Micron: An Actively Stabilized Handheld Tool for...

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IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1,FEBRUARY 2012 195 Micron: An Actively Stabilized Handheld Tool for Microsurgery Robert A. MacLachlan, Member, IEEE, Brian C. Becker, Student Member, IEEE, Jaime Cuevas Tabar´ es, Gregg W. Podnar, Member, IEEE, Louis A. Lobes, Jr., and Cameron N. Riviere, Senior Member, IEEE Abstract—We describe the design and performance of a hand- held actively stabilized tool to increase accuracy in microsurgery or other precision manipulation. It removes involuntary motion, such as tremor, by the actuation of the tip to counteract the effect of the undesired handle motion. The key components are a 3-degree- of-freedom (DOF) piezoelectric manipulator that has a 400-μm range of motion, 1-N force capability, and bandwidth over 100 Hz, and an optical position-measurement subsystem that acquires the tool pose with 4-μm resolution at 2000 samples/s. A control sys- tem using these components attenuates hand motion by at least 15 dB (a fivefold reduction). By the consideration of the effect of the frequency response of Micron on the human visual feedback loop, we have developed a filter that reduces unintentional motion, yet preserves the intuitive eye–hand coordination. We evaluated the effectiveness of Micron by measuring the accuracy of the hu- man/machine system in three simple manipulation tasks. Handheld testing by three eye surgeons and three nonsurgeons showed a re- duction in the position error of between 32% and 52%, depending on the error metric. Index Terms—Compensation, medical robotics, optical tracking, piezoelectric devices. I. INTRODUCTION N ORMAL hand tremor under microsurgical conditions is typically several hundred micrometers peak-to-peak [1], [2], yet from medical necessity, surgeons routinely manipulate much smaller structures (such as the 10-μm thick retinal in- ternal limiting membrane [3]) using handheld tools. Although such feats of dexterity are remarkable, it seems likely that some technical means for the stabilization of hand motion during microsurgery would allow more consistent outcomes for exist- ing procedures and (more importantly) allow the development Manuscript received February 16, 2011; revised August 15, 2011; accepted September 15, 2011. Date of publication November 18, 2011; date of current version February 9, 2012. This paper was recommended for publication by As- sociate Editor Y. Sun and Editor B. J. Nelson upon evaluation of the reviewers’ comments. This work was supported in part by the National Institutes of Health under Grant R21 EY016359, Grant R01 EB000526, and Grant R01 EB007969, by the National Science Foundation under a Graduate Research Fellowship, and by the Achievement Rewards for College Scientists Foundation. R. A. MacLachlan, B. C. Becker, G. W. Podnar, and C. N. Riviere are with the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: [email protected]; [email protected]; gwp@cs. cmu.edu; [email protected]). J. C. Tabar´ es was with the University of Valladolid, Valladolid 47011, Spain. He is now with the Sociedad Europea de An´ alisis Diferencial de Movilidad SL, Valladolid 47011, Spain (e-mail: [email protected]). L. A. Lobes, Jr., is with the Department of Ophthalmology, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TRO.2011.2169634 Fig. 1. Tremor signal with identified features. Low-frequency wander and nonperiodic jerk components dominate the peak-to-peak amplitude. of new procedures that are currently made impractical by the accuracy limits of unaided manipulation [4], [5]. We have con- centrated on applications to eye surgery because of the high accuracy that is required, but such technologies would likely be valuable in other areas of surgery [6] and for other applications, such as biological research [7] or industrial assembly tasks [8]. Before the discussion of the state of the art, we must review relevant properties of the human component in an aided manip- ulation system: tremor characteristics and human-in-the-loop dynamics. A. Tremor Characteristics For simplicity, we use tremor to mean any involuntary hand motion that creates position error. This differs somewhat from medical usage, where tremor is defined as a rapid quasi-periodic motion [9]. Furthermore, our concern is with the position error at the tip of a small tool that is manipulated using visual feedback under a microscope. Tremor characteristics may differ if there are changes in visual feedback or target motion amplitude [10]. Fig. 1 shows typical motion when a subject tries to hold a tool tip stationary (as in the experiments in Section III). In addition to the high-frequency quasi-periodic motion, there is also drift or wander (slow trends) and jerk (sporadic fast jumps). Whatever terminology is used, it is necessary to suppress all these motions to achieve useful stabilization. Fig. 2 shows the spectrum of the position error that results from averaging the power spectrum across 54 trials using six subjects [27 min of data (see Section III-A)] and then further averaging across 50 logarithmically spaced frequency bins [11]. In physiology research, tremor is generally measured using an accelerometer and then characterized by the peaks of the 1552-3098/$26.00 © 2011 IEEE Authorized licensed use limited to: Université de Strasbourg SCD. Downloaded on September 16,2020 at 16:14:20 UTC from IEEE Xplore. Restrictions apply.

Transcript of Micron: An Actively Stabilized Handheld Tool for...

Page 1: Micron: An Actively Stabilized Handheld Tool for Microsurgeryeavr.u-strasbg.fr/~bernard/education/3a_tis_gmcao/mac...ternal limiting membrane [3]) using handheld tools. Although such

IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012 195

Micron: An Actively Stabilized HandheldTool for Microsurgery

Robert A. MacLachlan, Member, IEEE, Brian C. Becker, Student Member, IEEE, Jaime Cuevas Tabares,Gregg W. Podnar, Member, IEEE, Louis A. Lobes, Jr., and Cameron N. Riviere, Senior Member, IEEE

Abstract—We describe the design and performance of a hand-held actively stabilized tool to increase accuracy in microsurgery orother precision manipulation. It removes involuntary motion, suchas tremor, by the actuation of the tip to counteract the effect ofthe undesired handle motion. The key components are a 3-degree-of-freedom (DOF) piezoelectric manipulator that has a 400-μmrange of motion, 1-N force capability, and bandwidth over 100 Hz,and an optical position-measurement subsystem that acquires thetool pose with 4-μm resolution at 2000 samples/s. A control sys-tem using these components attenuates hand motion by at least15 dB (a fivefold reduction). By the consideration of the effect ofthe frequency response of Micron on the human visual feedbackloop, we have developed a filter that reduces unintentional motion,yet preserves the intuitive eye–hand coordination. We evaluatedthe effectiveness of Micron by measuring the accuracy of the hu-man/machine system in three simple manipulation tasks. Handheldtesting by three eye surgeons and three nonsurgeons showed a re-duction in the position error of between 32% and 52%, dependingon the error metric.

Index Terms—Compensation, medical robotics, optical tracking,piezoelectric devices.

I. INTRODUCTION

NORMAL hand tremor under microsurgical conditions istypically several hundred micrometers peak-to-peak [1],

[2], yet from medical necessity, surgeons routinely manipulatemuch smaller structures (such as the 10-μm thick retinal in-ternal limiting membrane [3]) using handheld tools. Althoughsuch feats of dexterity are remarkable, it seems likely that sometechnical means for the stabilization of hand motion duringmicrosurgery would allow more consistent outcomes for exist-ing procedures and (more importantly) allow the development

Manuscript received February 16, 2011; revised August 15, 2011; acceptedSeptember 15, 2011. Date of publication November 18, 2011; date of currentversion February 9, 2012. This paper was recommended for publication by As-sociate Editor Y. Sun and Editor B. J. Nelson upon evaluation of the reviewers’comments. This work was supported in part by the National Institutes of Healthunder Grant R21 EY016359, Grant R01 EB000526, and Grant R01 EB007969,by the National Science Foundation under a Graduate Research Fellowship, andby the Achievement Rewards for College Scientists Foundation.

R. A. MacLachlan, B. C. Becker, G. W. Podnar, and C. N. Riviereare with the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA15213 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

J. C. Tabares was with the University of Valladolid, Valladolid 47011,Spain. He is now with the Sociedad Europea de Analisis Diferencial deMovilidad SL, Valladolid 47011, Spain (e-mail: [email protected]).

L. A. Lobes, Jr., is with the Department of Ophthalmology, School ofMedicine, University of Pittsburgh, Pittsburgh, PA 15213 USA (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TRO.2011.2169634

Fig. 1. Tremor signal with identified features. Low-frequency wander andnonperiodic jerk components dominate the peak-to-peak amplitude.

of new procedures that are currently made impractical by theaccuracy limits of unaided manipulation [4], [5]. We have con-centrated on applications to eye surgery because of the highaccuracy that is required, but such technologies would likely bevaluable in other areas of surgery [6] and for other applications,such as biological research [7] or industrial assembly tasks [8].Before the discussion of the state of the art, we must reviewrelevant properties of the human component in an aided manip-ulation system: tremor characteristics and human-in-the-loopdynamics.

A. Tremor Characteristics

For simplicity, we use tremor to mean any involuntary handmotion that creates position error. This differs somewhat frommedical usage, where tremor is defined as a rapid quasi-periodicmotion [9]. Furthermore, our concern is with the position error atthe tip of a small tool that is manipulated using visual feedbackunder a microscope. Tremor characteristics may differ if thereare changes in visual feedback or target motion amplitude [10].

