Estimating joint friction and tracking errors of robot end effectors

Abstract

A computerized method for estimating joint friction in a robotic wrist joint of an end effector is disclosed. A sensor measurement of force or torque is generated in a transmission device that mechanically couples the robotic wrist to an actuator. The joint friction in the robotic wrist joint driven by the actuator is calculated by applying the sensor measurement of force or torque to a closed form mathematical expression that relates a transmission force or transmission torque variable to a joint friction variable. A tracking error of the end effector is also calculated using a closed form mathematical expression that relates the joint friction variable to the tracking error. Other aspects are also described and claimed.

Description

[0001] This patent application claims the benefit of U.S. Provisional Application No. 62 / 858,937 filed on an earlier filing date of June 7, 2019. Technical Field

[0002] Embodiments related to robotic systems are disclosed. More specifically, embodiments related to surgical robotic systems and techniques for estimating joint friction and tracking errors of end effectors of surgical robotic tools are disclosed. Background Art

[0003] Endoscopic surgery involves viewing inside a patient's body and performing surgery inside the body using an endoscope and other surgical tools. For example, laparoscopic surgery can use a laparoscope to enter and view the abdominal cavity. Endoscopic surgery can be performed using manual tools and / or surgical robotic systems with robotic-assisted tools.

[0004] The surgical robotic system can be remotely operated by a surgeon to control a robotic-assisted tool located at the operating table. The surgeon can use a computer console located in the operating room, or it can be located in a different city, to command the robot to manipulate the surgical tool mounted on the operating table. The robotically controlled surgical tool can be a grasper mounted on a robotic arm. Thus, the surgical robotic system can be remotely controlled by the surgeon to grasp tissue during robotic surgery.

[0005] Control of the surgical robotic system may require control input from the surgeon. For example, the surgeon may hold in her hand a user input device (UID) such as a joystick or computer mouse that she manipulates to generate signals for control commands that drive actuators to control the movement of surgical robotic system components (e.g., a robotic arm) and / or surgical tools including their end effectors attached to the arm. Summary of the invention

[0006] There may be a tracking error between the commanded position x1 at the actuator (generated in part by the current state or posture of the UID) and the commanded position (e.g., angle) x2 of the end effector that is mechanically coupled to the actuator via a transmission (so as to be driven by the actuator). The following details how the tracking error may be mathematically estimated (e.g., calculated by a programmed processor) based on i) the value of the mechanical compliance (or equivalent stiffness or elasticity) of the transmission, and ii) the value of the joint friction that may resist the commanded motion of the end effector.

[0007] Another aspect of the present disclosure is a method for estimating (e.g., calculating) joint friction or frictional forces in a robotic wrist joint based on force measurements (e.g., cable force measurements, representing tension in a cable) through a transmission device that couples the robotic wrist to its actuators. The estimated joint friction can then be used to estimate the tracking error of an end effector.

[0008] In one aspect, the problem to be solved is how to determine (e.g., estimate) the amount of joint friction, and then use the estimated joint friction along with, for example, known (e.g., assumed) tool compliance or elasticity to estimate the tracking error of a controlled end effector. The solution to this problem helps the designer of a surgical robotic system understand and reduce the tracking error as needed. This can be accomplished by the designer selecting an appropriate value for the transmission stiffness (e.g., greater cable stiffness) or seeking ways to reduce the friction torque in the robotic wrist (e.g., by lubrication or by using different materials).

[0009] The above summary does not include an exhaustive list of all aspects of the invention. It is contemplated that the present invention includes all systems and methods that can be implemented by all suitable combinations of the various aspects summarized above and those disclosed in the detailed description below and specifically pointed out in the claims filed with this patent application. Such combinations have specific advantages not specifically recited in the above summary. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In various embodiments, description is made with reference to the accompanying drawings. However, certain embodiments may be implemented without one or more of these specific details, or may be implemented in combination with other known methods and configurations. Embodiments of the present invention are therefore illustrated in the drawings by way of example and not by way of limitation, and similar reference numerals in the drawings refer to similar elements. It should be noted that reference to "one" or "a kind of" embodiment of the present invention or "one" or "one" aspect of the present disclosure in this disclosure is not necessarily the same embodiment or aspect, and they refer to at least one. In addition, for the sake of brevity and to reduce the total number of drawings, a given drawing may be used to illustrate features of more than one embodiment of the present invention, and all elements in the drawings may not be required for a given embodiment.

