Patent Description:
Robotic surgical systems such as teleoperative systems are used to perform minimally invasive surgical procedures that offer many benefits over traditional open surgery techniques, including less pain, shorter hospital stays, quicker return to normal activities, minimal scarring, reduced recovery time, and less injury to tissue.

Robotic surgical systems can have a number of robotic arms that move attached instruments or tools, such as an image capturing device, a stapler, an electrosurgical instrument, etc., in response to movement of input devices by a surgeon viewing images captured by the image capturing device of a surgical site. During a surgical procedure, each of the tools is inserted through an opening, either natural or an incision, into the patient and positioned to manipulate tissue at a surgical site. The openings are placed about the patient's body so that the surgical instruments may be used to cooperatively perform the surgical procedure and the image capturing device may view the surgical site.

During the surgical procedure, the tools can include end effectors that are controlled by one or more open loop cables. The end effector can be manipulated by controlling the tension in the cables.

There is a continuing need for improved methods for controlling the tension in the cables to manipulate the end effector.

The invention is limited by the scope of independent claim <NUM>. Disclosed methods of treatment by surgery should only be seen as examples of how to use the device and are not claimed. In an aspect of the present disclosure, a method of controlling an end effector of a surgical robot includes receiving a desired pose, generating a motor torque for each motor, transmitting the motor torques for each motor, generating a null torque for each motor, generating a desired torque for each motor, and transmitting the desired torques to an instrument drive unit (IDU) such that the IDU moves the end effector to the desired pose. A primary controller receives the desired pose of the end effector in three degrees-of-freedom (DOF). The primary controller generates the motor torque for each motor of the IDU in response to receiving the desired pose. The primary controller transmits the motor torques which are received in a secondary controller. The secondary controller generates a null torque for each motor of the IDU to maintain tension in cables of a differential drive mechanism of the IDU. The desired torques are generated for each motor of the IDU which torques include a sum of the motor torques and the null torques for each motor.

In aspects, generating the null torque for each motor of the IDU also includes generating a clamping force between jaws of the end effector. Generating the clamping force may include modifying the desired pose such that a jaw angle between the jaws of the end effector is negative. The method may include verifying a position of the jaws of the end effector is less than a clamping threshold before generating the clamping force. The method may include releasing the clamp force when the jaws have a position greater than a releasing threshold. The releasing threshold may be greater than the clamping threshold.

In some aspects, generating the null torque for each motor includes the secondary controller receiving a sensed torque from the IDU. The sensed torque from the IDU may affect the null torque for each motor of the IDU. Generating the null torque for each motor may include adjusting the null torque for each motor in response to a sensed torque of the respective motor. Adjusting the null torque for each motor may include applying a gain to the motor torque of each motor. Generating the null torque for each motor may include adjusting the null torque for a puller motor for each pair of motors of the IDU in response to the sensed torques.

In certain aspects, generating a desired torque for each motor includes a tertiary controller receiving the motor torques and the null torques and combining the motor torques and the null torques into desired torques including the sum of the motor and null torques. The tertiary controller may transmit the desired torques to the IDU. Combining the motor torques and the null torques may include receiving sensed torques from the IDU and applying a gain to the sum of the motor and null torques to determine the desired torques such that the sensed torques approach the sum of the motor and null torques.

In particular aspects, the secondary controller generates the null torque for each motor in response to receiving a motor position for each motor of the IDU. The motor position received by the secondary controller may be in a joint space. A converter positioned between the IDU and the secondary controller converting a motor position from a motor space to the joint space.

In aspects, generating the motor torque for each motor includes calculating the motor torques in a joint space and compensating for friction. The method may include distributing the motor torques in the joint space to each motor before the secondary controller receives the motor torques for each motor.

In another aspect of the present disclosure, a controller for an end effector that is controlled by four cables of an open loop differential drive mechanism includes a primary controller and a secondary controller. The primary controller is configured to receive a desired pose for the end effector in yaw, pitch, and jaw degrees-of-freedom (DOF), to generate a motor torque for each motor of an instrument drive unit (IDU) to position the end effector in the desired pose, and to transmit the motor torques. The secondary controller is configured to receive the motor torques from the primary controller, and to generate null torques for each of the motors of the IDU to maintain tension in the cables of the differential drive mechanism, and an IDU configured to receive desired torques which include a sum of the motor torques and the null torques, and to manipulate the end effector to the desired pose in response to receiving the desired torques.

In aspects, the controller includes a combination controller that is configured to receive the null torques and the motor torques from the secondary controller, to generate the sum of the motor torques and null torques, and to transmit the sum to the IDU.

In another aspect of the present disclosure, an instrument drive unit (IDU) for controlling an end effector controlled by four cables of an open loop differential drive mechanism includes motors, couplers, and torque sensors. The IDU is controlled by a primary controller and a secondary controller. The motors are configured to receive desired torques and to manipulate the end effector to a desired pose in response to receiving the desired torques. The primary controller is configured to receive the desired pose for the end effector on yaw, pitch, and jaw degrees-of-freedom (DOF), to generate a motor torque for the motors to position the end effector in the desired pose, and to transmit the motor torques. The secondary controller is configured to receive the motor torques from the primary controller, to generate null torques for the motors to maintain tension in the cables of the differential drive mechanism, wherein the desired torques include a sum of the motor torques and the null torques.

In another aspect of the present disclosure, an adapter for a surgical tool that defines a longitudinal axis includes, a first drive screw, a first drive nut, a first cable, a first spring, a second drive screw, a second drive nut, a second cable, and a second spring. The first drive screw is longitudinally fixed and configured to rotate about a first screw axis that is parallel to the longitudinal axis and has a threaded portion. The first drive nut is disposed about the threaded portion of the first drive screw and is threadably coupled to the first drive screw such that the first drive nut longitudinally translates in response to rotation of the first drive screw and the first drive screw rotates in response to longitudinal translation of the first drive nut. The first cable has a proximal portion fixed to the first drive nut and a distal portion. The first spring is disposed about the first drive screw and configured to urge the first drive nut in a first longitudinal direction and has a first spring constant.

The second drive screw is longitudinally fixed and configured to rotate about a second screw axis that is parallel to the first screw axis and has a threaded portion. The second drive nut is disposed about the threaded portion of the second drive screw and is threadably coupled to the second drive screw such that the second drive nut longitudinally translates in response to rotation of the second drive screw and the second drive screw rotates in response to longitudinal translation of the second drive nut. The second cable has a proximal portion fixed to the second drive nut and a distal portion.

The distal portions of the first and second cables are operatively coupled to one another such that translations of the distal portions oppose one another. The second spring is disposed about the second drive screw and configured to urge the second drive nut in the first direction and has a second spring constant. The second spring biasedsuch that the second spring translates the second drive nut and the second cable in the first direction such that the second cable translates the first cable and the first drive nut in a second direction opposite the first direction and against the bias of the first spring such that the tool is biased towards a predetermined pose.

In aspects, the first screw includes a first proximal head that is configured to interface with a first motor and the second screw includes a second proximal head that is configured to interface with a second motor. The first direction may be proximal and the second direction may be distal. The first drive nut may define a first slot with the proximal portion of the first cable fixed in the first slot. The second spring constant may be larger than the first spring constant.

In another aspect of the present disclosure a surgical tool includes an elongate shaft, an end effector, and an adapter. The elongated shaft defines a longitudinal axis and has a proximal end and a distal end. The end effector is supported adjacent the distal end of the elongate shaft and includes a first jaw and a second jaw movable in pitch, yaw, and jaw DOFs. The adapter supports the proximal end of the elongate shaft and includes a first drive screw, a first drive nut, a first cable, a first spring, a second drive screw, a second drive nut, a second cable, and a second spring. The first drive screw is longitudinally fixed and configured to rotate about a first screw axis that is parallel to the longitudinal axis and has a threaded portion. The first drive nut is disposed about the threaded portion of the first drive screw and is threadably coupled to the first drive screw such that the first drive nut longitudinally translates in response to rotation of the first drive screw and the first drive screw rotates in response to longitudinal translation of the first drive nut. The first cable extends through the elongate shaft and has a proximal portion fixed to the first drive nut and a distal portion secured to the end effector. The first spring is disposed about the first drive screw and configured to urge the first drive nut in a first longitudinal direction and has a first spring constant.

The second drive screw is longitudinally fixed and configured to rotate about a second screw axis that is parallel to the first screw axis and has a threaded portion. The second drive nut is disposed about the threaded portion of the second drive screw and is threadably coupled to the second drive screw such that the second drive nut longitudinally translates in response to rotation of the second drive screw and the second drive screw rotates in response to longitudinal translation of the second drive nut. The second cable extends through the elongate shaft and has a proximal portion fixed to the second drive nut and a distal portion secured to the end effector.