Fig. 1 shows typical motion when a subject tries to hold a tooltip stationary (as in the experiments in Section III). In addition tothe high-frequency quasi-periodic motion, there is also drift orwander (slow trends) and jerk (sporadic fast jumps). Whateverterminology is used, it is necessary to suppress all these motionsto achieve useful stabilization.

Fig. 2 shows the spectrum of the position error that resultsfrom averaging the power spectrum across 54 trials using sixsubjects [27 min of data (see Section III-A)] and then furtheraveraging across 50 logarithmically spaced frequency bins [11].

In physiology research, tremor is generally measured usingan accelerometer and then characterized by the peaks of the

1552-3098/$26.00 © 2011 IEEE

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196 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 2. Spectra of position error and acceleration during the “hold-still” task.The acceleration spectrum shows a 10-Hz tremor peak, yet in the positionspectrum, low-frequency error dwarfs this 10-Hz peak, leveling off in the bandwhere visual feedback is effective. In this visual feedback band, the error isgreater in the vertical (visual depth) direction.

acceleration spectrum [11]. Therefore, for comparison, we havealso plotted the acceleration spectrum (obtained by multiplica-tion of the position spectrum and the frequency response of adouble differentiation). Although acceleration does have physi-cal meaning, the prominence of the 10-Hz peak in the acceler-ation spectrum is arguably an artifact of the choice to analyzeacceleration, with its implicit emphasis on high-frequency dy-namics. This acceleration peak (and the subsequent steeper low-pass roll-off in position error) result primarily from the biome-chanical resonance of the hand [12] and give the accelerationsignal its quasi-periodic character. The implicit high-frequencyemphasis of acceleration suits the medical definition of tremor,and accelerometers are convenient for medical diagnosis, butthis prevalent practice in the tremor literature [11]–[14] discardsimportant information about normal involuntary hand motionand, initially, led us astray in defining Micron’s performancerequirements (see Section I-D).

The bandwidth of human eye–hand feedback generally liesbetween 0.5 and 2 Hz (see Section I-B). It is only below thiscritical frequency that the eye–hand feedback becomes effective.This visual feedback contributes to the shift to a nearly flatposition spectrum that begins below 0.5 Hz. The microscopeview is vertical; therefore, the user relies on depth perception todiscern motion in this direction. At low frequencies, the verticalerror is twice as large as the horizontal error, apparently becauseof the inferiority of depth perception (see Section III-B1).

Fig. 3 shows the probability distribution of the magnitude ofthe tip velocity vector (the same data as in Fig. 2). At each speed,the curve shows the fraction of the samples having that speed orlower; for example, 90% of samples are below 2 mm/s.

B. Human-in-the-Loop Dynamics

We cannot design manipulation aids without considering thatthe aid is inside the eye–hand feedback loop. Although reducinga human to a linear system obviously neglects many details, thisapproach has been successfully used for over 50 years in the de-sign of aircraft control systems and flight instrumentation [15].

Fig. 3. Probability distribution of the tool tip velocity during the “hold-still”task. This is the empirical cumulative distribution function (CDF), plotted with alogarithmic vertical scale to show the detail in both distribution tails. A GaussianCDF would be a straight line on these axes, and therefore, the curvature showsstrong skewing.

Fig. 4. Simple feedback model of the human-in-the-loop system with a manip-ulation aid. Tremor is modeled as a disturbance DH added to the hand motion.The eye–hand feedback acts to minimize the effect of this disturbance. GA isthe dynamic contribution of the aid system, which may destabilize the overalleye–hand feedback.

Fig. 4 shows a simple human-in-the-loop feedback model. Theoperator internally develops a goal position RH and uses visualfeedback to move the hand to the desired position. The human“controller” CH functions well with a certain range of dynam-ics GH . An introduced manipulation aid transduces the handmotion X into some tool motion Y . If GA (the aid dynamics)is poorly chosen, it will destabilize the overall eye–hand feed-back. Of particular concern is the time delay or phase lag at theloop critical frequency (where the open-loop gain drops belowunity).

Human performance studies have shown that the Bode plot ofthe human frequency response exhibits a 45◦ intercept at the loopcritical frequency [16], generating the same sort of frequencyresponse as a classical feedback controller. It is only near thecritical frequency that the human controller is subject to theconstraints of loop stability; at lower frequencies, there is moreindividual and temporal variation of human control behavior.The critical frequency of the human eye–hand feedback loopvaries somewhat by task, but is generally found to be in therange of 0.5–2 Hz [17], [18].

C. State of the Art in Microsurgical Manipulation Aids

Table I summarizes the state of the art in manipulation aidsfor microsurgery, such as eye surgery. First, we classify systems(columns), and then, we consider characteristics (rows).

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MACLACHLAN et al.: MICRON: AN ACTIVELY STABILIZED HANDHELD TOOL FOR MICROSURGERY 197

TABLE ICOMPARISON OF MICROSURGERY MANIPULATION AIDS

The most common approach to surgical robots has beenmaster–slave teleoperation [19], which enables improved ac-curacy through motion scaling and low-pass filtering of tremor.This technology has been brought into the routine practice of en-doscopic surgery by the da Vinci robot (Intuitive Surgical) [20].Although not designed for eye surgery, the availability of daVinci has led to investigations of its applicability [21]; kine-matic limitations have led to the development of a prototypemicropositioner accessory [22]. Other investigations into teleop-erated eye surgery have generally involved purpose-built hard-ware [23]–[25]. Among such systems, we choose the Jet Propul-sion Laboratory RAMS robot [26] as the exemplar for the tablebecause its complete implementation allows performance to becompared.

Another approach is cooperative control, where the opera-tor guides the end of a robot arm using an attached grip thatsenses the force applied by the hand. The arm’s passive stiffnessprevents tremor from disturbing the tool position. Measuredhand force is converted into an arm velocity goal, which isimplicitly low-pass filtered by the biomechanical dynamics ofthe arm. This creates the effect of viscous damping that attenu-ates tremor. We choose the steady-hand robot [27], [28] as ourexemplar, since it was developed for eye surgery.

In the Micron approach, a handheld tool actuates its owntip to cancel tremor. This concept is analogous to the opticalimage stabilization in a handheld camera and uses no robot arm.The greater stability of the tool tip compared with the handle isentirely because of the active stabilization of the measured tipposition with respect to a goal point that is expressed in a fixedcoordinate system.

1) Manipulation Aid Characteristics: We now consider sys-tem characteristics (rows in Table I). A common technique forthe reduction of the effect of tremor is motion scaling: caus-ing the motion at the output to be a fraction of the hand motion.Then, the operator makes larger motions with greater relative ac-curacy. Scaling preserves the human-in-the-loop stability, sincethe flat frequency response need not add delay. Because of itsrigid connection between input and output, cooperative manip-ulation cannot support motion scaling. In effect, the damping ofcooperative manipulation attenuates tremor by low-pass filtra-tion alone. Because of the prompt force feedback to the hand,this does not destabilize the eye–hand feedback loop, as suchfiltering would in a position-input system (see Section II-F), butit limits voluntary control bandwidth.

Workspace intrusion denotes the additional hardware or otherergonomic constraints added to the surgeon’s workspace bythe aid system. This is a concern because there is a great dealof other equipment also in use, most importantly, the surgicalmicroscope, which must have a clear sightline. A slave arm orcooperative arm necessarily intrudes into the workspace, andMicron introduces optical constraints with its requirement for asensor sightline. In the steady-hand cooperative manipulation,the surgeon directly grasps the tool, preserving this familiarinterface. In master/slave operation, the input device has nomechanical connection to the output. A surgeon using da Vinciworks in a virtual environment that is entirely separated from thepatient, which enables telemedicine, and is also beneficial forlocal use because of the unfavorable ergonomics of conventionallaparoscopy. The situation is different in eye surgery, where thesurgeon directly views the interior of the eye through the lensusing a surgical microscope. The RAMS robot demonstratesthat a master/slave system for eye surgery can preserve thiswork pattern, but both the master and the slave intrude into thesurgeon’s workspace.

An aid supports force feedback if forces that are exertedon the tool can be directly felt by the operator. Micron pre-serves the 1:1 force feedback of unaided operation, but, havingno mechanical ground, it is fundamentally incapable of pro-viding scaled force feedback. In microsurgery, the 1:1 forcefeedback is of limited value because the tool tip is small andthe tissue is soft; therefore, an imperceptible force can createpressure high enough to cause damage. One study has foundthat in vitreoretinal surgery, 75% of the time contact forceswere below 7.5 mN, i.e., a level perceptible by only 19% ofsurgeons [29].

Scaling up such forces to be perceptible might offer a signifi-cant benefit [30]. However, force feedback in surgical robots re-mains an open research problem [31], [32]. The difficulty in eyesurgery is increased by the need to integrate the force sensor intothe intraocular portion of the 0.9-mm diameter tool shaft [33].A master/slave controlled aid with force feedback also facesfundamental stability challenges that tend to limit force scalingto small ratios [34]. Cooperative manipulation uses force input,avoiding these stability problems and, therefore, is well suitedto force feedback. Then, high scaling ratios must be used so thatfeedback remains clear when superimposed on the hand forcethat is needed to overcome the system’s damping effect. Greaterthan 60:1 force scaling has been demonstrated [35].

