Calibrating a surgical robot

Abstract

A control system for calibrating a surgical robot, the surgical robot comprising an arm 301 extending from a base 309 to an attachment structure for attaching to a surgical instrument, the arm compris

Description

BACKGROUND It is known to use robots for assisting and performing surgery. Figure 1 illustrates a typical surgical robotic system. A surgical robot 100 consists of a base 102, an arm 104 and an instrument 106. The base supports the robot, and may itself be attached rigidly to, for example, the operating theatre floor, the operating theatre ceiling or a cart. The arm extends between the base and the instrument. The arm is articulated by means of multiple flexible joints 108 along its length, which are used to locate the surgical instrument in a desired location relative to the patient. The surgical instrument is attached to the distal end of the robot arm. The surgical instrument comprises a shaft connected to a distal end effector 110 by a jointed articulation 111. The end effector engages in a surgical procedure at the surgical site. A surgeon controls the surgical robot 100 via a remote surgeon console 112. The surgeon console comprises one or more surgeon input devices 114. These may take the form of a hand controller or foot pedal. The surgeon console also comprises a display 116. A control system 118 connects the surgeon console 112 to the surgical robot 100. The control system receives sensory inputs from the robot 100 and command inputs from the surgeon input device(s) 114. The control system uses these inputs to calculate control signals to move the joints of the robot arm 104 and instrument 106. The control system sends these control signals to the robot, where the corresponding joints are driven accordingly. As shown in figure 2, the surgical instrument penetrates the body of the patient through a surgical port 200 so as to access the surgical site. The port comprises a hollow tube which passes through the outer subcutaneous tissues of the patient to help protect those tissues as surgical instruments are inserted and removed from the patient’s body, and as the robot manipulates the surgical instruments inside the body. The distance of subcutaneous tissue that the port extends through depends on the patient’s anatomy, but is generally of the order of 40 to 100mm. The surgical instrument is constrained at one end by its attachment to the surgical robot, and is further constrained by its passage through the port. The surgical instrument will have a natural centre of rotation at a point along the length of the port. The exact location of that natural centre of rotation will depend on a variety of factors, for example the position of the port on the body, the angle of entry of the port into the body, the patient’s position on the operating bed, and the patient’s anatomy. To reduce disruption to the tissue surroundingthe port by imposing a significant lateral force on the port, it is known to control the surgical robot so that as well as the end effector being located at a desired position at the surgical site as controlled by the surgeon, the surgical instrument always intersects an estimate of the natural centre of rotation of the surgical instrument in the port. That estimate is determined as part of a setup procedure before surgery starts. That estimate is determined by manually inserting the instrument through the port, and then manually moving the robot arm to alter the angle of the instrument relative to the body. Sensory data from the position sensors on the robot arm can be used to estimate the natural centre of rotation of the instrument in the port as the common point which the instrument intersects as it is moved. For patient safety, when a surgical instrument is inside the patient’s body, it is expected that the instrument is under the direct control of a person, that direct control being either manual control by a member of bedside staff, or remote control by a surgeon at the surgeon console. The instrument must be inside the patient’s body to estimate the natural centre of rotation of the surgical instrument in the port, and thus the sensory data required to generate the estimate is collected whilst the instrument is under the control of a person. SUMMARY OF THE INVENTION According to an aspect of the invention, there is provided a control system for calibrating a surgical robot, the surgical robot comprising an arm extending from a base to an attachment structure for attachingto a surgical instrument, the arm comprising a series of joints by which the configuration of thearm can be altered, the series of joints including a wrist proximal to the attachment structure, the wrist constrained to rotate about axes which intersect the longitudinal axis of the surgical instrument, each joint driveable by a motor, the arm further comprising a plurality of position sensors for sensing the position of each joint and a plurality of torque sensors for sensing the torque about each joint, the control system configured to, when a surgical instrument is attached to the attachment structure and captive in a port: receive a control input from a user to perform a calibration to estimate the natural centre of rotation of the surgical instrument in the port; respond to the control input from the user by: controllingthe motors to drive the joints to move the arm so that the position of the wrist follows a wrist path which is deterministic, smooth, and continuous; receiving sensor inputs from the position and torque sensors; responding to the sensor inputs from the torque sensors by controllingthe motors to drive the orientation of the wrist in a compliant manner, so as to respond to each external force applied to the surgical instrument from contact with the port as detected by the torque sensors by driving the wrist to adopt an orientation which causes the surgical instrument to move in the direction of the applied external force; from the sensor inputs from the position sensors, determining the orientation of the surgical instrument as the wrist follows the wrist path; and estimating the natural centre of rotation of the surgical instrument in the port from a set of straight lines, each straight line extending from a wrist position in the direction of the determined orientation of the surgical instrument corresponding to that wrist position. The control system may estimate the natural centre of rotation of the surgical instrument in the port as the point which has the least squares distance to the set of straight lines. The control system may iteratively update the set of straight lines as the wrist follows the wrist path, and iteratively update the estimate of the natural centre of rotation of the surgical instrument in the port from the updated set of straight lines. The control system may be operable in a driven mode in which the surgical instrument is attached to the attachment structure and a tip of the surgical instrument located at a surgical site. In this driven mode, the control system may: receive a demand signal indicating a desired location of the surgical instrument tip; respond to the received demand signal by: calculating a configuration of the arm in which the surgical instrument tip is at the desired location and the surgical instrument intersects the estimated natural centre of rotation of the surgical instrument in the port; and controlling the motors to drive the joints so that the arm adopts the calculated configuration. The position of the wrist may be non-repeating as it follows the wrist path. The wrist path may be symmetrical. The wrist path may be a circle of fixed radius. The fixed radius may be greater than 5cm. The wrist path may comprise a single complete circle or part circle. The surgical instrument may be a tissue manipulation instrument. The wrist path may comprise a single semi-circle or part semi-circle. The surgical instrument may be an endoscope. The control system may detect that the wrist has reached a workspace boundary limit, and respond by controlling the motors to drive the joints to move the arm so that the wrist follows an updated wrist path, the updated wrist path matching the wrist path except that the wrist moves alongthe updated wrist path in an opposing direction to the movement of the wrist along the wrist path. The control system may detect that the arm has clashed with another structure, and respond by controlling the motors to drive the joints to move the arm so that the wrist follows an updated wrist path, the updated wrist path matching the wrist path except that the wrist moves alongthe updated wrist path in an opposing direction to the movement of the wrist along the wrist path. The wrist path may be on the surface of a sphere, the radius of the sphere being the distance from the wrist to a tip of the surgical instrument. The control system may be further configured to assess a set of criteria, and if each criterion is satisfied: (i) store the estimated natural centre of rotation of the surgical instrument in the port for subsequent use in controlling movement of the arm whilst the instrument is attached to the attachment structure, and (ii) output a signal to the user indicatingthe calibration is complete. The criteria may include one or more of: (i) the number of straight lines in the set of straight lines used in the estimation of the estimated natural centre of rotation of the surgical instrument in the port exceeds a threshold number; (ii) the wrist has moved greater than a minimum distance on the wrist path; (iii) the quadratic average distance between the estimated natural centre of rotation of the surgical instrument in the port and the set of straight lines is less than a threshold value; and (iv) a calculated error of the estimated natural centre of rotation of the surgical instrument in the port in each dimension is less than a threshold error. If the set of criteria is not satisfied, the control system may: (i) iteratively update the estimate of the natural centre of rotation of the surgical instrument in the port, (ii) assess each updated estimate to the set of criteria, and (iii) only when an updated estimate satisfies the set of criteria save the estimated natural centre of rotation of the surgical instrument in the port for subsequent use in controlling movement of the arm whilst the instrument is attached to the attachment structure, and output a signal to the user indicatingthe calibration is complete. The control system may receive the control input from the user to perform the calibration whilst the surgical robot is operating in a setup mode prior to the start of a surgical procedure. The control system may receive the control input from the user to perform the calibration afterthe surgical robot has been operating in a surgical mode and the surgical instrument tip is located at a surgical site in the patient. The control system may control the motors to drive the joints to move the arm so that