[0011] Figure 1 is a pictorial view of an exemplary surgical robotic system 100 in a surgical setting.

[0012] Figure 2 The concept of tracking error using an exemplary simple mechanical system with friction and compliance is illustrated.

[0013] Figure 3A and Figure 3BExemplary robotic end effectors are shown that include a pair of jaws (for the pitch degree of freedom) at a robotic wrist in closed and open states, respectively.

[0014] Figure 4 A free body diagram of a pair of jaws and its robot wrist (for the pitch degree of freedom) is shown. DETAILED DESCRIPTION

[0015] In the following description, many specific details, such as specific configurations, dimensions and processes, are listed to provide a comprehensive understanding of the embodiments. In other cases, well-known processes and manufacturing techniques are not described in particular detail to avoid unnecessary fuzzy descriptions. "One embodiment", "embodiment" etc. mentioned throughout this specification means that the specific features, structures, configurations or characteristics described are included in at least one embodiment. Therefore, the phrases "one embodiment", "embodiment" etc. that appear everywhere in the entire specification do not necessarily refer to the same embodiment. In addition, in one or more embodiments, specific features, structures, configurations or characteristics can be combined in any suitable manner.

[0016] Relative terms are used throughout the specification to indicate relative positions or directions. For example, "distal" may indicate a first direction away from a reference point (e.g., away from an operator). Similarly, "proximal" may indicate a position in a second direction opposite to the first direction (e.g., toward an operator). However, such terms are provided to establish a relative frame of reference and are not intended to limit the use or orientation of the device to the specific configurations described in the various embodiments below.

[0017] Figure 1 1 is a pictorial view of an exemplary surgical robotic system 100 in a surgical setting. The robotic system 100 includes a user console 120, a control tower 130, and one or more surgical robotic arms 112 at a surgical robotic platform 111 (e.g., a table, a bed, etc.). The system 100 may incorporate any number of devices, tools, or accessories for performing a surgical procedure on a patient 102. For example, the system 100 may include one or more surgical tools 104 for performing a surgical procedure. The surgical tool 104 may include an end effector attached to a distal end of the surgical arm 112 for performing a surgical procedure.

[0018] Each surgical tool 104 can be manually manipulated, robotically manipulated, or both during a surgical procedure. For example, the surgical tool 104 can be a tool used to access, view, or manipulate the internal anatomy of the patient 102. In one embodiment, the surgical tool 104 is a grasper that can grasp tissue of the patient 102. The surgical tool 104 can be manually controlled by a bedside operator 106; or it can be robotically controlled via actuated movement of a surgical robotic arm 112 to which it is attached. The robotic arm 112 is shown as a table mounted system, but in other configurations, the arm 112 can be mounted in a cart, a ceiling or sidewall, or in another suitable structural support.

[0019] Generally, a remote operator 107 (such as a surgeon or other operator) can use a user console 120 to remotely manipulate the arm 112 and / or surgical tool 104, for example, via teleoperation. The user console 120 can be located in the same operating room as the rest of the system 100, such as in a Figure 1 As shown. However, in other environments, the user console 120 may be located in an adjacent or nearby room, or it may be located in a remote location, for example, in a different building, city, or country. The user console 120 may include a seat 122, a foot control 124, one or more handheld user input devices UID 126, and at least one operator display 128, which is configured to display, for example, a view of a surgical site in the body of the patient 102. In the exemplary user console 120, the remote operator 107 sits in the seat 122 and views the operator display 128, while manipulating the foot control 124 and the handheld UID 126 to remotely control the arm 112 and the surgical tool 104 (which is mounted on the distal end of the arm 112). The foot control 124 may be a foot pedal, such as seven pedals, which generate motion control signals when actuated. The user console 120 may include one or more additional input devices such as a keyboard or a joystick to receive manual input to control the operation of the user console 120 or the surgical robot system 100.