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198 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Set-and-forget hold allows the tool to be “parked” in a fixedlocation so that it can serve as a “third hand.” This is eas-ily implemented in a robotic-arm system. Micron is handheld;therefore, it cannot support this feature.

2) Aid Comparison Summary—Advantages of Micron: Ofthe two robot-arm approaches, master/slave operation has po-tential for a desirable combination of features, but the designcomplexity and production cost are significant practical barri-ers. Cooperative systems have a clearer path to force-feedbackoperation and several advantages in implementation cost andsimplicity, such as the elimination of the master and the use ofposition output (admittance) servomechanisms, but the sluggishforce-input response limits dexterity.

Compared with these robot-arm systems, the biggest advan-tages of Micron are intuitive operation, safety, and economy.Micron is handheld and, therefore, can offer the same intuitivefeel as a conventional unaided tool. This improves user accep-tance by preserving existing surgical skills. The handheld oper-ation also has a safety advantage because Micron requires a farsmaller range of motion than alternative systems, and becausethe surgeon remains in gross control of the tool motion at alltimes, able to quickly withdraw if the patient moves, or to finisha procedure unaided if the system fails. Micron does not needto duplicate the function of the surgeon’s arm and, therefore, ismechanically simpler, getting by with fewer degrees of freedom(DOF) and a much smaller range of motion.

D. Micron Implementation Challenges

Although the Micron approach is intuitively appealing andreasonably obvious, as far as we know, the only such systemsto reach the stage of implementation are the various versions ofMicron [36]–[38] and its descendant “ITrem” [39]. This is likelybecause of the considerable engineering challenges of achiev-ing adequate performance in the manipulator and position-measurement subsystems. Micron’s tremor suppression is en-tirely dependent on the control system performance, whereasin a robot arm system, the control bandwidth needs to only beadequate to pass the voluntary component of motion.

Micron development began 15 years ago [40]. In 2003, thefirst implementation of Micron was described that integrated a3-DOF manipulator and 6-DOF position sensing into a handheldinstrument [41]. During the course of this development, concur-rent studies of hand motion during simulated microsurgery [1]led to the realization that in order to achieve useful accuracy im-provement, motion must be suppressed at frequencies that arewell below 10 Hz, lower than could be accurately detected withthe inertial sensors in [41]. The amplitude of motion to be sup-pressed at these lower frequencies is also considerably larger, in-creasing the required range of motion. Although, in [41], the au-thors demonstrated measurable attenuation of simulated 10 Hztremor in bench-top tests, it had become clear that it was in-capable of canceling the lower frequency components of handmotion and, therefore, was never developed to the point wherehandheld operation could be demonstrated.

In this paper, we report on subsequent developments thathave enabled Micron to demonstrate a significant quantitative

Fig. 5. Micron system, showing tool, position sensors, and electronics.

improvement in handheld accuracy. The largest single changewas architectural, replacing inertial sensing and open-loop con-trol with dc-accurate optical sensing and closed-loop control.The challenges of manipulator range and control were also sub-stantial. We prototyped a magnetic manipulator and two otherpiezoelectric manipulators [36], [37] before developing the de-sign that is described here, which has a range of motion six timesof that in [41]. Mechanical refinements also reduced problemswith friction and backlash nonlinearities, fragility, and instabil-ity of kinematic parameters that necessitated frequent recali-bration. Combined with the use of charge control to minimizeactuator hysteresis (see Section II-L) and overall position feed-back, the contribution of actuator error to system performancewas drastically reduced so that tremor reduction is now limitedby the system delay (see Section II-N).

In Section II, we describe the design of the current Micronsystem (see Fig. 5), which includes solutions to a number ofintegration and control issues that appeared in handheld testing,notably the design of effective cancellation filters that do notdestabilize the human feedback loop (see Section II-F), devel-opment of ways to gracefully handle manipulator saturation (seeSection II-I), and robust closed-loop control of the manipulator(see Section II-K).

In Section III, we present experimental results from handheldtesting by three trained surgeons and three nonsurgeons. A 3-minvideo that is provided by the authors shows Micron operationand experimental results (available at http://ieeexplore.ieee.organd http://youtu.be/6Vt81EiXR5o).

II. DESIGN

A. System Architecture

The major system components (see Fig. 6) are the handpiece,optical tracking system, custom driver and signal conditioningelectronics, data acquisition cards, and a PC that runs real-timeLabVIEW control software. Optical measurement determinesthe 6-DOF pose of the handgrip and tool. A feedback looprunning at 2 kHz servos the tool tip to a goal position that iscomputed based on the measured hand motion. To achieve themanipulation accuracy that Micron makes possible, the operator

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MACLACHLAN et al.: MICRON: AN ACTIVELY STABILIZED HANDHELD TOOL FOR MICROSURGERY 199

Fig. 6. Micron system architecture. The handpiece contains the manipulator(which actuates the tip to cancel hand motion) and mechanically coupled LEDs(for position measurement by PSD cameras). Driver and signal conditioningelectronics interface these components to a controller PC.

Fig. 7. Micron handpiece, showing tool and position sensor LEDs (visiblethrough the window in the housing).

must have some high-power magnifier, but Micron does notrequire any integration with microscope optics.

B. Handpiece Design

The handpiece design packages the manipulator and position-measurement components into a small, lightweight (40 g) hand-held tool. The current design places the manipulator and LEDsin a housing of maximum diameter 50 mm, mounted on the dis-tal end of the handgrip (see Fig. 7). Although wider than desired,the indented star-like shape of the housing does allow the toolto be held within 15 mm of the microscope sightline. The gripitself contains only wiring.

The manipulator (see Fig. 8) has a 3-DOF parallel config-uration similar to [42], but the actuators and flexures undergoa complex distributed deformation (see Fig. 9) that does notpermit a simple geometric kinematic model. The manipulatoris under closed-loop control based on a direct output pose mea-surement; therefore, the kinematic approximation error does notcompromise system accuracy (see Section II-H). A flex-circuitconnects the electrical components, and a clear bore through thegrip allows passage of tool leads, such as optical fibers.

The requirement for a compact, high-bandwidth actua-tor with roughly 1-mm range of motion is challenging.The manipulator design depends on a unique piezoelectric

Fig. 8. Micron three-link parallel piezoelectric manipulator. Axes show theorientation of the tip coordinate system. Each leg of the manipulator has twoactuators mechanically series-connected in a folded configuration, generat-ing, approximately, 600 μm of motion (see Fig. 9). Each actuator assemblyis rigidly fixed to the base plate and is connected to the star-shaped output plateby a polypropylene flexure. See also the video at http://ieeexplore.ieee.org orhttp://youtu.be/6Vt81EiXR5o, which shows the manipulator in operation.

Fig. 9. Exaggerated depiction of the deformation of the actuator and flexurefor a single leg in the manipulator (twice the actual range of motion).

bending actuator (Thunder TH-10R, Face International Cor-poration, Norfolk, VA) that uses a laminated metal con-struction to achieve a large range of motion with a stiff-ness greatly exceeding that of all-ceramic bending actua-tors. High stiffness gives the manipulator a static force out-put capability far in excess of microsurgical requirements,as well as enhancing system performance by increasingthe frequency of manipulator resonances (see Section II-J).The piezoelectric actuators require high voltage (−240 to+480 V) but minimal current (4 mA peak). Hysteresis and non-linearity are reduced by controlling the total charge that is storedin the actuator rather than the applied voltage (see Section II-L).

In the current system, the most important performance limitsare determined by manipulator characteristics. See Section I-Dfor comparison with the previous design [41]. Greater rangeof motion, smaller size, and higher bandwidth would all bedesirable (in decreasing order of importance); the present force(>1 N) and slew rate (>100 mm/s) are more than adequate. Thebandwidth is discussed in Section II-N.

Fig. 10 shows the volume that can be reached by a typical40-mm tool tip. The lateral (XY) range varies with the tool lengthand is significantly larger than the Z range. Although the extentof the workspace is nearly 2 mm, the largest enclosed cube isapproximately 400 μm on a side.

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200 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 10. Manipulator workspace. Lateral (XY) tip motion is larger than axial(Z ) motion because of the tool lever arm. This volume defines the largestdisturbance that can be canceled and limits the achievable motion scaling.

C. Coordinate Systems and Notation

The human-in-the-loop Micron system (see Fig. 4) has a se-rial kinematic chain with two variable components: the hand andthe manipulator. This establishes three useful reference framesfor the coordinates of any point x: The fixed world coordinatesxw , the hand coordinates xh , and the manipulator coordinatesxm . The world coordinates are arbitrarily defined by the poseof the PSD cameras. The manipulator coordinate system moveswith the tool. Its origin is at the tool tip and its orientation isas shown in Fig. 8. The hand coordinates are defined to be theidentical to the manipulator coordinates when the manipulatoris in the null position, therefore, the origin of the hand coor-dinates is where the tip would be in a conventional rigid tool.If the pose of the manipulator is represented by a 4×4 linearhomogenous transform Pm , then this may be used to convertbetween coordinate systems:

xw = Pmxm .

In Fig. 4, the human-in-the-loop model is shown, and theresponse of the Micron manipulation aid is expressed as afunction:

Y (s) = GA (s)X(s).

