  FIG. 25 ). While this concept is described in greater detail below in connection with  FIGS. 24A-24C , for illustrative purposes,  FIG. 22A  shows the manipulator  102  supporting the instrument  112  of the tool  104  (here, the guide  208 ) spaced from the impactor assembly  210  secured to the implantable component  116  disposed in initial engagement with the target site TS supported on the work surface WS, with the tool center point TCP of the tool  104  and the target reference point TRP of the target site TS each shown comprising six respective degrees of freedom DOF represented in Cartesian format. 
     More specifically, the tool center point TCP and the target reference point TRP each define a respective x position XP degree of freedom DOF, y position YP degree of freedom DOF, z position ZP degree of freedom DOF, x orientation ZO degree of freedom DOF, y orientation YO degree of freedom DOF, and z orientation ZO degree of freedom DOF within a common coordinate system (e.g., the localizer coordinate system LCLZ or another suitable coordinate system). Here, the tool center point TCP is “fixed” relative to the tool  104  and is known by the controller  124  (e.g., based geometric relationships between the tool  104  and the coupling  110  of the manipulator  102 ). Similarly, the target reference point TRP is “fixed” relative to the target site TS and is known by the controller  124  (e.g., based on the tracked states of the first patient tracker  160 A coupled to the target site TS and defined by reaming the acetabulum). For illustrative purposes, the tool center point TCP and the target reference point TRP are depicted as coordinate systems in  FIGS. 22A-24C , with x, y, and z axes each representing two degrees of freedom DOF: translation of the coordinate system in a direction along the axis, and rotation of the coordinate system in a direction about the axis. In  FIG. 22A , for illustrative purposes, the tool center point TCP is arranged with its z axis parallel to the trajectory T and with its x axis transverse to the trajectory T, and the target reference point TRP is arranged with its z axis coincident to the trajectory T. 
     In some embodiments, the first constraint criteria C 1  may comprise a first number N 1  of degrees of freedom DOF in which movement of the tool  104  is restricted relative to the target site TS, and the second constraint criteria C 2  may comprise a second number N 2  of degrees of freedom DOF in which movement of the tool  104  is restricted relative to the target site TS, where the second number N 2  of degrees of freedom DOF is different from the first number N 1  of degrees of freedom DOF. Thus, in some embodiments, the controller  124  may be configured to operate the manipulator  102  in the first mode M 1  to maintain alignment of the tool  104  with respect to the target site TS based on the first number N 1  of degrees of freedom DOF, and in the second mode M 2  to maintain alignment of the tool  104  with respect to the target site TS based on the (different) second number N 2  of degrees of freedom DOF. 
     Here, the first number N 1  could represent the number of “active” degrees of freedom DOF which define the target state ST in the first mode M 1 , and the second number N 2  could represent the number of “active” degrees of freedom DOF which define the target state ST in the second mode M 2 . For example, where the sensing system  206  comprises the sensor  180  to detect force FD occurring between the target site TS and the manipulator  102  to define the system condition SYC, in some embodiments, the controller  124  could define the target state ST based on a total of six degrees of freedom DOF (e.g., the x position XP, the y position YP, the z position ZP, the x orientation XO, the y orientation YO, and the z orientation ZO) for operating the manipulator  102  in the first mode M 1 , and could automatically change how the target state ST is defined to operate the manipulator  102  in the second mode M 2  based on three degrees of freedom DOF (e.g., the x orientation XO, the y orientation YO, and the z orientation ZO) as soon as the force FD detected by the sensor  180  satisfies the predetermined condition PR. Here, the predetermined condition PR could be defined as the force FD detected by the sensor  180  (e.g., force and/or torque in one or more degrees of freedom DOF) that is indicative of a potential “runaway” condition defined such as by the implantable component  116  becoming “fixed” to the anatomy of the patient P at the target site TS, whereby the controller  124  effectively changes the target state ST in the second mode M 2  to no longer maintain the position (e.g., the x position XP, the y position YP, and the z position ZP) of the tool center point TCP relative to the target site TS. 
     Thus, in some embodiments, the controller  124  may be configured to operate the manipulator  102  in the first mode M 1  to restrict movement of the tool center point TCP away from the target site TS (or, the trajectory T) according to the first constraint criteria C 1  (e.g., which defines the target state ST based on a target orientation OT and a target position PT) and based on the first number N 1  of degrees of freedom DOF, and to operate the manipulator  102  in the second mode M 2  to permit movement of the tool center point TCP away from the target site TS according to the second constraint criteria C 1  (e.g., which defines the target state ST based on a target orientation OT but not a target position PT) and based on the (different) second number N 2  of degrees of freedom DOF. While this illustrative example is described in greater detail below in connection with  FIGS. 24A-24C , other configurations are contemplated, and the changing between modes based on satisfying the predetermined condition PR could occur in a number of different ways, based on various system conditions SYC determined via the sensing system  206 . 
