Integration of Predictive Feedforward and Sensory Feedback Signals for Online Control of Visually Guided Movement

doi: 10.1152/jn.91324.2008102:914-930, 2009. First published 27 May 2009;J Neurophysiol

V. Gritsenko, S. Yakovenko and J. F. KalaskaMovementFeedback Signals for Online Control of Visually Guided Integration of Predictive Feedforward and Sensory

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Integration of Predictive Feedforward and Sensory Feedback Signals forOnline Control of Visually Guided Movement

V. Gritsenko, S. Yakovenko, and J. F. KalaskaGroupe de Recherche sur le Systeme Nerveux Central, Departement de Physiologie, Universite de Montreal, Montreal, Quebec, Canada

Submitted 16 December 2008; accepted in final form 26 May 2009

Gritsenko V, Yakovenko S, Kalaska JF. Integration of predictivefeedforward and sensory feedback signals for online control of visu-ally guided movement. J Neurophysiol 102: 914–930, 2009. Firstpublished May 27, 2009; doi:10.1152/jn.91324.2008. Online controlof movement requires complex integration of predictive central feed-forward and peripheral sensory feedback signals. We studied the handtrajectories of human subjects pointing to visual targets that abruptlychanged locations by different amounts and modeled the mechanismof rapid online correction using a dynamic model of a two-joint limb.Small unperceived and large detected target displacements could beattributed to different origins (motor execution errors vs. environmen-tal changes, respectively) and compensated differently. However, thebehavioral findings indicate that the rapid feedback pathway is re-cruited regardless of the amplitude or subjective awareness of targetdisplacement and that the size of the earliest correction is alwaysproportional to the amplitude of the target displacement over thetested range of perturbations. The modeling findings suggest that therapid online corrections can be accomplished by superimposing adynamically appropriate error correction signal onto the outgoingfeedforward motor command to the original target. Furthermore, themodeling shows that the online correction mechanism must includecompensation for the dynamic mechanical properties of the limb andfor sensory delays in its error-correction pathway.

I N T R O D U C T I O N

The central goal of this study is to investigate the mecha-nisms of the online control of human reaching movements.One behavior that has provided a number of insights into theorganization of online motor control is the rapid initial adjust-ment of reach trajectories that occur in response to abruptchanges in target location immediately before or just after theonset of the reach (Day and Brown 2001; Day and Lyon 2000;Desmurget et al. 1999; Pelisson et al. 1986; Pisella et al. 2000;Prablanc and Martin 1992). The short-latency corrective re-sponses occur even when subjects are unaware of the targetdisplacement (Johnson and Haggard 2005; Pelisson et al. 1986;Pisella et al. 2000; Turrell et al. 1998) and are relativelyresistant to cognitive control (Castiello et al. 1991; Cressman etal. 2006; Day and Lyon 2000; Pisella et al. 2000; Rodriguez-Fornells et al. 2002), which suggests that it is an “automatic”correction process as distinct from a willful “voluntary” cor-rection. The short latency of trajectory correction suggests thatits mechanism involves a predictive efferent copy-based stateestimation process such as an internal forward model of futurelimb states (Cooke and Diggles 1984; Higgins and Angel 1970;Jaeger et al. 1979; Wolpert et al. 1995). Transcranial magneticstimulation (TMS) studies in neurologically normal subjects

and behavioral studies in optic ataxic patients have implicatedthe parietal lobe in this automatic correction mechanism (Bat-taglia-Mayer et al. 2001; Della-Maggiore et al. 2004; Desmur-get et al. 1999; Pisella et al. 2000; Rossetti et al. 2003; Tuniket al. 2005; van Donkelaarl et al. 2000).

This study focuses on two different aspects of the rapidonline correction mechanism that have not been studied indetail before. The first is how well the kinematics of the rapidcorrective response to an unpredictable change in the directionof the target from the starting location scales with the size ofthe directional change. The second concerns whether the cor-rective signal can be purely kinematic in nature or must insteadtake into account the dynamics of the limb. To address the firstquestion, we did a psychophysical study of reach trajectorycorrections in human subjects in response to target displace-ments. To address the second question, we did a modelingstudy to assess the ability of control circuits with differentcomputational architectures to replicate the reach trajectorykinematics observed in the human behavioral study.

No study to date has documented how closely the size of thetrajectory corrections scale with the amplitude of target direc-tion changes at different times after the target displacement.The scaling of trajectory corrections addresses the issue ofcredit assignment in motor control, i.e., to what degree themotor system attributes the origin of a sensed reaching error tointernal causes because of the subject’s own motor system or toexternal causes because of events in the world (Berniker andKording 2008; Kluzik et al. 2008; Malfait and Ostry 2004; Weiand Kording 2009). It is possible, for instance, that the mainfunction of the rapid automatic online correction mechanism isto correct for small performance errors that result from sto-chastic variability in the planning and execution of movements(“motor noise”; Gordon et al. 1995; Kording and Wolpert2006; Messier and Kalaska 1999; Stein et al. 2005; van Beerset al. 2004; Wolpert et al. 1995). As a result, there may be amaximum limit to the size of the trajectory correction thatcould be mediated by the rapid correction mechanism, beyondwhich the rapid corrective response would saturate. In contrast,the motor system might attribute large performance errors to anunexpected change in the environment and compensate forthem primarily by activation of a different corrective pathway,including longer-latency overt “voluntary” changes in motoroutput commands (Kluzik et al. 2008; Wei and Kording 2009).The hypothesized credit assignment dichotomy might result ina two-stage correction for large target displacements, involvingan early partial correction mediated by the saturated rapidonline correction mechanism, followed by a delayed “volun-tary” correction to compensate for the remainder of the dis-placement. This two-stage process would result in a sigmoidal

Address for reprint requests and other correspondence: V. Gritsenko, Dept.de Physiologie, Univ. de Montreal, C.P. 6128, Succursale Centre-ville, Mon-treal, Quebec H3C 3J7, Canada (E-mail: [email protected]).

J Neurophysiol 102: 914–930, 2009.First published May 27, 2009; doi:10.1152/jn.91324.2008.

914 0022-3077/09 $8.00 Copyright © 2009 The American Physiological Society www.jn.org


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relationship between target displacement size in opposite di-rections and the size of corrective trajectory deviations early inthe movement, which changes to a more linear relationshiplater in the movement. Alternatively, the rapid online correc-tion mechanism might not be activated by a large targetdisplacement, resulting in only a delayed correction at theusual voluntary visual reaction time.

This potential distinction is supported indirectly by differencesin learning, retention and generalization of adaptation to pertur-bations that the motor system might attribute to internal versusexternal origins, such as perturbations that are introduced gradu-ally and imperceptibly in small incremental steps versus abruptlyin one large step (Ingram et al. 2000; Kagerer et al. 1997; Kluziket al. 2008; Malfait and Ostry 2004) or that are in intrinsic versusextrinsic reference frames (Berniker and Kording 2008). Simi-larly, Wei and Kording (2009) showed that subjects made approx-imately linear trial-to-trial adaptive changes to reaching move-ments when they introduced small perturbations in the visualfeedback of final hand position, but that the adaptive responsebecame significantly nonlinear (saturated) for large feedback per-turbations. This suggested that the motor system tended to at-tribute small perturbations to its own performance and attemptedto adapt to the sensed error but tended to discount large infrequentperturbations as caused by an unpredictable external origin andtherefore irrelevant (Wei and Kording 2009).

We examined whether the rapid online correction of reachingerrors showed evidence of a similar two-stage credit-assignmentprocess by studying trajectory corrections evoked by target dis-placements that produced a larger range of directional errors thanused in most studies of automatic online corrections. We alsoassessed whether any possible transition point in the kinematics ofcorrective responses, i.e., nonlinear scaling of trajectory correc-tions with the amplitude of target displacements, might be coupledto the presence or absence of awareness of the occurrence of thetarget displacement.

