Abstract—In recent years, the use of robotics to augment MRI diagnostic and interventional procedures has increased significantly. However, the demanding MRI environment precludes the use of most common actuation approaches. Alternative actuation concepts have been proposed but these solutions do not lend themselves to linear control topologies. We present a new actuation method, using the motion of parallel ultrasonic motors combined through a differential mechanism, to address these limitations. A prototype of this device is constructed and evaluated. Results demonstrate the viability of the proposed approach while helping to clarify design improvements to further increase its utility.

I. INTRODUCTION

The use of robotic systems in an MRI environment has many applications, particularly in the area of diagnostic and interventional image-guided medical procedures. These systems have been proposed for an array of interventional procedures including prostate and breast biopsies [1-7], as well as diagnostics procedures such as fMRI studies requiring haptic feedback within the MR-bore [8-14].

However, working in an MRI environment is very demanding due to severe material and space constraints. The large magnetic fields present preclude the use of ferromagnetic materials in any part of the device, all but ruling out the use of electromagnetic actuators as well as many construction materials.

To avoid these limitations, a number of researchers have developed MR-compatible actuation methods using pneumatic, hydraulic, and ultrasonic components [3, 8-12, 15-19]. While these actuation approaches have met with considerable success, their use in applications that require actuation with high-bandwidth linear characteristics, such as position control with good disturbance rejection and force control, has been challenging.

Pneumatic actuation methods have primarily focused on stepper-motor implementations [3, 8, 10, 15, 18, 20]. In these cases, pneumatic valves are located outside the bore for MR-compatibility. Air-line compliance is generally not an issue as the actuator is operated open-loop, in that desired positions are achieved through the command of specified actuator steps. This configuration functions well for position

Manuscript received July 9, 2010. This work was supported in part by the University of Wisconsin – Madison Graduate School Industrial and Economic Development Research Program.

Christopher Esser is a graduate student in the Mechanical Engineering Department, University of Wisconsin – Madison, USA (e-mail: cesser@wisc.edu).

Michael Zinn is an Assistant Professor with the Mechanical Engineering Department, University of Wisconsin – Madison, USA (corresponding author phone: 608-263-2893; e-mail: mzinn@wisc.edu).

control applications but does not lend itself to force control or tele-robotic applications which required high-bandwidth linear actuator characteristics.

Hydraulic actuation has been implemented in a number of prototype systems [7, 8, 16, 21]. This approach works well for low frequency applications. However, due to fluid line compliance and valve nonlinearities, this approach does not lend itself to applications requiring high-bandwidth control.

Finally, ultrasonic motors (USMs) have been extensively used in MR-compatible robotic applications [4, 9, 22]. Ultrasonic motors create rotational motion by applying high- frequency, high-voltage signals to a ceramic stator. The stator is pressed against a ceramic rotor and vibrates in response to this signal, creating what is known as a traveling wave. This wave causes the rotor to advance with a velocity that is determined by the amplitude and frequency of the traveling wave. Because of these different operating principles, they do not rely on magnets or ferromagnetic material for motive torque. For this reason, they are well suited for MR-applications assuming they are located away from the MR-bore so as to avoid MR-image degradation.

While the drive electronics can vary, most commercially available USM systems are velocity controlled devices. The drivers are designed to drive the actuator at an output velocity proportional to input voltage regardless of the torque applied.

However, the driver has some serious limitations. Due to the USM’s physical limitations, it cannot be driven below a threshold velocity, typically 10% of the maximum velocity. This creates a velocity-dead zone, which can be seen in Figure 1. In addition, there is typically a delay associated with velocity reversals. These characteristics make high-bandwidth feedback control using linear design techniques nearly impossible.

In addition, other limitations must be considered when designing the controller, including limited USM output speed and inherently high output impedance. These limitations must be overcome before USMs can be used for force control or tele-robotic applications.