the surgical instrument is retracted from the surgical site along the longitudinal axis of the surgical instrument until the surgical instrument tip reaches the current estimated natural centre of rotation of the surgical instrument in the port used during the surgical mode. The control system may replace the current estimated natural centre of rotation of the surgical instrument in the port with the estimated natural centre of rotation of the surgical instrument in the port. The control system may cancel the current estimated natural centre of rotation of the surgical instrument in the port before performingthe calibration. The surgical instrument may comprise instrument joints to articulate an end effector at the surgical instrument tip, the instrument joints driveable by the arm joints. The control system may, prior to retracting the surgical instrument, control the motors to drive the arm joints to drive the instrument joints such that the surgical instrument adopts a straight configuration. The surgical instrument may comprise instrument joints to articulate an end effector at the surgical instrument tip, the end effector comprising opposable end effector elements, the instrument joints driveable by the arm joints. The control system may, prior to retracting the surgical instrument, control the motors to drive the arm joints to drive the instrument joints to open the end effector elements apart. The control system may, whilst the surgical instrument is being retracted, control the motors to drive the arm joints to drive the instrument joints to close the end effector elements together. The surgical robot may be supported at its base by a support structure, the control input being located either on the surgical robot or the support structure. The surgical robot may be remotely controllable by a surgeon console, the control input being located on the surgeon console. BRIEF DESCRIPTION OFTHE FIGURES The present invention will now be described by way of example with reference to the accompanying drawings. In the drawings: Figure 1 illustrates a surgical robot system for performing a surgical procedure; Figure 2 illustrates a surgical robot during a surgical procedure; Figure 3 illustrates a surgical robot; Figure 4 is a flowchart illustrating a calibration procedure for estimating the natural centre of rotation of the surgical instrument in the port; Figure 5a illustrates an exemplary wrist path for a tissue manipulation instrument, and figure 5b illustrates an exemplary wrist path for an endoscope; and Figure 6 is a flowchart illustrating additional steps of the calibration procedure when carried out mid-surgery. DETAILED DESCRIPTION The following describes a control system for calibrating a surgical robot. Figure 3 shows an example of a robot arm 301. The robot arm 301 may be comprised within a surgical robotic system, such as the surgical robotic system shown in figure 1. Although the surgical robotic system shown in figure 1 comprises one surgical robot arm, it is to be understood that the surgical robotic system described herein may comprise a plurality of surgical robot arms. The robot arm 301 comprises a base 309. The base supports the robot arm, and may itself be attached rigidly to, for example, a cart, the operating theatre floor, or the operating theatre ceiling. The robot arm has a series of rigid arm members. Each arm member in the series is joined to the preceding arm member by a respective joint 304a-g. Joints 304a-e and 304g are revolute joints. In order from the base 309, joint 304a is a roll joint, joint 304b is a pitch joint, joint 304c is a roll joint, joint 304d is a pitch joint, joint 304e is a roll joint, and joint 304g is a roll joint. Joint 304f is between joints 304e and 304g. Joint 304f is a compound joint composed of two revolute joints whose axes are orthogonal to each other, as in a Hooke’s or universal joint. Joint 304f may be co-located pitch and yaw joints. Joint 204f is referred to as a wrist in the following description. The robot arm may be jointed differently to that described with reference to figure 3. For example, joint 204d may be omitted and / or joint 204f may permit rotation about a single axis. The robot arm may include one or more joints that permit motion other than rotation between respective sides of the joint, such as a prismatic joint by which an instrument attachment can slide linearly with respect to more proximal parts of the robot arm. The arm joints are configured such that the configuration of the robot arm can be altered allowing the distal end 330 of the robot arm to be moved to an arbitrary point in a threedimensional working volume illustrated generally at 335. One way to achieve that is for the joints to have the arrangement illustrated in figure 3. Other combinations and configurations of joints could achieve a similar range of motion, at least within the zone 335. For example, the robot arm may comprise more or fewer arm members. The robot arm 301 comprises a series of motors 31 Oa-h. With the exception of the wrist 304f, which is served by two motors, each motor is arranged to drive rotation about a respective joint of the robot arm. The motors are controlled by a control system, such as control system 118 described with respect to figure 1. The control system comprises a processor and a memory. The memory stores, in a non-transient way, software code that can be executed by the processor to cause the processor to generate control signals to output to the robot arm to control the motors 31 Oa-h in the manner described herein. The robot arm 301 comprises a series of sensors 307a-h and 308a-h. These sensors comprise, for each joint, a position sensor 307a-h for sensing the rotational position of the joint and a torque sensor 308a-h for sensing torque applied about the joint’s rotation axis. Wrist 304f may have two pairs of sensors. One or both of the position and torque sensors for a joint may be integrated with the motor for that joint. The outputs of the sensors are sent to the control system where they form inputs to the processor. The distal end of the robot arm 330 has an attachment structure 316 by means of which a surgical instrument 306 can be releasably attached. The surgical instrument has a rigid linear shaft 361. The surgical instrument has an end effector 362 at the distal end of the shaft. The end effector 362 consists of a device for engaging in a procedure, for example a cutting, grasping or imaging device. Thus, the surgical instrument may be a tissue manipulation instrument for manipulating tissue, for example by grasping, cutting, heating, sealing, stitching or stapling it. Alternatively, the surgical instrument may be an endoscope for illuminating and imagingthe surgical site. As described herein, terminal joint 304g may be a revolute joint. The surgical instrument 306 and / or the attachment 316 may be configured so that the instrument extends linearly parallel with the rotation axis of the terminal joint 304g of the robot arm. In this example the instrument extends along an axis coincident with the rotation axis of joint 304g. Joints 304e and 304f of the robot arm are configured so that with the distal end of the robot arm 330 held at an arbitrary location in the working volume 335 the surgical instrument 306 can be directed in an arbitrary direction within a cone. Such a cone is illustrated generally at 336. One way to achieve that is for the terminal part of the arm to comprise the pair of joints 304e and 304f whose axes are mutually arranged as described above. Other mechanisms can achieve a similar result. For example, joint 304g could influence the attitude of the instrument if the instrument extends in a direction which is not parallel to the axis of joint 304g. For some types of minimally invasive procedure, the surgical instrument 306 may be inserted into the patient’s body through a synthetic port 317. For example, the minimally invasive procedure may be performed within the patient’s abdomen. The port 317 may comprise a hollow tube 317a. The hollow tube 317a passes through outersubcutaneous tissues 302 of the patient so as to limit disruption to those tissues as the surgical instrument is inserted into and removed from the patient, and as the instrument is manipulated within the patient’s body. The port 317 may comprise a collar 317b. The collar 317b prevents the port 317 being inserted too far through the outer tissues 302 of the patient. The surgical robot is calibrated in order to estimate a natural centre of rotation of the surgical instrument in the port. This estimate is then subsequently used when the surgical robot is being driven under the control of the surgeon console. For example, when the surgical robot is in a driven mode, such as a surgical mode, in which the surgical instrument is attached to the attachment structure of the arm and the tip of the surgical instrument is located at the surgical site. The tip of the surgical instrument is where the end effector is. When the surgical robot is driven under the control of the surgeon console, the control system receives a demand signal from a surgeon input device of the surgeon console indicating a desired location of the surgical instrument tip. The control system responds to the received demand signal by calculating a configuration of the robot arm in which the surgical instrument tip is at the desired location and the surgical instrument intersects the estimated natural centre of rotation of the surgical instrument in the port. The control system then controls the arm motors to drive the arm joints so that the arm adopts the calculated configuration. Problems may be encountered if the estimated natural centre of rotation of the surgical instrument in the port is inaccurate, i.e. is not coincident with the actual natural centre of rotation of the surgical instrument in the port. For example, because the instrument is being constrained to intersect a point which is not its natural centre of rotation, the instrument may also make sustained and significant contact with a side wall of the port, thereby exposing it to significant lateral forces. If the control system receives sensor inputs from one or more torque sensors which exceed a threshold value, it interprets this as indicating an unacceptable exogenous force is being applied to the arm. This could be due to a clash either between the robot arm and another structure, or between the instrument and another structure. This may cause the control system to issue an alarm and / or enter a protective state which prevents the surgeon from moving the instrument in the direction which causes the sensed torque to increase. If the estimated natural centre of rotation of the surgical instrument in the port is deeper into the patient’s body than the actual natural centre of rotation of the surgical instrument in the port, then this may result in the surgeon being unable to operate in areas close to the skin. This is because the