In addition to studying the extent to which the rapid feedbackpathway can compensate for visuomotor errors of different sizes,in a separate experiment, we used computational modeling toinvestigate the nature of the corrective signal responsible for thiscompensation. The objective of this modeling study was not toexplain the findings of the behavioral study for small versus largetarget displacements but rather to assess the ability of differentcomputational architectures to produce the general patterns oftrajectory corrections. The idea that the neural control of limbmovements encompasses both feedforward motor commands andsensory feedback components has been around since before theturn of the 20th century (Mott and Sherrington 1895; Woodworth1899). Nevertheless, how these components are integrated toproduce a motor command to the muscles that results in anaccurate movement of the limb to a desired goal are still beingintensely debated (Bhushan and Shadmehr 1999; Desmurget andGrafton 2000; Todorov and Jordan 2002; Wolpert and Kawato1998).

Recent experimental findings indicate that the hand trajectorycorrections result from two overlapping signals: the feedforwardmotor command to the original target, which is available beforethe start of movement, and an error-corrective signal that takesinto account any changes in the target position after the start ofmovement. This is supported by evidence that the online correc-tion can be selectively suppressed without interfering with themovement to the original target location (Desmurget et al. 1999;

Pisella et al. 2000). Computational studies have further exploredthe organization of online control of arm movement by showingthat the corrective signal can be computed based on the kinematicdifference between the continuous estimates of target and limbstates based on afferent and efferent signals (Flash and Henis1991; Henis and Flash 1995; Hoff and Arbib 1993; Nijhof 2003).Other studies argue for the importance of an internal model thatcompensates for the complex dynamics of a multisegment limb(Desmurget and Grafton 2003; Sabes 2000; Wolpert and Kawato1998). Furthermore, several studies suggest that a common inter-nal model may be used to compensate for limb dynamics duringboth planning and execution of movement (Kurtzer et al. 2008;Lacquaniti and Soechting 1984; Soechting and Lacquaniti 1988;Wagner and Smith 2008).

However, no study has addressed the question of what is thesimplest necessary error correction signal for successful onlinecorrections for target displacements during reaching. For example,if the feedforward motor command to the original target compen-sates for limb dynamics, a simple correction signal proportional tothe kinematic hand-to-target direction error might be sufficient todeviate the reach trajectory toward the new target location. This ismade more plausible because the requisite trajectory correctionsin most studies of rapid online control are usually fairly small.Furthermore, similar combinations of a feedforward motor com-mand and kinematic error feedback is an effective and commonway to control robotic devices in engineering (Braunl 2003;Goodwin and Sin 1984). In most robotic devices, the discrepancybetween the desired and actual robot position (kinematic error) issimply scaled by a constant (gain) and added to the outgoing(feedforward) torque signal. We tested the feasibility of a physi-ologically plausible model that includes a feedforward/feedbackcontroller and a multisegment arm with complex, nonlinear dy-namic properties to reproduce the online correction performanceobserved in humans.

M E T H O D S

Task apparatus

The task apparatus consisted of a digitizing tablet to capture reachtrajectories, an oculometer to detect onsets of ocular saccades, and asuspended LCD monitor to display visual targets on a semisilvered mirrormounted horizontally between the subjects’ eyes and their hand (Fig. 1A).The digitizing tablet (GTCO CalComp, Columbia, MD; 0.915 � 0.608m; spatial resolution, 0.006 � 0.127 mm) captured the movement of astylus that the subjects held in their hand, over the surface of the tablet at100 Hz. Both the stylus and the subject’s arm were visible through thesemitransparent mirror at all times. The monitor displayed visual targets7 mm in diameter, which reflected from the mirror and appeared to be onthe surface of the tablet in the plane of the subject’s hand movements.Images on the monitor were produced by a Visual Stimulus Generator(VSG, Cambridge Research Systems, Rochester, UK) PC card, whichwas programmed using Matlab 7 (The Mathworks, Natick, MA) soft-ware. Eye movements were captured using a Skalar IRIS IR oculometer(Cambridge Research Systems) and sampled at 2 KHz by the VSG card.Both hand and eye movements were synchronized using the VSG internalclock and recorded for analysis offline.

Behavioral task

Eight right-handed human subjects (3 women, 5 men; mean age, 27yr) with no known neurological deficits and normal or corrected tonormal visual acuity participated in the study. They all gave informedconsent before their inclusion and were naïve to the objectives of the

915MECHANISM OF ONLINE CORRECTION

J Neurophysiol • VOL 102 • AUGUST 2009 • www.jn.org


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study. The study was approved by the Human Research EthicsCommittee of the Faculte de Medicine, Universite de Montreal, andwas carried out in accordance with the ethical standards set by theCommittee.

The experiment consisted of two data collection sessions on sepa-rate days. During the sessions each subject performed five sets of 64trials per day separated by short breaks, for a total of 320 trials perdaily session and 640 trials per subject for the two sessions. Each trialstarted with the subject placing the tablet stylus and fixating his/hergaze on a visual target displayed on the surface of the tablet along themidline of their visual field (T0; Fig. 1B). After a 2-s delay, T0disappeared and a new target appeared in one of the two locations in

the right visual hemifield at a 30 (T130) or 60° (T160) angle to thehorizontal axis (x-axis; Fig. 1B). Both T1 locations were 15 cm awayfrom the initial position, which corresponded to a 15° visual angle.The subjects were instructed to look at the T1 target and simulta-neously to move the stylus to it as quickly and accurately as theycould, by making a reaching movement in the plane of the tablet. Inthe beginning of the first session, subjects performed 20 practice trialswithout target jumps to familiarize themselves with the task.

In one half of the trials, the T1 target changed its location before themiddle of the ocular saccade (jump trials). Saccade onsets weredetected online from the oculometer signal with a velocity thresholdalgorithm. The algorithm determined when the eye-movement veloc-

A

D

F

E

B

G

CFIG. 1. Experimental paradigm and methodol-

ogy. A: schematic of the experimental setup.B: coordinate system and target locations relative tothe subject: T0, starting location, T130 and T160,initial target locations 30 and 60° away from the xaxis; T2�14, example of a jumped target locationshowing a 14° jump clockwise relative to the T1direction. C: timeline of events during a typical trial.Thick gray lines indicate times of target appear-ances, solid black lines show times of hand-move-ment related events, and dashed black lines indicatetimes of eye movement–related events. D andE: illustration of the method to detect the onset ofon-line correction. Thin arrows in D shows how theinstantaneous trajectory angle was calculated. Solidline indicates control trajectory; dashed line indi-cates trajectory with a target jump. The calculatedinstantaneous trajectory angle is plotted in E forboth trajectories, together with the difference be-tween the 2 (thin solid line). The width of the graybox represents the time period used to estimatebaseline variability in the difference trace; the hightof the box shows the 95% CI used to detect the onsetof on-line correction, defined as the 1st value out-side the CI. F and G: functions fitted to the relation-ship between the target jump amplitude and the tan-gential angle of trajectories. Absolute tangential angleswere used for fitting a quadratic function in G.