     In some embodiments, the second number N 2  of degrees of freedom DOF is smaller than the first number N 1  of degrees of freedom DOF such that the controller  124  permits movement of the tool  104  relative to the target site TS in at least one more degree of freedom DOF in the second mode M 2  than in the first mode M 1 . Here too, in some embodiments, the first constraint criteria C 1  and the second constraint criteria C 2  may each comprise at least one orientational degree of freedom DOF (e.g., the x orientation XO, the y orientation YO, and/or the z orientation ZO), the first constraint criteria C 1  may comprise at least one more positional degree of freedom DOF (e.g., the x position XP, the y position YP, and/or the z position ZP) than the second constraint criteria C 2 , and both the first constraint criteria C 1  and the second constraint criteria C 2  may comprise at least one common degree of freedom DOF (e.g., the x orientation XO, the y orientation YO, and/or the z orientation ZO). Furthermore, in some embodiments, the first constraint criteria C 1  may comprise at least one positional degree of freedom DOF (e.g., the x position XP, the y position YP, and/or the z position ZP) and at least one orientational degree of freedom DOF (e.g., the x orientation XO, the y orientation YO, and/or the z orientation ZO). However, as will be appreciated from the subsequent description below, other configurations are contemplated, and the first criteria C 1  and/or the second constraint criteria C 2  could be defined in a number of different ways depending, for example, on the type of surgical procedure being performed at the target site TS, the specific arrangement and configuration of the tool  104  (and/or the energy applicator  114  or the implantable component  116 ), how the tool  104  is arranged by the manipulator  102  relative to the target site TS, and the like. 
     In some embodiments, the first constraint criteria C 1  may comprise a first resilience parameter R 1 , and the second constraint criteria C 2  may comprise a second resilience parameter R 2  different from the first resilience parameter R 1 . Thus, in some embodiments, the controller  124  may be configured to operate the manipulator  102  in the first mode M 1  to maintain alignment of the tool  104  with respect to the target site TS based on the first resilience parameter R 1 , and in the second mode M 2  to maintain alignment of the tool  104  with respect to the target site TS based on the (different) second resilience parameter R 2 . Here, the first resilience parameter R 1  could represent or otherwise correspond to tuning parameters TPA (e.g., spring parameters PS and/or damping parameters PD) of one or more guide constraints GC which define the first mode M 1 , and the second resilience parameter R 2  could represent or otherwise correspond to tuning parameters TPA (e.g., spring parameters PS and/or damping parameters PD) of one or more guide constraints GC which define the second mode M 2 . As will be appreciated from the subsequent description below, the first constraint criteria C 1  and/or the second constraint criteria C 2  may be configured or defined in a number of different way including, by way of non-limiting example, where resilience parameters are defined for each “active” degree of freedom DOF while operating in either the first mode M 1  or the second mode M 2 . Put differently, the first constraint criteria C 1  could comprise three “active” degrees of freedom DOF each having a respective first resilience parameter, which may be the same or could be different from each other. Other configurations are contemplated. 
     In some embodiments, the controller  124  may be configured to permit more resilient movement of the tool  104  relative to the target site TS in the second mode M 2  than in the first mode M 1 . Put differently, the second resilience parameter R 2  could be less “stiff” than the first resilience parameter R 1  such that deviation from the target state ST is more difficult in the first mode M 1  than in the second mode M 2 . However, other configurations are contemplated. In some embodiments, the first resilience parameter R 1  and the second resilience parameter R 2  are each associated with resilient movement of the tool  104  relative to the target site TS in at least one common degree of freedom DOF (e.g., in the x position XP, the y position YP, the z position ZP, the x orientation XO, the y orientation YO, or the z orientation ZO). By way of non-limiting example, the z orientation ZO degree of freedom DOF could be “active” and form part of both the first constraint criteria C 1  and the second constraint criteria C 2 , with the first and second resilience parameters R 1 , R 2  each being associated with the z orientation ZO degree of freedom DOF. 
     In some embodiments, the first constraint criteria C 1 , the second constraint criteria C 2 , and/or the predetermined condition PR may be adjustable and/or configurable by the user, such as via the user interface  142 . To this end, a threshold control  314  (see  FIG. 2 ; see also  FIG. 25 ) may be provided to facilitate adjusting how the predetermined condition PR is defined. By way of example, the threshold control  314  could be configured as an input device  146  which changes the amount of force FD detected by the sensor  180  (e.g., a system condition SYC) that is required to satisfy the predetermined condition PR, such as to require more or less force FD to be detected (e.g., force and/or torque in a particular direction) before the controller  124  will change from the first mode M 1  to the second mode M 2 . By way of further example, the threshold control  314  could be configured as an input device  146  which changes the amount of time that the tool  104  and the target site TS move together for (e.g., as determined via the navigation system  128 ) in order to satisfy the predetermined condition PR, such as to require concurrent movement for more or less time before the controller  124  will change from the first mode M 1  to the second mode M 2 . The examples provided above are illustrative and non-limiting, and other configurations are contemplated. 
     In some embodiments, a stiffness control  316  (see  FIG. 2 ; see also  FIG. 25 ) may be provided to facilitate adjusting how the first constraint criteria C 1  (or, in some embodiments, the second constraint criteria C 2 ) is defined. By way of example, the stiffness control  316  could be configured as an input device  146  which changes the tuning parameters TPA and/or the configuration parameters CPA of one or more of the guide constraints GC used to define the first mode M 1  (e.g., to facilitate maintaining the target state ST), such as by increasing or decreasing the first resilience parameter R 1  to result in a corresponding change in how the manipulator  102  restricts movement from the target state ST (e.g., with less or more “stiffness”). Here too, the forgoing example is illustrative and non-limiting, and other configurations are contemplated. 
     In other implementations, the first constraint criteria C 1  or the second constraint criteria C 2  can be dynamically determined or adjusted based on measurements from the sensing system or sensor  180 . The controller can correlate the magnitudes or values of the sensed measurements to stiffness values, e.g., using a look-up table stored in memory. This technique can be implemented with a threshold as described above, or without regard to any threshold. 