instrument cannot be controlled to reach the desired location close to the skin and also intersect the estimated natural centre of rotation of the surgical instrument in the port. To avoid problems of this nature, a more accurate estimate of the natural centre of rotation of the surgical instrument in the port is needed. The estimate may be inaccurate because of poor manual technique in moving the robot arm to generate the sensory data the control system uses to calculate the estimate. For example, if the robot arm is moved in a repetitive or jolty or minimally varying manner, then the sensory data may be insufficient to generate an accurate estimate. If the surgical instrument is not pushed far enough through the port initially, then the instrument may wobble as the robot arm is moved, resulting in sensory data which is insufficient to generate an accurate estimate. A sufficiently accurate estimate of the natural centre of rotation of the surgical instrument in the port may initially have been calculated, and successfully used during a surgical procedure, but then a change in circumstance mid-surgery has led to the estimate no longer being accurate. Such changes in circumstance include the patient moving, insufflation changes, obstructions in the body, or the surgeon moving the instrument to operate in a different area of the body. In such scenarios, it is important the estimate is re-calculated as quickly as possible so that the surgery can continue. The following description describes two scenarios in which the natural centre of rotation of the surgical instrument in the port is estimated. The first scenario is during a setup mode of the surgical robot prior to using it to perform a minimally invasive procedure on the patient. The second scenario is mid-surgery. In this scenario, the instrument tip is located at the surgical site in the patient. A current estimate of the natural centre of rotation of the surgical instrument in the port has been used in the surgery, but is to be recalculated. This may be due to problems occurring in the surgery, such as the detected exogenous forces described above. The following describes a calibration procedure carried out by the control system for calculating an estimate of the natural centre of rotation of the surgical instrument in the port which can be implemented in either the setup mode or mid-surgery when the robot has been in a surgical mode for performing surgery. Figure 4 is a flowchart illustrating steps of a calibration procedure carried out by the control system to estimate the natural centre of rotation of the surgical instrument in the port. This calibration procedure may be carried out during a setup mode of the surgical robot. This calibration procedure may be carried out mid-surgery after the surgical robot has already been operating in a surgical mode. For example, the control system may bring the surgical robot out of surgical mode into an impedance mode or compliance mode in order to perform the calibration procedure. Whilst performing the calibration procedure of figure 4, the surgical instrument 306 is attached to the attachment structure of the robot arm and captive in the port 317. Initially, at step 401, the control system receives a control input from a user to perform a calibration to estimate the natural centre of rotation of the surgical instrument in the port. The control input may be located on the robot itself, or on the support structure of the robot. For example, if the support structure of the robot is a cart, the control input may be located on the cart. The control input may be located on the surgeon console. The control input may be a physical input such as a button, switch, trigger, or pedal. The input may be on the surgeon console display. The input may be on a touchscreen device such as a tablet or phone. The input on these devices may be a selectable icon. The input may be via movement of the user, such as detected via eye-tracking or hand / body gesturing. The control system responds to receiving the control input from the user by performing steps 402 to 407. Firstly, at step 402, with the surgical instrument inside the port, the control system sends control signals to the arm motors. These control signals control the arm motors to drive the arm joints to move the arm to drive the position of the wrist along a wrist path. More specifically, the control system drives a dedicated point of the wrist along the wrist path. In the case that the wrist comprises two revolute joints whose axes are orthogonal to each other, the dedicated point of the wrist may be the intersection of those two orthogonal axes. In the case that the wrist comprises a single revolute joint, the dedicated point of the wrist may be a point along the rotation axis of that revolute joint which falls inside the casing of the robot arm. The wrist path is deterministic, smooth and continuous. The wrist path is entirely determined by the control system. The user does not manually move the wrist during the calibration process. The user does not apply force to the wrist during the calibration process. The wrist path is a standardised track. That track is preferably symmetrical. Ideally, each wrist position on the wrist path is unique. In other words, the path does not repeat. Figure 5a illustrates an exemplary wrist path for a tissue manipulation instrument. The wrist path is a circle of fixed radius. The radius of the circle may be greater than 2cm. The radius of the circle may be greater than 3cm. The radius of the circle may be greater than 5cm. The radius of the circle may be greater than 10cm. The wrist path is a single complete circle. If, as explained later, the control system acquires the sensory data it needs to generate a sufficiently accurate estimate before the wrist has traversed a complete circle, then the calibration procedure ends. Thus, in this case, the wrist path is a single part-circle. In either case, the wrist path is non-repetitive since the wrist does not complete more than one circle. The wrist may move along the circle in either a clockwise or anti-clockwise direction. The dotted line in figure 5a represents an initial movement of the wrist from a position in which the surgical instrument is colinear with the port, that movement being along the radius of the circle to a point on the circumference of the circle. The circular wrist path then begins. After the end of the circular wrist path, the wrist follows a final movement back along the dotted line from the circumference of the circle to the centre of the circle in a position in which the surgical instrument is colinear with the port. If sufficient measurements have been accrued prior to a whole circle being traversed by the wrist, then the control system may stop the calibration. In this case, the control system controls the wrist to stop moving along the circumference of the circle, and move back to the centre of the circle. Suitably, sensor measurements taken during motion of the wrist on the dotted lines, or otherwise along a direction towards or away from the centre of the circle are not used in the estimation of the natural centre of rotation of the tissue manipulation instrument in the port. Figure 5b illustrates an exemplary wrist path for an endoscope. The wrist path is a semicircle of fixed radius. The radius of the semi-circle may be greater than 2m. The radius of the semi-circle may be greater than 4cm. The radius of the semi-circle may be greater than 6 cm. The radius of the semi-circle may be greater than 10cm. The wrist path is a single semi-circle or part semi-circle. In either case, the wrist path is non-repetitive since the wrist does not complete more than one semi-circle. The wrist may move along the semi-circle in either a clockwise or anti-clockwise direction. The dotted line in figure 5b represents an initial movement of the wrist from a position in which the surgical instrument is colinear with the port, the movement being along the radius of the circle to a point on the circumference of the circle. The semi-circular wrist path then begins. After the end of the semi-circular wrist path, the wrist follows a final movement back along the dotted line from the circumference of the circle to the centre of the circle in a position in which the surgical instrument is colinear with the port. If sufficient measurements have been accrued prior to a full semi-circle being traversed by the wrist, then the control system may stop the calibration. The control system controls the wrist to stop moving along the circumference of the circle, and move back to the centre of the circle. Suitably, sensor measurements taken during motion of the wrist on the dotted lines, or otherwise along a direction towards or away from the centre of the circle are not used in the estimation of the natural centre of rotation of the endoscope in the port. The wrist path for the endoscope is suitably at most a semi-circle compared to the tissue manipulation instrument which may complete a whole circle. This is because the control system does not require as accurate an estimate of the natural centre of rotation of the endoscope in the port compared to the tissue manipulation instrument. This is because the endoscope is used only for illuminating and imagingthe surgical site, not for the more precise operations of tissue manipulation. Additionally, a robot arm holding the endoscope is less likely to move quickly compared to a robot arm holding the tissue manipulation instrument. Since the higher inertia of the camera head and telescope on the endoscope makes it a more lengthy process to find an estimate of the natural centre of rotation with a given accuracy, a lower accuracy estimate using a shorter wrist path is acceptable. Alternatively, the wrist path for the endoscope may be a single circle or part circle. In this case, the radius of the circle is smaller than the radius of the wrist path for the tissue manipulation instrument. A semi-circular wrist path or circular wrist path with a smaller radius reduces the likelihood of a clash between the robot arm and another structure. It also enables more robot arms to be calibrated ready for surgery in a smaller space, since the clearance volume around each robot arm needed to perform the calibration is smaller. Suitably, the wrist path itself is tracked out on the surface of a sphere. The radius of the sphere is the distance between the wrist and the tip of the surgical instrument. This is a safety feature which ensures that the instrument tip is maintained at the same depth in the patient’s body throughout the calibration procedure. Thus, the instrument is not pushed further into the patient’s body whilst the calibration procedure is carried out. In the examples described above, the wrist path is pre-determined, albeit that wrist path may be terminated prior to a complete circle (or semi-circle) having been traversed if sufficient measurements have been taken to determine a