916 V. GRITSENKO, S. YAKOVENKO, AND J. F. KALASKA



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ity exceeded 5% of the mean peak saccade velocity, which wasdetermined from the baseline recordings done during the practicetrials. The target changed position on the screen between 5 and 17 msafter the saccade onset detection. The target jumped to one of eightlocations along the arc of 15 cm radius with angular increments of 3.5(T2�3.5), 7 (T2�7), 10.5 (T2�10.5), and 14° (T2�14), where thepositive direction of target jumps was counterclockwise (Fig. 1B).These angular displacements relative to the original T1 directioncorresponded to visual angle changes from 1 to 4°. The timeline ofevents in a typical trial is shown in Fig. 1C. Before performing thetask, the subjects were told that the targets could change position insome trials, and at the end of each trial, subjects reported if they sawthe target jump in that trial or not. The sequence of trials with andwithout jumps and the values of amplitude and direction of targetjumps were presented in a randomized block design. Each blockincluded a trial for each combination of T1 and T2 target displacementconditions (16 trials) and an equal number of control trials withouttarget jumps (8 trials for each T1). Two blocks of 32 trials wererepeated consecutively with randomly permuted trials within eachblock creating one set of 64 trials. Subjects performed 20 jump trialsper T2 target and 160 baseline no-jump trials per T1 target in totalacross the two daily sessions. The subjects could see the position oftheir hand at all times through the semisilvered mirror relative to thereflected image of the target locations.

Analysis

Data analysis was carried out offline using Matlab 7. The handdisplacement traces were low-pass filtered at 20 Hz, and each trial wasaligned to the onset of reaching movement, when hand velocitysurpassed 0.03 m/s. The onset of online correction was determinedusing a method based on the difference between the mean target-jumptrajectories and the mean baseline trajectory (without target jumps) foreach subject in each condition (Fig. 1, D and E). First, tangential angle(�) of each trajectory was calculated using the formula � � arctan(�y/�x), where �x and �y are derivatives of the horizontal and verticalcomponents of mean hand trajectory at each 10-ms time step (Fig.1E). Second, the tangential angle of the baseline trajectory wassubtracted from that of the target-jump trajectory. Third, the 95% CIwas determined using a t-test of the baseline difference values in thefirst 100 ms after the start of movement before the earliest onlinecorrection is expected (Fig. 1E). Last, the onset of online correctionwas defined as the first value of the difference trace outside the CIafter the initial 100-ms period. Additional constraint on onset detec-tion was that the subsequent values of the angular difference trace hadto be outside the confidence interval for �80 ms. This analysis wasalso performed on trajectories aligned to the time of target jump, andresults were the same as those reported from trajectories aligned to theonset of movement (data not shown). Statistical analysis of trajectorycorrection onsets was performed using a repeated-measures ANOVAwith two main factors, initial target location (2 levels) and signedtarget jump amplitude (8 levels) using SYSTAT 11 (SYSTAT Soft-ware, San Jose, CA). When the sphericity assumption of ANOVA wasviolated, the Greenhouse-Geisser correction was used to estimate theP value.

Ideally, one would like to be able to detect the onset of thetrajectory corrections on a trial-to-trial basis. We initially attempted touse the correction-onset detection algorithm on single-trial basis.However, we found that the high variability of the moment-to-moment kinematic data for single trials reduced the sensitivity of thealgorithm to detect the onset of a trajectory correction, yielding muchlonger onset times on average than those detected by the methoddescribed above and also considerable scatter of onset times withinand across task conditions and subjects. Furthermore, the single-trialmethod was even less sensitive to small deviations during small targetjumps than to larger deviations during larger target jumps because thesmaller expected trajectory corrections were even more difficult to

detect in the noisy data traces (data not shown). As a result, we choseto present the analyses based on the mean trajectories as an acceptablecompromise.

To determine whether the amount of online correction was linearlyrelated to the amplitude of the target jump, we used tangential anglevalues of hand trajectories. We fitted a linear regression between thetangential angles and the amplitude of the target jump at every 10-mstime step after hand movement onset. The linear function was y(x) �ax � c, where y is the angle of trajectories with target jumps ofdifferent amplitudes taken at the same time after the onset of move-ment; x is the amplitude of the target jump; and a and b are constants.Furthermore, for data from individual subjects and the compoundmeans a comparison was made between linear, quadratic, and sigmoi-dal fits to the tangential angles taken at two instances: when the handreached peak velocity and when the hand decelerated to half of peakvelocity. The sigmoidal function used was y(x) � a/(1 � e�bx) � c,where y and x are the same as described above; a, b, and c areconstants; and e is exponent. The quadratic function used was y(x) �ax2 � b, where y is the absolute angle of trajectories with target jumpsof different amplitudes taken at the same time after the onset ofmovement; x is the same as described above; a and b are constants.Fitting was accomplished with the least-squares method, and good-ness of fit of the sigmoidal, quadratic, and linear functions wascompared for corresponding time periods using R2 values. A signif-icantly better fit to a sigmoidal function would indicate that the sizeof the trajectory correction saturated for larger target displace-ments in the two opposite directions while scaling linearly with thesize of smaller displacements in both directions (Fig. 1F). Asignificantly better fit to a quadratic function would indicate thattrajectory corrections scaled nonlinearly with the amplitude of thetarget jumps (Fig. 1G).

Model

The model arm comprising two segments connected with tworotational joints was built using Simulink and SimMechanics tool-boxes of MatLab (Fig. 2A). Segments were modeled as cylinders of 30cm length, 3 cm radius, and 2.5 kg mass each (Winter 1990). Thestarting posture of the virtual arm corresponded to a 60° shoulderangle (relative to the horizontal x-axis) and a 120° elbow angle(relative to the previous segment; Fig. 2A). Viscous resistance ofjoints modeled the intrinsic velocity-dependent property of musclesacting around the joints. The value of viscosity B � 0.2 Nms/rad waschosen within reported physiological values of 0.14 and 0.26 Nms/radin human subjects (Bennett 1993; Selen et al. 2006).

The arm controller was modeled as the sum of a feedforward motorcommand and an online correction signal, where the correction signalwith a constant gain (G) was superimposed on the feedforwardcommand to move to the initial target T1. The online correction signalcomprised a directional error between target location and current armstate. The purpose of this model was to infer the nature of thecorrective signals for the online correction mechanism. Consequently,the model was not designed to study such phenomena as multisensoryintegration or the effect of noise and uncertainty in sensory signals ormotor output commands. Therefore for simplicity, the model includedtwo feedback signals: target location and arm state. The modelassumed that they are accurate and they arrived at the central onlinecorrection circuitry at the minimal latencies reported in the literature.Also importantly, for the sake of simplicity, these feedback signals are“lumped” signals that are an amalgam of all possible sources ofinformation about target location and arm state. For instance, thetarget position signal can include both accurate retinal feedback aboutchanges in target position whether they are perceived or not, andfurther refinements of estimates of target location that can be calcu-lated from efferent copies of the saccade motor command to the initialtarget location and any subsequent corrective saccades.




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The target position feedback delay in the model (�v) was set at 80ms (Fig. 2B), which is based on the minimum time it takes to observecortical responses evoked by a novel target position before saccade orarm movement planning and execution reported for primates (Cisekand Kalaska 2005; Crammond and Kalaska 2000; Schall and Bichot1998). The total loop delay for this pathway was set to 140 ms, equalto the sum of descending delay (�d � 60 ms), which includedexcitation-contraction coupling time � 20 ms, and target positionfeedback delay (�v). Because we assume the minimal latency foraccurate feedback of target location, our model probably has anaccurate estimate of the new target location sooner than any re-estimate that can be derived from an efference copy of the correctivesaccade. We chose the shortest possible realistic value for the targetposition signal to provide the optimal conditions for the feedbackcontroller to work. Choosing a longer delay would only worsen theperformance.

Similarly, the arm state feedback signal can be considered as anamalgam of proprioceptive and visual feedback signals about limbposition and movement (Hillis et al. 2002; Rossetti et al. 1995; Soberand Sabes 2003; van Beers et al. 1996). The total loop delay was setto 100 ms, equal to the sum of descending delay (�d � 60 ms), whichincluded excitation-contraction coupling time � 20 ms and proprio-ceptive feedback delay (�p � 40 ms; Fig. 2B). Similar minimumdelays in response to kinesthetic stimuli were reported for humansubjects (Flanders and Cordo 1989; Jeannerod 1988). We used theshortest afferent delay for arm state feedback (proprioception ratherthan vision) to observe the best possible performance of a feedbackcontroller.

