A Preliminary Add-on Differential Drive System for MRI-Compatible Prostate Robotic System

Following our previous work [4, 5, 6, 7, 8, 9], a hollow shaft USM (HSM) based on the USR60-NM stator was designed and manufactured in this study. Figure 3 shows the design of MRI-compatible hollow shaft motor construction. The stator was harvested from a Shinsei USR60-NM motor, with a center hole of $\phi$32mm, other components were designed based on this stator. A plastic hollow type rotor, namely an internal rotor ring with a thin surface was covered by a plastic external rotor, where a $\phi$22mm hole was through the center. Between the two rotors, a layer of rubber rings contacted each other and provided both friction and damping space for the external rotor to apply prepressure. An M25$\times$1.5mm thread was manufactured on the bottom tube side of the external rotor. The stator was fixed onto the center hole enlarged original aluminum bottom stage by screws, and a plastic top cover enclosed the stator with rotors assembly, a sleeve bearing was holding the external rotor with the top cover. An additional layer of the plastic bottom stage was attached to the bottom of the stator stage, which was used for holding the bearing that the external rotor went through. A brass M25$\times$1.5mm panel nut matched the external rotor bottom tube thread, which was used to tighten the external rotor and adjust the prepressure applied onto the internal rotor. The top cover and bottom stage were fixed by 4 screws to enclose the whole motor. A manufactured hollow shaft USM can be found in Figure 4. Note that the motor had to contain the aluminum bottom stage as the first layer for the cable connector to attach onto, this is because the feedback (F.B.) terminal has a filter connected to the GND pin, this filter needs a large contacting aluminum area. Without the contact of the aluminum-made stage, the stator will not work functionally. This needs further research for the F.B. functionality.

The design drawing of a ball screw/spline (BSS) differential type is similar to the general ball screw/spline system, which consists of a $\phi$20x10mm ball screw nut, a ball spline nut with an ID $\phi$20mm center through-hole, and an OD $\phi$20mm shaft with both grooves. We designed a prototype of the main components, namely the ball screw nut, ball spline nut, and the shaft. Considering the MRI compatibility, we used a Markforged® 3D printer to print the parts. More specifically, the two nuts were cut in a specific method for easy support removal of the groove tunnel inside the nut body, and the shaft was designed into an identical unit with a 120mm length that can be assembled. The shaft is modular, so it can be extended. Parts of the BSS actuator can be found in Figure 5. Figure 6 shows the two nuts assemblies. Ball screw and spline nuts were both held by two 45$\times$58$\times$7mm nylon caged ceramic ball radial bearings (Kashima®  Bearing, Japan) UKB6809PP-A, two 3d printed housings were holding both nut-bearings assemblies for smooth rotation. The balls used between the grooves were all 5/32-inch glass balls.

Figure 7 shows the hollow type of differential drive using BSS configuration. Two hollow shaft motors were fixed with a ball screw nut and ball spline nut respectively to drive the rotary motion of nuts, the motor stage motor housings were fixed together relative to the robot, and a grooved shaft was through both nuts and motors contacting with glass ball fitting both grooves. Driving the nuts can perform different modes of motion. Note that the BSS actuator provides smooth motion performance due to the small friction caused by the ball bearings, however, the cost is high and the installation process will be hard with constrain of distance, otherwise the ball will be loose if the shaft is out of the nut bore.

Additional to the ball screw/spline design, another similar design based on a lead screw/bushing (LSB) actuator was also developed. Figure 8 shows the components of the lead screw/busing design, which consisted of a 4-start 20$\times$20mm lead screw nut (DST-J350RM4540DS20$\times$20, Igus, Germany), a custom-designed bushing nut with 3$\times$5/32in bushing fins equally distributed in the $\phi$20mm center hole, and a shaft with bushing groove and screw thread matching with two nuts above respectively. The two nuts were all Igus dryspin®  iglide®  J material, specifically, the screw nut was an in-stock product with additional modification, while the bushing was a custom 3D printing part using iglide material. In Figure 9 the two nuts assemblies are presented. Using the same housings and plastic bearing pairs, the two nuts were held and enclosed with housings and bearings.

Figure 10 shows the holly type of differential drive using LSB configuration. Same as the BSS configuration the two hollow shaft motors were fixed with two nuts and the housings were fixed with motors onto the robot, and a grooved shaft was through both nuts and motors directly contacting with screw thread and grooves. The LSB actuator design has fewer parts and is easier to manufacture, also it just is easier to recover from over-driving out of the nut compared to the BSS actuator since there are no free balls inside the nuts. Considering the ball spline and lead bushing were using the same dimension design, these two nuts actuators are exchanged. And for easy manufacturing purposes, we were using a combination of ball screw and lead bushing hybrid (BSLB) actuator in the next section.