sufficiently accurate estimate of the natural centre of rotation of the surgical instrument in the port. However, the control system may be configured to respond to certain scenarios by altering the predetermined path. This alternation may involve repeating some wrist positions. For example, the control system may detect that the wrist has reached a workspace boundary limit. That workspace boundary limit may be due to the working volume of the robot arm as defined by the joint limits (i.e. ranges of motion of the joints). That workspace boundary limit may be due to external structures with which the arm could collide, such as other robot arms. That workspace boundary limit may be due to the arm being close to colliding with itself. In response to detecting that the wrist has reached a workspace boundary limit, the control system responds by controlling the motors to drive the arm joints to move the arm so that the wrist changes direction. Thus, the wrist continues to follow the same wrist positions as in the original wrist path but in the opposing direction. The wrist therefore moves on an updated wrist path, the updated wrist path matching the original wrist path except that the wrist moves along the updated wrist path in an opposing direction to the movement of the wrist along the original wrist path. As another example, the control system may detect that the robot arm has clashed with another structure. The control system detects a clash if it receives sensory inputs from one or more torque sensors which indicate that the torque about one or more joints exceeds a threshold torque value. In response to a detected clash, the control system controls the motors to drive the arm joints to move the arm so that the wrist changes direction. Thus, the wrist continues to followthe same wrist positions as in the original wrist path but in the opposing direction. The wrist therefore moves on an updated wrist path, the updated wrist path matching the original wrist path except that the wrist moves along the updated wrist path in an opposing direction to the movement of the wrist along the original wrist path. During calibration, the surgical instrument is constrained at one end by being attached to the attachment structure of the robot arm, and at the distal end by passing through, and being captive in, the port. As the wrist follows the wrist path, the surgical instrument experiences forces acting on it where it contacts the port. The arm is controlled to be compliant to accommodate these external forces acting on it, as will now be explained. At step 403, the control system receives sensed inputs from the torque sensors. The control system then sends control signals to the motors 310a-h to control them to accommodate the torques detected about the joints. Joints which rotate about an axis which is notvertical will experience a gravitational torque. The control system stores, for each element of the robot arm and the surgical instrument, its mass, the distance of its centre of mass from the preceding joint of the robot arm and the relationship between the centre of mass and the positional outputof the position sensorforthe precedingjoint. Using this information, the control system models the effect of gravity on the components of the robot arm forthe current configuration of the robotarm and estimates a torque due to gravity on each joint of the robot arm. The processor then drives the motor 310a-h of each joint to apply a torque that will exactly oppose the calculated gravitational torque. During the calibration process, the control system receives sensed inputs from the torque sensors. The measured torque about a joint may be partially or completely due to gravity and / or external forces acting on the joint. The control system calculates any remaining sensed torque about each joint once the gravitational torque about that torque is discounted. Whilst the wrist position follows the wrist path, that remaining sensed torque is treated as being due to external force applied to the surgical instrument from contact with the port. At step 404, in response to that remaining sensed torque on each arm joint, the control system controls the motors to drive the orientation of the wrist in a compliant manner so as to cause the wrist to adopt an orientation which causes the surgical instrument to move in the direction of the applied external force from the port. Specifically, the control system controls the wrist motors 31 Of to drive the wrist orientation to reduce the measured torque. More specifically, the control system drives the wrist motors such that a vector having an origin at the dedicated point of the wrist (that being the point which is driven along the wrist path, such as the intersection of the two orthogonal axes of the compound wrist joint) and a direction parallel to the longitudinal axis of the shaft of the instrument adopts an orientation which causes the surgical instrument to move in the direction of the applied external force from the port. In this way, the angle of the instrument relative to the base of the robot changes as the wrist follows the wrist path. As the wrist moves along the wrist path, at step 405, the control system receives sensor inputs from the position sensors 307a-h. At step 406, from the position sensors and the stored parameters of the robot arm mentioned above, the control system calculates the current configuration of the robot arm, including both the wrist position and wrist orientation as it moves along the wrist path. The wrist position is already known to the control system from the deterministic wrist path. Thus, in the following calculations, the control system may use the known wrist positions on the wrist path that it commanded the wrist to move on. Alternatively or additionally the control system may use the wrist positions on the wrist path as measured by the position sensors. The current configuration of the robot arm could be inferred by other means than direct measurement by position sensors 307a-h. For example, a camera-based positioning system may be used to track points in space, such as fiducial markers attached to the robot arm. This technique could be used to determine the angle of each joint. As another example, joint positions may be inferred using current sensors. For example, the position of a joint can be inferred from the amount of current passing through the motor and assuming a given relationship to be constant. Both the position and torque sensors record sensor data at discrete times. The data may be recorded irregularly or at predetermined intervals, such as every millisecond. At step 407, the control system estimates the natural centre of rotation of the surgical instrument in the port. To do this, the control system first determines a set of straight lines, each line extending from a wrist position in the direction of the determined orientation of the surgical instrument corresponding to that wrist position. For example, the control system may calculate a set of data pairs [a,b]. a is the position of the wrist relative to the base, b is the vector of the instrument shaft 361 relative to the distal end of the robot arm, i.e the wrist orientation. The data pairs are temporally connected. In other words, each pair is calculated from sensory data taken at the same time t, in the motion of the wrist in the wrist path, t, are discrete times between t= 0 at the beginning of the wrist path, and t=T at the end of the wrist path. The control system may calculate a data pair for each instance at which the position sensors record position information. That is, for each instance, the control system determines both a position of the wrist and a vector of the surgical instrument from the determined position of the wrist in dependence on the recorded joint positions. Since the rigid linear axis of the instrument shaft 361 passes through the port, the natural centre of rotation of the surgical instrument lies along that vector. As the distal end of the robot arm moves along the wrist path, the control system calculates multiple pairs of wrist positions and instrument shaft vectors. Those vectors converge, from their respective wrist position, on the natural rotation centre of the surgical instrument in the port. By collecting a series of those data pairs and then solving for the location where the instrument shaft vectors converge, the control system estimates the location of the natural centre of rotation of the surgical instrument in the port relative to the robot arm. The control system then stores the estimate in non-transient form in memory for use in generating control signals to control movement of the robot arm during surgery. The control system may calculate the natural centre of rotation of the surgical instrument in the port to be a point p which has the least squares distance to the set of straight lines defined by the [a,b] data pairs. The control system can calculate a value for the natural centre of rotation of the surgical instrument in the port from two data pair sets. However, because the port is wider than the surgical instrument, the vectors b of those two data pair sets are very unlikely to intersect at the actual natural centre of rotation of the surgical instrument in the port. Thus, that estimate will be very inaccurate. Thus, the control system follows a process in which it iteratively updates the estimate of the natural centre of rotation of the surgical instrument in the port that it calculates. The control system starts calculating the estimate as soon as it has generated data pairs from the sensory data it receives. This is whilst the wrist is being moved along the wrist path. With every iteration, the wrist has moved further along the wrist path, and further sensor inputs have been received by the control system, thus the control system has calculated an updated set of data pairs from which to calculate the estimate. The control system may recalculate the estimate in an iteration every time it receives position and torque sensor inputs, i.e. every time it calculates a new data pair. Alternatively, the iteration rate may be slower, and the control system recalculate the estimate once it has calculated a set of new data pairs, for example 10 new data pairs. Suitably, once the control system has calculated an estimate for the natural centre of rotation of the surgical instrument, it assesses a set of criteria to establish whether the estimate is sufficient to use in surgery. That criteria may include any one, combination or allot the following: (i) The number of data pairs [a,b] calculated exceeds a threshold number; (ii) The wrist has moved greater than a minimum distance along the wrist path; (iii) The quadratic average distance between the estimate and the set of straight lines used in the estimation is less than a threshold value; (iv) A calculated error of the estimate in each dimension is less than a threshold error; (v) The difference between the penultimate