     In some embodiments, the surgical system  100  also comprises a mode indicator  318  (see  FIG. 2 ; see also  FIG. 25 ) coupled to the controller  124  to communicate a change in operation of the manipulator  102  from the first mode M 1  to the second mode M 2  (or between other modes). Here, the mode indicator  318  may form part of the user interface  142  (e.g., as an alarm, a speaker, an indicator light, a part of a display screen, and/or another type of output device  144 ), and the controller  124  could be configured to activate the mode indicator  318  in response to determining that at least one of the one or more system conditions SYC satisfies the predetermined condition PR. 
     As noted above,  FIG. 22A  shows the manipulator  102  supporting the instrument  112  of the tool  104  (here, the guide  208 ) spaced from the impactor assembly  210  secured to the implantable component  116  disposed in initial engagement with the target site TS supported on the work surface WS, with the tool center point TCP of the tool  104  and the target reference point TRP of the target site TS spaced from each other. Comparing  FIG. 22A  with  FIG. 22B  illustrates movement of the tool  104  in the x position XP degree of freedom DOF (e.g., in a direction along the x axis of the tool center point TCP), whereby the shaft  224  of the impactor assembly  210  has passed through the opening  268  of the guide  208  and into the channel  262  to bring the tool center point TCP onto the trajectory T (and also onto the z axis of the target reference point TRP). 
     Comparing  FIG. 22B  with  FIG. 22C  illustrates movement of the tool  104  in the z position ZP degree of freedom DOF (e.g., in a direction along the z axis of the tool center point TCP), whereby the flange  216  of the impactor assembly  210  has become disposed within the channel  262  of the guide  208 , with the first engagement surface  218  abutting the second engagement surface  270 , and with the tool center point TCP arranged coincident to the flange reference point FRP and still disposed along the trajectory T. 
     In some embodiments, the controller  124  may be configured to operate the manipulator  102  in the second mode M 2  to permit movement of the tool  104  relative to the target site TS in at least one degree of freedom DOF according to the second constraint criteria C 2 . Similarly, in some embodiments, the controller  124  may be configured to operate the manipulator  102  in the first mode M 1  to permit movement of the tool  104  relative to the target site TS in at least one degree of freedom DOF according to the first constraint criteria C 1 . Here, for example, comparing  FIG. 22C  with  FIG. 23  illustrates movement of the tool  104  in the z orientation ZO degree of freedom DOF (e.g., in a direction about the z axis of the tool center point TCP), whereby the guide  208  has moved relative to the impactor assembly  210  and the target site TS from the arrangement depicted in  FIG. 22C  (depicted as a phantom outline in  FIG. 23 ), but the tool center point TCP of the tool  104  remains arranged coincident to the flange reference point FRP and is likewise disposed along the trajectory T. 
     Put differently, the movement of the tool  104  illustrated by comparing  FIGS. 22C-23  could represent a scenario where the first constraint criteria C 1  comprises five active degrees of freedom DOF (e.g., the x position XP, the y position YP, the z position ZP, the x orientation XO, and the y orientation YO) and permits movement in one degree of freedom DOF (e.g., the Z orientation ZO) to define the target state ST while operating in the first mode M 1 . This configuration could, for example, be implemented in order to allow the user to “rotate” the guide  208  about the trajectory T (e.g., between mallet strikes to the head  214  of the impactor assembly  210 ) to a different arrangement that is maintained by the manipulator  102  (e.g., by re-defining the target state ST based on the wherever the guide  208  was positioned by the user). 
     However, the first constraint criteria C 1  could be configured in a number of different ways to define the target state ST while operating in the first mode M 1 . For example, rather than permitting the user to adjust the orientation of the guide  208  about the trajectory T in the first mode M 1  in such a way that the manipulator  102  re-defines the target state ST based on the user “rotating” the guide  208  about the trajectory T, the first constraint criteria C 1  could instead be configured to define the target state ST in all six degrees of freedom DOF while permitting more resilient movement (e.g., less “stiff” movement) in one or more degrees of freedom DOF than in others. By way of illustrative example, the arrangement depicted in  FIG. 22C  could instead represent the target state ST in the first mode M 1 , with the first constraint criteria C 1  configured such that the first resilience parameter R 1  associated with the z orientation ZO degree of freedom DOF has a relatively “weak” value that permits the user to “rotate” the guide  208  about the trajectory T as shown in  FIG. 23  but nevertheless urges the tool  104  toward the target state ST. Here in this example, the arrangement of the tool  104  depicted in  FIG. 23  would represent a current state SC, with the target state ST shown as a phantom outline (see also  FIG. 22C ). 