[0020] In some variations, the bedside operator 106 can also operate the system 100 in an "in bed" mode, where the bedside operator 106 is now located on the side of the patient 102 and is manipulating the robotically driven tools (which are attached to the end effector of the arm 112) at the same time, for example, holding the handheld UID 126 and the manual laparoscopic tools with one hand. For example, the left hand of the bedside operator can manipulate the handheld UID 126 to control the robotic components, while the right hand of the bedside operator can manipulate the manual laparoscopic tools. Therefore, in these variations, the bedside operator 106 can perform both robotic-assisted minimally invasive surgery and manual laparoscopic surgery on the patient 102.

[0021] During the exemplary procedure (surgical operation), the patient 102 is prepared and draped in a sterile manner and anesthetized. Initial access to the patient's anatomical structure can be achieved using known techniques, such as by forming an incision in the skin. Trocars and / or other surgical tools can be inserted into the incision through the patient's visual entrance. The trocar can then be positioned at the surgical site (in the patient's body). The initial access to the surgical site can be performed manually when the arm of the robotic system 100 is in a stowed configuration or a retracted configuration (to facilitate access to the surgical site) or a stay posture set by the operator. Once the initial access is completed, the initial positioning or preparation of the robotic system can be performed, including docking the arms 112 to their trocars, respectively, and attaching tools (with end effectors) to the arms 112, respectively. Then, the surgical operation continues, wherein the remote operator 107 at the user console 120 uses foot controls 124 and UID 126 to manipulate various end effectors and possible imaging systems to perform the surgical operation. Manual assistance may also be provided at the surgical bed or table by a bedside person (e.g., bedside operator 106) in sterile clothing who may perform tasks on one or more of the robotic arms 112, such as retracting tissue, performing manual repositioning, and tool changes. Non-sterile personnel may also be present to assist the teleoperator 107 at the user console 120. When the procedure or surgical procedure is completed, the system 100 and / or the user console 120 may be configured or arranged to be in a state that facilitates postoperative procedures (such as cleaning or disinfection) and the entry or printing of healthcare records via the user console 120.

[0022] In one embodiment, the remote operator 107 holds and moves the UID 126 to provide input commands to move the robotic arm actuator 114 in the robotic system 100. The UID 126 can be communicatively connected to the rest of the robotic system 100, for example, via the console computer system 110. The UID 126 can generate spatial state signals corresponding to the movement of the UID 126, such as the position and orientation of the handheld housing of the UID, and the spatial state signals can be input signals to control the movement of the robotic arm actuator 114. The robotic system 100 can generate control signals based on the spatial state signals to control the proportional movement of the actuator 114. In one embodiment, the console processor of the console computer system 110 receives the spatial state signals and generates corresponding control signals. Based on these control signals that control how the actuator 114 is powered to move the segments or connectors of the arm 112, the movement of the corresponding surgical tool, including the end effector attached to the arm, can simulate the movement of the UID 126. Similarly, interaction between the teleoperator 107 and the UID 126 may generate, for example, a grasp control signal that drives an actuator in the arm 112 , thereby causing the jaws of a grasper of a surgical tool (which is attached to the arm 112 ) to close and grasp tissue of the patient 102 .

[0023] Alternatively, sensing motion of the UID 126 may be provided to control other aspects of the surgical robotic system 100. For example, a gesture detected by a finger clutch may generate a clutch signal to pause motion of the actuator 114 and the corresponding surgical tool 104. For example, when an operator contacts the finger clutch of the UID 126 with a finger, the finger clutch may generate a clutch signal, and the clutch signal may be an input signal for pausing motion of the actuator 114. Similarly, one or more capacitive sensing pads may be located on the UID 126, and an operator may touch the capacitive sensing pads to control an endoscope's camera view, a cursor on a display of the user console 120, etc., while performing a diagnostic, surgical, laparoscopic, or minimally invasive surgical procedure, or another robotic procedure.