The feedforward motor program in the model consisted of jointtorques (�T1; Fig. 2B) necessary to move the endpoint of the virtualarm along the mean control trajectory of human subjects for baselinemovements to the T1 target (Fig. 1D, solid line). Without targetjumps, the feedforward motor program brought the model endpoint tothe target within 390 ms after the start of movement, which was equalto the mean duration of the unperturbed reaching movements of thehuman subjects. We used the mean subject trajectory to one of thetargets, T160, for constructing the feedforward movement to both T1targets. This removed the confounding differences between feedfor-ward trajectories to different targets and left only the differencesbetween trajectories caused by error correction. To simulate baselinemovements to the T130 target, the horizontal and vertical componentsof the endpoint trajectory toward the T160 target were scaled to end onthe T130 target. However, all simulations were also repeated with thesubject’s mean T130 trajectory with the same results. To generatefeedforward joint torques, the endpoint trajectories for the two move-ment directions were recalculated into the appropriate joint kinematicsfollowed by joint torques using the inverse dynamic model (IDM) ofthe limb in SimMechanics. The IDM included a virtual arm identicalto the plant (Fig. 2, A and B), which it used to predict joint torquesnecessary to produce any desired movement.

We studied the performance of four controllers. The first twocontrollers (Kin1 and Kin2) included kinematic error correction (Fig.2B, both switches a and b are in position 1). The torque �j that wasdriving the dynamic model of the limb consisted of the followingcomponents

�j � �jT1 � G �pj

err � B ��j (1)

where j is joint index (elbow or shoulder); �jT1 is feedforward torque

to the T1 target (main target before jump); G is gain constant; pjerr is

kinematic error in the joint-based coordinate system; B is viscosityconstant; and �j is joint angular velocity.

The correction signal in the Kin1 controller was proportional to theerror between the desired and sensed endpoint trajectories, convertedinto the joint-based reference frame (perr in Fig. 2, B and C). The errorin the joint-based coordinate system (pj

err) was calculated from theendpoint error using a kinematic transformation in SimMechanics.The mediolateral (px

err) and anterio-posterior (pyerr) components of

the endpoint error were calculated as follows

pxerr � �t � �d � �p� � cosT�t � �v�� cosEP�t � �d � �p��

(2)

pyerr � �t � �d � �p� � sinT�t � �v�� sinEP�t � �d � �p��

(3)

where is endpoint distance away from the starting position; �d isdescending delay; �p is proprioceptive delay; T is target angularposition (angle of T1 or T2 target relative to horizontal); �v is visualdelay; and EP is endpoint angular position (angle of endpoint relativeto horizontal).

The endpoint error vector pointed in the direction of the target jumpwith its amplitude proportional to the change in the direction ofmovement (perr in Fig. 2C). This type of error correction was inspiredby the idea of vectorial control of movement, in which amplitude anddirection are separately controlled variables (Gordon et al. 1994;Rossetti et al. 1995; Sarlegna et al. 2003).

The Kin2 controller included a kinematic error that was calculatedas in Kin1 (Eqs. 2 and 3). However, instead of the delayed peripheralarm-state feedback used in Kin1, the correction in Kin2 relied on acentrally estimated arm state signal that led the actual movement bythe value of �d. This simulated an internal prediction of sensed armposition �d � �p into the future by a forward dynamic model (FDM)based on the efference copy of the outgoing motor command (Fig. 2B,switch a is in position 2, switch b is in position 1). In theory, the FDM

Elbow

Shoulder 60o

120oA

DC

τx

τy

τT1

τerr

T130

T2-14

T0T0

py

pEPθT

px

T130

T2-14perr

θEP

B

+ PlantτT1 pEP

perrerr

FDMτ* pEP*

θT

τerrIDM

+-

1

2

1

2

a

b

τ

FIG. 2. Model summary. A: structure and starting configuration of themodel arm. B: control circuit diagram. Plant, model arm; FDM, forwarddynamic model; IDM, inverse dynamic model; err, error feedback; G, feed-back gain; �T1, torque toward the T1 target; �*, efference copy of the outgoingmotor command; T, angular direction of the target; pEP, pEP*, position of thecurrent sensed and predicted hand position, respectively; �err, perr, torque andposition error feedback, respectively; �d, �p, and �v, descending, propriocep-tive, and visual delays, respectively. Controller Kin1 is implemented whenboth switches a and b are in position 1; controller Kin2 is implemented whena is 2, and b is 1; controller Dyn1 is implemented when a is 1, and b is 2;controller Dyn2 is implemented when both a and b are 2. C: schematic of theperr calculations for controllers Kin1 and Kin2. D: schematic of the �err

calculations for controllers Dyn1 and Dyn2.




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includes a model of the plant (Fig. 2, A and B), which it uses to predictmovement that would result from any given torque. A practicalimplementation of this in our model is to set the delays to 0 (�d ��p � 0 in the Eqs. 2 and 3), thus obtaining predicted arm state valuesfor error correction.

The other two controllers, Dyn1 and Dyn2, were in essence theKin1 and Kin2 controllers with the IDM added to their error correc-tion pathways, which compensated for limb dynamics. For thesecontrollers the driving torque �j was

�j � �jT1 � G ��j

err � B ��j (4)

where �jerr is joint torque error calculated by IDM from pj

err and itsderivatives. The Dyn1 controller used the IDM to convert the delayedsensed kinematic error, calculated as in Kin1, into joint torques (Fig.2, B and D, switch a is in position 1, switch b is in position 2). TheDyn2 controller, in contrast, used the predicted arm-state signal(calculated the same way as in Kin2) as the input signal to the IDM(Fig. 2B, both switches a and b are in position 2). The IDM in Fig. 2Bcould be the same putative internal inverse-dynamics model thatgenerated the feedforward torque output signal or a separate IDM thatis a component of the online correction mechanism.

The gain (G; Fig. 2B) of the correction signal was systematically variedto find the best fits of model arm movements to human trajectories. Therange for Kin1 and Kin2 controllers was 0.05–0.5, in 0.05 increments;the range for Dyn1 and Dyn2 controllers was 0.005–0.05, in 0.005increments. The difference between the gain values of the kinematic anddynamic controllers is because of the differences in units of position andtorque used for correction in the Kin and Dyn controllers, respectively.

Model and human trajectories were compared across controllers withdifferent gains and all other parameters (feedback delays and viscosity)being equal to determine the best performance for each controller. Threemeasures were used to evaluate the similarity between the simulated andhuman trajectories: velocity error, onset error, and endpoint error. Thesemeasures were relatively independent with correlation coefficients be-tween them being 0.5. The velocity error was calculated by summingacross time the perpendicular distances between model and humanendpoint velocity values for each T2 location. The onset error wascalculated as the difference between the onsets of online correction inhuman and simulated trajectories. The onset of correction in the modeltrajectories were calculated by measuring the human tangential angles atthe onsets of online correction described above (see Analysis) and findingthe times at which the model tangential angles reached the same values.The endpoint error was the difference between the human and simulatedendpoint errors. The human endpoint errors were calculated as distancesbetween the target positions and the corresponding human trajectories atthe end of movement. The endpoint errors of the simulated trajectorieswere calculated the same way at times equal to the mean durations ofhuman control and target-jump trajectories. The best performance of thefour controllers was defined as the smallest sum of the squared normal-ized error measures described above. The errors were normalized to theirmeans for equal contribution to the sum. Combinations of other measuresand different combinations of the same three measures were also testedfor comparing performance of the four models to human performance.All measure combinations selected the same two controllers to be the bestand the worst performers, but the distinction between the other twocontrollers depended more on the particular choice of measures.