Therefore, x will be used to denote the null tip position, and ywill be used to denote the actual tip position (xh ≡ ym ≡ 0).

D. Position Measurement

Position measurement for Micron imposes demanding re-quirements for noise and latency because measurement noisecreates undesirable tip motion, and latency fundamentally lim-its canceling performance (see Section II-N). The measurementsubsystem optically tracks the pose of both the tool and the hand-grip at 2 kilosamples/s over a 4-cm workspace [43]. The majorcomponents are two position-sensitive-detector (PSD) cameras,signal conditioning electronics, infrared light-emitting diodes(IR LEDs), and an LED driver.

A PSD is a specialized large-area photodiode that makes ananalog position measurement of the centroid of a light source. Alens focuses the IR light onto the PSD. A long-pass IR filter ex-cludes much ambient light, reducing interference and shot noise.(We cite this lens/filter/PSD combination as a camera, thoughit does not capture an image.) Each camera allows measure-

Fig. 11. Position servo loop small-signal model with disturbance. This servoloop stabilizes the tip position without any direct measurement of hand motion,canceling disturbance from any source.

ment of an LED position in 2 DOF. Each PSD tracks multipleLEDs, simultaneously, using frequency domain multiplexing.The LEDs are modulated at distinct frequencies between 8 and20 kHz [43].

Two separated PSD cameras allow each LED position to betriangulated in three dimensions. The manipulator pose Pm isrecovered from the positions of a triad of LEDs that are mountedon the tool holder [44]. Because the manipulator has only 3 DOF,the hand pose Ph can be reconstructed from the tool pose usingonly one additional LED that is mounted on the handle. Theorigin of the hand pose is xw , i.e., the null tip position.

The measurement noise of the LED position is white, with avector amplitude of 0.74-μm rms in the full 1-kHz measurementbandwidth. The tip position yw is, by definition, the origin ofthe manipulator coordinates, but achieving this desired refer-ence requires calibration of the tip location with respect to theLEDs (using a pivot calibration procedure). Since the LEDs areoffset from the tip, an error in the pose orientation creates alateral error in the tip position proportional to this offset. Witha typical tool length, the resulting tip noise is 5.7-μm rms atfull bandwidth. Although the control loop runs at the 2 kilo-samples/s measurement rate, the control bandwidth is consider-ably less, about 100 Hz (see Section II-N), and this is also thebandwidth of the 200 samples/s data collection in Section III.The tip position noise in this reduced 100-Hz bandwidth is1.8-μm rms.

E. Small-Signal Model

To understand the operation of Micron, first consider a genericsmall-signal model of a feedback system with disturbance (seeFig. 11). In Micron, the manipulator generates a motion that ismechanically added to the hand tremor and other disturbancesD(s) to generate the tip motion Y (s). A suitably chosen con-troller C(s) can compensate for the manipulator dynamics G(s),driving the tip to the goal position R(s). This negative feedbacksubtracts out the disturbances without requiring any direct mea-surement of D(s).

The Micron small-signal model (see Fig. 12) includes thisposition servo loop (see Fig. 11) as a component. In thehuman-in-the-loop system (Fig. 4), the manipulation aid con-verts hand motion X into tool motion Y . The hand mo-tion X is a combination of the human’s desired motionRH and the tremor disturbance DH . The cancellation fil-ter H(s) computes R(s), i.e., the reference for the posi-tion servo loop, from a measurement of this hand motion.

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MACLACHLAN et al.: MICRON: AN ACTIVELY STABILIZED HANDHELD TOOL FOR MICROSURGERY 201

Fig. 12. Micron small-signal model with cancellation filter. Hand motion isa combination of the desired motion RH and tremor DH (see Fig. 4). Thismotion is measured and filtered to establish the goal position so that voluntarymotion is possible. The position servo loop is from Fig. 11.

Conceptually, R(s) is an estimate of the human reference posi-tion RH . If H(s) perfectly recovered RH , and the position servoloop perfectly tracked R(s), then Y (s) = RH . It is inherent inMicron’s handheld implementation that there is a unity-gainfeedforward path from input to output (X to Y ). Nonintuitively,this mechanical connection sums the desired motion RH intothe disturbance that the position servo loop must reject:

D(s) = RH + DH + DO .

If the RH disturbance component is imperfectly canceled, thenit sums with R(s) ≈ RH through the C(s) G(s) forward path,creating position error. In practice, the interaction between thesetwo paths is negligible because the bandwidth of the positionservo loop is necessarily much greater than that of the cancella-tion filter (see Section II-N and Figs. 14 and 24).

F. Cancellation Filter

H(s) has a generally low-pass response, since it must haveunity gain at low frequencies so that the goal remains within themanipulator workspace in spite of gross hand motion and shouldhave high attenuation at 10 Hz to suppress high-frequencytremor components. The filter requirements are defined bothby the nature of tremor (see Section I-A) and the dynamics ofthe human eye–hand feedback loop (see Section I-B).

From the human-in-the-loop system model (see Fig. 4),Micron’s dynamics GA can be approximated by the cancellationfilter H(s), because the other dynamics are too fast to be relevantto the human operator. Although we have not performed systemidentification for the human-in-the-loop Micron system, our ex-perience with cancellation filter design suggests that the criticalfrequency is near 1 Hz. We have found that if H(s) is a simplelow-pass filter, the corner frequency must be set above 1 Hz inorder for the intuitive eye–hand coordination to be preserved.From Fig. 2, it is evident that the amplitude of tremor below 1 Hzis considerably greater than the peak near 10 Hz. As the cutofffrequency is reduced, the response begins to feel “bouncy” eventhough the step response of H(s) is well damped. The responsecontinues to deteriorate to near-unusability at 0.5 Hz, belowwhich there is a transition to a different control regime, where

Fig. 13. Cancellation filter structure. This implements the shelving responseof the scaling algorithm, as well as limiting the goal velocity.

Fig. 14. Simulated Micron low-frequency response, hand to tip. The scalingresponse is labeled with the corresponding filter parameters.

all sense of manipulation of a rigid tool is lost, and it feels morelike operating a flight simulator.

Motion scaling provides tremor attenuation withoutcompromising eye–hand stability (see Section I-C). TheMicron handle and tip can move independently; therefore,Micron can implement motion scaling. However, given a scalinggain kS < 1, to permit a desired voluntary tip motion yv , themanipulator range must accommodate the differential hand/tipmotion yv (1/ks − 1). Unfortunately, a handheld manipulatorhas a very small workspace, making impractical the sort ofmanual “clutching” [20] or “reindexing” [45] feature that isusually used in motion-scaling master/slave systems to allowlarge voluntary motions during scaling. However, motion scal-ing can be approximated by a shelving filter with a low cornerfrequency fL , a flat shelf near 1 Hz with amplitude kS (the scal-ing region), and, a high corner frequency fH (above 1 Hz). Theunity gain at dc ensures that the manipulator remains centeredduring large voluntary motions, yet there is still considerable at-tenuation at tremor frequencies. From a control perspective, thiscan be viewed as lead–lag compensation of the human feedbackloop in Fig. 4.

Fig. 13 shows the structure of the Micron cancellation filter.In addition to implementation of the shelving response, it alsoincorporates a velocity limiter. The two component filters areinfinite impulse response second-order sections with qualityfactors QL = 0.7 and QH = 0.62. Fig. 14 shows the simulatedfrequency response of Micron with the two sets of parametersthat are given in Table II.

The scaling response has no more phase lag than the low-passresponse at 1 Hz, even though it provides 10 dB more attenuation

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202 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 15. Control system with kinematics, showing the coordinate transformsthat implement the 3-D signal flow. The optical tracker measures both the systeminput (hand motion xw ) and the output (manipulator pose Pm ). Inversion ofthe pose creates negative feedback that forces the tip to track rw (an estimateof the voluntary motion).

from 0.4 to 4 Hz. The delay from disturbance motion measure-ment to the compensating tip motion causes the decrease inattenuation above 4 Hz (see Section II-N).

In Fig. 3, we see that 1 mm/s is exceeded 30% of the time;therefore, the velocity limiter operates frequently (not only onsporadic jerky motion, such as in Fig. 1). Fig. 14 does not reflectthe amplitude-dependent effect of velocity limiting. As long asthe voluntary motion does not exceed the limit, there is nodestabilizing effect on the eye–hand feedback.

G. Three-Dimensional Kinematics

To generalize the single-input-single-output (SISO) small-signal model (see Fig. 12) to 3-D kinematic operation, Micronuses transform matrices to convert positions between three coor-dinate systems: world, manipulator, and link-length space (seeFig. 15). The optical tracker measures the positions of the han-dle and tip LEDs (see Section II-D), computing the manipulatorpose Pm and the null tip position xw , which is where the tipwould be in a conventional tool. This is filtered by H(z) tofind rw , i.e., the goal position in world coordinates. Pose Pm

is a linear homogenous transform (see Section II-C); therefore,multiplication with the matrix inverse P−1

m rw converts the goalposition into manipulator coordinates, giving rm , i.e., an offsetrelative to the current tip position. This transform is analogousto the R(s)–Y (s) node in the small-signal model (see Fig. 12);therefore, rm plays the role of the error signal in the feedbackloop. High frequencies have been removed from rw , giving theeffect of passing forward the high-frequency content in Pm witha negative sign, creating negative feedback at high frequencies.