[0024] The surgical robotic system 100 may include several UIDs 126, wherein respective control signals are generated for each UID that controls the actuators of the respective arm 112 and the surgical tool (end effector). For example, the teleoperator 107 may move the first UID 126 to control the movement of the actuator 114 located in the left robotic arm, wherein the actuator responds by moving the linkage, gears, etc. in the arm 112. Similarly, the movement of the second UID 126 by the teleoperator 107 controls the movement of another actuator 114, which in turn moves other linkages, gears, etc. of the robotic system 100. The robotic system 100 may include a right arm 112 fixed to a bed or table on the right side of the patient, and a left arm 112 located on the left side of the patient. The actuator 114 may include one or more motors, such as a motor housed in the arm, included in a tool drive housing on the arm 112. A mechanical transmission device (partially in the arm 112, particularly in the tool drive housing, and partially in the housing of the surgical tool) couples the actuator motor to the joint of the end effector. The actuator motors are controlled so that they drive the rotation of the joints of the end effector to change the orientation of the grasper (a part of the end effector). The movement of several actuators 114 in the same arm 112 can be controlled by a spatial state signal generated from a specific UID 126. The UID 126 can also be used to convert finger squeezes into corresponding movements of the jaws of the grasper. For example, the UID 126 can generate a grasp signal to control the movement of an actuator (e.g., a linear actuator) that opens or closes the jaws of the grasper (which is at the distal end of the surgical tool) to grasp tissue in the patient 102.

[0025] In some aspects, communication between the platform 111 and the user console 120 may be through a control tower 130, which may convert operator commands received from the user console 120 (and more specifically from the console computer system 110) into robotic control commands transmitted to the arm 112 on the robotic platform 111. The control tower 130 may also transmit status and feedback from the platform 111 back to the user console 120. The robotic platform 111, the user console 120, and the control tower 130 may be communicatively connected via wired and / or wireless links using any suitable data communication protocol among a variety of data communication protocols. Any wired connection may optionally be built into the floor and / or walls or ceiling of the operating room. The robotic system 100 may provide video output to one or more displays, including displays within the operating room and remote displays accessed via the Internet or other networks. The video output or feed may also be encrypted to ensure privacy, and all or part of the video output may be saved to a server or electronic health record system.

[0026] It should be understood that Figure 1 The operating room scenes are illustrative and may not accurately represent certain medical practices.

[0027] Tracking Error

[0028] See now Figure 2 , which is used to illustrate the concept of tracking error. It depicts an exemplary simple system in which a force F pulls a mass m through a cable with stiffness k. The friction between the mass and the ground is Ff, and the velocity is assumed to be constant (or the mass m is negligible compared to F and Ff). This gives the result F=Ff. The tracking error between the command position (x1) and the controlled position (x2) is e=x1-x2, which is essentially equal to the elongation of the cable (spring). Therefore, the tracking error can be given by e=Ff / k (ignoring external forces and inertial forces of the mass). This means that the following can be shown: the error is proportional to the friction; the error is inversely proportional to the stiffness; and if the friction is zero (Ff=0), or the stiffness is infinite (the cable is rigid), the tracking error is essentially zero e=0, and in the absence of friction, the external load (applied on m) can play the same role as friction. In this case, in order to reduce the tracking error, efforts should be made to increase the stiffness k.

[0029] Some formulas

[0030] In order to perform control tasks (via a microprocessor configured or programmed according to instructions stored in a computer-readable storage medium such as a microelectronic memory) to control the movement of an end effector, it is often beneficial to define a consistent coordinate system for the joint angles of the end effector associated with such movement. For example, consider an exemplary end effector comprising a robotic wrist coupled to two jaws of a grasper, such as Figure 3A and Figure 3B 10,166,082, which is incorporated herein by reference. The jaws pivot about axis 410, wherein the jaw angle (θ jaw ) can be defined as the angle between the two jaws 401A and 401B, and the yaw angle (θ yaw ) is defined as the angle between axis 452 and the line that bisects the jaw angle. Therefore:

[0031]

[0032] exist Figure 3B The conversion between the angles in and these newly defined angles is as follows:

[0033]

[0034]

[0035] This newly defined coordinate system is called the extrinsic joint angle. In addition, the following nomenclature can be established for the pulley geometry:

[0036] a)r 11 is the radius of the outer pulley 425A and the outer pulley 425C, on which the cable 405A and the cable 405C are located respectively;

[0037] b)r 12 is the radius of the inner pulley 425B and the inner pulley 425D on which the cables 405B and 405D are located respectively (r 11 May or may not be equal to r 12 );

[0038] c)r 21 is the radius of the pulley 415A on the side where the cable 405A is located (see the center of the pulley 415A and the axis 412, as shown in FIG. Figure 3A shown);

[0039] d)r 22 is the radius of the pulley 415A on the side where the cable 405B is located (see the center of the pulley 415A and the axis 412, as shown in FIG. Figure 3A shown);

[0040] e)r 31 is the radius of pulley 415B on the side where cable 405C is located; and

[0041] f)r 32 It is the radius of the pulley 415B on the side where the cable 405D is located.