R E S U L T S

Human behavioral performance

Visually guided movements were studied in a double-stepparadigm, which required subjects (n � 8) to both look andpoint to visual targets projected in the plane of their movement(Fig. 1A). Subjects responded to the appearance of a visualtarget, T1, in one of two locations (T130 or T160) 15 cm away

from the start location. Subjects first initiated an ocular saccadeat 204 � 40 (SD) ms latency and later moved their hand towardthe T1 target 264 � 35 ms after its appearance (Fig. 1C;Supplementary Table S1).1 The arm movement was carried outat the subject’s preferred speed, and the peak velocity was onaverage 0.75 � 0.2 m/s across subjects. Characteristic exam-ples of hand trajectories are shown from a subject with meanpeak velocities of 0.63 � 0.09 and 0.70 � 0.09 m/s averagedacross trials to T160 and T130, respectively (Fig. 3A) and froma different subject with mean peak velocities of 0.94 � 0.26and 1.07 � 0.27 m/s averaged across baseline trials to T160 andT130, respectively (Fig. 3B).

In one half of the trials, T1 did not change position (baselinetrials). In the other half, the target jumped to one of eight otherlocations centered on T1 (T2�3.5, T2�7, T2�10.5, T2�14; Fig.3). This corresponded to target displacements ranging from 1to 4° visual angle. The jump was triggered by the onset of thesubject’s ocular saccade and occurred on average 50 ms beforethe start of arm movement, during the period of saccadicsuppression of vision (Bridgeman et al. 1975; Mackay 1970;Matin 1974). The target jump triggered a corrective saccadedirected toward the new target location, which occurred onaverage 233 � 76 ms after the target jump or 208 � 77 msafter the termination of the first saccade (Supplementary TableS1). Furthermore, all subjects responded to the target jumps byinitially following their baseline reach trajectory toward the T1target and later deviating the trajectory toward the T2 target(Fig. 3). Most subjects corrected their trajectories graduallywith one smoothly curved movement whose deviation from thebaseline began about half way to T1 and scaled with the size ofthe target jump from its onset (Fig. 3C). However, the twofastest-moving subjects showed relatively small trajectory de-viations until their hand was close to T1 and made a sharpchange in movement direction (Fig. 3D). This was not causedby delayed corrective responses or inattention to the targetjumps because the time of onset of the trajectory deviationswas similar in all subjects (Fig. 3, C and D). This suggests thatthe fast-moving subjects had nearly reached T1 before theon-line correction mechanism could influence the reachingtrajectories, possibly compounded by the lower effectivenessof the error feedback pathway in overcoming the higher mo-mentum of the fast-moving arm. This interpretation is exploredfurther with modeling.

Consistent with earlier studies (Blouin et al. 1995; Bridge-man et al. 1975; Niemeier et al. 2003), the amplitude of thetarget jumps determined whether the subjects were aware ofthe perturbation. Subjects’ reports at the end of each trialshowed that small target jumps went unperceived in most trialscaused by saccadic suppression, whereas most large targetjumps were noticed and reported by the subjects (Fig. 4A).Subjects also reported a false positive rate of 6% perceivedjumps in baseline trials when none had occurred (Fig. 4A). Themean trajectory path for trials with unreported target displace-ments tended to be displaced further away from the unper-turbed trajectory to T1 and appeared to be slightly less curvedthan trials in which the displacement was detected and reportedby the subjects (Supplementary Fig. S1A). However, for thesmaller target displacements the mean paths for the unreported-displacement trials were within the confidence intervals of the

1 The online version of this article contains supplemental data.




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trajectories in the reported-displacement trials (SupplementaryFig. S1B). In contrast, for the largest two displacements, themean paths of the few unreported-displacement trials clearlylay outside of the CI of the majority of reported-displacementtrials for part of their path, and there was even some indicationthat the trajectories lay outside of the usual range of trajectoriesdirected at T1 from the onset of the reaching movements(Supplementary Fig. S1A).

On average, the trajectory corrections started at the sametime regardless of the amplitude of the target jump and theaccompanying changes in overall degree of perceptual aware-ness of the displacements (Figs. 3, C and D, and 4B). Note thatthe onset of trajectory corrections was calculated relative to theonset of hand movement, whereas the target jump was trig-gered on average 50 ms before the onset of hand movement(Fig. 1C). Statistical analysis of mean trajectory-correctiononset times using repeated-measures ANOVA with main fac-tors initial target position (T1 factor with 2 levels) and signedtarget jump amplitude (T2 factor with 8 levels) found nosignificant differences between the onset values (T1 factor:F � 0.22, P � 0.65; T2 factor: F � 2.31, P � 0.12; interactionbetween factors: F � 0.29, P � 0.77). Therefore these resultssuggest that early trajectory corrections begin at about the sametime regardless of both the size of the jump (at least down to3.5° reach direction changes) and the level of conscious aware-ness of the target jump by the subjects. Trial-by-trial analysisyielded essentially the same results (data not shown).

Both angular and perpendicular linear deviations betweenthe jump-trial trajectories and the baseline trajectories, aver-aged across both movement and target jump directions andacross subjects, gradually increased with the amplitude of thetarget jump (Fig. 5, A and B). When the angular and perpen-dicular deviations for each target-jump amplitude were nor-malized to their maximal deviations at 0.48 s after the start ofmovement, all traces closely overlapped (Supplementary Fig.S2). This further supports our conclusion that trajectory cor-rections for all target jumps started at the same time and scaledlinearly with the amplitude of the target direction displacementthroughout the duration of the corrective response. The amountof scaling of trajectory deviations was estimated by fitting alinear regression between the amplitude of the target jump andthe tangential angles of jump-trial trajectories at different timesduring movement. The angle of the fitted linear regression lineincreased gradually following the target jump so that by thetime the hand reached peak velocity the trajectory correctionswere already scaled proportionally to the amplitude of thetarget jump (Fig. 5C). The regressions shown in Fig. 5C werehighly statistically significant for trajectory deviations at andfollowing peak velocity (R2 � 0.984 and 0.964 for trajectoryangles at 165 ms for T160 and T130, respectively, R2 � 0.998and 0.996 for trajectory angles at 290 ms for T160 and T130,respectively, P 0.01 in all cases). However, no significanttrajectory deviations were observed before peak velocity andconsequently regressions were insignificant (R2 � 0.176 and

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0.256, P � 0.65 and 0.51 for trajectory angles at 64 ms forT160 and T130, respectively). Residuals of these linear fitsshowed no obvious pattern and were of similar amplitudeacross the regression slopes (Fig. 5D), which indicates thatlinear regression is an appropriate fit for the trajectory-devia-tion data. To further test the linearity of error correction wecompared the quality of linear, quadratic, and sigmoidal fits tothe scaling of individual-subject trajectories at and followingpeak velocity (Fig. 6, A and B). Better sigmoidal fit than alinear fit would indicate a saturation of error correction at largetarget jumps in the two opposite directions (Fig. 1F), whereasbetter quadratic fit would indicate a nonlinear scaling of tra-jectory corrections with the target jumps (Fig. 1G). However,linear fits explained a large percentage of the variance intrajectory deviations at peak velocity in six of eight subjects(Fig. 6A; R2 for subjects 1–8 � 0.72, 0.57, 0.95, 0.97, 0.91,0.99, 0.98, and 0.01, respectively); the same was true in allsubjects for trajectory deviations 125 ms after peak velocity(Fig. 6B; R2 for subjects 1–8 � 0.99, 0.95, 0.98, 0.98, 0.996,0.99, 0.998, and 0.88, respectively). Fitting a sigmoidal func-tion increased the amount of explained variance by 5% com-