H. Inverse Kinematics

The manipulator is a 3-DOF parallel linkage. Continuing withthe signal flow in Fig. 15, we convert the desired tip positioninto link lengths rll using the inverse kinematics transform K−1 ,which is calibrated by an offline procedure that generates po-sition sweeps in the manipulator link-length space, measures

TABLE IICANCELLATION ALGORITHM PARAMETERS

the resulting tip motion, and, finds the linear transform ma-trix that best generates this motion. The kinematics of evenan ideal parallel manipulator are nonlinear, but the maximumMicron angular deflection is less than 2◦; therefore, this errorsource is negligible. The significant manipulator nonlinearitiescome from other sources, such as nonidealities in the actuators(see Fig. 9). The typical calibration error is 40-μm rms, out of±400 μm actuator travel. This level of error does not signif-icantly affect the performance of the closed-loop system (seeSection II-N and Fig. 31).

I. Alternate Goal Substitution

Large hand motions often cause manipulator saturation, cre-ating two problems: first, when the manipulator is saturated, nocancellation can take place, and second, although the controllerdoes manage saturation (see Section II-K.1), this is done on aper-axis basis, creating undesirable tip motion during prolongedsaturation. To avoid this, when the goal position is not reachable,the controller substitutes a reachable alternate goal position rll

that is in the direction of the goal. This largely eliminates spuri-ous tip motion on saturation by keeping the position servo loopclosed and maintains at least partial cancellation by pointing thetip toward the goal. rll is computed by the renormalization of rll

to fall within the workspace, assuring a smooth transition backto normal operation.

Another layer of saturation control adaptively increases thecutoff frequency of the cancellation filter H(z) when the manip-ulator nears saturation, gracefully avoiding saturation by com-promising this filter response. This adaptation begins at 50% ofthe manipulator travel, rising to a tenfold increase at saturationonset. The cancellation filter also limits the goal displacementthat is introduced by the velocity limiter to 300 μm. Because ofthe manipulator range, it is not possible to suppress jerks muchlarger than this, and therefore, allowing a larger difference wouldonly prolong recovery from saturation.

J. System Identification

System identification was performed to experimentally de-termine a linear discrete-time model G(z)z−L . This is an ap-proximation of the behavior of the entire signal path, excludingthe controller C(z). The term z−L models the pure delay in thesystem, which results from the actual processing latency as wellas other sources of lag, such as the antialias/antiimaging filterson the input and output. The estimated delay was L = 4 samples(2 ms).

The Micron manipulator is a multiple input multiple out-put (MIMO) system because it has three degrees of free-dom. In three open-loop response tests, a swept-sine signal(transformed by the inverse kinematics) was used to excite tip

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MACLACHLAN et al.: MICRON: AN ACTIVELY STABILIZED HANDHELD TOOL FOR MICROSURGERY 203

Fig. 16. Experimental manipulator frequency response that is superimposedon the response of the identified system models. There are poorly damped res-onances above 100 Hz, and the dynamics differ significantly between lateraltip motion (x, which is implemented by manipulator angular motion) and axialtranslation (z). Identification was focused below 500 Hz, deliberately compro-mising high frequency accuracy to reduce the model order.

motion along each of the three Euclidian tip coordinate axes.The MATLAB system identification toolbox was used to gener-ate both nonparametric (spectral) frequency response estimatesand state-space models for motion in each direction. Using thenonparametric response as a reference, we found the lowestorder models with good fidelity over the 10– 500 Hz range(see Fig. 16). The response is flat at low frequencies, but thereare pronounced manipulator resonances above 100 Hz. Thereare two distinct dynamic operating modes. Moving all threeactuators together generates axial translation, while opposedactuator motion creates angular deflection, causing a lateraldisplacement of the tip. The z stimulus excites axial motion,giving the axial model Ga(z) (order 8). The x and y stim-uli generate lateral motion, giving two similar models Gx,y (z)(order 11).

K. Controller Implementation

The availability of a linear model from system identifica-tion enables use of theoretically grounded control methodolo-gies. Although less general than state-space approaches, suchas linear-quadratic optimal control, we chose internal modelcontrol (IMC) because we preferred a frequency-domain ap-proach, and we found that it was a good match for particularcontrol issues that Micron faces: Manipulator resonances arepoorly damped, dynamics vary because of tool changes and ma-nipulator aging, and different tasks demand different tradeoffsbetween speed, noise, and settling time.

1) Internal Model Control: IMC, which was originally de-veloped for process control in the chemical industry, has alsofound use in control of electromechanical systems [46]. IMCuses a control topology that incorporates a system (plant) modelin a straightforward way (see Fig. 17) and has an associatedcontrol design methodology that permits proofs of robustnessand optimality [47]. There is also a wide body of practice thatprovides specific guidance for the management of a wide rangeof control problems, including those listed earlier [48]. IMCcan handle underdamped dynamics, is robust in the presenceof model error, and has two parameters that can be varied to

Fig. 17. IMC architecture. The actual plant and the model receive the samecommand. The difference of the measured and predicted positions (disturbanceor modeling error) is fed back to the input.

achieve a range of stable responses. IMC also addresses timedelay and saturation nonlinearity.

First, the plant models G and L are determined by analysisor system identification. Then, F and Q must be designed. InMicron, G is stable and minimum phase, making control designfairly straightforward (although IMC could still be applied if itwere otherwise). Note that if G(z)z−L = G (no modeling error),and we set F = 1, and Q = G−1 , then the output tracks the inputperfectly, with only a time delay. In practice, this is impossible,both because of inevitable modeling error and because G−1 isusually improper (having more zeros than poles); therefore, itcannot be realized as a digital filter. This is more than a numericaldifficulty—it represents the physical reality that the plant hasa low-pass characteristic, and therefore, infinite bandwidth isunattainable.

The IMC architecture has a feedforward character—duringthe system time delay, a step change in R(z) passes directly tothe output, modified only by F . F is a unity-gain low-pass filterthat creates robustness by rolling off the modeling error at highfrequencies (where uncertainty is greater). The system’s closed-loop response is, approximately that of F . Then, the controlbandwidth goal that is specified by F is a “robustness knob” onthe controller that can be varied over a wide range without com-promising stability. Even after significant changes in the plant, astable (but slow) response can usually be restored by setting thecontrol bandwidth sufficiently low. F also serves to attenuatehigh-frequency measurement noise that would otherwise be fedinto the plant control input. Since low-pass filtering in the IMCcontroller benefits robustness, additional poles can be added toQ (or F ) to make FQ proper.

In Fig. 17, note the straightforward compensation for thedestabilizing effect of time delay by including a delay in thesystem model. The factoring of G into G and L allows the con-struction of a causal inverse G−1 , a system with lag cannot bedirectly inverted. In practice, L serves as an additional knob onthe controller that can be used to adjust the phase margin (andthus, the gain flatness and step response damping). The unmod-eled poles in FQ create additional lag that may be compensatedby increasing L.

Fig. 17 can be redrawn in various nearly equivalent forms.In particular, from an optimal control perspective, IMC can beseen to be a special case of state feedback with an observer [49].More interesting, for our purposes, is Fig. 18, which placesIMC in the framework of classical control by the rearrangement

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204 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 18. Block diagram, which is equivalent to that in Fig. 17, drawn with unitynegative feedback, showing similarity to PID and other conventional controllers.

Fig. 19. IMC architecture simplification possible when Q = G−1 , giving alead–lag controller with approximate inversion of plant dynamics.

of the architecture into an equivalent unity-gain negativefeedback configuration (see Fig. 12). If G is a single pole, thena proportional-integral differential (PID) controller can be usedto implement IMC. One of the most common uses of IMC inindustrial process control is to derive PID control parametersfrom a model [48].

In Micron the system dynamics are more complicated, andtherefore, PID control is inadequate, but Fig. 19 shows a con-troller that is equivalent to Fig. 18 when Q = G−1 and that rivalsPID control for simplicity. As noted earlier, G−1 is usually im-proper, and therefore, this transformation implicitly replaces Gwith the proper Q−1 , in effect adding zeros to the plant model.This approximation is benign, being almost the same as addingadditional poles to F . A tunable F is still needed; therefore, inMicron, we use the following first-order filter:

F (z) =(1 − p)zz − p

.

Continuing with the signal flow in Fig. 15, we see that the con-troller operates in the link-length space. This choice does notaffect the small-signal response, but makes it easier to avoidactuator saturation. In the presence of saturation, an IMC con-troller is susceptible to integral windup, which can be avoidedin several ways. In the IMC architecture (see Fig. 17), satura-tion and other nonlinearities can be incorporated directly into thesystem model, but this is not robust to modelling error. There areoptimal anti-windup techniques for IMC [50], but a simple androbust technique incorporates a conservative saturation into thecontroller so that the plant never actually saturates [51]. Fig. 20is a more detailed view of the Micron controller, including arate and position saturation block that avoids overshoot on sat-uration at the cost of a slower response that does not expoit thefull control authority. This sub-optimal response is acceptable inMicron because position saturation is prevented by other means(see Section II-I) and rate saturation is rare because of the high

Fig. 20. Micron controller C (z), including saturation and MIMO decoupling.See Fig. 15 for the larger system context.