[0042] Although in the above example, the design is symmetrical, 31 =r 21 ,r 32 =r 22 And r 21 ≠r 22 (like Figure 3A ), but in some other designs, there may be r 31 =r 21 =r 32 =r 22 , and r 11 =r 12 .

[0043] The following equation gives the cable tension or force in the transmission device, Zeta, (ξ [4×1] ) and joint torque, Tau,(τ [3×1] )

[0044] Tau [3×1] =B [3×4] Zeta[4×1] (3)

[0045] The square matrix (B) has the following form

[0046]

[0047] and (ξ1, ξ2, ξ3, ξ4) correspond to the cable tensions on cables 405A, 405B, 405C and 405D, respectively.

[0048] In formula (3), (τ [3×1] ) is the vector of virtual joint torques applied by the cables, which may cause the joints shown in Figures 3a and 3b to move against friction and against external forces (which may be present on the end effector). The vector (τ [3×1] ) has three components:

[0049] τ [3×1] =[τ1 τ2 τ3] T (6)

[0050] Where (τ1) is the pitch joint torque, and (τ2) and (τ3) are the joint torques of jaw 401A and jaw 401B, respectively.

[0051] The kinematic relationship that relates the ideal cable displacement (assuming the cable is inelastic) to the jaw angle is as follows:

[0052] q [4×1] =[q1 q2 q3 q4] T =B T ·θ [3×1] (7)

[0053] Among them (q [4×1] ) is a four-element vector containing the desired displacements of cables 405A-405D, and (θ [3×1] ) is in Figure 3B The angle vector is shown in:

[0054] θ [3×1] =[θ1 θ2 θ3] T (8)

[0055] In actual situations, the cable is elastic, and the actual cable displacement and the ideal cable displacement are related as follows:

[0056] ξ [4×1] = k(x [4×1] -B T ·θ [3×1] ) (9)

[0057] where ξ [4×1]is the cable tension, k is the cable elastic constant in N / m (assuming all cables are similar), and (x [4×1] -B T ·θ [3×1] ) is the actual cable displacement x [4×1] and ideal cable displacement B T ·θ [3×1] The difference between.

[0058] Tracking error as a function of friction and stiffness

[0059] From formula (7), we get:

[0060] θ [3×1] =B -T ·q [4×1] (10)

[0061] Using Hooke's law for each cable, the cable force is related to the displacement on either side of the cable as follows:

[0062] ξ [4×1] = k(x [4×1] -q [4×1] ) (11)

[0063] where k is the elastic constant of the cable in N / m, a measure of stiffness (assuming all cables are similar).

[0064] Using formulas (10) and (11), we obtain:

[0065] θ [3×1] =B -T ·(x [4×1] -k -1 ξ [4×1] ) (12)

[0066] Here θ [3×1] is the vector of actual joint angles. On the other hand, since x [4×1] is the cable displacement at the proximal end, B - T x [4×1] is the joint angle vector we believe to be obtained using the proximal measurement. The difference between the actual joint angles in equation (12) and these angles (the angles we believe to be obtained) is the joint angle error, as follows:

[0067] θ e[3×1] =B -T ·x [4×1] -θ [3×1] =k -1 B -T ξ [4×1] (13)

[0068] It is obvious from this formula that the tracking error is inversely proportional to the stiffness k.

[0069] In order to study how friction affects tracking error, it is necessary to convert cable force into joint torque using the following formula: Formula (3):

[0070]

[0071] Among them, BB T is a non-singular square matrix of size 3×3. In addition, is the vector of joint torques - see equation (6).

[0072] To proceed further, consider the case where there is a gripping force but no lateral load, but this does not affect the more general applicability of this case. This case is considered here only for the sake of illustrating the broader concept. Figure 4 The free body diagram of the two jaws and the proximal wrist (for pitch degrees of freedom, DOF) is shown, where ∑F1 to ∑F4 and ∑τ4 are the composite reaction forces and torques at the joints, τ f1 is the friction at the pitch joint, and τ f2 and τ f3 are the joint frictions of Jaw1 and Jaw2 respectively. In addition, F g is the gripping force between the two jaws, and τ i is the joint torque. Finally, F ext_pitch and F ext_yaw is the lateral load applied at the jaw tips and is assumed to be evenly distributed across the two jaws.

