MINARO HD: control and evaluation of a handheld, highly dynamic surgical robot

A miniaturized robot with a total weight of 2.5 kg, including power tool and cables, was designed (Fig. 1), based on a five-bar linkage mechanism and a linear drive. The workspace of this manipulator is shown in Fig. 2.

A standard surgical high-speed burr is mounted onto the end of the kinematic chain together with a rigid body for the localization of the tool. The position of the burring tip in relation to the rigid body is calibrated prior to each intervention since the clamping of the tool onto the draped robot cannot be reproduced perfectly. Using a spherical rosen burr, the burr axis for the unicompartmental knee arthroplasty procedure can be chosen freely by the surgeon within the limits of the surgical approach and does not need to follow a specific plan. Therefore, three DOF of the robot are sufficient to maneuver the tool along a preplanned trajectory.

The user can hold and position the robot using a single-hand grip at the rear end, which also hosts a button to activate the burr. The second hand can be placed on the patient’s lower leg while stabilizing and supporting the front end of the robot.

After the manipulator has been pre-positioned and activated by the surgeon, the burring tool is automatically moved by the robotic system along a previously planned trajectory. In case the burring tool cannot be moved further at one position, as it would then exceed the manipulator’s workspace, the burring tool is stopped by the system and the surgeon is informed to re-align the manipulator.

The entire procedure is closely monitored by the surgeon. In case of any unforeseen event, the manipulator can be stopped at any time or, since it is a handheld device, just being withdrawn from the surgical site by the operator.

The centerpiece of the MINARO HD robotic system (Fig. 3) is a real-time control system development platform with a DS1006 processor board (dSPACE GmbH, Paderborn, Germany). It is equipped with several expansion cards for CAN and serial communication, analog and digital in- and outputs, and host PC communication.

The robotic manipulator is equipped with three motion controllers that communicate with the control system via the CiA 402 profile (CAN in Automation) with a 3 ms cycle time. Position and velocity demand values are sent to the manipulator from the control system, whereas the motion controllers return actual position, velocity and current measurements.

The burring tool mounted on the manipulator can be activated by the dSpace control system. It is set to a fixed rotational speed of 60,000 rpm. The current drawn by the burring tool can be measured with an added shunt resistor through the dSpace DS2004 High-Speed A/D expansion board. Thus, the relative course of the machining force can be monitored.

The patient is simulated by a fixture for a synthetic bone substitute material and a rigid body localized by the tracking camera. An FTS-Mini-45 force torque sensor (SCHUNK GmbH & Co. KG, Lauffen/Neckar, Germany) is mounted between the bone phantom and the rigid fixture to measure the machining forces directly. The sensor is read out by the DS2004 card of the dSpace system.

Both the bone phantom and the robot’s tool are tracked by a fusionTrack 500 tracking camera (Atracsys LLC, Puidoux, Switzerland) with an update interval of 3 ms. The compressed stereo images are sent through a Gigabit Ethernet connection to a dedicated tracking PC running on Windows Embedded Compact. The atracsys software development kit is used to compute the 6D poses of both rigid bodies. Those poses are then sent to the control system via an RS 422 connection running at 1.2 MBaud. A direct connection of the tracking camera to the dSpace real-time system is not possible because the atracsys software development kit cannot be compiled for this platform.

A host PC is connected to the control system via an optical link and shares information with the running real-time control using the ASAM (Association for Standardization of Automation and Measuring Systems) standard XIL API (model/software/processor/hardware-in-the-loop application programming interface). The software of the host PC guides the user through the intervention, from homing all axes of the robot, registering the patient dummy and uploading a trajectory to the real-time control prior to the intervention, up to showing a compensatory navigational display for the rough prepositioning of the manipulator by the user. The user is guided through the different steps of the intervention by using a medical multifunction foot switch (steute Technologies GmbH & Co. KG, Löhne, Germany).