     Referring now to  FIGS. 24A-24C , in some embodiments, the controller  124  may be further configured to operate the manipulator  102  in a third mode M 3  to maintain alignment of the tool  104  with respect to the target site TS according to a third constraint criteria C 3  different from both the first constraint criteria C 1  and the second constraint criteria C 2 . Here in this embodiment, the controller  124  is configured to change operation of the manipulator  102  from the first mode M 1  to the second mode M 2  in response to determining that at least one of the one or more system conditions SYS satisfies a first predetermined condition PR 1 , and to change operation of the manipulator  102  from the second mode M 2  to the third mode M 3  in response to determining that at least one of the one or more system conditions SYS satisfies a second predetermined condition PR 2  different from the first predetermined condition PR 1 . Here in this illustrative embodiment, the first constraint criteria C 1  comprises a first number N 1  of degrees of freedom DOF in which movement of the tool  104  is restricted relative to the target site TS, the second constraint criteria C 2  comprises a second number N 2  of degrees of freedom DOF in which movement of the tool  104  is restricted relative to the target site TS, and the third constraint criteria C 3  comprises a third number N 3  of degrees of freedom DOF in which movement of the tool  104  is restricted relative to the target site TS. Furthermore, in this illustrative embodiment, the first constraint criteria C 1  also comprises a first resilience parameter R 1 , the second constraint criteria C 2  also comprises a second resilience parameter R 2 , and the third constraint criteria C 3  also comprises a third resilience parameter R 3 . 
     Thus, in the representative embodiment illustrated in connection with  FIGS. 24A-24C , the controller  124  is configured to operate the manipulator  102 : in the first mode M 1  to maintain alignment of the tool  104  with respect to the target site TS based on the first number N 1  of degrees of freedom DOF and also based on the first resilience parameter R 1 ; in the second mode M 2  to maintain alignment of the tool  104  with respect to the target site TS based on the second number N 2  of degrees of freedom DOF and also based on the second resilience parameter R 2 ; and in the third mode M 3  to maintain alignment of the tool  104  with respect to the target site TS based on the third number N 3  of degrees of freedom DOF and also based on the third resilience parameter R 3 . Here, the third number N 3  of degrees of freedom DOF is different from one or more of the first number N 1  of degrees of freedom DOF and the second number N 2  of degrees of freedom DOF. More specifically, in this embodiment, the third number N 3  of degrees of freedom DOF is smaller than the first number N 1  of degrees of freedom DOF such that the controller  124  permits movement of the tool  104  relative to the target site TS in at least one more degree of freedom DOF in the third mode M 3  than in the first mode M 1 . Similarly, in this embodiment, the third number of degrees of freedom DOF is smaller than the second number N 2  of degrees of freedom DOF such that the controller  124  permits movement of the tool  104  relative to the target site TS in at least one more degree of freedom DOF in the third mode M 3  than in the second mode M 2 . 
     More specifically, in this representative embodiment, the first number N 1  of degrees of freedom DOF is equal to the second number N 2  of degrees of freedom DOF, both of which are different from the third number N 3  of degrees of freedom DOF. However, other configurations are contemplated. Here in this embodiment, the difference between the first constraint criteria C 1  and the second constraint criteria C 2  is based on the first and second resilience parameters R 1 , R 2  as described in greater detail below, rather than on the first and second number N 1 , N 2  of degrees of freedom DOF that are “active” in the first and second modes M 1 , M 2 . 
     In some embodiments, such as the embodiment illustrated in connection with  FIGS. 24A-24C , the first constraint criteria C 1  and the second constraint criteria C 2  each comprise at least one positional degree of freedom DOF (e.g., the x position XP, the y position YP, and/or the z position ZP) and at least one orientational degree of freedom DOF (e.g., the x orientation XO, the y orientation YO, and/or the z orientation ZO); and each of the first constraint criteria C 1 , the second constraint criteria C 2 , and the third constraint criteria C 3  comprise at least one orientational degree of freedom (e.g., the x orientation XO, the y orientation YO, and/or the z orientation ZO). Here too, the first constraint criteria C 1  and the second constraint criteria C 2  each comprise at least one more positional degree of freedom DOF than the third constraint criteria C 3 . However, other configurations are contemplated. 
     As noted above, in the representative embodiment illustrated in  FIGS. 24A-24C , the difference between the first constraint criteria C 1  and the second constraint criteria C 2  is based on the first and second resilience parameters R 1 , R 2  rather than on the first and second number N 1 , N 2  of degrees of freedom DOF which are “active” in the first and second modes M 1 , M 2 . Here, the third resilience parameter R 3  is different from one or more of the first resilience parameter R 1  and the second resilience parameter R 2 , which are also different from each other in this embodiment. More specifically, and as is described in greater detail below, the controller  124  permits more resilient movement (e.g., less “stiff” movement) of the tool  104  relative to the target site TS in the second mode M 2  than in the first mode M 1 , and permits more resilient movement (e.g., less “stiff” movement) of the tool  104  relative to the target site TS in the second mode M 2  than in the third mode M 3 . Here too, the forgoing is intended to be a non-limiting example, and other configurations of the surgical system  100  are contemplated. 
     In  FIG. 24A , the controller  124  is operating the manipulator  102  in the first mode M 1  according to the first constraint criteria C 1  which, in this representative embodiment, defines the target state ST as illustrated, with the tool  104  arranged such that there is coincident alignment of the axes A 1 , A 2  with the trajectory T as noted above. To this end, the first constraint criteria C 1  comprises both the first number N 1  of degrees of freedom DOF and the first resilience parameter R 1 . For the purposes of this illustrative example, the first number N 1  comprises six “active” degrees of freedom DOF: the x position XP, the y position YP, the z position ZP, the x orientation XO, the y orientation YO, and z the orientation ZO. Furthermore, in this illustrative example, the first resilience parameter R 1  is set such that the tool  104  is maintained in the target state ST with a relatively “stiff haptic,” defined for example by tuning parameters TPA of guide constraints GC where the spring parameters PS are set relatively high to resist movement in each of the six active degrees of freedom DOF. 