pared with linear fits for trajectory deviations at peak velocity.However, this increase was driven by only two of eightsubjects, whose trajectory deviations were fitted better withsigmoidal compared with linear fits (12 and 9% increases inexplained variance for subjects 2 and 5, respectively). How-ever, this difference all but disappeared 125 ms later, wheresigmoidal fits of trajectory deviations increased the explainedvariance by only 1% over the linear fits. Fitting a quadraticfunction decreased the amount of explained variance comparedwith linear fits by �43 and �23% for trajectory deviations atand following peak velocity, respectively. The comparison ofsigmoidal, quadratic, and linear fits of the mean trajectorydeviations shown in Fig. 5C yielded similar results (linear fitR2 � 0.968, 0.960, 0.998, 0.995, quadratic fit; R2 � 0.655,0.478, 0.886, 0.852; sigmoidal fit R2 � 0.985, 0.999, 0.999,0.996 for T160 at 165 ms, T130 at 165 ms, T160 at 290 ms, andT130 at 290 ms, respectively). This amounts to the meandifference in explained variance between the linear and sig-moidal fits of 3 and 0.1% for trajectory deviations at andfollowing peak velocity. The mean difference in explainedvariance between the linear and quadratic fits is �41 and�13% for trajectory deviations at and following peak velocity.Thus this analysis indicates that most subjects showed essen-tially linear scaling of trajectory adjustments with the ampli-tude of the target jump. Regression on a sigmoidal function,consistent with saturation of error corrections for large targetdisplacements, did not account for a significantly greateramount of the variance of the performance overall for mostsubjects at any time during the reaching movements.

When linear regressions were fitted to trajectory deviationsin 10-ms steps from the onset of hand movement (Fig. 6C), theangle of the regression line was statistically significantly dif-ferent from zero starting at 123 � 24 ms (averaged acrosssubjects) after the start of movement. The data from individualsubjects also show that the temporal evolution of trajectorycorrections was scaled to the duration or peak velocity of eachsubject’s movement, so that corrections were always com-pleted just as the hand arrived at the target (Fig. 6E).

These results show that the trajectory correction was pro-portional to the amplitude of the target jump from its onset,linear across the entire tested range of target jump amplitudes,and scaled to the speed of movement of each subject. Further-more, there was no evidence of an early correction phase thatsaturated for large target jumps, followed by a later correctionthat scaled for the entire range of tested target displacements,which would be consistent with a two-stage online correctionprocess. This suggests that a single corrective mechanism thatis proportional to error amplitude may underlie online correc-tion for target jumps in this study. Furthermore, the observedlinear relationship between the amplitude of the target jumpand trajectory correction suggests a constant gain of errorfeedback in the corrective mechanism.

Modeling studies

Assuming a one-stage proportional correction mechanism assuggested by the human performance in the target-displace-ment study, we next assessed the ability of four simple controlcircuits with different types of error feedback and motorcommand corrective signals to replicate the kinematics of theonline corrections. Two general types of error correction path-

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ways were tested: kinematic correction (controllers Kin1 andKin2) and dynamic correction (controllers Dyn1 and Dyn2)(Fig. 2). Controller Kin1 relied on the kinematic error betweenthe desired and sensed direction of reach movement toward thetarget. Controller Kin2 calculated the error signal the same wayas Kin1, but instead of the delayed peripheral feedback-medi-ated estimate of arm state, the FDM was used to predict reachdirection based on an efference copy of the outgoing motorcommand. The other type of error correction circuit simulatedhere included an IDM, which transformed the kinematic direc-tional error into the corrective joint torques appropriate for thedynamics of the virtual arm. The internal IDM of the Dyncontrollers could be the same putative IDM that calculated �T1

or could be a separate internal model that is integral to theonline correction mechanism. The kinematic error before itstransformation by the IDM in the Dyn1 and Dyn2 controllerswas calculated the same way as in the Kin1 and Kin2 control-lers, respectively.

The best performance of the four controllers is shown inFigs. 7–9. The feedback delays were the same across control-lers, but the gains of the error signal were chosen so that themodels generated trajectories that were the closest to those ofhuman subjects for movements toward the T160 target (Fig. 7).All controllers drove the virtual arm with gradually deviatingtrajectories that scaled with the target jump amplitude (Fig. 8).However, there were large differences in the success of trajec-tory corrections for the target jumps by different types ofcontrollers (Supplementary Table S2).

The Kin1 controller with a delayed kinematic error signalcan accomplish trajectory corrections during very slow move-ments (Supplementary Fig. S3). However, during movementsat the speeds performed by the subjects, the Kin1 controllerproduced asymmetric trajectory deviations that were hypomet-

ric for clockwise target jumps and hypermetric for counter-clockwise target jumps (Fig. 7B). Choosing a smaller or alarger gain of error signal decreased or increased, respectively,the amount of deviation at any given time between the jump-trial trajectories, but did not appreciably change the under-shoot/overshoot pattern of corrections. Furthermore, the over-all fit between the model and human trajectories was poor(Figs. 8A and 9, A and B; Supplementary Table S2). Thisshows that a simple delayed kinematic error correction mech-anism is insufficient for online correction for target jumps andproduces trajectories that are very dissimilar to trajectoriesobserved in humans.

The failure of the Kin1 controller was clearly movementspeed dependent, which may indicate that the delay of the armstate estimation based only on peripheral afferent feedbackcaused the error signal to be too delayed to correctly adjust theongoing movement at the movement speeds performed by thesubjects. Compensation for the delay by the FDM in the Kin2controller slightly improved the performance of the simulation(Figs. 7C and 8B; Supplementary Table S2). However, theKin2 controller still produced asymmetric trajectory correc-tions with inappropriate velocities (Fig. 9C) so that the end-point trajectory did not come close to the targets at the meanmovement time of human subjects. Note, that the illustratedtrajectories only show the first 500 ms of model performance.When the model was allowed to run longer, it could eventuallybring the endpoint to the target after a few terminal oscillations(Supplementary Fig. S4), provided that the gain of the error-correction pathway was not too high to cause instability.

In contrast, the Dyn1 and Dyn2 controllers produced muchmore symmetric trajectory corrections (Figs. 7, D and E, 8, Cand D). The Dyn1 controller largely eliminated the targetovershoots and undershoots evident in the Kin1 and Kin2

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models because the IDM compensated for the interactiontorques produced by the error-driven path deviations, but stillproduced trajectories with hypermetric deviations because ofthe delayed arm state estimation used for the error calculation(Figs. 8, C and D, and 9; Supplementary Table S2). The bestperformance was achieved by the Dyn2 controller, which used

the internal forward model-based predicted arm state estimateto calculate the kinematic error and passed the error signalthrough an IDM to calculate the additive joint torque signalnecessary to implement the correction while simultaneouslycompensating for limb dynamics.

The Dyn2 controller can also simulate the differences inperformance of the individual subjects illustrated in Fig. 3. Weused the same model parameters that produced the best fit tothe mean trajectories (Fig. 7E), but scaled the feedforwardtorque command to produce movements to the T1 target withthe same peak velocities as that of the two subjects in Fig. 3(Fig. 10). The peak velocities of baseline movements to theT160 target in subjects shown in Fig. 3, A and B, were 0.63 �0.09 and 0.94 � 0.26 m/s, respectively, whereas the peakvelocities of the model arm produced by the Dyn2 controllerwith scaled �T1 in Fig. 10, A and B, were 0.62 and 0.95 m/s,respectively. Both trajectory shapes and temporal evolution ofsubject’s movements were reasonably well matched by themodel with the same values of gain, viscosity, and delays, butwith different velocity of the feedforward motor command.This simulation indicates that the differences in the trajectoriesof the two subjects in Fig. 3, C and D, were explained primarilyby the kinematics and dynamics of the more rapid movementsof the subject in Fig. 3D and not because of differences in thetiming or gain of the rapid on-line correction mechanism.