The distal portions of the first and second cables are operatively coupled to one another such that translations of the distal portions oppose one another. The second spring is disposed about the second drive screw and configured to urge the second drive nut in the first direction and has a second spring biased such that the second spring translates the second drive nut and the second cable in the first direction such that the second cable translates the first cable and the first drive nut in a second direction opposite the first direction and against the bias of the first spring such that the tool is biased towards a predetermined pose.

In aspects, the distal portions of the first and second cables are each coupled to the first jaw.

In some aspects, the adapter includes a third drive screw, a third drive nut, a third cable, a third spring, a fourth drive screw, a fourth drive nut, a fourth cable, and a fourth spring. The third drive screw is longitudinally fixed within the adapter and configured to rotate about a third screw axis parallel to the longitudinal axis and has a threaded portion. The third drive nut is disposed about the threaded portion of the third drive screw and is threadably coupled to the third drive screw such that the third drive nut longitudinal translates in response to rotation of the third drive screw and the third drive screw rotates in response to longitudinal translation of the third drive nut. The third cable extends through the elongate shaft and has a proximal portion that is fixed to the third drive nut and a distal portion secured to the end effector. The third spring is disposed about the third drive screw and is configured to urge the third drive nut in a third longitudinal direction and has a third spring constant.

The fourth drive screw is longitudinally fixed within the adapter and is configured to rotate about a fourth screw axis that is parallel to the third screw axis and has a threaded portion. The fourth drive nut is disposed about the threaded portion of the fourth drive screw and is threadably coupled to the fourth drive screw such that the fourth drive nut longitudinally translates in response to rotation of the fourth drive screw and the fourth drive screw rotates in response to longitudinal translation of the fourth drive nut. The fourth cable extends through the elongate shaft and has a proximal portion fixed to the fourth drive nut and a distal portion secured to the end effector. The distal portions of the third and fourth cables are operatively coupled to one another such that translations of the distal portions oppose one another. The fourth spring is disposed about the fourth drive screw, is configured to urge the fourth drive nut in the first direction, and has a fourth spring biased such that the fourth spring translates the fourth drive nut and the fourth cable in the first direction. The fourth cable translating the third cable and the third drive nut in the second direction and against the bias of the third spring such that the end effector is biased towards the predetermined pose.

In certain aspects, the distal portion of the first cable is secured to a first side of the first jaw, the distal portion of the second cable is secured to a second side of the first jaw, the distal portion of the third cable is secured to the second side of the second jaw, and the distal portion of the fourth cable is secured to the first side of the second jaw such that the first and fourth cables are disposed on the same side of the first and second jaws, respectively, and the second and third cables are disposed on the same side of the first and second jaws, respectively. The end effector may include a yoke and a clevis. The clevis may be fixed to the distal end of the elongate shaft and the yoke may be pivotally coupled to the clevis about a first axis perpendicular to and intersected by the longitudinal axis. The jaw may be pivotally coupled to the yoke about a second axis perpendicular to the first axis. The first jaw may have a first spindle pivotal about the second axis and the second jaw may have a second spindle pivotal about the second axis. The distal portions of the first and second cables may be secured to opposite sides of the first spindle and the distal portions of the third and fourth cables may be secured to opposite sides of the second spindle.

In particular aspects, the second and fourth springs are configured to maintain the tool in a pose with the first and second jaws in a closed position, the first and second jaws longitudinally aligned with the longitudinal axis, and the yoke aligned with the longitudinal axis. The first, second, third, and fourth cables may be configured to manipulate the pose of the end effector in pitch, yaw, and jaw DOFs.

In another aspect of the present disclosure, a surgical tool configured to selectively connect to a drive unit includes an elongate shaft, an end effector, a first cable, a second cable, a third cable, a fourth cable, and an adapter. The elongate shaft defines a longitudinal axis and has a proximal end and a distal end. The end effector is supported adjacent the distal end of the elongate shaft and includes a first jaw and a second jaw. The first cable extends through the elongate shaft and has a distal portion secured to a first side of the first jaw. The second cable extends through the elongate shaft and has a distal portion secured to a second, opposite side of the first jaw. The third cable extends through the elongate shaft and has a distal portion secured to the second side of the second jaw.

The fourth cable extends through the elongate shaft and has a distal portion secured to the first side of the second jaw. The adapter supports the proximal end of the elongate shaft and is configured to selectively connect to a drive unit. The adapter includes a differential drive mechanism configured to manipulate proximal portions of each of the first, second, third, and fourth cables to manipulate the end effector in pitch, yaw, and jaw DOFs. Each of the first, second, third, and fourth cables are biased proximally and configured to maintain the end effector in a desired pose with the tool is disconnected from a drive unit.

In aspects, the adapter urges each of the first and third cables proximally with a first force and urges each of the second and fourth cable proximally with a second force greater than the first force. The desired pose may be straight in pitch and yaw with the first and second jaws in a closed position such that the first and second jaws are closed and aligned with the longitudinal axis. Alternatively, the desired pose may be straight in pitch and yaw with the first and second jaws in an open position such that the first and second jaws are spaced apart from one another and aligned with the longitudinal axis.

In some aspects, the end effector includes a yoke and a clevis. The clevis may be fixed to the distal end of the elongate shaft. The yoke is pivotally coupled to the clevis about a first axis that is perpendicular to and intersected by the longitudinal axis. The jaws may be pivotally coupled to the yoke about a second axis perpendicular to the first axis. The first jaw has a first spindle pivotal about the second axis and the second jaw has a second spindle pivotal about the second axis.

In certain aspects, the differential drive mechanism includes a drive screw, a nut threadably coupled to the drive screw, and a spring biasing the nut proximally for each of the first, second, third, and fourth cables with the proximal portion of each of the first, second, third, and fourth cables fixed to a respective nut.

Further, to the extent consistent, any of the aspects described herein may be used in conjunction with any or all of the other aspects described herein.

Various aspects of the present disclosure are described hereinbelow with reference to the drawings, which are incorporated in and constitute a part of this specification, wherein:.

Embodiments of the present disclosure are now described in detail with reference to the drawings in which like reference numerals designate identical or corresponding elements in each of the several views. As used herein, the term "clinician" refers to a doctor, a nurse, or any other care provider and may include support personnel. Throughout this description, the term "proximal" refers to the portion of the device or component thereof that is closer to the clinician or surgical robot manipulating the device or component and the term "distal" refers to the portion of the device or component thereof that is farther from the clinician or surgical robot manipulating the device.

Referring to <FIG>, a robotic surgical system <NUM> in accordance with the present disclosure is shown generally as a robotic system <NUM>, a processing unit <NUM>, and a user interface <NUM>. The robotic system <NUM> generally includes linkages or arms <NUM> and a robot base <NUM>. The arms <NUM> moveably support a tool <NUM> which is configured to act on tissue. The arms <NUM> each have an end <NUM> that supports a tool <NUM> which is configured to act on tissue. In addition, the ends <NUM> of the arms <NUM> may include an imaging device <NUM> for imaging a surgical site. The user interface <NUM> is in communication with robot base <NUM> through the processing unit <NUM>.

The user interface <NUM> includes a display device <NUM> which is configured to display three-dimensional images. The display device <NUM> displays three-dimensional images of the surgical site which may include data captured by imaging devices <NUM> positioned on the ends <NUM> of the arms <NUM> and/or include data captured by imaging devices that are positioned about the surgical theater (e.g., an imaging device positioned within the surgical site, an imaging device positioned adjacent the patient, imaging device <NUM> positioned at a distal end of an imaging linkage or arm <NUM>). The imaging devices (e.g., imaging devices <NUM>, <NUM>) may capture visual images, infra-red images, ultrasound images, X-ray images, thermal images, and/or any other known real-time images of the surgical site. The imaging devices transmit captured imaging data to the processing unit <NUM> which creates three-dimensional images of the surgical site in real-time from the imaging data and transmits the three-dimensional images to the display device <NUM> for display.

The user interface <NUM> also includes input handles <NUM> which are supported on control arms <NUM> which allow a clinician to manipulate the robotic system <NUM> (e.g., move the arms <NUM>, the ends <NUM> of the arms <NUM>, and/or the tools <NUM>). Each of the input handles <NUM> is in communication with the processing unit <NUM> to transmit control signals thereto and to receive feedback signals therefrom. Additionally or alternatively, each of the input handles <NUM> may include input devices (not shown) which allow the surgeon to manipulate (e.g., clamp, grasp, fire, open, close, rotate, thrust, slice, etc.) the tools <NUM> supported at the ends <NUM> of the arms <NUM>.