One system developed to overcome the limitations used an ultrasonic motor in combination with a powder brake [22]. This device was capable of force control, and used the USM in an admittance force control topology. The USM created active torques while the brake created resistive torques. This approach successfully created forces mimicking springs and walls. However, the bandwidth of the system was limited because of the non-linearities inherent to the USM (i.e. delays switching direction and velocity-dead-zone).

Development of a Differential Actuator Concept for MR-Compatible Robotic Applications

Christopher Esser, Michael Zinn, Member, IEEE

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Fig. 1. General velocity non-linearity typical of ultrasonic motor

II. PROPOSED ACTUATION CONCEPT

To overcome the limitations of USMs, we propose a new actuation concept that combines the output motion of parallel USMs through the use of a differential mechanism. The differential mechanism will act as a motion summer, where the output is a linear combination of the two parallel USM’s motion. Using this approach, the velocity of each USM can be constrained to the linear region of operation, avoiding the dead band nonlinearity and delay associated with velocity reversals. Output motion is controlled by creating a velocity bias favoring either the clockwise or counter clockwise direction. By combining the motion of USMs in this fashion, we can achieve an actuation system that has a linear velocity to command relationship.

By eliminating the non-linearities, force and position control topologies can be created with much higher bandwidths.

III. CONTROL APPROACH

There are many ways to combine the velocities of the parallel USMs. One option is to set the nominal velocity of each motor at the midpoint between its maximum velocity and the upper limit of its dead-zone region. With one USM set at this positive value and the other set at the negative value, the resulting output velocity is zero. Changes in output velocity are achieved by changing the velocity of both USMs simultaneously around that point. Using this approach, the output velocity of the differential actuator is given as

∗ ∗ (1)

where c1 and c2 are the scaling factors caused by gear ratios, A is a user defined gain, and wdesired is the commanded output velocity. In this case, the USM actuators are commanded to follow a velocity profile given as

∗ ∗ (2)

∗ ∗ (3)

This approach is summarized in Figure 2.

Fig. 2. Description of Motion Summer. In this figure, A is the user defined gain and c1 and c2 are the individual gear ratios from each individual USM to the output. Ideally c1 and c2 are both unity. Both USM’s velocities are changed simultaneously.

Alternatively, power can be minimized (assuming power dissipation is proportional to output velocity) by setting the nominal velocity for both USMs at the non-linearity threshold and increasing the velocity of only one USM at a time to create an output velocity. Using this approach, the system velocity equations are given as:

0∗ ∗

∗ ∗ (4)

0 ∗ ∗∗ ∗

(5)

Using the previously described velocity heuristic, we have created a ‘black box’ that can be treated as a linear component in the control model. The overall system is now linear and we can use linear techniques to analyze and design a controller. In the case of position control, a simple proportional gain is sufficient. As shown in Figure 3, the plant is modeled as a simple integrator. Presumably, similar control schemes could be designed for force control applications.

Fig. 3. Position Control. Block diagram of simplified model of the USM differential actuation position controller. The velocity heuristic can effectively be treated as a block with unity gain.

IV. HARDWARE IMPLEMENTATION

To validate our approach, we have constructed a differential actuation prototype. We choose to implement the differential mechanism using a planetary gear train (see Figures 4 and 5). The two input ultrasonic motors drive the sun gear and ring gear, respectively. The planet gears, coupled to an output shaft, provide the actuator output. This

1 ωdesired ωout

∗ ∗

∗ ∗

∗ ∗

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configuration was chosen because it possesses simple kinematics and is easily fabricated. An additional gear stage, using a pulley and timing belt, was added between the planetary gear set and each USM to equalize their contribution to the differential actuator output velocity. The system was designed such that the output velocity was a simple summation of the input USM actuator velocities.

Fig 4. Differential Arrangement. The timing pulleys are used to counteract the gear ratios introduced by the planetary gear box. For MRI testing the USM drivers are removed to a greater distance.

Fig. 5. Internal view of the planetary gear. The ring gear and gear housing are rigidly attached and driven by one USM. The sun gear is driven by the other USM. The planet gears are rigidly attached to the output, which extends out the back.