The objective of the outer control loop, running on the real-time dSpace platform, is a dynamic compensation for introduced disturbance movements by the user and the patient, while following a planned milling path. Therefore, the positioning error of the burring tool \({}^{P}\Delta p\) is constantly monitored by the tracking camera and deviations are compensated in a control loop similar to [14], as can be seen in Fig. 4.

Forward and inverse kinematics must be calculated for the control loop. An analytical solution using the geometric dimensions derived from the CAD model has been implemented for both transformations, i.e., from the robot base’s coordinate system to the tool’s coordinate system and vice versa. The origin of the robot base’s right-handed coordinate system is centered between the motor axes of both lower motors driving the five-bar linkage and in the plane that also goes through the center of the ball joint in the coupling point. The y vector of the coordinate system points upwards, perpendicular to the robot’s base plate. The z vector points frontwards, towards the patient.

The origin of the tool’s right-handed coordinate system is in the center of the burring tool. The z vector points towards the patient, in the direction of the tool’s shaft. The y vector also points upwards, perpendicular to the linear guide.

The actual joint positions, measured by the motion controllers, are transmitted via CANopen. Since measurement and transmission of the joint positions is faster than the tracking camera, an extra delay must be added to the joint positions such that both measurements originate from the same real event. The exact duration of the delay required will be measured during the following experiments.

The transformation \({}_{B}{}^{R}{T}_{M}\) from the robot’s base R to the burring tool B is calculated with the direct kinematic model of the manipulator and the measured joint positions \({q}_{M}\). In parallel, the tracking camera measures the patient’s pose P as \({}_{P}{}^{C}{T}_{M}\) and the burring tool pose \({}_{B}{}^{C}{T}_{M}\) in its own coordinate system C. The former is inverted and multiplied with the latter to receive the burring tool’s pose in the patient’s reference frame \({}_{B}{}^{P}{T}_{M}\). Multiplying this transformation with the known robot base pose in the burring tool’s frame \({}_{R}{}^{B}{T}_{M}\) from the encoder position leads to the robot base pose in the patient’s coordinate system \({}_{R}{}^{P}{T}_{M}\), which is inverted to \({}_{P}{}^{R}{T}_{M}\).

From the transformation \({}_{B}{}^{P}{T}_{M}\) of the current burring tool pose in the patient’s coordinate system, the translational part is taken and subtracted from the desired position \({}_{B}{}^{P}{T}_{D}\), resulting in the distance vector \({}^{P}\Delta p\), resembling the current position error in the patient’s coordinate system.

This error vector is multiplied to the rotational part of the transformation \({}_{P}{}^{R}{T}_{M}\). This results in the vector \({}^{R}\Delta p\), which is the error vector in the robot’s base coordinate system. This translational vector is added to the measured transformation \({}_{B}{}^{R}{T}_{M}\) of the burring tool in the robot’s base coordinate system, resulting in the desired position \({}_{B}{}^{R}{T}_{D}\) of the burring tool in the robot’s base coordinate system. After applying the inverse kinematic model of the manipulator, the desired joint positions \({q}_{D}\) are ready to be sent to the motion controllers.

This outer loop is executed on the dSpace system every millisecond, even though an update from the motion controllers and the tracking camera is only received every 3 ms. The trajectory handler updates the burring tool’s required position every millisecond, following the trajectory that was programmed into the control system by the host PC. The feed rate of the burr on the planned trajectory can be defined by the user.

The three motion controllers on the manipulator are operated in the profile position mode. The position controller computes a position trajectory from the actual and the joint position required, taking into account the maximum acceleration defined, deceleration and speed of the motors. Using cascaded PI controllers, consisting of a position controller, velocity controller and current controller, the motion controller follows this trajectory until a new joint position requirement is received from the control running on the dSpace system.