Fig. 21. Manipulator x and y frequency response data, shown superimposedon Gl (z), i.e., the lateral response model. Filtered is Ql Gl , which is thedesigned frequency response including the effect of the lateral inverse filter.This low-pass response robustly suppresses high-frequency resonances but addsphase lag.

speed of the manipulator. This limiter is distinct from the veloc-ity limiter in the cancellation filter (see Fig. 13).

2) MIMO Control: In Fig. 15, the controller input rll is avector of link-length errors and the output cll is a vector of theupdated link lengths. As with other frequency-domain designtechniques, IMC most naturally controls SISO systems, but itcan be extended to MIMO systems when the dynamics can bedecoupled into noninteracting SISO systems. In the simplifiedIMC architecture (see Fig. 19), only the inverse filter Q(z) incor-porates system dynamics; therefore, it is only there that MIMOinteractions must be considered. In the Micron controller (seeFig. 20), the decoupled systems are axial and lateral motion (asdiscussed in Section II-J). In the inverse filter, the 3-vector ofcommanded manipulator link-lengths dm is decoupled into ascalar axial component and a 3-vector of lateral components dl .The axial component da is the mean of dm , and dl = dm − da .

3) Design Parameter Specifics: The high-order models fromsystem identification (see Section II-J) can be used directly forsimulation, but for conceptual simplicity and implementationefficiency, we reduced the xyz model orders to 5, 5, and 6 bydiscarding states with low Hankel singular values (MATLABbalred). Then, the xy models were, combined into a singlelateral model by taking the mean of the complex pole/zero lo-cations (see Fig. 21). Because the lateral mode has a lower first

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Fig. 22. Structure of Ql (z), inverse filter for the lateral mode, compared withthe manipulator model. Low-frequency resonances are approximately canceled,while a low-pass filter ensures a robust high-frequency gain margin.

resonance than the axial mode, the lateral controller design isperformance limiting and will be presented in more detail.

Fig. 22 shows the sixth-order design of Ql(z), i.e., the in-verse filter for the lateral mode. Two pairs of zeros are used tocancel the lowest frequency manipulator poles (peaks in modelresponse, see Fig. 21). One pair of poles approximately cancelsthe lowest manipulator zero pair (valley in model response). Thedamping of this pole pair has been increased to 0.1, leaving aslight dip in Fig. 21 filtered response. This increases robustness,since modeling error can reveal Ql’s underdamped response,creating long settling times [48].

Because the response becomes overly sensitive to model-ing error, control bandwidth cannot be robustly extended muchabove the first manipulator resonance (150 Hz), yet the ma-nipulator has considerable gain well above this frequency (seeFig. 21). It is futile to attempt inversion of plant dynamics outto arbitrarily high frequencies; therefore, realistic controller de-sign amounts to a decision of what low-pass response the systemshould have. Although IMC design is done in the frequency do-main to facilitate understanding of high-frequency stability, innormal operation, the time-domain response is more relevant—the open-loop step response should have minimal overshootand ringing. For this reason, the remaining poles of Ql(z) areconfigured as a Bessel filter.

Because F (z) was chosen to be first order, an additional polepair was added to Ql(z) to ensure adequate high-frequency gainmargin near the 400 Hz resonance, which is strongly dependenton the mass of the (interchangeable) tool tip. Since a low-passresponse creates phase lag, there is inevitably some compro-mise between bandwidth and robustness. This compromise isreflected in filtered response that is shown in Fig. 21, which ismuch more well behaved than the uncompensated manipulator,having a nearly ideal Bessel response, but has considerably morephase lag than the uncompensated system as well, limiting thestable unity gain bandwidth, as well as more directly affectingthe ability to resist tremor disturbance (see Section II-N).

Allowing for the lag that is introduced by this nonideal in-verse, the nominal system delay time L was eight cycles (4 ms).Both L and the control bandwidth FBW can be varied to achievedifferent responses. We experimentally determined two sets of

TABLE IIICONTROLLER TUNING PARAMETERS

tuning parameters (see Table III), which we cite as (approxi-mately) critically damped and underdamped.

L. Charge Control

Continuing with signal flow that is shown in Fig. 15, nowthe new link lengths cll are converted to charge increments. Asdiscussed in Section II-B, Micron implements charge control tolinearize the piezoelectric actuators. Although a voltage drivescheme is relatively straightforward to implement using a high-voltage amplifier, the position response from a voltage signalis difficult to characterize, being both nonlinear and hysteretic,with dependence on frequency [52]. Because of the high levelof piezoelectric strain that is made possible by the Thunderactuator, this nonlinearity can reach extreme levels, exceedingone third of full scale. In contrast, the position response to charge(the integral of current) is far more linear and repeatable [53].

Current errors are inevitable, and a charge source has high out-put impedance; therefore, any practical charge control schememust have some way to keep the output voltage under control.This is usually done by rolling off the output impedance at lowfrequencies, transferring back to voltage control. In Micron, thecharge control is implemented by a PID controller that acts tominimize the difference between the measured actuator voltageand that of a simulated ideal capacitor. The integral gain can-cels slowly varying current errors, while the proportional gaincompensates the feedback loop, resulting in a transfer to volt-age mode below 0.8 Hz (where the optical position feedback ishighly effective). The derivative gain damps manipulator reso-nances in a manner similar to [54].

M. Closing the Loop

To close the Micron position servo loop (see Fig. 15), thecomputed charge increment is used to determine the outputcurrent for the next cycle, giving a first-order-hold discrete-to-continuous-time conversion, which reduces the sample-rateharmonics sent to the actuators. During the next cycle, the re-sulting actual position is once again read by the optical tracker,closing the feedback loop. This feedback counteracts all effectsthat disturb the tip from the desired goal position: hand tremor,inverse kinematics error, and output loading.

N. System Characterization

From a user’s perspective, Micron’s performance comes downto how the tool tip moves when the handle is moved: whetherdesired motion is passed through and undesired motion is re-jected. No apparatus was available for generation of handpiecemotion with the necessary accuracy and bandwidth for systemcharacterization; therefore, we obtained equivalent frequencyand transient response results by perturbing the digital position

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206 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 23. High-frequency motion disturbance rejection (sensitivity) for bothcontrol tunings. “Delay only” is a theoretical limit. Inevitably disturbance ismagnified at high frequencies, but this is harmless because tremor disturbancedrops off above 10 Hz (see Fig. 2). Note linear frequency scale.

TABLE IV3-D POSITION TRACKING ERROR

signal in the running real-time system, creating the same actualtip motion that would have been generated by the simulatedhandle motion. The frequency responses vary depending on themanipulator mode excited, but the overall performance is lim-ited by the lowest resonance, which is lateral. For brevity, wepresent only lateral responses.

At low frequencies, the position servo loop has high gain;therefore, the closed-loop response from handle to tip is verysimilar to the simulation in Fig. 13. More interesting is the por-tion of the response above 4 Hz that is determined by the servoloop’s declining ability to reject the tremor disturbance. Fig. 23shows the frequency response in this disturbance-dominated re-gion, where tuning parameters (see Table III) become importantand the cancellation algorithm is irrelevant. From a control per-spective, the ability to resist disturbance is the sensitivity, andthe Bode integral theorem states that in a plot, such as Fig. 23,the areas between the curve and the 0-dB line are equal aboveand below the line. Feedback cannot resist disturbance at allfrequencies, but it can move the sensitivity to high frequencies,where it is less harmful. Fig. 2 shows a tremor disturbance peaknear 10 Hz, followed by a rapid drop-off. For tremor rejection,the greater attenuation of the underdamped tuning at 10 Hz is farmore important than its threefold magnification of nonexistent90-Hz disturbance. We confirmed this conclusion by measuringthe position servo tracking error in each tuning when disturbedby the same prerecorded tremor signal (see Table IV).

Another perspective on output sensitivity is given by the delayonly curve in Fig. 23. This is the frequency response of anidealized Micron-like system that measures the handle motionand actuates the tip to perfectly cancel this motion with thesame 3-ms delay as Micron. This involves no considerations offeedback at all—it is simply the destructive and constructiveinterferences as the frequency is varied of two sine waves that

Fig. 24. Open-loop Bode plots for both controller tunings. The underdampedtuning mainly increases the gain (reducing the phase margin).

have a fixed time offset. In the relevant band (<30 Hz), the servoloop implements a pure delay (as designed); therefore, the onlyway to reduce sensitivity is to reduce the delay time (or predictthe future disturbance).

Active stabilization inevitably introduces some noise into thetrue tip position because the negative feedback moves the tipto cancel out measurement noise. Although there is little actualdisturbance at frequencies with high sensitivity, any measure-ment noise is also magnified. The amplitude of this inducedtip noise is 1.6-μm rms (underdamped tuning) and 1.2-μm rms(critically damped) when measured with a fiber optic displace-ment sensor (Model D63, Philtec, Inc., Annapolis, MD). Thismotion is invisible in handheld operation because it is smallcompared with the residual tremor. This scalar measurementis not directly comparable with the measurement noise vectoramplitude in Section II-D, but is, approximately, the expectedmagnitude of this noise passing through the system bandwidth.