and final iterative estimates is less than a threshold difference; (vi) The distance of the estimate from the wrist is greater than the distance from the wrist to the start of the instrument shaft; and (vii) The distance of the estimate from the wrist is less than the distance from the wrist to the instrument tip. The criteria may be different for a tissue manipulation instrument compared to an endoscope. For example, for a tissue manipulation instrument compared to an endoscope the threshold number of data pairs for criterion (i) may be higher, and / or the minimum distance for criterion (ii) may be higher, and / orthe threshold value for criterion (iii) may be smaller, and / or the threshold error for criterion (iv) may be smaller, and / or the threshold difference for criterion (v) may be smaller. If the control system determines that each criterion in the set of criteria is satisfied, then it stores the estimated natural centre of rotation of the surgical instrument in the port from the final iteration it has performed. That stored estimate is then used for subsequent use in controlling movement of the robot arm whilst the instrument is attached to the attachment structure. In response to determining that the set of criteria is satisfied, the control system outputs a signal to the user indicating that the calibration is complete. That output signal may be a visual signal, either on the surgeon console, such as an icon on the surgeon console display, or on the robot arm and / or robot arm support structure, such as illumination of a light on the robot arm and / or support structure, or a visual signal on both the surgeon console and robot arm and / or robot arm support structure. The output signal may be an audible signal, such as a beep or spoken confirmation played out through a speaker at the surgeon console and / or robot arm and / or robot arm support structure. The output signal may be visual and audible. The output signal may alternatively or additionally be a haptic signal. The haptic signal may be output through the surgeon’s hand controllers and / or on the robot arm and / or robot arm support structure. If the control system determines that at least one criterion in the set of criteria is not satisfied, then it does not deem the calibration to be complete. Instead, it continues to a further iteration of the calibration process. In other words, it continues to control the wrist to move along the wrist path, receives further position and torque sensor data, determines one or more further data pairs [a,b], and calculates an updated estimate of the natural centre of rotation of the surgical instrument in the port. The control system then assesses that updated estimate against the set of criteria. It continues this process for the estimate of each iteration. Only when an updated estimate satisfies the set of criteria does it deem the calibration complete and save the estimate for use in surgery and output the calibration compete signal to the user. The control system may be configured to deem the calibration has failed if no estimate of the natural centre of rotation of the instrument in the port has satisfied the criteria in a limit. That limit may be a time limit. That limit may be a number of data pairs [a.b]. That limit may be a number of generated estimates of the natural centre of rotation of the instrument in the port. In the case that the limit has reached, the control system may output a signal to the user that the calibration has failed. Additionally, the control system may send control signals to the robot arm to control the arm joints to stop moving the wrist. The control system may control the arm to stop moving the wrist along the wrist path, and instead move the wrist to the central port position and then stop all movement of the arm. Once the control system has determined that an estimate of the natural centre of rotation of the instrument in the port has satisfied the set of criteria, and calibration is complete, it may transition the surgical robot out of the calibration mode to a locked mode. In this locked mode, the estimated natural centre of rotation of the instrument in the port is adopted as the current estimated natural centre of rotation of the instrument in the port. In subsequent use of the arm to perform a minimally invasive procedure, the configuration of the robot arm is remotely controlled in response to inputs received at a remote surgeon console, such as remote surgeon console 112 shown in figure 1. During the minimally invasive procedure, the surgeon uses the remote surgeon console to signal a desired position of the end effector 362. The control system determines a configuration of the joints of the robot arm that will result in the end effector 362 being placed in that desired position. The control system uses the current estimated natural centre of rotation of the instrument in the port to control the configuration of the robot arm when the robot arm is performing surgery. The control system is configured, for example by software stored in memory, to select a configuration of the arm for which both (i) the end effector 362 is at the desired position and (ii) the rigid shaft 361 of the instrument 306 passes through the current estimated natural centre of rotation of the instrument in the port, and to move the arm to that configuration. In that way the end effector 362 can be provided at the desired position with relatively little disruption to the outer tissues of the patient. Although steps 401 to 407 are shown in an order in figure 4, it will be understood that these steps may occur in a different order and / or alongside each other. Typically, sensor inputs from the position and torque sensors (steps 403 and 405) will be received continually throughout the calibration procedure. The control system drives the wrist position (step 402) and wrist orientation (step 404) together in time. Suitably, the control system iteratively estimates (step 407) the natural centre of rotation of the surgical instrument in the port whilst driving the wrist to follow the wrist path (step 402). The calibration procedure described above with reference to figure 4 applies to both estimating the natural centre of rotation of the surgical instrument in the port during a setup mode of the surgical robot prior to surgery starting, and also mid-surgery after the surgical robot has already been used in a minimally invasive manner to operate on the patient. In the case of the setup mode, priorto the user providing the control input to instruct the control system to perform the calibration procedure of figure 4, the user attaches the instrument to the robot arm and manually moves the arm so as to position the instrument in the port. The manual movement is done in a compliant mode of the robot in which the control system responds to torque sensed about the robot arm’s joints by the torque sensors by controlling the motors to drive the arm joints to move in compliance with those torques. Thus, if the user applies a force to the robot arm, the control system controls the robot arm to move in the direction of the applied force. Once the instrument is pushed into the port, the user provides the user input to initiate the calibration procedure of figure 4. In the case that the user initiates the calibration procedure mid-surgery, the control system may perform one or more further steps after receiving the control input from the user at step 401 but before performing the remaining calibration steps described with reference to figure 4. These additional steps are illustrated in figure 6. When the calibration procedure is performed mid-surgery, the surgical instrument is initially at the surgical site where it has been used in the surgery. The robot arm has a current estimated natural centre of rotation of the surgical instrument in the port previously calculated, for example during a setup mode of that surgical instrument. The control system may carry out any one, combination, or all of steps 601 to 604 of the flowchart of figure 6 in order to move the instrument into position for performing the calibration procedure to calculate a new estimate of the natural centre of rotation of the surgical instrument in the port. As shown in figure 1, the instrument may comprise joints at its tip. The end effector 110 itself may be jointed, for example the end effector may comprise a pair of opposing end effector elements. Each end effector element is attached to the instrument by a joint about which it is permitted to rotate. Suitably, the axis of rotation of the joint of each end effector is the same, thereby enabling the end effector elements to open apart and close together in a gripping motion for a pair of jaws, or a cutting motion for a pair of scissors. Suitably, the end effector is connected to the shaft of the instrument by an articulation 111. This articulation comprises one or more joints, to enable the end effector to articulate relative to the shaft. For example, the articulation may comprise a pitch joint. The articulation may further comprise a yaw joint and / or a roll joint. Joints at the distal end of the robot arm in the attachment structure drive the joints of the instrument to move. This may be carried out, for example, by joints in the attachment structure of the robot arm transferring linear or rotational drive to drive cables of the instrument, those cables passing through the shaft of the instrument and being constrained to move about the joints of the instrument thereby transferring drive to rotation about the instrument joints. In the case that the surgical instrument comprises opposable end effector elements 110, after the control system has received the control input from the user to perform the calculation at step 401, it may, at step 601, send control signals to the motors of the robot arm which drive the end effector elements to rotate to control the end effector elements to open apart from each other. This action is a safety measure to cause the end effector elements to release any tissue they are grasping. In the case that the surgical instrument comprises an articulation 111, after the control system has received the control input from the user to perform the calculation at step 401, it may, at step 602, send control signals to the motors of the robot arm which drive the articulation to drive the instrument joints such that the instrument adopts a straight configuration. This straight configuration is one in which the end effector is aligned with the instrument shaft. For example, the longitudinal axis of the end effector may be colinear with the longitudinal axis of the shaft. Thus, the end effector elements are straightened, and the articulation is straightened. This action is a safety measure to minimise likelihood of the instrument snagging on the patient’s tissue or the port as it is subsequently retracted. After the control system has received the control input from the user to perform