[0073] The motion equation for the proximal wrist about the pitch axis is as follows:

[0074]

[0075] where τ ext_pitch It is the external force rotation around the pitch axis caused by the external force on the jaws.

[0076] For the jaws, the external load is usually applied by the object held between the jaws. Therefore, it is assumed that each jaw carries half of the load. As a result, we get:

[0077]

[0078]

[0079] In equation (15-17), the right-hand side consists of inertia, Coriolis, centrifugal, and gravity terms. However, when the moving parts (wrist and jaw) have very small mass and inertia, these terms are negligible compared to friction and drive torque. Therefore, the right-hand side of equation (15-17) can be ignored. Therefore, we will get:

[0080]

[0081] Therefore, we find that the vector of joint torques is:

[0082]

[0083] Substituting this vector back into equation (14), we obtain:

[0084]

[0085] Using equation (2), the error angle in the external reference coordinate system will be as follows:

[0086]

[0087] Substituting equation (20), we obtain:

[0088]

[0089] To eliminate the effects of friction and grip force on tracking error, the terms in parentheses can be further decomposed as follows:

[0090]

[0091] The first term on the right-hand side of the above equation captures the effect of friction on the external reference joint angle error and shows that the tracking error is linearly proportional to the joint friction. The second and third terms capture the effect of the grip force and external load on the tracking error.

[0092] Replace B and D from equations (4) and (2.b) respectively, and assume r 31 =r 21 , and r 32 =r 22 , we get:

[0093]

[0094] Several observations can be made from Equation (24). It can be seen that the pitch and yaw tracking errors due to friction are only affected by τ f1 , and τ f2 +τ f3 On the other hand, the tracking error of the jaw DOF is only affected by τ f2 -τf3 As expected, it is also observed that the gripping force only affects the jaw DOF. However, we know that the jaws are closed during the application of the grip. Therefore, the actual measured jaw angle should be zero (or should be the jaw closing angle at the contact point). The second term in equation (20) represents the additional quantity read (as the joint state) when the jaws are closed. In order to estimate the joint angle, this value needs to be subtracted from the estimated jaw angle obtained based only on the cable displacement and inverse kinematics. In addition, an approximation / simplification for the case where a gripping force is applied can be considered. In this case, since the jaws move in the same direction and at the same speed, and the forces on the jaw pins are very similar, the joint friction values ​​will also be similar. Therefore, in this special case it can be assumed that

[0095] In addition, from the third term on the right hand side of equation (24), we can observe that τ ext_pitch and τ ext_yaw The effect on tracking error is very similar to τ f1 and τ f2 +τ f3 Basically plays a similar role to providing resistance on the distal end of the device. Without knowing the magnitude of the external loads, and without any distal sensors, they are essentially indistinguishable from joint friction.

[0096] As seen in equation (24), joint friction values ​​(e.g., Tauf1, which is the friction torque at the pitch joint, and Tauf2 and Tauf3, which are the joint frictions for Jaw1 and Jaw2, respectively) are needed to calculate the tracking error of the end effector. The friction in the joint is proportional to the normal force on the joint pin. These forces can change with the magnitude of the gripping force or external load on the jaws, thereby changing the amount of friction. In the following, the relationship between friction / torque and cable force is explored, where a sensor can be used to measure the cable force.

[0097] As defined in equation (6), the driving torque can be expressed using equation (3) as a function of the cable force:

[0098]

[0099] Solving equation (25) to eliminate the drive torque, and assuming r21 = r31 and r22 = r32, we obtain:

[0100]

[0101] As mentioned above, when the jaws grasp an object and move together, it follows that Using the third formula in equation (26), we get the formula that can be used to estimate the gripping force:

[0102]

[0103] As long as cable force measurements (measured by sensors generating forces in the transmission device that mechanically couples the robot wrist to its actuator) are available, the joint friction torque can be calculated by equation (26), which is a closed form mathematical expression that relates the transmission force or torque variables Zeta1, Zeta2, Zeta3, Zeta4 to the joint friction variables Tauf1, Tauf2, Tauf3 of the joints of the end effector. The joint friction values ​​thus calculated can then be substituted back into equation (24), which is a closed form mathematical expression that relates the joint friction variables to the tracking error, for example for calculating the estimated tracking error of the end effector The designer can then determine an appropriate value for cable stiffness (k), or may decide to reduce the friction torque (eg, by lubrication, or using a different material) as a way to reduce tracking error.