A hollow-type differential drive (HDD) subsystem with a robot switchable configuration is shown in Figure 11. The left figure shows the design of a hollow differential drive actuator sitting on the prostate robot (robot reported in [10, 11, 12, 13, 2, 14, 15]) connection mechanism. Two 2-inch encoder discs were fixed on the external side of two nuts, and the matching encoders were fixed onto the support with the robot body. The needle was inserted and fixed into the shaft. A prototype of the HDD is shown in the right figure. Two hybrid HSMs integrated with the original aluminum stage were used in the system to drive both nuts accordingly. A Luer lock needle connector was fixed on the top of the shaft for needle installation, and a monitoring oscilloscope was used to monitor the signal of two HSMs.

The HDD subsystem shown above is the original design with the most compact configuration. However, because of the limitation and dimensional tolerance of manual fabrication, the performance of HSMs was not very good, which was not capable of driving nuts with friction. What’s worse, the rotary speed provided by the motor was slow, measurement of rotary speed yields approximately 75rpm, which was enough for a normal biopsy procedure. However for a later application like CURV steering mentioned in [12, 16, 14, 15] which required high rotary speed motion, the direct drive from HSMs was not sufficient. An acceleration mechanism integrated differential drive system needs to be developed to fulfill the requirement.

To address the need for rotary speed at a high level, a side-pulley type of differential drive (PDD) was developed and presented in this study. Figure 12 shows the PDD design based on the LSB actuator. Instead of using HSMs for direct drive, two modified $\Phi$1.528in, 24 teeth nylon pulleys with $\phi$22mm center hole were used as master pulley connected to each nut of the LSB actuator, where the whole system was seated onto the prostate robot connection mechanism. A holder with a chamfered hole was located on the top of the LSB actuator with multiple slave pulley pairs, and two USR60-NM were driving the slave pulleys. The right figure shows the multiple-speed transmission generated by different pulley pairs, and four different transmission ratios were shown. Detailed configuration can be found in Table I.

The prototype of the PDD system is shown in Figure 13. For proof of concept and easy fabrication purposes, we used a combination of BSLB actuators same as the hollow type. Two 3D-printed housings enclosed the ball screw nut and lead bushing nut and hold by two paired plastic bearings. Two modified nylon master pulleys were fixed on the inner surface of the ball screw nut and lead bushing nut respectively and paired with slave pulley 1 configuration of a 1:2.5 transmission ratio. A Timing XL belt was connected with the master and slave pulleys and held by the top motor assembly. Two USR60-NM motors were connected with the slave pulleys on one side and the center mutual side, there was a small housing holding two small bearings to balance the pulleys. Motor-slave pulleys assembly was designed to be adjustable on vertical location to load and release tension to the belts. Three ball screw/spline shaft units with 120mm length were connected making the main shaft to be a 360mm length. A male Luer lock was fixed on the top of the shaft for needle installation. In this study, the main validation and testing were using this PDD setup as the main switchable subsystem for prostate robot needle driving.

A conception of a smaller-size PDD system was also designed for our previous MRI-compatible NeuroAblation robot [17] which is shown in Figure 14. The advantages of using HCM are significant, and another solution of using a differential drive system to control the motion of the needle-based probe is presented here. By using small USM USR30-NM motors, a differential drive system was integrated into the NeuroAblation robot to replace the needle insertion and rotation motion. More studies about brain tumor ablation procedures can be found in our previous work [18, 19, 20, 21, 22, 23, 24, 25]. Similar to the PDD top motors holding mechanism, two USR30-NM were fixed onto the robot arm and connected with pulleys respectively. Belts connected the master and slave pulleys and transmitted motion to the master pulleys. To minimize the volume, master pulley teeth were manufactured on the lateral wall of the lead screw and bushing nuts directly. An ablation probe integrated with screw thread and bushing groove on the body was inserted into the minimized LSB nuts center hole and controlled by the LSB-type PDD system. The whole subsystem was designed based on the current NeuroAblation robot 2D orientation module, which was also compatible with the current probe driver module with switchable ability. This subsystem should be developed further in future work.

A PDD system integrated prostate robot design is shown in Figure 16. The PDD subsystem was attached to the 4-DOF prostate robot top with an L-shape needle guide connected, the biopsy needle was connected on the initial top of the shaft and through the guide. The patient, Z-frame fiducial, and robot system were all fixed onto the base platform, and all the components shown in the figure were located on the MRI table. A PDD-integrated prostate robot system can be found in Figure 17, which follows the same configuration mentioned above. Note that the motors used in the robot were USR60-S4N, which had a back shaft at the back of the motor, so the encoder (EM1-0-1250-N, US Digital) and disc can be attached to the back of the motors.