Each of the input handles <NUM> is moveable through a predefined workspace to move the ends <NUM> of the arms <NUM> within a surgical site. The three-dimensional images on the display device <NUM> are orientated such that movement of the input handle <NUM> moves the ends <NUM> of the arms <NUM> as viewed on the display device <NUM>. It will be appreciated that the orientation of the three-dimensional images on the display device may be mirrored or rotated relative to a view from above the patient. In addition, it will be appreciated that the size of the three-dimensional images on the display device <NUM> may be scaled to be larger or smaller than the actual structures of the surgical site permitting a clinician to have a better view of structures within the surgical site. As the input handles <NUM> are moved, the tools <NUM> are moved within the surgical site as detailed below. As detailed herein, movement of the tools <NUM> may also include movement of the ends <NUM> of the arms <NUM> which support the tools <NUM>.

For a detailed discussion of the construction and operation of a robotic surgical system <NUM>, reference may be made to <CIT>.

With reference to <FIG>, a portion of an exemplary arm <NUM> of the surgical robot <NUM> of <FIG>. The arm <NUM> includes a carriage <NUM> that is translatable along a rail <NUM>. An instrument drive unit (IDU) <NUM> is secured to the carriage <NUM>. The IDU <NUM> has one or more motors (not shown) that are configured to control a tool <NUM> as detailed below. For a detailed discussion of an exemplary IDU including one or more motors, reference may be made to <CIT>.

The tool <NUM> includes an adapter <NUM>, an elongate shaft <NUM> that extends distally from the adapter <NUM>, and an end effector <NUM> supported by a distal portion of the elongate shaft <NUM>. The adapter <NUM> is releasably coupled to the IDU <NUM> such that the tool <NUM> receives input from the IDU <NUM>.

With additional reference to <FIG>, the adapter <NUM> includes an IDU interface <NUM> including a first motor interface <NUM>, a second motor interface <NUM>, a third motor interface <NUM>, a fourth motor interface <NUM>, and a control interface <NUM>. Each of the motor interfaces <NUM>-<NUM> is configured to mechanically couple to a respective motor of the IDU <NUM>. The motor interfaces <NUM>, <NUM>, <NUM>, <NUM> are arranged about the longitudinal axis A-A of the shaft <NUM>. The motor interfaces <NUM>, <NUM>, <NUM>, <NUM> may from a rectangle or square in a plane orthogonal to the longitudinal axis A-A of the shaft <NUM>. The control interface <NUM> is configured to couple to a control interface of the IDU <NUM> or the carriage <NUM> to receive instructions from the surgical robot <NUM> and/or the processing unit <NUM> and/or to transmit data to the surgical robot <NUM> and/or the processing unit <NUM>.

Referring to <FIG> and <FIG>, the first motor interface <NUM> includes a first drive screw <NUM>, a first drive nut <NUM>, a first spring <NUM>, and a first cable <NUM>. The first drive screw <NUM> includes a first head <NUM> and a distal nub <NUM>. The first head <NUM> may have radial teeth, a slot, a female connector, a male connector, or any suitable interface for coupling coaxial rotating shafts such that the first head <NUM> is configured to mechanically couple the first drive screw <NUM> to a motor of the IDU <NUM>. The first drive screw <NUM> is supported within the adapter <NUM> by a first bearing <NUM> positioned adjacent the first head <NUM>. The distal nub <NUM> is received within a first opening <NUM> defined by the adapter <NUM> such that the first bearing <NUM> and the distal nub <NUM> support the first drive screw <NUM> within the adapter <NUM> and enable the first drive screw <NUM> to rotate about its longitudinal axis, maintain the longitudinal axis of the first drive screw <NUM> parallel to a longitudinal axis of the elongate shaft <NUM>, and prevent the first drive screw <NUM> from translating along its longitudinal axis.

The first drive nut <NUM> is disposed over a threaded portion of the first drive screw <NUM> such that the first drive nut <NUM> and the first drive screw <NUM> are threadably coupled with one another. Specifically, as the first drive screw <NUM> is rotated in a first direction, e.g., clockwise rotation about the longitudinal axis of the drive screw as shown with arrow D<NUM> in <FIG>, the first drive nut <NUM> translates proximally along the first drive screw <NUM> towards the first head <NUM> and when the first drive screw <NUM> is rotated in a second direction opposite the first direction, e.g., counter-clockwise, the first drive nut <NUM> is translated distally along the first drive screw <NUM> away from the first head <NUM>. The first drive nut <NUM> defines a first slot <NUM> that receives a portion of the first cable <NUM> such that as the first drive nut <NUM> translates along the first drive screw <NUM>, the first cable <NUM> cooperates with translation of the first drive nut <NUM>. Specifically, the first cable <NUM> is retracted as the first drive nut <NUM> translates proximally and the first cable <NUM> is relaxed as the first drive nut <NUM> translates distally.

The first spring <NUM> is disposed about the first drive screw <NUM> distal of the first drive nut <NUM> and engages a distal surface of the first drive nut <NUM>. The first spring <NUM> is supported within the adapter <NUM> such that the first spring <NUM> urges the first drive nut <NUM> proximally. The first spring <NUM> may have a spring constant large enough to urge the first drive nut <NUM> proximally such that the first drive screw <NUM> is rotated in the first direction absent a force applied to the first head <NUM>. The first spring <NUM> may have a constant or progressive spring constant.

The second motor interface <NUM> includes a second drive screw <NUM>, a second spring <NUM>, and a second cable <NUM>; the third motor interface <NUM> includes a third drive screw <NUM>, a third spring <NUM>, and a third cable <NUM>; and the fourth motor interface <NUM> includes a fourth drive screw <NUM>, a fourth spring <NUM>, and a fourth cable <NUM>. The drive screws <NUM>, <NUM>, <NUM>, the springs <NUM>, <NUM>, <NUM>, and the cables <NUM>, <NUM>, <NUM> are similar to the first drive screw <NUM>, the first spring <NUM>, and the first cable <NUM>, respectively, detailed above and will not be detailed herein for brevity except where the differences are relevant to the function of the tool <NUM>.

With reference to <FIG>, the cables <NUM>, <NUM>, <NUM>, <NUM> extend through the shaft <NUM> and are connected to the end effector <NUM> to control movement of the end effector <NUM> in three degrees-of-freedom (DOF), e.g., yaw, pitch, and jaw. The end effector <NUM> includes a clevis <NUM>, a yoke <NUM>, a first jaw <NUM>, and a second jaw <NUM>. The clevis <NUM> includes a first idler <NUM> and the yoke <NUM> includes a second idler <NUM> distal of the first idler <NUM>. The first and second idlers <NUM>, <NUM> each define an idler axis I<NUM>, I<NUM> that is perpendicular to the longitudinal axis A-A of the shaft <NUM> and parallel to one another.

The first jaw <NUM> includes a first spindle <NUM> and the second jaw <NUM> includes a second spindle <NUM>. The first spindle <NUM> and the second spindle <NUM> each define a spindle axis S<NUM>, S<NUM> that is perpendicular to the longitudinal axis A-A of the shaft <NUM>, when the shaft <NUM> is in a straight configuration as shown in <FIG>, and perpendicular to the second idler axis I<NUM>. The first and second spindle axes S<NUM>, S<NUM> may be coaxial with one another.

The clevis <NUM> pivotally supports the yoke <NUM> about the second idler axis I<NUM> in a yaw DOF. The yoke <NUM> pivotally supports the first and second jaws <NUM>, <NUM> about the first and second spindle axes S<NUM>, S<NUM> in pitch and jaw. Specifically, when the first and second jaws <NUM>, <NUM> pivot about the first and second spindle axes S<NUM>, S<NUM> in the same direction in concert with one another, the first and second jaws <NUM>, <NUM> move in a pitch DOF. Alternatively, when the first and second jaws <NUM>, <NUM> pivot about the first and second spindle axes S<NUM>, S<NUM> in opposite directions or independent of one another, the first and second jaws <NUM>, <NUM> move in a jaw DOF. The first and second jaws <NUM>, <NUM> can move in the same direction but at different speeds, e.g., not in concert, such that the first and second jaws <NUM>, <NUM> move in both the pitch DOF and the jaw DOF.

Continuing to refer to <FIG>, the cables <NUM>, <NUM>, <NUM>, <NUM> wrap around the first and second idlers <NUM>, <NUM> and are secured to a respective one of the first and second spindles <NUM>, <NUM>. The first and second cables <NUM>, <NUM> are secured to opposite sides of the first spindle <NUM> of the first jaw <NUM>. Specifically, the first cable <NUM> may be secured to a top side of the first spindle <NUM> and the second cable <NUM> may be secured to a bottom side of the first spindle <NUM>. The first and second cables <NUM>, <NUM> may form a continuous monolithic cable with one another that wraps about the first spindle <NUM>. The third and fourth cables <NUM>, <NUM> are secured to opposite sides of the second spindle <NUM> of the second jaw <NUM>. Specifically, the third cable <NUM> may be secured to a bottom side of the second spindle <NUM> and the fourth cable <NUM> may be secured to a bottom side of the second spindle <NUM>. The third and fourth cables <NUM>, <NUM> may form a continuous monolithic cable with one another that wraps about the second spindle <NUM>.