[0104] Although certain aspects have been described and illustrated in the above drawings, it should be understood that such description is merely illustrative of the invention and not limiting, and the invention is not limited to the specific constructions and arrangements shown and described, as various other modifications may occur to those of ordinary skill in the art. For example, although the above description describes a method of estimating joint friction, particularly joint friction associated with controlling the jaw angle and pitch and yaw of a surgical robot wrist, using a pair of wrist-pivoting jaws, the method is also applicable to estimating joint friction in other types of surgical robot end effectors (e.g., needle drives). Therefore, this description should be regarded as illustrative and not limiting.

Claims

1. A computerized method for estimating joint friction in a robotic wrist joint of an end effector, the method comprising: a. A sensor measurement of the cable force generated in the transmission device that mechanically couples the robot wrist to the actuator; b. calculating joint friction in the robot wrist joint driven by the actuator, wherein the joint friction is calculated by applying the sensor measurement of the cable force to a closed form mathematical expression that relates a transmission cable force variable to a joint friction variable; as well as c. Calculating the tracking error of the end effector using a closed form mathematical expression that relates the joint friction variable to the tracking error.

2. The method of claim 1, wherein the cable force measurement is a measurement of the force or tension of a plurality of cables that are part of the transmission means mechanically coupling the robot wrist to the actuator.

3. The method of claim 2, wherein the closed form mathematical expression relates a plurality of cable tension variables to a plurality of joint friction torque variables, wherein the plurality of joint friction torque variables represent friction at a plurality of joints of the end effector.

4. The method of claim 1 wherein the end effector comprises a pair of pivoting jaws having a jaw angle therebetween and mechanically coupled to the wrist to be driven by the actuator, and wherein the tracking error refers to the jaw angle. The method of claim 4 , wherein the joint friction variable represents friction at the wrist joint.

6. The method of claim 1, wherein the cable force measurement is a measurement of force or tension of a plurality of cables that are part of the transmission mechanically coupling the robotic wrist to the actuator.

7. The method of claim 6, wherein the closed form mathematical expression relates a plurality of cable tension variables to a plurality of joint friction torque variables, wherein the plurality of joint friction torque variables represent friction at a plurality of joints of the end effector.

8. An article of manufacture comprising a computer readable storage medium having stored therein instructions that configure a processor to estimate joint friction in a robotic wrist joint of an end effector that is part of a surgical tool, comprising: a. generating a sensor measurement of a cable force in a transmission device, wherein the transmission device mechanically couples the robot wrist to an actuator so that the actuator can drive the robot wrist; as well as b. calculating joint friction in the robot wrist by applying the sensor measurement of the cable force to a closed form mathematical expression that relates a transmission cable force variable to a joint friction variable; Wherein the computer-readable storage medium has additional instructions stored therein, the additional instructions configuring the processor to calculate a tracking error of the end effector using a closed form mathematical expression that relates the joint friction variable to the tracking error.

9. The article of claim 8, wherein the cable force measurement is a measurement of force or tension of a plurality of cables that are part of the transmission mechanically coupling the robotic wrist to the actuator.

10. The article of claim 9, wherein the closed form mathematical expression relates a plurality of cable tension variables to a plurality of joint friction torque variables, wherein the plurality of joint friction torque variables represent friction at a plurality of joints of the end effector.

11. The article of claim 8, wherein the end effector comprises a pair of pivoting jaws having a jaw angle therebetween and mechanically coupled to the robotic wrist to be driven by the actuator, and the tracking error refers to the jaw angle.

12. The article of manufacture of claim 11, wherein the joint friction variable represents friction at the robot wrist joint.

13. The article of manufacture of claim 8, wherein the cable force measurement is a measurement of force or tension of a plurality of cables that are part of the transmission mechanically coupling the robotic wrist to the actuator.

14. The article of claim 13, wherein the closed form mathematical expression relates a plurality of cable tension variables to a plurality of joint friction torque variables, wherein the plurality of joint friction torque variables represent friction at a plurality of joints of the end effector.

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