The principle of “differential” is based on the combination motions of the two nuts or two driving motors specifically. In this study, we only discuss the basic functionality of general BSS system motion, namely linear motion, and rotary motion, and a supplementary argument code was implanted into our prostate robot controlling code both in high-level C++ and engineering UI. The schematic image of PDD is shown in Figure 18. The shaft rotary and insertion motion was achieved by the combination motions of the ball screw and lead bushing nut, which were driven by two motors respectively. In our current controlling system, each DOF motion was one-to-one mapping with a single motor, and encoders were used to send position feedback to the control box and display it on the UI page. The new differential drive segment controller was using two motors mapping to rotary motion, so when rotary motion was processed, two motors were spinning simultaneously, under this circumstance one of the encoders had to stop reading or sending any position feedback to the control box for compensation. We labeled the two motors and encoders as insertion motor (IM)/insertion encoder (IE) and rotary motor (RM)/rotary encoder (RE), and a general position feedback equation of the 2-DOF differential drive position algorithm can be found in Equation 1, where the insertion and rotary represented the positioning value showing on the UI, and IE and RE described the value reading from each encoder. This equation indicates that the insertion position was always subtracted from the reading value of the rotary encoder. This equation was defined as the general controller pattern, however, in this study considering the goal of proof of concept, a simplified control method was developed.

After labeling the motors and encoders, we set the primary motor/encoder for each motion. In this preliminary study, we developed a bang-bang controller for updating the motors’ enable/disable status and the encoders updating regulation to perform insertion, rotary, and mixed motion for needle driving purposes. For insertion motion, it was the same one-to-one mapping as the current controller, however, for rotary motion, the IE reading value will affect the current position value of insertion motion. By forcing the IM to follow the RM and stop counting IE, the interference from IE was reduced. We first set up a trigger from the UI, which was the Needle Rotation Enable button to trigger an additional controller mode with IM following RM and IE stop counting. When the Rotation Enable button was disabled, the robot set back to the original controller with normal motion control. This method solves the issue of multi-mapping and can achieve the basic motion function of the new PDD system.

After validating the basic function and proving the new controller, system accuracy validation is required. In this section, a preliminary accuracy validation experiment and results are discussed. For proof of concept purposes, the PDD system was validated using a caliper and protractor for insertion and rotary accuracy test. For the insertion accuracy experiment, we chose the front gantry surface as the baseline and the top surface of the Luer lock as the testing surface. By using the control system to the target point enable the insertion motion, and read the displacement of the baseline and target surface with five trials for each target distance. Figure 19 shows the needle rotation validation setup, which was using the difference of two protractors as experimental data. The two protractors were located on the front side of the shaft, where the base protractor was fixed on the front gantry surface with a through hole in the center for the shaft being through, while the rotary protractor was fixed onto the needle side of the Luer connection to prevent any contact interference generated from the two protractors.

The rotary speed was measured, which reached up to approximately 168rpm, and Table II summarizes the insertion axis ($I_{i}$) accuracy test results. The highest insertion means error ($\mu_{I_{i}}$) is -1.9mm and the highest insertion standard deviation ($\sigma_{I_{i}}$) is 3.43mm. Results indicate that the larger the distance insertion applied, the larger the error it performed. This was because of the manually manufactured dimensional error and tolerance which accumulated that error with long-distance of operation. Table III summarizes the needle driver rotation axis ($R_{i}$) accuracy test results. The largest rotation mean error ($\mu_{R_{i}}$) is 1.45^∘, and the largest rotation standard deviation ($\sigma_{R_{i}}$) is 1.789^∘. Repeatability in this axis was expected since the needle will require over 360^∘ rotation, as well as the requirement of the CURV steering method for needle targeting compensation. Note that the error of rotary accuracy was only performed within the two-cycle (at most 720^∘) range, where the interference to the IM and IE was small and can be neglected. A further experiment of multiple cycle rotation for accumulation error observed a large error, namely every seven circles of needle rotation (2520^∘) there was approximately 2.1mm insertion accumulation feed-in error displacement. This was because of the speed misalignment between the RM and IM, and this tiny amount of difference in speed caused a tiny spiral motion instead of pure rotary motion. With the accumulation of these spiral motions after a huge amount of rotation motion, the insertion error will be large. To solve this issue, a delicate motor speed controller like a PID compensation controller is desired for further study.