A single infrared (IR) LED connected to the dSpace control system is used to measure the latency of the tracking system. After the IR LED is turned on by the dSpace system, it is recognized as a stray fiducial by the tracking camera. The dedicated tracking PC processes the information received from the camera and sends the location of the IR LED to the dSpace system. The dSpace system measures the time between turning on the IR LED and receiving its location from the tracking system. Subsequently, the dSpace system turns off the IR LED and measures the latency again, this time until the LED location is no longer received from the tracking system.

Only the lower row of the diagram in Fig. 4 is evaluated to test the motion controllers separately. Cartesian steps of 2 mm are applied to the target tool position \({}_{B}{}^{R}{T}_{D}\) and the actual tool position \({}_{B}{}^{R}{T}_{M}\) is recorded. One step is applied in the z direction of the manipulator (“forward,” feed axis) that mainly requires the spindle drive to move. A second step is applied in the x direction (“sideways”) that mainly requires the two motors of the five-bar linkage to move. The third and last step is applied in a diagonal direction.

The three-dimensional movement of the tool position, measured by the joint positions and calculated using the forward kinematic, is projected to a one-dimensional movement along the direction of the step. From this, the latency, overshoot, rise time and settling time are extracted. In this context, latency is the time until the tool position movement passes the 5% mark, i.e., 0.1 mm. Overshoot will be given in percent and the rise time is the time required to rise from 5 to 95%, i.e., from 0.1 to 1.9 mm. The error window for the settling time is 10%, i.e., ± 0.2 mm. This is set as the accuracy required of the manipulator itself, so that some safety cushion remains, e.g., for tracking inaccuracies and movements due to reaction forces by the burring tool. To evaluate the maximum frequency f of the disturbing movement that can be compensated for by the robot, the 0 to 90% rise time will be read off and be called the reaching time T. The maximum frequency f then equals \(1/(2T)\).

This and all subsequent measurements are only taken once. Due to the repeatability of robotic behavior, this is assumed to be sufficient.

The step response of the whole control loop is evaluated analogously to the step response of the manipulator. Only the step is applied to the target tool position \({}_{B}{}^{P}{T}_{D}\) in the patient’s coordinate system and the actual tool position \({}_{B}{}^{P}{T}_{M}\) in the patient’s coordinate system, recorded by the tracking camera, is taken as the response. Since the manufacture and calibration of the manipulator is not perfect, the joint positions required are updated with every tracking frame, converging to the burr position needed.

Regarding these experiments, disturbing movements of 50 mm amplitude and with various speeds and directions are added to the location \({}_{P}{}^{C}{T}_{M}\) of the patient. The movements are applied in the same directions as the step responses and the speeds range from 1 up to 50 mm/s. The maximum positioning error \({}^{P}\Delta p\) is recorded during each test run.

The latency between a change in the real world and the corresponding data reaching the dSpace control system could be measured between 6 and 8 ms, with rare dropouts of up to 16 ms.

Since the reception of the manipulator joint positions via the CANopen bus takes between 2 and 4 ms until it is processed by the dSpace system, the extra latency \({z}^{-T}\) of the control loop (seen in Fig. 4) is set to 4 ms for all following experiments.

The step response measurements of the manipulator alone can be seen in Fig. 6; the evaluation is summarized in Table 1. The reaching time (sum of the latency and rise time) of the step responses varies between 27 and 39 ms, depending on the direction of the step. This results in a maximum compensation frequency of 13–19 Hz.

The step response measurements with the tracking camera in the control loop can be seen in Fig. 7; the evaluation is summarized in Table 2. The reaching time varies between 27 and 42 ms, resulting in a maximum compensation frequency of 12–19 Hz.

The positioning error (Fig. 8) is mostly linear with no distinct variation depending on the direction of the disturbing movement. The slope of a linear fit to the three curves is \(0.025 \frac{\mathrm{mm}}{\mathrm{mm}/\mathrm{s}}=25\, \mathrm{ms}\) with 0.048 mm error offset.

A positioning accuracy of 0.5 mm can be achieved with relative movements between the patient and burring tool of up to 18 mm/s.