The ultrasonic motors selected for the prototype system were from Shinsei Corporation (Tokyo, Japan). The ultrasonic motor (model USR60E) and its drive (model D6060E) come as a matched pair. The Shinsei USM is constructed entirely of non-ferromagnetic materials and is equipped with a 1000 CPR encoder.

The USMs were controlled using Matlab xPC. The xPC target was equipped with a Contec DA12-16 digital to analog convertor card for command voltages and digital outputs. It has 16 channels with 12-bit resolution. In addition, the target had an 8-channel, 32-bit encoder counter card to manage the encoder signals.

V. EXPERIMENTAL RESULTS

A. Single USM Characterization Experiments

To verify the assumptions made about the characteristics of a single USM, a set of open-loop experiments was performed. The first experiment obtained the steady-state velocity output of a single USM actuator as a function of input voltage. Figure 6 shows the measured relationship between input voltage and output velocity for the Shinsei ultrasonic motor/driver set used (model USR60E/D6060E) . As seen in Figure 6, the output velocity is linear with commanded voltage away from the dead band. In addition, the dead band region around low velocities is clearly visible. Here, the dead band region magnitude is approximately 10% of the full scale output velocity.

Fig. 6. Experimentally obtained USM velocity vs Command Voltage. Note that negative command voltages are actually positive, but with the direction bit flipped. The negative values are used for visual clarity.

To assess dynamic response, the frequency response of a single USM actuator was experimentally obtained, with commands ranging from 0.1 Hz to 35 Hz. To avoid the low-velocity dead band, the experiments were performed with a constant velocity offset. This created a position output with a constant ramp component. To improve the quality of the measured frequency response, this ramp signal was eliminated from the data prior to processing using a high-pass filter, the cutoff frequency of which is two-orders of magnitude below the lowest frequency of interest. The position output can be seen in Figure 7.

The frequency response of the velocity-offset USM was constructed by assembling the experimental data obtained for the tests spanning the frequency range from 0.1 to 35 Hz (see Figure 8). It shows that the measured position response as a function of input voltage closely matches that of a pure velocity source for frequencies below approximately 10 Hz. For frequencies above 10 Hz, the frequency response shows evidence of a damped resonance, either electrical or mechanical. The plots in Figures 6 and 8 verify our USM model assumptions provided the closed-loop bandwidth of the prototype system is lower than estimated system resonance. For control implementations with high desired closed-loop bandwidths, alternative control topologies would likely produce better results.

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Fig. 7. Output position with the constant velocity offset and resulting position output after high pass filter was applied.

Fig. 8. Frequency Response of a single USM. The plot relates the command voltage to measured position.

B. Differential Actuator Control Experiments

To assess the performance of the proposed differential actuation approach, a position controller of the type shown in Figure 3 was implemented. Position measurements from encoders mounted directly on the USM were used as the feedback signal. To emulate a typical MR-robotic application, additional inertia was added to the output stage of the differential mechanism. The control system was adjusted to provide the highest closed-loop bandwidth attainable without inducing appreciable system oscillations.

To assess the performance of the position control implementation, a series of step inputs were applied to the closed loop system. Position measurements were made at the output of the USMs as well as at the output of the differential mechanism. As seen in Figure 9, the closed-loop system time constant is approximately 0.024 seconds, resulting in a 6.6 Hz closed-loop bandwidth.

The plot shows three signals including the position command, the output position as calculated from the

incremental positions of the motor encoders, and the output position as measured by the encoder on the output shaft.

Fig. 9. Step response of differential actuator position control system. The system has a time constant of 0.024 seconds, which puts its closed loop bandwidth at 6.6 Hz.

The offset error between the measured output position and the incremental calculated position is due to compliance in the timing pulleys and flexible couplings. The harmonics visible in the measured position are caused by the inertia of the planetary gear assembly and output inertia and the compliance of the timing pulleys and flexible couplings.

Fig. 10. Response of system to steps of variable magnitude. The output error and harmonics are caused by compliance in the timing belts and the inertia of the planetary gear box.