     With continued reference to  FIG. 24A , impaction force FI is shown being improperly applied to the head  214  of the impactor assembly  210  (e.g., transverse to the trajectory T). Here, the improper application of impact force FI (e.g., relatively high in magnitude and/or misaligned with the trajectory T) may result in the implantable component  116  becoming partially-seated into the target site TS in a way that is misaligned with the trajectory T, such as is depicted in  FIG. 24B  with exaggerated misalignment between axes A 1 , A 2  and the trajectory T for illustrative purposes. Here in  FIG. 24B , the sensor  180  detects force FD between the target site TS and the manipulator  102  resulting from the deviation of the illustrated current state SC from the target state ST (depicted here in phantom outline), with the sensor  180  serving as part of the sensing system  206  to detect system condition SYC (e.g., the force FD). In this scenario, rather than continuing to move the manipulator  102  so as to bring the tool  104  to the target state ST (e.g., by moving the tool center point TCP back onto the trajectory T), the controller  124  changes from the first mode M 1  to the second mode M 2  in response to the force FD detected by the sensor  180  having satisfied the first predetermined condition PR 1  which, in this embodiment, is defined as a first force F 1  detected by the sensor  180  (e.g., force and/or torque in one or more degrees of freedom DOF). Thus,  FIG. 24B  depicts operation of the manipulator  102  in the second mode M 2  according to the second constraint criteria C 2 . 
     In  FIG. 24B , the controller  124  is operating the manipulator  102  in the second mode M 2  according to the second constraint criteria C 2 , with the target state ST still being defined by the arrangement depicted in  FIG. 24A  (shown in  FIG. 24B  as a phantom outline). Here, the second constraint criteria C 2  comprises the second number N 2  of degrees of freedom DOF and the second resilience parameter R 2 . For the purposes of this illustrative example, the second number N 2  comprises six “active” degrees of freedom DOF: the x position XP, the y position YP, the z position ZP, the x orientation XO, the y orientation YO, and z the orientation ZO. However, in this illustrative example, the second resilience parameter R 2  is set such that the tool  104  is urged toward the target state ST with a relatively “loose haptic” (e.g., the second resilience parameter R 2  is smaller than the first resilience parameter R 1 ), defined for example by tuning parameters TPA of guide constraints GC where the spring parameters PS are set relatively low to permit a certain amount of resilient movement in each of the six active degrees of freedom DOF. With this configuration, the manipulator  102  is still attempting to return to the target state ST (e.g., by bringing the tool center point TCP back onto the trajectory T), but the “loose haptic” afforded by the second constraint criteria C 2  permits a certain amount of deviation from the target state ST to occur, thereby preventing a “runaway” condition when the implantable component  116  is partially-seated into the target site TS while misaligned, and keeping the target site TS supported on the work surface WS. 
     With continued reference to  FIG. 24B , additional impaction force FI is shown being improperly applied to the head  214  of the impactor assembly  210  (e.g., transverse to the trajectory T). Here, the improper application of impact force FI (e.g., relatively high in magnitude and/or misaligned with the trajectory T) may still result in the implantable component  116  becoming seated further into the target site TS in a way that is further misaligned with the trajectory T, such as is depicted in  FIG. 24C  with exaggerated misalignment between the axes A 1 , A 2  and the trajectory T for illustrative purposes. Here in  FIG. 24C , the sensor  180  similarly detects force FD between the target site TS and the manipulator  102  resulting from the further deviation of the illustrated current state SC from the target state ST (depicted here as an endpoint of the trajectory T). Here too in this scenario, rather than continuing to move the manipulator  102  so as to bring the tool  104  to the target state ST (e.g., by moving the tool center point TCP back onto the trajectory T), the controller  124  changes from the second mode M 2  to the third mode M 3  in response to the force FD detected by the sensor  180  having satisfied the second predetermined condition PR 2  which, in this embodiment, is defined as a second force F 2  detected by the sensor  180  (e.g., force and/or torque in one or more degrees of freedom DOF) where the second force F 2  is larger than the first force F 1 . In some embodiments, the second force F 2  may be smaller than an amount of force and/or torque acting on the target site TS in one or more directions via engagement with the implantable component  116  that could otherwise “unseat” the partially or fully-seated implantable component  116 . 
     In  FIG. 24C , the controller  124  is operating the manipulator  102  in the third mode M 3  according to the third constraint criteria C 3 , with the target state ST still being defined by the arrangement depicted in  FIG. 24A  (shown in  FIG. 24C  as an endpoint of the trajectory T). Here, the third constraint criteria C 3  comprises the third number N 3  of degrees of freedom DOF and the third resilience parameter R 3 . For the purposes of this illustrative example, the third number N 3  comprises three “active” degrees of freedom DOF: the x orientation XO, the y orientation YO, and z the orientation ZO. Put differently, no positional degrees of freedom DOF are active according to the third constraint criteria C 3 . Here in this illustrative example, the third resilience parameter R 3  is set such that the tool  104  is urged toward the target state ST with a relatively “stiff haptic,” defined for example by tuning parameters TPA of guide constraints GC where the spring parameters PS are set relatively high to resist movement in each of the three active degrees of freedom DOF. Here, the tool  104  is urged toward the target state ST based on orientation but not position. With this configuration, the manipulator  102  is still attempting to return to the target state ST (e.g., by orientating the tool center point TCP toward the target site TS), but the lack of active positional degrees of freedom DOF prevents a “runaway” condition from occurring when the implantable component  116  is further seated into the target site TS while misaligned, and the target site TS similarly remains supported on the work surface WS. Here, the surgeon or another user may be alerted to the change to the third mode M 3  via the mode indicator  318  which, as noted above, may form part of one or more of the user interfaces  142 . By way of non-limiting example, when the controller  124  switches from the first mode M 1  to the second mode M 2 , a “low level” alert (e.g., a sound played on a speaker, a warning displayed by a flashing light or graphic presented on a screen, and the like) could be generated to alert the user, and when the controller  124  switches from the second mode M 2  to the third mode M 2  (or from the first mode M 1  to the third mode M 3 ), a different or “high level” alert could be generated to alert the user. The alerts could be defined in a number of different ways sufficient to differentiate each other (e.g., one being visual and the other being audible, or combinations thereof) and, as noted above, the mode indicator  318  could be of a number of different styles, types, and/or configurations. 