The first and second idlers <NUM>, <NUM> may define a separate groove to guide each of the cables <NUM>, <NUM>, <NUM>, <NUM> around the respective idler <NUM>, <NUM> such that the cables <NUM>, <NUM>, <NUM>, <NUM> are secured within the respective groove without interfering with the other cables <NUM>, <NUM>, <NUM>, <NUM>.

Continuing to refer to <FIG>, displacement of the cables <NUM>, <NUM>, <NUM>, <NUM> are used as a differential drive to control the end effector <NUM> in the yaw DOF, the pitch DOF, and the jaw DOF. Initially referring to <FIG>, the end effector <NUM> is in a straight configuration in which the cables <NUM>, <NUM>, <NUM>, <NUM> are in a neutral position relative to one another. In the neutral position, the tension in each of the cables <NUM>, <NUM>, <NUM>, <NUM> may be substantially equal to one another. To move the end effector <NUM> in a positive yaw direction, the third and fourth cables <NUM>, <NUM>, which are each secured to the second spindle <NUM>, are each retracted a distance and the first and second cables <NUM>, <NUM>, which are each secured to the first spindle <NUM>, are each extended or relaxed the same distance as shown in <FIG>. As shown, the positive yaw direction is pivoting the yoke <NUM> to the right and the negative yaw direction is pivoting the yoke <NUM> to the left. To move the end effector <NUM> in the negative yaw direction, the first and second cables <NUM>, <NUM> are retracted and the third and fourth cables <NUM>, <NUM> are extended or relaxed the same distance that the first and second cables <NUM>, <NUM> are retracted.

Referring now to <FIG>, to move the end effector <NUM> in a positive pitch direction, upwardly as shown, the first and fourth cables <NUM>, <NUM>, which are each secured to the top side of different spindles <NUM>, <NUM>, are retracted a distance and the second and third cables <NUM>, <NUM>, which are each secured to the bottom side of different spindles <NUM>, <NUM>, are relaxed the same distance. To move the end effector <NUM> in the negative pitch direction, downwardly as shown, the second and third cables <NUM>, <NUM> are retracted a distance and the first and fourth cables <NUM>, <NUM> are relaxed the same distance.

With reference to <FIG>, to move the end effector <NUM> in a positive jaw direction, to pivot the jaws <NUM>, <NUM> apart from one another, the first and third cables <NUM>, <NUM>, which are each secured to different sides of different spindles <NUM>, <NUM>, are retracted and the second and fourth cables <NUM>, <NUM>, which are secured to different sides of different spindles <NUM>, <NUM>, are relaxed. The first and third cables <NUM>, <NUM> may be retracted the same distances or different distances. However, the second cable <NUM> is relaxed the same distance that the first cable <NUM> is retracted and the fourth cable <NUM> is relaxed the same distance that the third cable <NUM> is retracted. To move the end effector <NUM> in the negative jaw direction, e.g., to move the jaws <NUM>, <NUM> towards one another, the second and fourth cables <NUM>, <NUM> are retracted and the first and third cables <NUM>, <NUM> are relaxed.

It is contemplated that one jaw, e.g., second jaw <NUM>, may be stationary as the other jaw, e.g., first jaw <NUM>, is pivoted such that the end effector <NUM> moves in the jaw direction. To move the end effector <NUM> in the positive jaw direction with second jaw <NUM> stationary, the first cable <NUM> can be retracted and the second cable <NUM> is relaxed an equal amount while the third and fourth cables <NUM>, <NUM> remain stationary. Similarly to move the end effector <NUM> in the positive jaw direction with the first jaw <NUM> stationary, the third cable <NUM> is retracted and the fourth cable <NUM> is relaxed and equal amount while the first and second cables <NUM>, <NUM> remain stationary. Each of these movements can be reversed to move the end effector <NUM> in the negative jaw direction with one of the jaws <NUM>, <NUM> stationary.

Referring now to <FIG>, the end effector <NUM> may be moved in more than one DOF sequentially or simultaneously. For example, the end effector <NUM> may be moved from the straight configuration (<FIG>) to the position in <FIG> by retracting the fourth cable <NUM> and relaxing the second cable <NUM> while substantially maintaining the position of the first and third cables <NUM>, <NUM> to move the end effector <NUM> in the positive yaw, pitch, and jaw directions simultaneously.

While several movements of the end effector <NUM> in the yaw DOF, the pitch DOF, and the jaw DOF are described above, these are meant to be exemplary movements and not an exhaustive list of all possible movements or combination of movements of the end effector <NUM> in the yaw, pitch, and jaw DOFs.

Referring to <FIG>, <FIG>, and <FIG>, it may be desirable to maintain the end effector <NUM> in a known or neutral position when the tool <NUM> is disconnected from the IDU <NUM>. By maintaining the tool <NUM> in a known position, the robotic system <NUM> can know the position or pose of the end effector <NUM> when the tool <NUM> is connected to the IDU <NUM> without the need for running a calibration sequence. This may reduce the time required to calibrate a surgical robot <NUM> each time a new tool <NUM> is attached. In addition, the robotic system <NUM> can know the position of the end effector <NUM> without requiring absolute encoders which may reduce the cost of each tool <NUM>. This known pose may be stored in memory (not shown) of the tool <NUM> and communicated to the robotic system <NUM> through the control interface <NUM> when the tool <NUM> is attached to the surgical robot <NUM>.

To maintain the end effector <NUM> in a known or neutral pose, the springs <NUM>, <NUM>, <NUM>, <NUM> can be used as pretension springs. For some tools, e.g., clip appliers or staplers, it may be beneficial to have end effectors maintained in a fully open, or fully positive jaw, configuration when the tool <NUM> is disconnected from the IDU <NUM>. For example, clip appliers and staplers may need to be in an open position to load clips or staples into a jaw of the end effector. For such instruments, the first and third springs <NUM>, <NUM> each have a large, first spring constant and the second and fourth springs <NUM>, <NUM> each have a smaller, second spring constant such that the first and third springs <NUM>, <NUM> overpower the second and fourth springs <NUM>, <NUM> to move the jaws <NUM>, <NUM> towards the fully open configuration. In addition, as the second and fourth springs <NUM>, <NUM> maintain tension in the second and third cables <NUM>, <NUM>, such that the end effector <NUM> remains straight with respect to the yaw and pitch directions. Additionally or alternatively, the first and third springs <NUM>, <NUM> may have the same or substantially the same spring constant as the second and fourth springs <NUM>, <NUM> and be biased such that the first and third springs <NUM>, <NUM> overpower the second and fourth springs <NUM>, <NUM> to move the jaws towards the fully open configuration.

Alternatively, it may be beneficial for some end effectors to be maintained in a fully closed, or fully negative jaw, configuration when the tool <NUM> is disconnected from the IDU <NUM>. For such instruments, the second and fourth springs <NUM>, <NUM> each have a large, first spring constant and the first and third springs <NUM>, <NUM> each have a smaller, second spring constant such that the second and fourth springs <NUM>, <NUM> overpower the first and third springs <NUM>, <NUM> to move the jaws <NUM>, <NUM> towards the full closed configuration. In addition, as the first and third springs <NUM>, <NUM> maintain tension in the first and third cables <NUM>, <NUM>, the end effector <NUM> remains straight with respect to the yaw and pitch directions. Additionally or alternatively, the second and fourth springs <NUM>, <NUM> may have the same or substantially the same spring constant as the first and third springs <NUM>, <NUM> and be biased such that the second and fourth springs <NUM>, <NUM> overpower the first and third springs <NUM>, <NUM> to move the jaws towards the fully closed configuration.

The springs <NUM>, <NUM>, <NUM>, <NUM> may be configured to maintain the tool <NUM> in other neutral positions which may be beneficial for a tool <NUM> with a particular end effector <NUM>. The configuration of the tool <NUM> may be maintained by varying spring constants of one or more of the springs <NUM>, <NUM>, <NUM>, <NUM> and/or biasing one or more of the springs <NUM>, <NUM>, <NUM>, <NUM>. The neutral position of the tool <NUM> may be communicated to the surgical robot <NUM> and/or the processing unit <NUM> through the control interface <NUM>, when the tool <NUM> is connected to the IDU <NUM>.