Fig. 24 shows the open-loop frequency response of the po-sition servo loop. The underdamped tuning increases the low-frequency gain, but at the cost of reducing the phase marginfrom 64◦ to 42◦. The corresponding closed-loop bandwidth (notshown) increases from 84 to 123 Hz, but with 5-dB gain peaking.

Fig. 25 shows Micron’s response to a 200-μm step. Thereis an initial transient, where the position servo loop works tocancel the disturbance. The remainder of the response is simplythe step response of the cancellation filter Q(s). The fH regionis in common to both curves and lasts about 300 ms. Note thatthe scaling ks region has a constant slope, rather than beinghorizontal. It was not certain a priori that users would toleratesuch a response, but we have found that this recentering actionis imperceptible in practice because the natural open-loop driftin hand position has a similar speed.

Fig. 26 shows the initial transient, which is determined by theresponse of the position servo loop. The spike to 200 μm is thedisturbance itself. With the underdamped tuning, the recoveryis followed by 70 μm of overshoot and ringing (correspondingto the negative attenuation at 90 Hz).

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Fig. 25. Tip motion caused by a 200-μm step in handle position, for both algo-rithms (underdamped tuning). The labels show the cancellation filter parametercontrolling each part of the response. The initial transient is the leading edge ofthe disturbance step; see Fig. 26 for details.

Fig. 26. Details of initial transient in response to handle position step. Thedisturbance is injected numerically, and therefore, the rise time is one sampleperiod. The critically damped tuning has hardly any overshoot but is slower inbringing the tip back to zero (less bandwidth).

III. EVALUATION

A. Experimental Design

To evaluate the true performance of Micron with a human inthe loop, a series of handheld positioning tests was performedby six subjects under a board-approved protocol. The subjectsincluded three who had no significant prior experience withmicromanipulation or use of a microscope (novice group, age25 ± 1) and three ophthalmic surgeons (surgeon group, age41 ± 21).

The experiment involved moving the tool tip above the sur-face of a laser-engraved rubber target. The subject viewed theworkspace through a 29× stereo surgical microscope (ZeissOPMI 1). The tool was a 27-gauge hypodermic needle (400-μmshaft diameter). An oblique lighting source was used to createa strong tool shadow depth cue, as is also present in retinalsurgery. Fig. 27 shows the target and tool tip as seen through themicroscope. The following tasks were performed.

1) Hold still: Hold the tip stationary above the lower rightcross for 30 s.

Fig. 27. Target and tool tip (hypodermic needle). The target is laser-engravedrubber; oblique lighting creates a tool shadow depth cue.

2) Circle trace: Trace continuously for 60 s around a 500-μmdiameter circle.

3) Move and hold: On a tone cue, move to the next cross(600 μm) and then hold there for 15 s. Repeat four times.This task resembles common procedures in microsurgery,allowing evaluation of Micron during (relatively) rapidmotion. The elapsed time for the move portion was alsorecorded.

In all tasks, the subjects were instructed to try to maintain thetool tip just above the target surface. Lifting the tool during themove portion of the move and hold task was permitted. Therewere also three test conditions: cancellation using the low-passand scaling algorithms (see Section II-F), and off, where can-cellation was disabled. This gave nine different task/conditioncombinations.

We expected that subjects’ performance would vary duringthe experiment, initially improving because of practice and thendropping because of fatigue. In order to prevent this nuisancevariable of task ordering from biasing the results, the order oftest conditions and tasks was systematically varied in a nestedLatin square design. Each experiment had three groups of ninetasks, which are separated by two 4-min rest periods. This gave27 tasks per experiment (approximately 45 min).

There is a clear performance difference between the test con-ditions; therefore, it was impossible for testing to be blind. Inorder to aid learning of the different operation modes, we toldthe subject before each task whether they would use “AlgorithmA” (scaling) or “Algorithm B” (low pass) or that cancellationwas off. To address the possibility that motivated subjects mightbias the results, we analyzed how handgrip motion changedunder the different conditions.

Data from the trials were logged at 200 Hz for analysis. Inorder to separate the perceptual depth error from the horizontalposition error, the analysis rotated the data so that the Z axiswas parallel to the microscope view. Because experiments withan earlier prototype of Micron exhibited a learning curve [38],each subject did the experiment six times to allow time for con-vergence. Data from sessions 4 to 6 were pooled, and ANOVAwas used to determine the statistical significance of the results.These experiments were conducted with an earlier version of theMicron controller that is described in Section II-K, which imple-mented a response intermediate between the critically dampedand underdamped responses in Table III and Section II-N.

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208 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 28. Learning curves for the 3-D max error (mean across all tasks), brokendown by the experience level. The flatter curve for surgeons suggests that theirexperience did generalize to the experimental tasks.

Fig. 29. Main effect of algorithm on the 3-D max error. The error bars are 95%confidence intervals. Cancellation significantly reduced error in comparisonwith the control condition (off).

B. Results

Fig. 28 gives an overview of the experimental results in theform of learning curves. The curves were similar across tasksand error metrics; therefore, we have shown the mean acrosstasks of the 3-D max error. Performance has largely convergedby the fourth experiment, and the final ranking, i.e., scaling <low-pass < off, is already established by the second session.The learning curve for the surgeons is much flatter, especially,in the off condition, suggesting that their existing skills didtransfer to this experiment. The low-pass algorithm requireslittle training, already showing benefit on the first day, while thescaling performance improves with experience.

Fig. 29 shows the effect on the 3-D max error of the experi-mental variable algorithm. The Tukey–Kramer procedure withthe error criterion p < 0.05 was used to generate 95% confidencebounds. In comparison with the control condition, i.e., off, theeffect of the two cancellation algorithms is both significant andsubstantial, with scaling superior to the low-pass algorithm.

The task and the subject experience level also had signif-icant effects on error; however, these results are unsurprisingand do not reveal anything about the performance of Micron.The reason for the introduction of multiple tasks was to evaluatewhether cancellation was more effective for some tasks than oth-ers. The high probability of no effect that ANOVA found for theinteraction between task and algorithm (p = 0.54) means thatthe relative benefit of the algorithms was similar across all threetasks. Likewise, the high probability of no effect on the interac-tion between experience and algorithm (p = 0.66) indicates thatthe benefit of cancellation was similar for novices and surgeons.A nested analysis of individual subjects within the groups re-vealed only one significant interaction: subject(experience) bytask (p = 0.001). That is, some subjects did significantly bet-ter on some tasks (independent of algorithm), but there was nodetectable variation by subject of the improvement because of

Fig. 30. Effect of cancellation on point clouds of the low-frequency positionerror during the “hold-still” task. With or without cancellation, the error is largerin the visual depth direction, but cancellation is more effective at reducing thehorizontal error than the depth error because the positioning accuracy ultimatelydepends on the eye–hand feedback. The user does not perceive this depth error,and therefore, the accuracy of the human-in-the-loop system becomes limitedby perception and not by tremor.

TABLE VCOMPARISON OF THE 3-D MAX ERROR BY GROUP (in micrometers)

TABLE VIEFFECT OF CANCELLATION BY ERROR METRIC

cancellation. Except where marked with “∗,” all of the reportedmeasures of both algorithms were found to be significantly dif-ferent from the off condition and from each other.

Table V shows the effect of cancellation broken down byexperience level. Both surgeons and novices benefited signif-icantly from scaling, but only surgeons showed a significantimprovement for low pass.

Table VI shows the relative performance of the algorithmsunder several error metrics. While the rms error is familiar toengineers, in surgical applications, the maximum error is likelyto be more important. Note that cancellation has a greater rela-tive effect on the maximum error than on the rms error.

1) Depth Perception Error: Although we do not expect the2-D error (excluding depth error) to be a superior predictorof surgical outcomes, the 2-D error reveals how depth per-ception affects task performance. The 3-D error is necessarilygreater than the 2-D error, but the expected increase because ofthe added DOF is

√3/2 = 1.22. The larger measured ratios of

3-D/2-D error show that vertical (depth) error is larger than thehorizontal error. Fig. 30 directly shows the increased magnitudeof the depth error compared with the horizontal error in the

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TABLE VIIOTHER EFFECTS OF CANCELLATION

hold-still task. This distribution is aligned within 5◦ of the mi-croscope sightline.

Although the stereo surgical microscope permits binoculardepth perception, this is a weak cue. To a considerable extent,microsurgeons rely on other cues, such as tool shadow andtissue deformation [55]. Therefore, these experiments used anoblique light source that gives a strong shadow cue and used adeformable rubber target. Because the depth error results from aperceptual limitation, it is not improved by cancellation; there-fore, its predominance increases when cancellation is on [seeFig. 30(b)].

2) Other Effects of Cancellation: A frequently expressedconcern about the Micron concept is that the tool motion causedby active cancellation might cause injury at the sclerotomy (thesurgical opening, where the tool passes inside the eye). Weexamined the mean across all trials of the 3-D maximum motionduring the hold-still task at both the tip and the sclerotomylocation and found that while motion is reduced by 44% at thetip, it is also reduced by 30% at the sclerotomy. Thus, Micron isless likely, not more likely, to damage the sclera than a traditionalinstrument. This finding that motion at the sclera is reduced bycancellation is inevitable. Kinematically, the tip is fixed duringcancellation, while the handle is free to move. This constraintthat the tip remains fixed also constrains the motion of otherpoints on the tool shaft (to a lesser degree).