     While the representative embodiment described above in connection with  FIGS. 24A-24C  employs three constraint criteria C 1 , C 2 , C 3 , three modes M 1 , M 2 , M 3 , and two predetermined conditions PR 1 , PR 2 , similar functionality could be afforded with two modes and one predetermined condition PR in some embodiments. By way of non-limiting example, when utilizing the sensor  180  to monitor system conditions SYC where the predetermined condition PR is defined as the detected force FD (e.g., force and/or torque in one or more degrees of freedom DOF), with the controller  124  configured to switch from the first mode M 1  (e.g., to maintain six degrees of freedom DOF according to a first constraint criteria C 1 ) to the second mode M 2  (e.g., to maintain only orientational degrees of freedom DOF according to a second constraint criteria C 2 ), the controller  124  could be configured to operate the manipulator  102  in the first mode M 1  to resist movement of the tool  104  relative to the target site TS with increasing resilience as the force FD detected by the sensor  180  increases toward the predetermined condition PR. Put differently, rather than  FIG. 24B  depicting operation in a different mode than what is depicted in  FIG. 24A ,  FIG. 24B  could instead represent a part of the same mode (e.g., the first mode M 1 ) where the first constraint criteria C 1  comprises a resilience parameter that is defined as a function of the force FD detected by the sensor  180  until, for example, the detected force FD satisfies the predetermined condition PR (e.g., where the force FD exceeds the second force F 2  described above in connection with  FIG. 24C ). However, the forgoing example is illustrative and non-limiting, and other configurations are contemplated. 
     In embodiments which utilize the sensor  180  as a part of the sensing system  206  to facilitate changing between modes (e.g., the first mode M 1  and the second mode M 2 ), the sensor  180  may be further defined as a force-torque sensor  180  that is configured to detect, in one or more degrees of freedom DOF, force FD (e.g., force and/or torque) occurring between the manipulator  102  and the target site TS. To this end, and as is depicted generically in  FIGS. 1 and 15 , the sensor  180  may be coupled to the robotic arm  108  (e.g., as a part of the coupling  110 ). However, the sensor  180  could be arranged in any suitable way sufficient to detect force FD occurring between the manipulator  102  and the target site TS, and could be of a number of different types, styles, or configurations without departing from the scope of the present disclosure. By way of non-limiting example, the sensor  180  could be realized as a part of the coupling  110 , as a part of the robotic arm  108  (e.g., arranged at one of the joints), and/or as a part of the tool  104  (e.g., arranged at the instrument  112  and/or at the implantable component  116 ). Similarly, the sensor  180  could be arranged at the mount  148  and/or the body  260  of the guide  208 . Moreover, while the representative embodiment illustrated herein is directed toward a single, multiple degree of freedom DOF force-torque transducer that is coupled to the manipulator  102 , the sensor  180  could also be realized by multiple components, arranged in the same location or in different locations (e.g., one at the guide  208  and one at the coupling  110 ), which cooperate to facilitate detecting force FD occurring between the target site TS and the robotic arm  108 . Other configurations are contemplated. 
     In some embodiments, the amount of force FD detected by the sensor  180  which satisfies the predetermined condition PR (e.g., the first force F 1 , the second force F 2 , or other values) either represents or is based on the amount of torque (or force) being applied at the implantable component  116 . Here, the known properties of the tool  104  and the implantable component  116  can be used to relate force/torque at the sensor  180  to the force/torque applied at the implantable component  116 . Calculating the rigid body Jacobian from the sensor  180  to the implantable component  116  may be performed according to F IMPLANT =J SENSOR_TO_IMPLANT   −T *F SENSOR . The force FD detected by the sensor  180  could define the predetermined condition PR in a number of different ways, and may be application and/or procedure specific. In some embodiments, the type, style, size, or other parameters of the implantable component  116  could at least partially define one or more predetermined conditions PR. Here, for example, a relatively “large” implantable component  116  may require a different amount of torque (or force) applied thereto before becoming unseated at the target site TS in comparison to a relatively “small” implantable component  116 . The specific parameters of the predetermined condition PR based on the sensor  180  (e.g., the magnitude of force and/or torque in one or more degrees of freedom DOF) could be determined in other ways, including using by performing experiments. For example, in determining the baseline force at which to start to release the translational constraint on the impaction assembly  210 , lever-out torques were analyzed for acetabular cups. By knowing an approximate torque at which a well-fixed cup  116  would likely move or de-seat, cup placement accuracy can be optimized while avoiding cup lever-out by releasing the constraint at a specified limit or range. With a range of approximately 5 to 25 Nm of lever-out strength of the cup  116 , the possible force limits at the impaction assembly  210  could range from 20 N to 100 N (assuming 0.25 m lever arm from end effector attachment to cup center) to address different cup fixation scenarios. In one implementation, the amount of force FD to satisfy the predetermined condition PR per lab evaluation is approximately 64 N (approximately 16 Nm lever out torque). However, other values or ranges of values are contemplated or possible depending on cup types, press-fits, testing methods and materials. In other examples, the amount of force FD to satisfy the predetermined condition PR is between 58-66 N, 50-70 N, or 40-80 N or any values in between these ranges. 