In Figure 10, a set of consecutive step inputs of variable magnitude were commanded to assess the systems stability due to velocity saturation of the ultrasonic motors. As seen in Figure 10, the step input which commences at 1.5 seconds causes velocity saturation with the resulting lag in response. However, system stability is maintained.

In addition, the frequency response of the closed-loop position controlled system was experimentally obtained. Sinusoidal input commands, ranging in frequency from 0.2-

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35 Hz, were applied to the closed-loop system. The commanded amplitude was limited to avoid saturating the ultrasonic motors. Figure 11 shows three examples of the system’s sinusoidal tracking performance. Figure 12 shows the complete closed-loop frequency response. As seen from Figures 11 and 12, the system tracks the output commands well for frequencies below approximately 8 Hz. In addition, the differential tracking approach has eliminated all traces of the velocity dead band nonlinearity. For the 1 Hz tracking experiment shown, the output velocity varies from -1 rad/sec to +1 rad/sec. This low tracking velocity, which includes zero-crossings, would be impossible to achieve with a single USM.

Fig. 11. Sine tracking at 1, 10, and 30 Hz. The figure is adjusted to show only the steady state response. The output position as calculated from the incremental positions of the motor encoders was used.

Fig. 12. This bode plot summarizes the frequency response for the differential actuator. The output position as calculated from the incremental positions of the motor encoders was measured. From the plot, a close loop bandwidth of 7Hz is determined.

As noted previously, the response of the differential actuator prototype, as measured at the output of the actuator, is offset from the desired position. In addition, higher-frequency oscillations are present. These effects are caused by compliance and, to a lesser extent, backlash and mechanical run out in the prototype differential mechanism. The authors believe that a redesign of the differential mechanism would address the majority of these issues. In addition, it is expected that higher closed-loop position control bandwidths are also achievable.

In addition to the modifications discussed above, the steady-state offset error could be eliminated through the use of a non-collocated control approach. Specifically, feedback of position measurements from the output of the differential mechanism would allow the controller to drive the steady-state error to zero. However, a non-collocated control approach is generally more difficult to stabilize and will invariably result in a system with a lower closed-loop bandwidth [23]. As seen in Figure 13, a non-collocated control approach has eliminated the steady-state position error. However, the resulting closed-loop bandwidth has been significantly reduced resulting in a slower response.

Fig. 13. Non-colocated multistep response

VI. CONCLUSION

We have successfully created a new actuation method for use in MR-compatible applications. This new actuator design eliminates the velocity reversal delays and the low velocity dead band associated with a single ultrasonic motor. With the elimination of these non-linearities, this device can be used for force control applications for MR-compatible applications.

The closed loop bandwidth of this system was around 7Hz. While this is relatively low for high performance applications, it can easily be increased by modifying the prototype design. The timing belt compliance can be reduced by adding additional pre-tensioning or selection of better materials. Also, the size of the planetary gear box can be reduced through strategic redesign using a smaller internal

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gear pitch. This reduction in size will significantly reduce the inertia of the assembly.

Future iterations of this design will incorporate a torque sensor on the output shaft to allow force control to be implemented using an admittance approach.

REFERENCES [1] A. Krieger, R. C. Susil, C. Menard et al., “Design of a novel MRI

compatible manipulator for image guided prostate interventions,” Biomedical Engineering, IEEE Transactions on, vol. 52, no. 2, pp. 306-313, 2005.

[2] P. W. Mewes, J. Tokuda, S. P. DiMaio et al., "Integrated system for robot-assisted in prostate biopsy in closed MRI scanner." pp. 2959-2962.

[3] G. S. Fischer, I. Iordachita, C. Csoma et al., “MRI-Compatible Pneumatic Robot for Transperineal Prostate Needle Placement,” Mechatronics, IEEE/ASME Transactions on, vol. 13, no. 3, pp. 295-305, 2008.

[4] N. V. Tsekos, J. Shudy, E. Yacoub et al., "Development of a robotic device for MRI-guided interventions in the breast." pp. 201-208.

[5] X. Zhai, R. Harter, C. Moran et al., "Image-guided interventional device for 3D access and localization of breast lesions."