the calculation at step 401, it may, at step 603, send control signals to the motors of the robot arm to move the arm so that the surgical instrument is retracted from the surgical site along the longitudinal axis of the surgical instrument. The control system may control the instrument to be retracted out of the patient, following which the bedside staff reinsert the instrument into the port prior to carrying out the calibration procedure as described above for the setup mode. Alternatively, the control system controls the instrument to be retracted until the surgical instrument tip reaches the current estimated natural centre of rotation of the surgical instrument in the port used during the surgical mode. The control system then leaves the instrument at that depth in the patient’s body and performs the calibration procedure of figure 4 with the surgical instrument at that depth in the body. As mentioned above, an inaccurate estimate of the natural centre of rotation of the surgical instrument in the port may stem from the instrument not having been pushed sufficiently far through the port prior to the calibration procedure being initiated. This feature of robotically controlling the instrument retraction until the instrument tip reaches the current estimated natural centre of rotation of the surgical instrument in the port ensures the instrument is in a stable position not at risk of significant wobbling. Thus, “good” data pairs [a,b] will be generated for the calibration procedure, leading to a more accurate estimate of the natural centre of rotation of the surgical instrument in the port. Whilst, or after, performing the retraction of step 603, for an instrument which has opposable end effector elements 110, the control system may, at step 604, send control signals to the motors of the robot arm which drive the end effector elements to rotate to control the end effector elements to close together. This action is a safety measure to minimise likelihood of the instrument snagging on the patient’s tissue or the port as it is retracted. After the control system has received the control input from the user to perform the calculation at step 401, it may, at step 605, cancel the current estimated natural centre of rotation of the surgical instrument in the port. It may do this prior to performing the remainder of the calibration procedure described with reference to figure 4. Alternatively, the control system may maintain the current estimated natural centre of rotation of the surgical instrument in the port until it has calculated a new estimate which satisfies the set of criteria. Once the control system has calculated a new estimate which satisfies the set of criteria, the current estimated natural centre of rotation of the surgical instrument in the port is replaced with the estimated natural centre of rotation of the surgical instrument in the port. By driving the wrist along a deterministic wrist path entirely determined by the control system, better data is generated from which to estimate the natural centre of rotation of the surgical instrument in the port compared to when the wrist path is manually driven by a user. This is because a poor data set caused by that data being generated by poor manual technique is eliminated. The deterministic wrist path has a sufficiently large radius that the data pairs [a,b] representing the straight lines used to form the estimate are all sufficiently different, thereby enabling a more accurate estimate to be generated. When the wrist is manually driven to generate the calibration data, it is often driven on a linear track or in repetitive circular movements which have too small a radius. This results in a large number of very similar data pairs, i.e. straight lines which are close to parallel with each other. This leads to large errors in the accuracy of the estimate of the natural centre of rotation of the instrument in the port, that estimate often being too deep into the patient’s body. The deterministic path controlled by the control system with the large radius generates very different data pairs, i.e. straight lines which are at large angles to each other. This leads to a more accurate estimate of the natural centre of rotation of the instrument in the body being generated. The wrist path driven by the control system is smooth and continuous. As described above, the wrist is driven along the wrist path in a compliant mode in which the orientation of the wrist accommodates the forces acting on the instrument from contact with the port. The control system calculates the compliant movement to drive the wrist to adopt using an impedance model. The impedance model has inertial parameters. Sudden stops or changes in direction are thereby not instantly accommodated but rather responded to over a period of time in accordance with the inertia parameters in the impedance model. If the wrist is suddenly brought to a stop, or its direction suddenly changed during the calibration procedure, as is often the case when the wrist path is manually commanded by a user, the data pairs calculated from the sensory data received for a time after the stop / direction change is affected by the impedance model determining the compliant motion of the wrist. Thus, this data is not “good” data. The wrist path driven by the control system is preferably non-repetitive. It may be a single circle, or a single semi-circle. There is a mathematical benefit to using non-repetitive data in calculatingthe estimate of the natural centre of rotation of the instrument in the port. Since the estimate is calculated as the least squares distance to all the straight lines from the data pairs [a,b], repetitive data skews the calculated estimate to being closer to the straight lines of that repetitive data. A more accurate estimate is generated from a data set having fewer data pairs [a,b] which are all different and widely varying, than from a larger data set in which pairs [a,b] are repeated or very similar. A more accurate estimate is calculated from a small “good” data set than from a large data set which has both “good” and “bad” data in it. Since the data set that is generated for use in calculating the estimate of the natural centre of rotation of the instrument in the port is better, a more accurate estimate is generated. This has benefits when that estimate is subsequently used during surgery. The more accurate estimate reduces shaft forces caused by the instrument contacting the port. Thus, the torque sensed about the joints is less likely to exceed the threshold torque at which the control system determines a clash to have occurred. Thus, the surgical team will experience fewer clash events and fewer alarms causing them to have to stop the surgical procedure, move the instrument away from the determined clash and re-calibrate the estimate of the natural centre of rotation of the instrument in the port. An estimate of the natural centre of rotation of the instrument in the port that is too deep is less likely to happen, and so the surgeon will be permitted to operate with the instrument closerto the skin if desired. Because better data is used to generate the estimate, the estimate will satisfy the set of criteria after fewer iterations of the calibration method. Thus, an acceptable estimate will be generated and adopted for use in surgery more quickly. This is particularly important if the calibration is being performed mid-surgery, since minimising time away from performing the surgery is important for improving patient outcomes. If a manual calibration is performed mid-surgery, the instrument is retracted fully out of the patient’s body, and then detached and reattached, in order to restart the calibration procedure the same as if it was being done in the setup mode prior to the surgery starting. This is time consuming. If the calibration is performed mid-surgery as described herein in which it is fully controlled by the control system, and the procedure includes the step of the control system automatically retracting the instrument to the correct position for re-calibration to occur, then this also reduces the time taken to re-calibrate. The instrument is not taken out of the patient’s body. Again, this minimises time away from performing the surgery, thereby improving patient outcomes. Since better data is generated by the wrist being driven along a wrist path entirely determined by the control system, the criteria against which each iterative estimate of the natural centre of rotation of the instrument in the port is assessed may be more restrictive than the criteria used when the wrist path is determined manually. A more accurate estimate can be reliably calculated from the data generated by the wrist path determined by the control system in the same timeframe as is allocated to the calibration procedure when the wrist path is determined manually. Thus, a more accurate estimate can be required by the criteria and still result in a successful calibration occurring at the same or a better rate than occurs when the wrist path is manually determined. Referring to the set of criteria described above, the control system may, compared to when a manual wrist path is used: - Reduce the threshold number of required data pairs, for example from 40 to 30; - Reduce the minimum distance the wrist is required to move along the wrist path, for example from 40cm to 30cm; - Reduce the threshold value for the quadratic average distance between the estimate and the set of straight lines; - Reduce the threshold error of the estimate in each dimension; - Reduce the threshold difference between the penultimate and final iterative estimates from 0.5mm to 0.25mm. The control system may be configured to enable a user to command that the wrist path be determined either wholly by the control system or manually by the user. The control system may require a clearance zone around the robot arm which is a volume in which no other structures may be present in order for the calibration described herein to be performed. If the robot arm to be calibrated is physically located close to another robot arm or other obstacle, then the manual calibration method may be selected by the user. The surgical robot described herein could be used for purposes other than surgery. For example, the robot could be used to control a viewing instrument for inspecting a manufactured article, such as the inside of a car engine. The applicant hereby discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the present specification as a whole in the light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems disclosed herein, and without limitation to the scope of the claims. The applicant indicates that aspects of the present invention may consist of any such individual feature or combination of features. In view of the foregoing description it will be evident to a person skilled in the artthatvarious modifications may be made within the scope of the invention.