     In some embodiments, the threshold control  314  (and/or the stiffness control  316 ) could be manually-adjusted by the user intraoperatively based on subjective considerations, observations, and the like (e.g., a certain predetermined condition PR is adjusted higher or lower based on user preference). In some embodiments, the predetermined condition PR may be based on patient-specific data (e.g., height, weight, age, bone density, body-mass-index BMI, and the like) that can be entered using an input device  146  of the user interface  142 . In some embodiments, the predetermined condition PR may be at least partially determined intraoperatively, such as by a “wiggle test” similar to as is described in U.S. Patent Application Publication No. US 2015/0094736 A1, entitled “System and Method of Controlling a Robotic System for Manipulating Anatomy of a Patient During a Surgical Procedure,” the disclosure of which is hereby incorporated by reference in its entirety. However, other configurations are contemplated. 
     In other implementations, the first constraint criteria C 1  or the second constraint criteria C 2  can be dynamically determined or adjusted based on measurements from the sensing system or sensor  180 . The controller can correlate the magnitudes or values of the sensed measurements to stiffness values, e.g., using a look-up table stored in memory. This technique can be implemented with a threshold as described above, or without regard to any threshold. 
     As noted above, the functionality afforded by the surgical system  100  in switching between the first and second modes M 1 , M 2  (and/or other modes) could be carried out using other components of the sensing system  206  besides (and/or in addition to) the sensor  180 . By way of non-limiting example, and referring again to  FIGS. 24A-24C , the localizer  158  and one or more trackers  160  (e.g., the first patient tracker  160 A and the second tool tracker  160 I) could be utilized to monitor system conditions SYC such as concurrent movement of the target site TS with the impactor assembly  210  in ways that satisfy predetermined conditions PR. Here, movement which satisfies one or more predetermined conditions PR could be based on various combinations of duration and direction, such as movement which suggests that the impactor assembly  210  is fixed” to the target site TS with misalignment between the first axis A 1  and the trajectory T, movement which suggests that the target site TS is being lifted off of the work surface WS or is otherwise moving in an unintended direction, and the like. Here, combinations of components of the sensing system  206  could be used together such that satisfying predetermined conditions PR to effect changing between modes M 1 , M 2  requires multiple predetermined conditions PR to be satisfied based on the same or different types of system conditions SYC. By way of non-limiting example, the sensor  180  could be used to detect when the user is applying impact force FI, and could change how the predetermined conditions PR are defined for a period of time encompassing the impaction event, such as to briefly interpret movement of the target site TS via the first patient tracker  160 A in a different way during impaction to prevent false detection of a “runaway” condition as the target site TS initially reacts to the application of impact force FI. Other configurations are contemplated. 
     The surgical system  100  can detect impact forces FI (or off-axis forces) and ignore or disregard such impact forces FI for the runaway condition control algorithm. In doing so, the surgical system  100  can identify that the event is an expected impact force FI and not an undesired “runaway” condition. In turn, the surgical system  100  can determine that there is no need to control the manipulator according to the second mode M 2 . In one example to distinguish between runaway condition and impact forces FI, the system  100  analyzes X and Y component force signals from the force torque sensor  180 . The Z-component force was disregarded because the Z-axis force is not constrained in the mechanical design. To detect a runaway condition, in one implementation, the system  100  can average magnitude force over a certain duration of time (125 ms as an example) of X and Y axis forces combined and determine if this average magnitude force is greater than a force threshold. A standard deviation over that same duration can be computed to determine if the same is below a threshold. If the threshold is satisfied, then the system  100  can determine that the runaway condition exists. In one experiment, example force deviations in the X and Y directions in the runaway condition were in the range of +/−10-60 N. There may be other manners of determining that the runaway condition exists. For example, the measured X and Y forces can be individually compared to threshold limits over time. Other factors can be considered when determining thresholds for detecting the runaway conditions. 
     On the other hand, to detect the impaction force FI (as compared with a runaway condition), the X, Y and Z components of force as obtained by the sensor  180  can be analyzed by the sensing system  100  over a period of time (e.g., 30-60 seconds) during which impaction occurs. In one example, the majority of the forces during the impaction event occur in the Z-direction due to the mechanical nature of the assembly. However, X and Y forces occur depending on the manner or accuracy in which a user hits the impactor. During this period of time, each of the X, Y and Z components produce individual signal spikes indicative of each impact. The sensing system  100  can isolate each of the signal spikes indicative of each impaction. In one example, each signal spike was experimentally determined to last for a duration within the range of 100-150 ms. The sensing system  100  can then compute the duration of each impaction event and compute a standard deviation during that computed duration. From there, a threshold is set to define the impaction event. If the threshold is satisfied, then the system  100  can determine that the impact event occurred. In one experiment, example force deviations in the X and Y directions in response to impaction events were in the range of +/−10-30 N and example force deviations in the Z direction in response to impaction events were in the range of +/−20-40 N. There may be other manners of determining that the impaction event occurs. For example, the measured forces can be individually compared to thresholds over time. Also, thresholds for detecting the runaway conditions can vary depending on factors such as cup type, cup size, patient data, impactor parameters, expected impaction forces or the like. By being able to filter between runaway and impact events, the system  100  can intelligently modify the constraint criteria only when needed to counteract runway condition. 