In summary, modeling results of this study show that a motorcontroller that sums a feedforward motor command with an errorcorrection signal is capable of rapidly correcting for unexpectedtarget displacements. The best performance was obtained with acontroller circuit that used a forward model to compensate forafferent delays in arm state estimation and an inverse-dynamicsmodel to account for limb dynamics to calculate the error correc-tion signal. This controller produced responses of a simple armmodel that closely approximated the performance of human sub-jects as they correct ongoing movements for target displacements.

D I S C U S S I O N

This study yielded two main findings. First, we found noevidence of a hypothesized change in the scaling of the short-latency corrections for small versus large target displacements thatwould be consistent with a two-stage mechanism of online cor-rection. Thus we found no evidence in the moment-to-momentkinematics of the reach trajectories of a credit-assignment processthat influenced how the motor system responded to random targetdisplacements of different sizes. However, this does not precludethe possibility of a credit-assignment process that influences howthe motor system responds to and gradually adapts to repeatedtarget displacements of different sizes (Berniker and Kording2008; Ingram et al. 2000; Kagerer et al. 1997; Kluzik et al. 2008;Malfait and Ostry 2004; Wie and Kording 2009). Second, wefound that the kinematics of online corrections of human subjects,at least for the tested range of target jumps, could only beapproximated reasonably well by a single error correction mech-anism that uses an internal forward model to compensate forperipheral feedback delays and uses an inverse model of the limbto adjust the outgoing predictive motor command to the originaltarget location in a way that takes into account the dynamicalproperties of the limb. A number of modeling studies havesuggested that the motor circuits that control unperturbed reachingmovements and that compensate for external force-field perturba-

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tions require combinations of forward and inverse internal modelsto generate the appropriate predictive feed forward motor outputcommands (Bhushan and Shadmehr 1999; Haruno et al. 2001;Wolpert and Kawato 1998). Our modeling study indicates that thesame control architecture is also necessary to reproduce thefeedback-mediated trajectory adjustments observed as humansubjects correct for trajectory errors resulting from unexpectedtarget displacements. Without the forward and inverse internalmodels, feedback delays and the inherent dynamics of the limbwould result in reach trajectories that cannot compensate rapidlyfor even small shifts in target location.

One-stage versus two-stage online correction

Our results showed that the early online correction is trig-gered at the same onset time by all target jump amplitudes anddirections (Figs. 4–6; Supplementary Fig. S2). The onsetlatency values are consistent with previous findings for thetiming of responses to visual perturbations (Day and Lyon2000; Prablanc and Martin 1992; Sarlegna et al. 2003). Fur-thermore, our results have shown that the amount of trajectory

correction at all times during the movement is linearly propor-tional to the amplitude of the target jump across the entirerange of tested target displacements (Fig. 3C; SupplementaryFig. S2). If the size of the correction of reach trajectorymediated by the rapid online mechanism does saturate at somemaximum value, it must only occur for target displacementsthat are larger than those used in this study. Finally, theperformance of the human subjects did not show evidence ofan abrupt transition in the kinematics of the rapid correctiveresponses for small versus large target displacements. Therewas therefore no evidence in this study of a process thatmight have attributed performance errors to different causessuch as motor execution variability versus changes in theenvironment and corrected for them with different mecha-nisms. This suggests that a single error correction mecha-nism may be responsible for the observed online correction.However, it is important to point out that the absence ofobservable nonlinearities in the kinematics of correctionsfor target displacements of different amplitudes does notpreclude the possibility of two corrective mechanisms withoverlapping or staggered delays and variable gains. This

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complex situation cannot be discounted using the currentparadigm. Moreover, it is possible that the inherent dynam-ical properties of the arm may have filtered out any physicalevidence of a two-stage correction mechanism for largertarget displacements, especially if the latency differencebetween the two processes was not too large.

Consistent with published observations, we found that sub-jects were largely unaware of small target jumps but becameprogressively more aware of target jumps as their amplitudeincreased (Blouin et al. 1995; Niemeier et al. 2003). Neverthe-less, subjects succeeded in reaching the final target positionswhether or not they were aware of the displacement. Thissupports previous studies showing that awareness of the visuo-motor errors does not have a causal relationship with the onlinecorrection of hand trajectories (Castiello et al. 1991; Fecteau etal. 2001; Johnson et al. 2002). However, there was somesuggestion of a relationship between reach trajectory shape andthe likelihood of being aware of the target displacement.Especially for the largest target displacements, the reach tra-jectory during the relatively infrequent trials in which the

subjects failed to report the displacement tended to be directedaway from the original target location and toward the dis-placed position almost from the beginning of the movementand showed less curvature of the corrected trajectory com-pared with those trials in which the subjects reported thedisplacement. It is unlikely that these trajectories that devi-ated away from T1 from their outset were produced by avery precocious rapid correction response. Instead, theymay simply be trials whose initial direction was at theextreme of the natural distribution of variability of initialreach directions toward T1. Although very speculative atthis point, it is possible that when subjects make a reachingmovement to T1 with an initial directional error that islarger than normal and by chance is in the same direction asthe ensuing target jump, they may be less likely to detect alarge target displacement in the same direction.

Previous studies of the rapid online error correction mech-anism for target displacements during reaching movementsfocused primarily on such issues as its short latency, indepen-dence from perceptual processes, insensitivity to cognitive

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control, and the possible implication of dorsal stream visuo-motor pathways (Day and Lyon 2000; Goodale et al. 1986;Pelisson et al. 1986; Prablanc and Martin 1992; Rossetti et al.1995; Sarlegna et al. 2003). This study provides the mostdetailed description to date of the kinematics of the earlycorrective response and its relation to the size of target direc-tional changes.

Online correction by summation of feedforward andfeedback error signals

To investigate the mechanism of the simplest necessaryerror-correction signal for successful online corrections fortarget displacements we tested the performance of 4 versions ofa controller with features inspired by experimental observa-tions in moving a dynamic model of the arm with physiologicalparameters. The simplest model of the observed linear rela-tionship between the error and trajectory correction in humansis one that multiplies the error with a constant scaling factor(gain) and incorporates the result into the ongoing motorcommand. Similarly, the simplest model of the observed com-mon onset of trajectory corrections for target jumps of different

amplitudes is one with a single corrective pathway and aconstant feedback delay. Our modeling results show that acontroller with such attributes can produce motions of a simpledynamic model of a 2-joint arm that closely approximate keyfeatures of human reach trajectories. This suggests that a singleproportional error-correction mechanism can compensate forvisuomotor errors of different amplitudes and that this mech-anism is of sufficient gain to adjust for even the largest errorstested in this study.

Further support for this hypothesis is that the rate at which thetrajectories deviate away from the baseline also scaled as a functionof the overall movement velocity for each subject (Fig. 3D). Thisprovides indirect evidence that the error signal is continually propor-tional to the difference between the target location and current esti-mate of hand position but also suggests that the rate at which the erroris corrected is proportional to the overall speed and movement dura-tion of each subject. This indicates a close coordination between thetime course of the online correction mechanism and the time courseof the ongoing movement. This coordination could be achieved byafferent feedback signals about the speed of movement, an efferencecopy-based estimate of the time course of changes in arm state, orboth.

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This hypothesis does not preclude the possibility that thesubjects may have intervened to make more “voluntary” ad-justments to the outgoing feedforward motor command tore-aim the ongoing movement to the new target location,especially during the latter stages of the reach movement. Infact, the small errors in final position and velocity shown by thebest-performing controller may be due in part to the lack ofsuch delayed “voluntary” corrections implemented in themodel. The simulations only suggest that this voluntary inter-vention may not have been necessary until near the end of themovement for the target displacements used in this study.Nevertheless, the proposed proportional error correction mech-anism may be inadequate for large target displacements such asreversals in target location. In such circumstances, it is verypossible that most of the correction involves voluntary inter-vention by the subject to truncate the ongoing motor output tothe original target location and to substitute a motor commandappropriate for the new location (Georgopoulos et al. 1981,1983).