Claims

1. A control system for calibrating a surgical robot, the surgical robot comprising an arm extending from a base to an attachment structure for attaching to a surgical instrument, the arm comprising a series of joints by which the configuration of the arm can be altered, the series of joints including a wrist proximal to the attachment structure, the wrist constrained to rotate about axes which intersect the longitudinal axis of the surgical instrument, each joint driveable by a motor, the arm further comprising a plurality of position sensors for sensing the position of each joint and a plurality of torque sensors for sensing the torque about each joint, the control system configured to, when a surgical instrument is attached to the attachment structure and captive in a port:receive a control input from a user to perform a calibration to estimate the natural centre of rotation of the surgical instrument in the port;respond to the control input from the user by:controlling the motors to drive the joints to move the arm so that the position of the wrist follows a wrist path which is deterministic, smooth, and continuous;receiving sensor inputs from the position and torque sensors;responding to the sensor inputs from the torque sensors by controlling the motors to drive the orientation of the wrist in a compliant manner, so as to respond to each external force applied to the surgical instrument from contact with the port as detected by the torque sensors by driving the wrist to adopt an orientation which causes the surgical instrument to move in the direction of the applied external force;from the sensor inputs from the position sensors, determining the orientation of the surgical instrument as the wrist follows the wrist path; andestimatingthe natural centre of rotation of the surgical instrument in the port from a set of straight lines, each straight line extending from a wrist position in the direction of the determined orientation of the surgical instrument corresponding to that wrist position.