A forward kinematic model to relate measured motor positions of the motors of the IDU <NUM> to calculated yaw, pitch, and jaw positions of the end effector <NUM> is required to determine a pose of the end effector <NUM>. This is different than traditional robots where joint angles are generally directly measured by position sensors, such as potentiometers or encoders. However, as space is extremely limited within the end effector <NUM>, it is difficult to place encoders, potentiometers, or other devices which directly measure the pose of the end effector <NUM> within the end effector <NUM>. Thus, it is advantageous to calculate the pose of the end effector from the measured position of the motors of the IDU <NUM>. In addition, inaccuracies of the calculated pose can be compensated for by observations of the end effector <NUM> within the surgical site by a clinician interfacing with the robotic surgical system <NUM> (<FIG>).

Kinematic control methods for controlling the end effector <NUM> in the yaw DOF, the pitch DOF, and the jaw DOF are described below with reference to the tool <NUM> detailed in <FIG>. In the model below, the first jaw <NUM> will be referred to as jaw a and the second jaw <NUM> will be referred to as jaw b to avoid confusion with integers used in the following equations. It will be appreciated that the arm <NUM> of the surgical robot <NUM> is configured to move the end effector <NUM> in an additional four DOFs such that the end effector <NUM> is moveable in six DOFs and the jaw DOF.

As detailed above, the jaws "a, b" are moved by displacing one or more of the cables <NUM>, <NUM>, <NUM>, <NUM> with the motors (not shown) of the IDU <NUM>. A first torque τa is the torque applied to the first jaw "a" and a second torque τb is the torque applied to the second jaw "b". As shown, the first and second jaws "a, b" are typically mirror images of each other with only minor differences and both of the first and second jaws "a, b" pivot about the same pin or axis, e.g., spindle axes S<NUM>, S<NUM>. As such, the first and second torques τa, τb can be represented by the following equations: <MAT> where µ<NUM> is the coefficient of friction between the respective jaw "a, b" and the pin (not explicitly shown) that the respective jaw "a, b" is pivotal about, ca, cb are dampening terms, and "m" is an inertial term. The dampening terms ca, cb and the inertial term "m" are a function of a joint angle θ.

In addition, the first jaw a is directly articulated by the first and second cables <NUM>, <NUM> and the second jaw b is directly articulated by the third and fourth cables <NUM>, <NUM> with the first and fourth cables <NUM>, <NUM> being secured to the top side of the respective jaw "a, b", and the second and third cables <NUM>, <NUM> being secured to the bottom side of the respective jaw "a, b". As such the torque τa, τb can also be represented by the following equations: <MAT>.

If each jaw "a, b" is considered separately, the inertial term "m " and the dampening term "c " are independent of the joint angle θ. Since the jaws "a, b", are substantial mirrors of each other, it can be assumed that the combined term of the inertial term "m" and the dampening term "c" is twice the respective term from a single jaw such that mp ≡ <NUM>ma ≈ <NUM>mb and cp ≡ <NUM>ca ≈ <NUM>cb. Thus, combining Equation (<NUM>) into Equation (<NUM>), and rearranging the equation, results in the following: <MAT>.

Next, a synthetic joint of pitch, for the pitch DOF, is formed by combining jaw "a" and jaw "b". As noted above, the inertial term "mp" and the dampening term "cp" of the synthetic pitch joint are twice that of the dampening terms and inertial terms for each of the individual jaws "a, b". The pitch angle θp is defined by a line bisecting an angle between the first and second jaws "a, b". thus, the articulation torque in pitch is defined as: <MAT>.

A synthetic joint of jaw, for the jaw DOF, is formed by the combination of the first and second jaws "a, b" with j oint pitch as: <MAT>.

Substituting Equations (<NUM>) and (<NUM>) into Equation (<NUM>) provides basic dynamic equations for the synthetic joint of pitch and the synthetic joint of jaw as: <MAT>.

As detailed above, Equations (<NUM>) and (<NUM>) describe the relationship between forces in the cables <NUM>, <NUM>, <NUM>, <NUM> and the articulation torque for the synthetic joints of pitch and jaw. The final DOF of the end effector <NUM> is the yaw DOF which is articulated by all four cables. For the joint of yaw, the dynamic equation depends on the configuration of the end effector <NUM> in pitch and jaw. Generally, in medical applications the motion in pitch and jaw are quick. As such, for simplicity, this dependency can be ignored to provide: <MAT> where inertial term "m" and Coriolis and centrifugal term "c" are lumped parameters that take the pitch and jaw joints into account and µ<NUM> is a friction coefficient of the yoke <NUM> about the idler <NUM>. Equation (<NUM>) is rearranged to define articulating torque of yaw τy as: <MAT>.

Equation (<NUM>) can be substituted into Equation (<NUM>) to simplify a dynamic equation for the yaw joint as: <MAT>.

Thus the dynamic equations for the yaw, pitch, and jaw joints are: <MAT>.

Further, a set of equations to relate articulating torques to forces in the cables <NUM>, <NUM>, <NUM>, <NUM> can be determined from Equations (<NUM>), (<NUM>), and (<NUM>) such that: <MAT> This can be simplified by defining the following variables: <MAT> Such that Equations (<NUM>) can be expressed in matrix form as: <MAT>.

An inverse kinematic model can be formed to determine desired yaw, pitch, and jaw angles of the end effector <NUM> to motor positions for each the motors of the IDU <NUM>. As detailed above, movements in the yaw, pitch, and jaw DOFs of the end effector <NUM> can be achieved with the differential drive mechanism of the adapter <NUM>. Further, movement in the negative of each of the DOF uses the same cables, e.g., cables <NUM>, <NUM>, <NUM>, <NUM>, but with the opposite direction or sign on each of the cables. It is noted that a negative sign on movement of a cable does not necessarily represent retraction of the cable but that the respective cable is kept under minimal tension to prevent the cable from going slack. Table <NUM>, below, shows the combinations of movement in the positive direction in each of the DOFs. It is noted that translations of the jaw DOF are half due to each jaw "a, b" moving and contributing to the total jaw angle.

The movement of each of the cables in a linear combination of the cable movements in yaw, pitch, and jaw such that: <MAT>.

Thus, the movement of each cable <NUM>, <NUM>, <NUM>, <NUM> for each of the movements can be given by: <MAT> Such that the displacement, e.g., translation, of each cable <NUM>, <NUM>, <NUM>, <NUM> for movement in each of the DOFs is: <MAT>.

As described above, the IDU <NUM> includes a motor (not shown) that is associated with each of the motor interfaces <NUM>, <NUM>, <NUM>, <NUM> to rotate a respective one of the drive screws <NUM>, <NUM>, <NUM>, <NUM> which in turn retract or relax a corresponding cable <NUM>, <NUM>, <NUM>, <NUM>. The motors are rotated as a function of the desired pose of the end effector <NUM> from the following: <MAT> Noting that s is the overall translation of the respective cable such that a desired rotation of a motor can be shown as a function of the desired end effector pose as: <MAT> The desired rotation of each motor as a function of the desired end effector pose can be combined in a single matrix as: <MAT> If it is assumed that radii of each of the idlers <NUM>, <NUM> and spindles <NUM>, <NUM> are equal for each of the cables <NUM>, <NUM>, <NUM>, <NUM>, then Equation (<NUM>) can be simplified to: <MAT>.

From the inverse kinematic model of Equation (<NUM>), a forward kinematic model can be obtained to relate motor position to the yaw, pitch, and jaw angles of the end effector <NUM>. It is noted that Equation (<NUM>) has three unknowns and four equations. However, if proper tension is maintained in each of the cables <NUM>, <NUM>, <NUM>, <NUM>, Equation (<NUM>) can be solved in the reverse direction. For example, to solve for θj, the first and third equations or the second and fourth equations can be added together. Since it is no more likely that either one of the sums is more accurate, an average of the two can be taken. Following this reasoning, a forward relationship can be expressed as follows: <MAT> It will be appreciated that Equation (<NUM>) can be obtained by taking a pseudoinverse, e.g., the Moore-Penrose inverse, of Equation (<NUM>).

Referring to <FIG>, the motors of the IDU <NUM> can be controlled by a proportional-integral-derivative (PID) controller <NUM> as detailed below in accordance with the present disclosure. The desired motor position gd is calculated from a desired jaw angle θd using Equation (<NUM>). The motor position is then sensed as qs and subtracted from the desired position to generate a motor position error qe. The PID controller <NUM> then calculates a motor torque τm. which is outputted to the IDU <NUM>. Propositional, integral, and derivative gains Kp, Ki, Kd. can be expressed in a control law as: <MAT> where qe is calculated from Equation (<NUM>) as follows: <MAT>.