     Furthermore, combining different types of predetermined conditions PR to be satisfied before changing between modes M 1 , M 2  could also be implemented with other types of tools  104 , such as the powered surgical device  150  described above in connection with  FIGS. 12-14D . For example, predetermined conditions PR associated with system conditions SYC defined by operation of the power generation assembly  152  (e.g., motor speed, load, and the like) could be compared against predetermined conditions PR associated with system conditions SYC defined by the navigation system  128 , the sensor  180 , and the like, such as to avoid changing between modes M 1 , M 2  if the energy applicator  114  is still rotating even where there is concurrent movement of the tool  104  and the target site TS that would otherwise cause the controller  124  to change between modes M 1 , M 2 . Here too, the example provided above is intended to be illustrative and non-limiting, and other configurations are contemplated. 
     In one example, and with reference to  FIG. 26 , the “runaway” condition may exist in a situation where a tool  104 , such as a tool having a bur  154  as the energy applicator  114 , engages with the target site TS bone while being constrained by a virtual boundary  174  associated with the target site TS. More specifically, the runaway condition may exist if the bur  154  becomes trapped, disposed, or wedged between the virtual boundary  174  and the target site TS bone. As a result of this situation, the bur  154  can be pushed partially outside of the virtual boundary  174 . Because the virtual boundary  174  is configured to constrain tool  104  motion, the system controls the manipulator to apply a reactive force RF to the bur  154 . This reactive force RF causes the bur  154  push against the target site TS bone causing the target site TS bone to move. The target site TS is tracked by the navigation system through tracker  160 A. Therefore, the pushing of the target site TS will cause a corresponding movement of the associated virtual boundary  174 , in turn causing the reactive force RF to persist to the runaway condition. Implementations of the systems, methods and techniques described above can be fully applied to prevent this scenario. In this example, the first constraint criteria C 1  and second constraint criteria C 2  can be like any of those described above to prevent the runaway condition. Additionally or alternatively, the constraint criteria C 1 , C 2  may relate to a magnitude or direction of the reactive force RD, a stiffness or damping parameter associated with the reactive force RF, a shape of the virtual boundary  174 , a flexibility of the virtual boundary  174 , a stiffness or damping parameter associated with the orientation of the tool  104  and/or energy applicator  114 , or enabling position or orientational degrees of freedom for the tool  104  and/or energy applicator  114 . 
     In one implementation, the present disclosure is also directed toward a method of operating the surgical system  100  comprising the impactor assembly  210  having the interface  212  for releasably securing the implantable component  116 , the guide  208  having the channel  262  formed to receive the impactor assembly  210 , the manipulator  102  configured to support the guide  208  relative to the target site TS along the trajectory T, the sensor  180 , and the controller  124  coupled to the manipulator  102  and the sensor  180  and being configured to perform different steps. The steps include: operating the manipulator  102  in the first mode M 1  to maintain alignment of the guide  208  with respect to the trajectory T according to the first constraint criteria C 1 ; operating the manipulator  102  in the second mode M 2  to maintain alignment of the guide  208  with respect to the trajectory T according to the second constraint criteria C 2  different from the first constraint criteria C 1 ; detecting force FD occurring between the target site TS and the manipulator  102  with the sensor  180 ; and determining that the force FD detected by the sensor  180  satisfies the predetermined condition PC and changing operation of the manipulator  102  from the first mode M 1  to the second mode M 2  in response. 
     In this way, the techniques, methods, and embodiments of the surgical system  100  of the present disclosure afford significant advantages in connection with various types of surgical procedures carried out using manipulators  102  to support different types of tools  104  relative to target sites TS. The functionality afforded by the controller  124 , the sensing system  206 , and the manipulator  102  helps ensure that surgeons and other users are able to carry out surgical procedures in a safe, reliable, and predictable manner. Specifically, the ability to change between modes M 1 , M 2  in response to detecting different types of system conditions SYC which satisfy predetermined conditions PR helps prevent “runaway” conditions (and other types of undesired movement of tools  104 ) that could otherwise “lift” or “turn” the patient P via the manipulator  102 . 
     Those having ordinary skill in the art will appreciate that aspects of the embodiments described and illustrated herein can be interchanged or otherwise combined. 
     It will be further appreciated that the terms “include,” “includes,” and “including” have the same meaning as the terms “comprise,” “comprises,” and “comprising.” Moreover, it will be appreciated that terms such as “first,” “second,” “third,” and the like are used herein to differentiate certain structural features and components for the non-limiting, illustrative purposes of clarity and consistency. 
     Several configurations have been discussed in the foregoing description. However, the configurations discussed herein are not intended to be exhaustive or limit the invention to any particular form. The terminology which has been used is intended to be in the nature of words of description rather than of limitation. Many modifications and variations are possible in light of the above teachings and the invention may be practiced otherwise than as specifically described.