Table VII shows that the move time for the move and holdtask increased with cancellation. It may be that subjects learnedthat, to get the best results with canceling, they had to movemore slowly. Scaling also makes it more natural to move slowlybecause it scales down speed.

As mentioned in Section III-A, the experimental design isnot blind; therefore, results are vulnerable to subject bias. Torule out this possibility, we analyzed the hand motion whencancellation was on and compared it with the motion when off.This was done by scoring the accuracy as described earlier, butusing the null tip position xw instead of the actual tip position.Table VII shows that hand motion increased with cancellation;however, this can be explained without supposing that subjectswere biased against the cancellation condition. Because Micronattenuates all hand motion, it reduces the gain of the visuomotorfeedback loop (see Fig. 4), impairing the ability of eye–handfeedback to stabilize the hand position. Tremor is reduced atthe tip, but not by as much as one might expect, given themeasured attenuation from handle to tip. The increase in handlemotion was not significant under the low-pass condition but wassignificant in the scaling condition.

3) Qualitative Results: Fig. 31 shows the effect of Micronwith the low-pass algorithm on magnitude of the 3-D posi-

Fig. 31. Effect of low-pass cancellation algorithm on tremor. Although the tiptracks the goal position quite well, the 1.5-Hz low-pass filter allows most of thetremor to pass through into the goal position.

Fig. 32. Effect of scaling cancellation algorithm on tremor. Low-frequencycomponents are now attenuated in the goal position, as well as at the tip.

tion error during a hold-still task. Although the high-frequency(≈10 Hz) shaking is nearly eliminated, the larger low-frequencymotion passes through unattenuated; therefore, the effect of can-cellation is modest. Even so, the filter introduces a fraction of asecond of lag, which destabilizes the eye–hand feedback loop,limiting the effectiveness of a low-pass filter alone. Fig. 32shows another hold-still task, where the scaling algorithm wasused. In this case, the tremor is larger, in part because of theeffect discussed earlier, yet the resulting tip motion is signif-icantly smaller because motion below 1.5 Hz is attenuated. Inboth Figs. 31 and 32, the tip position tracks the goal quite well,rejecting the tremor disturbance and canceling open-loop er-rors. Therefore, performance is limited primarily by the abilityof the goal filter to attenuate tremor and not by the active posi-tion stabilization feedback loop (see Section II-N and Tables IVand VI).

Fig. 33 shows the effect of the different algorithms on tip mo-tion during the circle tracing task. Accuracy is greatly improvedunder the scaling condition, although the invisible depth errormay be significant (see above).

IV. DISCUSSION

These results show the feasibility of the concept of an ac-tively stabilized handheld tool for tremor suppression—such a

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210 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Fig. 33. Effect of cancellation on 2-D tip motion. These are typical results from three different circle tracing tasks (approximately 15 s each circle).

system can give a statistically significant reduction in positionerror for both trained surgeons and nonsurgeons. The motionscaling cancellation algorithm gave a 46% reduction in the 3-Dmax error, while the improvement with low-pass cancellationwas also significant at 21%. The performance improvement wassimilar across all three tasks that were tested and all six subjects.

Error in depth perception is an issue in any micromanipulationwith handheld tools using a microscope, and it limits the benefitsof Micron in the experiments that are presented here. In future,the precision measurement intrinsic in Micron could be usedas part of a surgical navigation system to help the operatoraccurately control the depth of the tool tip.

The tracking system that is presented here has high accu-racy, high bandwidth, and measures both tip and handle motionwith the same sensor. Other position sensors could be used, of-fering their own advantages, such as relaxing the line-of-sightconstraints on tool motion and workspace layout.

An increased manipulator range of motion and a smaller hand-piece would both be beneficial. A manipulator design under de-velopment uses piezoelectric linear motors to improve the rangeof motion and size (with reduced force and slew rate).

This study has described Micron’s principles of operationand has experimentally demonstrated significant manipulationaccuracy improvements. The use of synthetic tasks has enabledprecise quantification by eliminating anatomic variability, butdistances the results from the ultimate medical application. Anaccuracy improvement may not always give improved clinicaloutcomes [56], but medical instruments and techniques coe-volve, creating more effective interventions. We have encour-aging preliminary results on the use of Micron on biologicaltissues [57] and the use of procedure-specific goal position com-putation [58]. Duplicates of the system that is described here arenow being evaluated in two other laboratories, and future workwith Micron will involve realistic surgical tasks.

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Robert A. MacLachlan (M’01) received the B.S. de-gree in applied mathematics from Carnegie MellonUniversity (CMU), Pittsburgh, PA, in 1987.

He has been a Research Software Developer andEngineer with CMU since 1983 and has been in-volved in electronic design since 1993. In 1999, hejoined the Robotics Institute, CMU, where he has de-signed and developed sensor and control hardwareand software for mobile robots and, currently, is in-volved in the development of intelligent medical in-struments with the Surgical Mechatronics Labora-

tory. His research interests include medical robotics, sensor design, signal pro-cessing, and control systems, with particular emphasis on exploiting the com-bination of sensitive measurements and effective data-interpretation algorithmsin order to enable the construction of novel mechatronic systems that solve thereal-world problems.

Brian C. Becker (S’05) received the B.S. degree incomputer engineering from the University of Cen-tral Florida, Orlando, and the M.S. degree in roboticsfrom Carnegie Mellon University, Pittsburgh, PA, in2007 and 2010, respectively. Since 2007, he has beenworking toward the Ph.D. degree in medical roboticswith the Robotics Institute, Carnegie Mellon Univer-sity.

His current research interests include computer vi-sion, control systems, and microsurgical instruments.

Jaime Cuevas Tabares received the B.S. degree inelectrical engineering from the University of Leon,Leon, Spain, and the M.S. degree in electrical engi-neering from the University of Valladolid, Valladolid,Spain, in 2007 and 2010, respectively.

Since 2011, he has been a Research Engineer withSociedad Europea de Analisis Diferencial de Movili-dad SL, Valladolid, working on electronic design forhigh sensitivity vapor analysis instruments.

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212 IEEE TRANSACTIONS ON ROBOTICS, VOL. 28, NO. 1, FEBRUARY 2012

Gregg W. Podnar (M’08) received the B.S. degree,self-defined, in 1976 from Carnegie Mellon Univer-sity (CMU), Pittsburgh, PA, where he has also donegraduate work in computer science.

He is currently a Program Manager with theRobotics Institute, CMU. He is a Principal in a com-pany that builds computer-based vision examinationequipment. He was a Visiting Fellow with the Min-erals Down Under Flagship, CSIRO, Australia; aVisiting Professor of computer science with JiangXiUniversity, China; a Research Associate with the En-

gineering Design Research Center, CMU; and a Research Fellow with the Studiofor Creative Inquiry, College of Fine Arts, CMU. He holds many U.S. and inter-national patents. He has authored or coauthored more than three dozen papers onrobotics, planetary mineral prospecting, ocean and surface water quality, aircraftskin inspection, predictive energy management for electric commuter vehicles,stereoscopic imaging, and engineering design. Over the past three decades ofwide-ranging research, he has developed many task-specific mobile robots andmanipulators; stereoscopic telepresence systems; and surgical instruments.

Louis A. Lobes, Jr., received the M.D. degree fromthe Medical College, Cornell University, New York,in 1970.

He has been a Clinical Associate Professorwith the Department of Ophthalmology, School ofMedicine, University of Pittsburgh, Pittsburgh, PA,since 1984, with clinical concentration on vitreo-retinal surgery, macular degeneration, and diabeticretinopathy. He has been Coinvestigator in an en-dophthalmitis vitrectomy study, age-related eye dis-ease study, submacular surgical trial, comparison of

age-related macular degeneration treatments trial, and studies that are fundedby National Institutes of Health. His main research interest includes the Micronrobotics project.

Dr. Lobes is a member of the Retina Society, the Macular Society, and theAmerican Academy of Ophthalmology.

Cameron N. Riviere (S’94–M’96–SM’10) receivedthe B.S. degrees in aerospace engineering and oceanengineering from the Virginia Polytechnic Instituteand State University, Blacksburg, in 1989 and thePh.D. degree in mechanical engineering from theJohns Hopkins University, Baltimore, MD, in 1995.

Since 1995, he has been with the Robotics In-stitute, Carnegie Mellon University, Pittsburgh, PA,where he is currently an Associate Research Pro-fessor and the Director of the Surgical Mechatron-ics Laboratory. His research interests include med-

ical robotics, control systems, signal processing, learning algorithms, andhuman–machine interfaces for biomedical applications, including surgery andrehabilitation.

Dr. Riviere is an Associate Editor with the Conference Editorial Boards of theIEEE Robotics and Automation and the Engineering in Medicine and BiologySocieties. He was the Guest Editor of the special issue on medical robotics inthePROCEEDINGS OF THE IEEE in 2006.

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