The PID controller <NUM> as shown in <FIG> may also be used to control stiffness in one or more DOF of the end effector <NUM>. In addition, the PID controller <NUM> may calculate error in joint space instead of motor space as shown by utilizing the forward kinematics model of Equation (<NUM>).

As detailed above, the PID controller <NUM> alone does not directly or explicitly account for force within the cables <NUM>, <NUM>, <NUM>, <NUM>. For example, maintaining tension, e.g., preventing slack in the cables, is a requirement of the kinematics models detailed above. It will be appreciated that if the motors of the IDU <NUM> track the desired motor position with high precision and in sync with one another, that tension will be maintained in the cables <NUM>, <NUM>, <NUM>, <NUM>. In contrast, if the motors are unable to move to a desired motor position in sync with one or more of the other motors, then one or more of the cables <NUM>, <NUM>, <NUM>, <NUM> may become slack. In embodiments, the cables <NUM>, <NUM>, <NUM>, <NUM> may be pre-tensioned by a predetermined amount by monitoring current of the motors of the IDU <NUM> and/or monitoring torques sensors before the PID controller <NUM>. By pre-tensioning the cables <NUM>, <NUM>, <NUM>, <NUM>, tension in the cables will be kept positive even if the motors of the IDU <NUM> move the cables <NUM>, <NUM>, <NUM>, <NUM> out of sync.

In addition, the PID controller <NUM> alone does not maintain a clamping force in the jaws "a, b" when the jaws "a, b", are closed. For example, when the motors of the IDU <NUM> close the position loop according to Equation (<NUM>), the net clamping force is approximately zero. In embodiments, when the end effector <NUM> cannot reach a zero position, some closure force may remain when the jaws "a, b" are in the closed position. In embodiments, the jaw angle can be commanded to be negative such that closure force may remain when the jaws "a, b" are in the closed position. In such embodiments, a desired angle in the jaw DOF may be scaled and the inverse kinematic equation may be modified once the jaw angle is past zero such that the clamping force is modulated by changing a magnitude of the desired negative angle. However, this approach may cause confusion for a clinician as the end effector <NUM> may not open when it is commanded until the commanded jaw angle exceeds the desired negative angle. Further, there may be tracking errors in the jaw DOF due to the rescaling.

In accordance with embodiments of the robotic surgical system <NUM> (<FIG>), the surgical robot <NUM> or processing unit <NUM> includes a null space (NS) controller <NUM> that is configured to provide cable tension and/or jaw clamping force. In such embodiments, the PID controller <NUM> is a primary positional controller and the NS controller <NUM> is a secondary controller.

The PID controller <NUM> continues to control a pose of the end effector <NUM> using Equation (<NUM>) as detailed above. As the PID controller <NUM> controls the pose of the end effector <NUM>, another DOF, cable force, is created in the motor space from Equation (<NUM>) which can be related to the motor torque through the screws <NUM>, <NUM>, <NUM>, <NUM>. The cable force in each cable <NUM>, <NUM>, <NUM>, <NUM> is related to torque of the respective motor as: <MAT> where kls is a conversion coefficient that accounts for direction and efficiency of the respective screw <NUM>, <NUM>, <NUM>, <NUM>.

Assuming that the screws <NUM>, <NUM>, <NUM>, <NUM> have the same radius, Equation (<NUM>) can be combined with Equation (<NUM>) such that: <MAT> which can be simplified to: <MAT>.

As shown above, Equation <NUM> is under constrained such that for the same articulating torque, there may be different ways to generate the motor torque to balance Equation (<NUM>). For example, motor torques τmotor may satisfy Equation (<NUM>) and the requesting articulating joint torques τjoint such that: <MAT> where the motor torques τmotor could be torques that are generated from the PID controller <NUM> as shown above with respect to Equation (<NUM>). As Equation (<NUM>), and thus the matrix S of Equation (<NUM>), is unconstrained, additional motor torques Δτmotor may be added to the right side of Equation (<NUM>) such that: <MAT> This is satisfied by constraining the additional motor torques Δτmotor within null space of matrix S as: <MAT> such that there is no net change in the articulating joint torques Δτjoint determined by the PID controller <NUM>.

From the above, it is possible to develop the secondary NS controller <NUM> to adjust the motor torques Δτmotor generated by the PID controller <NUM> such that the NS controller <NUM> cascades after the PID controller <NUM> to directly adjust the motor torques Δτmotor. The motor torques Δτmotor may be measured directly by additional torque sensors that detect the output torque of the motors of the IDU <NUM>. For a detailed description of suitable torque sensors, reference can be made to U. Patent No. <NUM>,<NUM>.

First, maintaining tension in the cables <NUM>, <NUM>, <NUM>, <NUM> will be addressed in accordance with the present disclosure. During normal operation the end effector <NUM> has three DOF with the articulating torques defined in Equation (<NUM>). These torques can be adjusted without impacting the position of the end effector <NUM> as long as the additional motor torques Δτmotor satisfy Equation (<NUM>) such that vectors in null space can be expressed as: <MAT> where matrix I is a 4x4 identity matrix; ST is the transpose of matrix S, and z is an arbitrary vector with a dimension of <NUM>. The arbitrary vector z can be projected or decomposed through a helper matrix by: <MAT>.

Then, substituting Equation (<NUM>) into Equation (<NUM>) and setting the friction coefficients µ<NUM> and µ<NUM> to zero produces: <MAT>.

Next, the influence of the constant rKls is extracted from the null space defined in Equation (<NUM>) by assuming that the arbitrary vector z has the same unit of measure as the motor torques τmotor. By substituting Equation (<NUM>) into Equation (<NUM>): <MAT> which is rearranged as: <MAT> where the additional motor torque vector Δτmotor is explicitly expressed by its elements as: <MAT> and since arbitrary vector z is an arbitrary vector, another arbitrary scalar Δτ can be defined as: <MAT> which results in: <MAT>.

As shown by inserting Equation (<NUM>) into Equation (<NUM>), it is clear that the same torque can be added to each motor of the IDU <NUM> without changing the articulating torques for the yaw, pitch, and jaw DOFs. Thus, if the additional motor torque for each motor is the same, a position determined by the PID controller <NUM> will not be impacted. As detailed above with respect to Equation (<NUM>) this assumes that the friction is ignored which is allowed as the additional torque of each motor does not articulate the joints but generates internal forces within the system and contributes to a stiffness of the system.

However, when the friction coefficients µ<NUM> and µ<NUM> are significant, the matrix S is solved symbolically such that the null space of Equation (<NUM>) is expressed as: <MAT> It is noted that if the friction coefficients µ<NUM> and µ<NUM> are zero, Equation (<NUM>) degrades to Equation (<NUM>) such that Equation (<NUM>) is a first order approximation of Equation (<NUM>). Thus, Equation (<NUM>) provides relationships of the additional motor torques Δτmotor that can be adjusted without impacting the articulating torques in jaw, pitch, and jaw DOFs to avoid impacting the position determined by the PID controller <NUM>.

As Equation (<NUM>) is flexible in the implementation of the NS controller <NUM>, several methods may be used to adjust the torque for each motor of the IDU in view of a measured torque τs.

In a first method of maintaining cable tension, torque is adjusted at each motor according to a measured torque τs which can be taken from a measured current or from a physical torque sensor as detailed above. In practice, when the NS controller <NUM> is operating in the first method, positional gain of the PID controller <NUM> as shown in Equation (<NUM>) is necessarily high. Further, to maintain minimum tension fmin in the cables <NUM>, <NUM>, <NUM>, <NUM>, two of the four motors of the IDU <NUM> keep minimum tensions in the respective cables while the other two motors of the IDU <NUM> take over a workload from the two motors maintaining the minimum tension fmin in addition to the expected workload. This is reflected in Table <NUM>, above, which requires the positional change be distributed to the motor pairs with different signs by the same amounts such that each pair of motors of the IDU <NUM> that are physical connected by a pair of cables, e.g., first and second cables <NUM>, <NUM> and third and fourth cables <NUM>, <NUM>.

The differential drive mechanism detailed above is a push-pull mechanism with two pairs of motors. However, in the first method the pusher does not actively push but maintains the minimum tension and the puller motor pulls the pusher motor to the desired position such that the puller motor of each pair closes the positional loop for both motors of the pair which requires the proportional gains to be high and the maximum current of the puller motor to be increased significantly. Even in view of the increased gains, the first method is extremely good at maintaining the minimum tension fmin in each cable.

To keep the tension of each cable <NUM>, <NUM>, <NUM>, <NUM> at a minimum tension fmin as the motors of the IDU <NUM> articulate the end effector <NUM>, a minimum Δτ is determined as: <MAT> If the adjustment torque Δτ is the minimum torque that satisfies Equation (<NUM>), the adjustment torque Δτ from the NS controller <NUM> is expressed as: <MAT>.