Our study is the first to address the minimum necessarycomplexity of the error correction signal for online control ofa multisegment limb with dynamic properties during correc-tions of reach movements to displaced targets. We manipulated

the complexity of the error signal independently from thefeedforward signal and had the two signals summate to drive atwo-joint arm model. We found that the controller that summeddynamic feedforward and corrective signals can reproduce therecorded human movements reasonably closely, suggestingthat it is a viable control strategy for fast online motor control.This is consistent with multiple modeling studies suggestingthat movement planning and execution includes multiple over-lapping pathways that accomplish optimal multisensory inte-gration based on both afferent feedback and internal predictivesignals (Bhushan and Shadmehr 1999; Flanagan et al. 1993;Mehta and Schaal 2002; Nijhof 2003; Sabes 2000; Shadmehrand Krakauer 2008; Wolpert and Kawato 1998). Althoughmost of these studies include both dynamic and kinematicsignals in their models of motor control, this is the first studyto address the need for dynamics and delay compensation inthe error correction pathway separately from the feedforwardmotor command.

The results of our study strikingly show that controllers withonly kinematic error correction (Kin1 and Kin2) were unsuc-cessful in compensating for target jumps: even though thelargest target displacements were only 14°, the feedforwardmotor command included all the necessary compensation forlimb dynamics for movements to the original target, and themodel incorporated joint viscosity that simulated resistance toimposed movement by soft tissues of the limb and providedintrinsic partial dynamics compensation. This failure to repro-duce human trajectories by Kin controllers is not because of theinherent inability of kinematic correction to compensate formotor errors (Supplementary Fig. S3). When the models sim-ulated slow movements to minimize interaction torques (Sup-plementary Fig. S3) or were allowed to run beyond the averagehuman movement time (Supplementary Fig. S4), the kinematiccorrection signal by itself was sufficient to eventually bring themodel arm endpoint to the target position after multiple oscil-lations around the target, provided that the gain of the errorsignal was not too large to make the model behavior unstable.However, both controllers with delayed and delay-compen-sated kinematic error correction caused large and asymmetrictrajectory deviations and did not bring the model arm close tothe targets within a realistic time frame. These large asymmet-ric deviations produced by Kin controllers arose because thecorrective movements evoked by the purely kinematic errorsignals produced additional interaction torques that were notaccounted for in the original motor command to T1 or in thekinematic correction signal itself. This result suggests that theerror signal of the online correction mechanism has to accountfor the complex dynamics of whole arm movements, such asthe interaction torques that arise during movement of a multi-segment limb (Hollerbach and Flash 1982). This conclusion isconsistent with a recent study showing that adaptation to noveldynamics modifies not only movement planning but also theonline control of movement (Wagner and Smith 2008). To-gether the results of Wagner and Smith (2008) and our mod-eling results suggest that both movement planning and onlinecontrol rely on a common internal model of limb dynamics.

Based on the observations that the onset of online correctioncan be shorter than the usual “voluntary” motor responses tosensory stimuli, it was suggested that the nervous system mayrely on predictive internal estimates of current arm state tocompute corrections for target jumps (Cooke and Diggles

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1984; Higgins and Angel 1970; Jaeger et al. 1979). In ourstudy, both kinematic and dynamic controllers that relied onlyon delayed arm state estimation performed worse than thecorresponding controllers with delay-compensated internal es-timation of arm state. This improvement occurred despitesetting the delayed feedback controllers according to the “bestcase scenario” by including the shortest feedback delays re-ported in the literature and using the feedforward motor com-mand that produced movements of average speed. Thereforeour simulations suggest that the predictive estimation of armstate is an important part of the error computation for onlinecorrection for target displacements, especially if the motorsystem relies on superimposed feedforward and correctivepathways. This is in agreement with multiple studies arguingthe importance of efference copy signals for online control ofmovement (Desmurget and Grafton 2000; Kording and Wolp-ert 2006; Sabes 2000).

Model limitations

Mathematical models of how the hybrid feedforward/feed-back motor command can be generated by the motor systemand how it interacts with the musculoskeletal system tend to becomplex, and, therefore can simulate various aspects of humanbehavior (Bhushan and Shadmehr 1999; Flanagan et al. 1993;Shadmehr and Krakauer 2008; Wolpert and Kawato 1998).Higher model complexity can increase its predictive power, butit inevitably requires many ad hoc assumptions because of thelack of experimental data measuring all the necessary param-eters, which can limit the physiological relevance of the model.In our study, we used a simple dynamic model of a two-jointarm driven by a controller with either kinematic or dynamicerror correction signals. All four parameters that defined thebehavior of the model were varied to find the simplest workingcontroller. However, this simplicity also created a few limita-tions. The main limitation is the lack of musculature with allthe complexity of muscle anatomy and physiology. This com-plexity of the muscular system may simplify neural controlsignals, for example, by providing some inherent dynamicscompensation (Feldman 1986; Flanagan et al. 1993; Gribble etal. 1998). The second limitation is that the controllers tested inthis study all combined feedforward and corrective signals withconstant gains throughout the movement. However, it is some-times proposed that a shift from preplanned to online controloccurs during movement by changing the gain of feedback(sensory) pathways (Wolpert et al. 1995). Third, the controllerstested here do not take into account any long-loop (voluntary)error-correction pathways that may contribute to online con-trol, for example those that would change the feedforwardmotor command to be more appropriate for the newly dis-placed target location. Instead, the controllers used a feedfor-ward motor command aimed at the original target location forthe duration of the response. The absence of voluntary correc-tions and changing feedback gains may explain larger finalerrors shown by the model compared with those shown by thesubjects. These more complex pathways may also be morecritical for recalculating the outgoing motor command to cor-rect for larger target jumps than those used here, such asreversals of target locations (Georgopoulos et al. 1983). Last,the horizontal planar configuration of the model only partiallycaptures the kinematics of the full three-dimensional configu-

ration of the arm associated with the observed two-dimensionalhand trajectories in humans. This difference between modeland human arm configurations may also account for some ofthe observed differences between the human and the bestsimulated model trajectories in this study. However, thatshould not explain the relative ability of the different control-lers to produce effective corrective responses of the simple armmodel to the target displacements. Nevertheless, a more quan-titative comparison between human and model performancewould undoubtedly require a three-dimensional model of thearm and full three-dimensional kinematics of human move-ment.

Conclusions

Our study has shown that goal-directed reaching movementscan be supervised by a single fast online correction controllerthat robustly compensates for visuomotor perturbations ofdifferent amplitudes and directions. Furthermore, this studyfound that online control of reaching movements can be ac-complished by superimposing a dynamically appropriate errorcorrection gated by a constant gain onto the outgoing feedfor-ward motor command to the original target. This organizationof the human online correction mechanism may be exploited todevelop new strategies for assessment and rehabilitation ofmotor deficits following brain damage. For example, it may bepossible to dissociate between damage to the feedforward andcorrective components of the proposed controller and custom-ize the rehabilitative intervention to target the identified path-way. Furthermore, the proposed importance of dynamics com-pensation for the online control of goal-directed movementssuggests that focusing rehabilitation on movement dynamics,i.e., retraining appropriate muscle activity patterns, may bemore beneficial than focusing on recreating normal movementkinematics alone.

G R A N T S

This work was supported by Canadian Institutes of Health Research (CIHR)Grant MOP 62983, an infrastructure grant from the Fonds de la Recherche enSante (FRSQ), and a CIHR Postdoctoral Fellowship to V. Gritsenko and aFRSQ Postdoctoral Fellowship to S. Yakovenko.

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Integration of Predictive Feedforward and Sensory Feedback Signals for Online Control of Visually Guided Movement

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