2. A control system as claimed in claim 1, configured to estimate the natural centre of rotation of the surgical instrument in the port as the point which has the least squares distance to the set of straight lines.

3. A control system as claimed in claim 1 or 2, configured to iteratively update the set of straight lines as the wrist follows the wrist path, and iteratively update the estimate of the natural centre of rotation of the surgical instrument in the port from the updated set of straight lines.

4. A control system as claimed in any preceding claim, operable in a driven mode in which the surgical instrument is attached to the attachment structure and a tip of the surgical instrument located at a surgical site, the control system configured to, in the driven mode:receive a demand signal indicating a desired location of the surgical instrument tip;respond to the received demand signal by:calculating a configuration of the arm in which the surgical instrument tip is at the desired location and the surgical instrument intersects the estimated natural centre of rotation of the surgical instrument in the port; andcontrolling the motors to drive the joints so that the arm adopts the calculated configuration.

5. A control system as claimed in any preceding claim, wherein the position of the wrist is non-repeating as it follows the wrist path.

6. A control system as claimed in any preceding claim, wherein the wrist path is symmetrical.

7. A control system as claimed in any preceding claim, wherein the wrist path is a circle of fixed radius.

8. A control system as claimed in claim 7, wherein the fixed radius is greater than 5cm.

9. A control system as claimed in any preceding claim, wherein the wrist path comprises a single complete circle or part circle.

10. A control system as claimed in claim 9, wherein surgical instrument is a tissue manipulation instrument.

11. A control system as claimed in any of claims 1 to 8, wherein the wrist path comprises a single semi-circle or part semi-circle.

12. A control system as claimed in claim 11, wherein the surgical instrument is an endoscope.

13. A control system as claimed in any preceding claim, further configured to detect thatthe wrist has reached a workspace boundary limit, and respond by controlling the motors to drive the joints to move the arm so that the wrist follows an updated wrist path, the updated wrist path matching the wrist path except that the wrist moves along the updated wrist path in an opposing direction to the movement of the wrist along the wrist path.

14. A control system as claimed in any preceding claim, further configured to detect that the arm has clashed with another structure, and respond by controlling the motors to drive the joints to move the arm so that the wrist follows an updated wrist path, the updated wrist path matching the wrist path except that the wrist moves along the updated wrist path in an opposing direction to the movement of the wrist along the wrist path.

15. A control system as claimed in any preceding claim, wherein the wrist path is on the surface of a sphere, the radius of the sphere being the distance from the wrist to a tip of the surgical instrument.

16. A control system as claimed in any preceding claim, further configured to assess a set of criteria, and if each criterion is satisfied: (i) store the estimated natural centre of rotation of the surgical instrument in the port for subsequent use in controlling movement of the arm whilst the instrument is attached to the attachment structure, and (ii) output a signal to the user indicating the calibration is complete.

17. A control system as claimed in claim 16, wherein the criteria include one or more of:(v) the number of straight lines in the set of straight lines used in the estimation of the estimated natural centre of rotation of the surgical instrument in the port exceeds a threshold number;(vi) the wrist has moved greater than a minimum distance on the wrist path;(vii) the quadratic average distance between the estimated natural centre of rotation of the surgical instrument in the port and the set of straight lines is less than a threshold value; and(viii) a calculated error of the estimated natural centre of rotation of the surgical instrument in the port in each dimension is less than a threshold error.

18. A control system as claimed in claim 16 or 17, configured to, if the set of criteria is not satisfied: (i) iteratively update the estimate of the natural centre of rotation of the surgical instrument in the port, (ii) assess each updated estimate to the set of criteria, and (iii) only when an updated estimate satisfies the set of criteria save the estimated natural centre of rotation of the surgical instrument in the port for subsequent use in controlling movement of the arm whilst the instrument is attached to the attachment structure, and output a signal to the user indicating the calibration is complete.

19. A control system as claimed in any preceding claim, configured to receive the control input from the user to perform the calibration whilst the surgical robot is operating in a setup mode prior to the start of a surgical procedure.

20. A control system as claimed in any of claims 1 to 18, configured to receive the control input from the user to perform the calibration after the surgical robot has been operating in a surgical mode and the surgical instrument tip is located at a surgical site in the patient.

21. A control system as claimed in claim 20, configured to control the motors to drive the joints to move the arm so that the surgical instrument is retracted from the surgical site along the longitudinal axis of the surgical instrument until the surgical instrument tip reaches the current estimated natural centre of rotation of the surgical instrument in the port used duringthe surgical mode.

22. A control system as claimed in claim 21, configured to replace the current estimated natural centre of rotation of the surgical instrument in the port with the estimated natural centre of rotation of the surgical instrument in the port.

23. A control system as claimed in claim 22, configured to cancel the current estimated natural centre of rotation of the surgical instrument in the port before performingthe calibration of claim 1.

24. A control system as claimed in any of claims 21 to 23, wherein the surgical instrument comprises instrument joints to articulate an end effector at the surgical instrument tip, the instrument joints driveable by the arm joints, wherein the control system is configured to, prior to retracting the surgical instrument, control the motors to drive the arm joints to drive the instrument joints such that the surgical instrument adopts a straight configuration.

25. A control system as claimed in any of claims 21 to 24, wherein the surgical instrument comprises instrument joints to articulate an end effector at the surgical instrument tip, the end effector comprising opposable end effector elements, the instrument joints driveable by the arm joints, wherein the control system is configured to, prior to retracting the surgical instrument, control the motors to drive the arm joints to drive the instrument joints to open the end effector elements apart.

26. A control system as claimed in claim 25, further configured to, whilst the surgical instrument is being retracted, control the motors to drive the arm joints to drive the instrument joints to close the end effector elements together.

27. A control system as claimed in any preceding claim, wherein the surgical robot is supported at its base by a support structure, the control input being located either on the surgical robot or the support structure.

28. A control system as claimed in any of claims 1 to 26, wherein the surgical robot is remotely controllable by a surgeon console, the control input being located on the surgeon console.

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