In this first method, torque is adjusted at each individual motor of the IDU <NUM>. The measured torque τs is checked and adjusted to ensure that the tension in each of the cables <NUM>, <NUM>, <NUM>, <NUM> is greater than the minimum tension fmin.

In a second method of maintaining cable tension, the physical connection between each pair of cables, e.g., first and second cable <NUM>, <NUM> and third and fourth cable <NUM>, <NUM>, are considered such that the constraints defined in Equation (<NUM>) are relaxed. Specifically, instead of verifying torque of each motor, the torque of each pair of motors of the IDU <NUM> is constrained by an average of each motor group or pair of motors of the IDU <NUM>.

If the average of the measured torque τs meets the requirements as detailed below, then the puller motor of each pair is working harder than the pusher motor but since there is still a net torque in each of the motors of the pair, e.g., the pusher and puller, it means that the cable of the pusher motor is also likely under tension. However, as each motor is not individually checked, the second method may not provide as consistent result in maintaining tension in each of the cables greater than the minimum tension fmin. However, as the puller motor of each pair of motors is not required to take the entire load of the pusher motor of each pair of motors such that the load on the motors of the IDU <NUM>, and the stiffness of the joint, can be reduced.

In the second method, the average of each of the motor groups is expressed as: <MAT>.

Similar to the first method, the minimum adjustment torque Δτ is determined that fulfills Equation (<NUM>) such that output from the NS controller <NUM> takes the form of Equation (<NUM>). It is not necessary to show that if Equation (<NUM>) holds that Equation (<NUM>) will also hold. However, it is also clear that Equation (<NUM>) provides a less certain constraint that the minimum tension fmin of each cable is maintained. However, as detailed above, as a result of each pair of cables being coupled together, as long as the puller motor of each pair of motors has a measured torque τs greater than the average, then it is likely that the pusher motor is also maintaining the minimum tension fmin in its related cable. Further, it is noted that Equation (<NUM>) accounts for an influence of friction in the calculation of the adjustment torque Δτ.

In a third method of maintaining cable tension, the measured torque τs of each motor of the IDU <NUM> is tracked and maintained above a targeted minimum torque τmin based on a measured torque τs that corresponds to the minimum tension fmin desired in each of the cables <NUM>, <NUM>, <NUM>, <NUM>. The third method has a simple controller in the form of: <MAT> where τmin is the targeted a minimum torque; τs, min is a sensed minimum torque, and K is a gain factor.

The adjustment torque Δτ in Equation (<NUM>) can provide varying degrees of certainty of maintaining tension in the cables <NUM>, <NUM>, <NUM>, <NUM>. For example, when the gain factor K=<NUM>, the adjustment torque Δτ will adjust every motor torque τmotor by the minimum torque τs, min such that each motor torque τmotor will be at or above the targeted minimum torque τmin to maintain the minimum tension fmin in the cables <NUM>, <NUM>, <NUM>, <NUM>. This will have a similar result as the first method detailed above where the puller motor of each pair of motors will take on the entire workload of the respective pusher motor while providing certainty that the minimum tension fmin is maintained. When the gain factor K<<NUM>, certainty of maintaining the minimum tension fmin is reduced while the additional workload on the puller motor of each pair of motors is reduced. In an extreme case, when the gain factor K=<NUM>, a constant is added to each motor torque τmotor to maintain the minimum tension fmin.

The third method allows for consideration of friction from Equation (<NUM>) by scaling the four elements of Equation (<NUM>) to account for friction and to make the highest adjustment torque Δτ equal to the output of Equation (<NUM>).

The third method allows for allowing for tuning of the gain factor K to account for performance requirements of other controllers such as an overall power, a maximum current that the motors of the IDU <NUM> can provide, and/or a stiffness of the j oint. This allows for the gain factor K to be increased when certainty of maintaining cable tension is critical and workload on the motors of the IDU <NUM> can be increased and to be reduced when certainty of maintaining cable tension is less critical and workload on the motors of the IDU <NUM> needs to be reduced.

Second, generating a clamping force between jaws "a, b" will be addressed in accordance with the present disclosure. It may be beneficial to adjust the clamping force between jaws "a, b" depending on the type of instrument of the end effector <NUM>. For example, when the jaws "a, b" form a needle driver, a high clamping force is required and when the jaws "a, b" are a bowel grasper a much lower clamping force is required.

In a first method or technique of generating clamping force, the clamping force is generated by over clamping the jaws, e.g., commanding the desired jaw angle θd to a negative value. In the first technique, an amount of clamping force generated depends on the overall stiffness of the PID controller <NUM> and a magnitude of the desired negative angle. To maintain cable tension, Equation (<NUM>) is modified after the actual jaw angle passes zero as follows: <MAT> By modifying Equation (<NUM>), the puller motors of each pair of motors continue to pull while the pusher motors are prevented from relaxing.

As a commanded jaw angle θj does not go negative, the commanded jaw angle θj must be remapped in the first technique. As detailed above, if the commanded jaw angle θj is remapped linearly, a clinician may notice a significant difference between a commanded jaw angle θj and an actual jaw angle. To improve a clinician's experience and more closely track the commanded jaw angle θj with the actual jaw angle, the commanded jaw angle θj can be mapped to the actual jaw angle nonlinearly. The commanded jaw angle θj can be mapped using different slopes where for most of a range of the commanded jaw angle θj the slope is substantially linear and as the commanded jaw angle θj approaches zero, a steeper slope is used. For example, a logarithmic function may be used such that when the commanded jaw angle θj ∈ [<NUM>,<NUM>] can be mapped to [-<NUM>, <NUM>] roughly through 6log<NUM>(θj + <NUM>). When the commanded jaw angle θj changes from <NUM> to <NUM>, the mapped angle θm changes from <NUM> to <NUM> such that the mapping is substantially linear. In contrast, when the commanded jaw angle θj changes from <NUM> to <NUM>, the mapped angle θm changes from -<NUM> to <NUM> such that the slope is significantly non-linear and steep.

In a second method or technique for generating a clamping force between jaws "a, b", the NS controller <NUM> can be used to generate the clamping force when the jaws "a, b" are in closed position. When the jaws "a, b" are in the closed position, the end effector <NUM> has two DOF such that Equation (<NUM>) degrades, as the articulating torque τj of in the jaw DOF is now zero, to the following: <MAT> Two new variables can be defined as follows: <MAT> to simplify Equation (<NUM>) to: <MAT> Similarly, Equation (<NUM>) also degrades to: <MAT> which can be expressed for null space of matrixes S<NUM> to S<NUM> as defined in Equation (<NUM>) as: <MAT> where Δτ<NUM> and Δτ<NUM> are arbitrary scalars.

By setting the friction coefficients µ<NUM> and µ<NUM> to zero it can be shown that the additional motor torques Δτmotor for motors <NUM> and <NUM> are equal and that the additional motor torques Δτmotor for motors <NUM> and <NUM> are equal: <MAT> Thus, to balance internal forces in the end effector <NUM>: <MAT> which constrains the additional motor torques Δτmotor to: <MAT> <MAT> Equation (<NUM>) illustrates that the difference between Δτ<NUM> and Δτ<NUM> can be used to adjust the clamping force Δτclamp between jaws "a, b" which is defined as: <MAT> Such that Equation (<NUM>) can be rewritten as: <MAT> When Equation (<NUM>) is compared to Equation (<NUM>) it is clear that cable tension can be maintained in the first, second, and third methods while adjusting the clamping force Δτclamp between jaws "a, b" once the jaws "a, b" are in the closed position.

When the friction coefficients µ<NUM> and µ<NUM> are included, the clamping force Δτclamp of Equation (<NUM>) depends on the sign in Equation (<NUM>). For example, when sgn(θ̇p) is positive, the second part of Equation (<NUM>) is rearranged as: <MAT> In this example, the articulating torque for pitch τp is provided by the fourth cable <NUM>. To provide the articulating torque for pitch τp, the frictional forces that must be overcome by the fourth cable <NUM> are proportional to the total force of the third and fourth cables <NUM>, <NUM> and represented by µ<NUM>(f<NUM> + f<NUM>). In addition, the fourth cable <NUM> must also overcome a countering force provided by the opposite jaw which is shown as f<NUM> - f<NUM>. Further, the fourth cable <NUM> must also overcome the friction of the other jaw represented as µ<NUM>(f<NUM> + f<NUM>). The internal torque or clamping force Δτclamp can be expressed as: <MAT> Further, the motor torques Δτmotor can absorbed the coefficient kls as: <MAT>.

To maintain the clamping force Δτclamp between jaws "a, b", Equation (<NUM>) can be expressed as: <MAT> Substituting Equation (<NUM>) into Equation (<NUM>) in which Δτ<NUM> is expressed as a function of Δτ<NUM> and the clamping force Δτclamp yields: <MAT>.