[6] B. T. Larson, N. V. Tsekos, and A. G. Erdman, "A robotic device for minimally invasive breast interventions with real-time MRI guidance." pp. 190-197.

[7] R. Kokes, K. Lister, R. Gullapalli et al., "Towards a needle driver robot for radiofrequency ablation of tumors under continuous MRI." pp. 2509-2514.

[8] Y. Ningbo, C. Hollnagel, A. Blickenstorfer et al., “Comparison of MRI-Compatible Mechatronic Systems With Hydrodynamic and Pneumatic Actuation,” Mechatronics, IEEE/ASME Transactions on, vol. 13, no. 3, pp. 268-277, 2008.

[9] M. Flueckiger, M. Bullo, D. Chapuis et al., "fMRI compatible haptic interface actuated with traveling wave ultrasonic motor." pp. 2075-2082 Vol. 3.

[10] Y. Ningbo, W. Murr, A. Blickenstorfer et al., "An fMRI compatible haptic interface with pneumatic actuation." pp. 714-720.

[11] D. Chapuis, R. Gassert, G. Ganesh et al., "Investigation of a Cable Transmission for the Actuation of MR Compatible Haptic Interfaces." pp. 426-431.

[12] N. V. Tsekos, A. Khanicheh, E. Christoforou et al., “Magnetic Resonance–Compatible Robotic and Mechatronics Systems for Image-Guided Interventions and Rehabilitation: A Review Study,” Annual Review of Biomedical Engineering, vol. 9, no. 1, pp. 351-387, 2007.

[13] R. Gassert, R. Moser, E. Burdet et al., “MRI/fMRI-compatible robotic system with force feedback for interaction with human motion,” Mechatronics, IEEE/ASME Transactions on, vol. 11, no. 2, pp. 216-224, 2006.

[14] N. Vanello, V. Hartwig, M. Tesconi et al., “Sensing Glove for Brain Studies: Design and Assessment of Its Compatibility for fMRI With a Robust Test,” Mechatronics, IEEE/ASME Transactions on, vol. 13, no. 3, pp. 345-354, 2008.

[15] K. Uffmann, and M. E. Ladd, “Actuation Systems for MR Elastography,” Engineering in Medicine and Biology Magazine, IEEE, vol. 27, no. 3, pp. 28-34, 2008.

[16] G. Ganesh, R. Gassert, E. Burdet et al., "Dynamics and control of an MRI compatible master-slave system with hydrostatic transmission." pp. 1288-1294 Vol.2.

[17] M. Rajendra, A. Yamamoto, T. Oda et al., “Motion Generation in MR Environment Using Electrostatic Film Motor for Motion-Triggered Cine-MRI,” Mechatronics, IEEE/ASME Transactions on, vol. 13, no. 3, pp. 278-285, 2008.

[18] B. Vigaru, D. Petrisor, A. Patriciu et al., "MR compatible actuation for medical instrumentation." pp. 49-52.

[19] F. Carpi, A. Khanicheh, C. Mavroidis et al., “MRI Compatibility of Silicone-Made Contractile Dielectric Elastomer Actuators,” Mechatronics, IEEE/ASME Transactions on, vol. 13, no. 3, pp. 370-374, 2008.

[20] I. Bricault, N. Zemiti, E. Jouniaux et al., “Light Puncture Robot for CT and MRI Interventions,” Engineering in Medicine and Biology Magazine, IEEE, vol. 27, no. 3, pp. 42-50, 2008.

[21] R. Moser, R. Gassert, E. Burdet et al., "An MR compatible robot technology." pp. 670-675 vol.1.

[22] D. Chapuis, X. Michel, R. Gassert et al., "A Haptic Knob with a Hybrid Ultrasonic Motor and Powder Clutch Actuator." pp. 200-205.

[23] R. H. Cannon, and E. Schmitz, “Initial experiments on the end-point control of a flexible one-link robot,” International Journal of Robotics Research, vol. 3, no. 3, pp. 62-75, 1984.

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