In a similar manner, when sgn(θ̇p) is negative, the second part of Equation (<NUM>) can be rearranges as: <MAT> In this example, the articulating torque for pitch is provided by the second cable <NUM> such that the internal torque or clamping force Δτclamp can be expressed as: <MAT>.

To maintain the clamping force Δτclamp between jaws "a, b", Equation (<NUM>) can be expressed as: <MAT> Substituting Equation (<NUM>) into Equation (<NUM>) provides: <MAT> A governing equation can be developed in view of the symmetry between Equations (<NUM>) and (<NUM>) as: <MAT> which has two independent variables, the clamping force Δτclamp and Δτ<NUM>. The clamping force Δτclamp can be used to control an amount of force between jaws "a, b" such that Equation (<NUM>) provides a direct means for managing a clamping torque and force in the jaw DOF. Further, the free variable Δτ<NUM> can be used to maintain cable tension as detailed above.

Equation (<NUM>) depends on the assumption that the jaws "a, b" of the end effector <NUM> are closed such that the DOF of the end effector <NUM> are reduced to two such that Equation (<NUM>) holds. In use, this condition can be evaluated through the forward kinematic model of Equation (<NUM>). To verify the forward kinematic model of Equation (<NUM>) it may be advantageous to use the motor positions provided by encoders for the motors of the IDU <NUM> due to the physical separation of the motors and the end effector <NUM>. As the motor encoders will induce some uncertainty, a clamping threshold can be set such that once the calculated jaw angle is smaller than the clamping threshold, the clamping torque adjustment as noted in Equation (<NUM>) can be applied gradually over a short period of time, e.g., <NUM> seconds. Further, as the adjustments are proportional to the two free variables, the clamping force Δτclamp and Δτ<NUM>, if the adjustments are increased proportionally, the position controlled by the PID controller <NUM> may be impacted.

As the clamping force is only provided on instruction from a clinician interfacing with the robotic surgical system <NUM> (<FIG>), when a clinician signals an intent to open the jaws "a, b" of the end effector <NUM> the clamping force may be released faster than the addition of clamping force, e.g., <NUM> seconds. As the clinician can visually observe the jaws "a, b" opening once the intent is clear, a desired jaw angle θd can be used to determine a releasing threshold instead of a calculated jaw angle as detailed above. Once the desired jaw angle θd crosses the clamping threshold, the clamping torque in the form of the clamping force Δτclamp can be quickly applied. In addition, a hysteresis can be built between the clamping threshold and the releasing threshold to avoid a constant crossing between applying a clamping force and releasing a clamping force.

Referring now to <FIG>, a total controller <NUM> that combines the PID controller <NUM>, the NS controller <NUM>, and a combination controller <NUM> provided in accordance with the present disclosure to control the position of the end effector <NUM> in yaw, pitch, and jaw and to maintain cable tension and generate a clamping force when needed. The PID controller <NUM> receives the desired jaw angle θd and outputs motor torques τm to the NS controller <NUM>. In addition, the PID controller <NUM> receives the position of the motors qs of the IDU <NUM> as part of a feedback loop.

The NS controller <NUM> receives the motor torques τm from the PID controller <NUM> and the desired jaw angle θd. The NS controller <NUM> can utilize any of the methods for maintaining cable tension and/or techniques for generating a clamping force as detailed above. The desired jaw angle θd can be used to calculate a desired angular velocity about each joint and to pick a corresponding sign for the friction coefficients µ<NUM> and µ<NUM>, e.g., opposite the direction of desired angular velocity. Alternatively, friction may be ignored to simplify the NS controller <NUM>. The NS controller <NUM> also receives the position of the motors qs of the IDU <NUM> as part of a feedback loop and uses the forward kinematics model to generate calculated joint angles θs to detect when the system loses a DOF, e.g., when the calculated joint angles θs are less than a clamping threshold, to determine when to apply a clamping torque. In addition, the NS controller <NUM> may also receive a sensed torque τs to maintain cable tension.

The NS controller <NUM> outputs the motor torques τm and null torques τnull to the combination controller <NUM>. The combination controller <NUM> adds the null torques τnull to the motor torques τm to calculate a desired torque τd from a sum of the motor torques τm and null torques τnull for output to the IDU <NUM>. In embodiments where a sensed torque τs is available, the combination controller <NUM> receives the sensed torque τs and closes the desired combination controller <NUM> then outputs the desired torque τd. The proportional gain Ks is implemented to reduce error between the desired torque τd and the sensed torque τs. Specifically, a sum of the motor torques τm and null torques τnull may be the desired torque τd and the proportional gain Ks is implemented such that the sensed torque τs approaches the sum of the motor torques τm and null torques τnull. Thus, when an error between the desired torque τd and the sensed torque τs is small, the proportional gain Ks is also small. As detailed herein, the combination controller <NUM> is a tertiary controller.

Referring to <FIG>, another total controller <NUM> that combines the PID controller <NUM> and the NS controller <NUM> is disclosed in accordance with the present disclosure to control the position of the end effector <NUM> in yaw, pitch, and jaw and to maintain cable tension. As shown, the NS controller <NUM> adds the motor torques τm and the null torques τnull and outputs the desired torque τd directly to the IDU <NUM>. The total controller <NUM> may be used when the NS controller <NUM> maintains cable tension but does not generate a clamping force.

With reference to <FIG>, another total controller <NUM> that combines the PID controller <NUM> and the NS controller <NUM> is disclosed in accordance with the present disclosure to control the position of the end effector <NUM> in yaw, pitch, and jaw and to maintain cable tension and generate a clamping force when needed. The total controller <NUM> also includes a joint space converter <NUM> that converts the motor positions qs of the IDU <NUM> from the motor space to joint angles θs in the joint space by using the forward kinematics model of Equation (<NUM>). The joint space converter <NUM> delivers the joint angles θs to the PID controller <NUM> and the NS controller <NUM>. The total controller <NUM> may also include a distribution controller <NUM> as detailed below which also receives the joint angles θs from the joint space controller <NUM>. The distribution controller <NUM> may be a separate controller or may be integrated into the PID controller <NUM>.

By operating the PID controller <NUM> directly in the joint space, the yaw, pitch, and jaw joints can have different controlled stiffnesses if desired. The output from the PID controller <NUM> in the joint space is joint torque τj which is calculate as: <MAT>.

The distribution controller <NUM> receives the joint torques τj from the PID controller <NUM> and distributes the joint torques τj to the motor torques τm. However, there is not an equation that directly distributes the joint torques τj to motor torques τm. Equation (<NUM>) relates motor torques τm to joint torques τj but is not invertible. Similar to the forward kinematics, a pseudoinverse of Equation (<NUM>) can be used to distribute the joint torques τj to motor torques τm. The distribution controller <NUM> may account for friction when distributing the joint torques τj to the motor torques τm. The distribution controller <NUM> then outputs the motor torques τm to the NS controller <NUM>. As noted above, the distribution controller <NUM> may be separate from or integrated into the PID controller <NUM>.

The NS controller <NUM> then receives the motor torques τm from the distribution controller <NUM> and calculates the null torques τnull, adds the motor torques τm and the null torques τnull, and outputs the desired torque τd directly to the IDU <NUM> in a manner similar to those detailed above.

The overall controllers <NUM>, <NUM>, <NUM> are examples of contemplated overall controllers and should not be seen as limiting. Other overall controllers are also considered to accommodate the differential drive mechanism which controllers maintain cable tension and generate clamping forces using a null space controller. For example, another overall controller may verify the desired torque τd before the desired torque τd is delivered to the IDU <NUM> to verify that the desired torque τd is within an acceptable range for the IDU <NUM>. In such a controller, if one or more of the desired torques τd is outside of a range for the IDU <NUM>, then a null space technique may be used to adjust the desired torques τd before outputting the desired torques τd to the IDU <NUM>, e.g., the cable tension may be reduced and/or the clamping force may be reduced.

Claim 1:
A controller for an end effector the end effector controlled by four cables of an open loop differential drive mechanism, the controller comprising:
primary controller configured to receive a desired pose for the end effector in yaw, pitch, and jaw degrees-of-freedom (DOF), to generate a motor torque for each motor of an instrument drive unit (IDU) to position the end effector in the desired pose, and to transmit the motor torques; characterized in that,
a secondary controller configured to receive the motor torques from the primary controller, to generate null torques for each of the motors of the IDU to maintain tension in the cables of the differential drive mechanism; and
an IDU configured to receive desired torques which include a sum of the motor torques and the null torques and to manipulate the end effector to the desired pose in response to receiving the desired torques.