illusions of force perception: the role of sensori-motor...

doi: 10.1152/jn.01076.200697:3305-3313, 2007. First published 7 March 2007;J Neurophysiol

Jörn Diedrichsen, Timothy Verstynen, Andrew Hon, Yi Zhang and Richard B. IvryPredictions, Visual Information, and Motor ErrorsIllusions of Force Perception: The Role of Sensori-Motor

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Illusions of Force Perception: The Role of Sensori-Motor Predictions, VisualInformation, and Motor Errors

Jorn Diedrichsen,1* Timothy Verstynen,2* Andrew Hon,3 Yi Zhang,3 and Richard B. Ivry3,4

1Wolfson Center for Cognitive Neuroscience, School of Psychology, University of Wales, Bangor, United Kingdom; 2W. M. KeckFoundation Center for Integrative Neuroscience, Department of Physiology, University of California, San Francisco; 3Department ofPsychology, University of California, Berkeley; and 4Helen-Wills Neuroscience Institute, University of California, Berkeley, California

Submitted 9 October 2006; accepted in final form 25 February 2007

Diedrichsen J, Verstynen T, Hon A, Zhang Y, Ivry RB. Illusions offorce perception: the role of sensori-motor predictions, visual infor-mation, and motor errors. J Neurophysiol 97: 3305–3313, 2007. Firstpublished March 7, 2007; doi:10.1152/jn.01076.2006. Internal predic-tions influence the perception of force. When we support an objectwith one hand and lift it up with the other, we expect the force todisappear from the first, postural hand. In a virtual reality system, weviolated this prediction by maintaining the force on the postural hand,whereas the object was still seen and felt to be lifted by the liftinghand. In this situation, participants perceived an illusionary increase inforce on the postural hand, which was, in reality, constant. We testthree possible mechanisms of how force perception may be influencedin this context. First, we showed that part of the illusion can be linkedto a sensorimotor prediction—the predicted sensory consequencesbased on an efference copy of the lifting action. The illusion isreduced when the object is lifted by an external force. We also showedthat the illusion changes on a trial-by-trial basis, paralleling the fastadaptation of the postural response. Second, motor errors that arisefrom a miscalibrated forward model do not contribute to the illusion;the illusion was unchanged even when we prevented motor errors bysupporting the postural hand. Finally, visual information signaling theremoval of the object is sufficient to elicit part of the illusion. Theseresults argue that both sensorimotor predictions and visual objectinformation, but not motor errors, influence force perception.

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

The perception of forces that act on the body is influenced byour expectations. The football player who sees the approachingopponent is likely to anticipate the tackle and perceive theimpact as less jolting than the player who is tackled withsimilar force from an unseen angle. Predictions about forcescan arise from observation of external agents and from theexperience with consequences of our own action; furthermore,these predictions in turn alter our own motor output. To studyhow these factors contribute to the perception of force, weexplored a new illusion, in which a change in force is experi-enced even though the force, in reality, is constant.

We discovered this illusion accidentally during a series ofexperiments studying the dynamics of bimanual coordination(Diedrichsen et al. 2003, 2005a). Using a virtual reality system,participants supported an object in one hand, the postural hand(Fig. 1A) and, when cued, lifted it with the other hand, thelifting hand (Fig. 1B). The visual feedback of the rising objectand the forces that acted on the lifting hand were always

veridical. However, on a small percentage of trials, the loadforce of the object remained on the postural hand as the objectwas lifted. In this situation, participants perceived a strongincrease in the force acting on the postural hand, although thetrue load force remained constant.

This misperception is similar to a number of related illu-sions, all of which have in common the influence of internalpredictions on the actual sensory data. In the classic size-weight illusion, we expect a larger object to be heavier than asmaller object. When both objects have the same weight andare lifted, the larger object is perceived to be lighter (Charp-entier 1891). Another example comes from the recent work ofBays et al. (2005, 2006) and Shergill et al. (2003). Force pulsesapplied to the fingers were judged to be stronger when theywere externally generated rather than when the same forceswere the consequence of self-produced actions. In this case, thevoluntary action seems to give rise to a detailed predictionabout the sensory inflow, and in the absence of this prediction,the force is perceived to be stronger.

What are the mechanisms by which these internal predic-tions influence the perception of force? Considering the forceillusion we observed in our lifting task, we can identify threepossibilities. First, the illusion may arise because our sensori-motor system continuously generates a prediction concerningthe expected sensory consequences of self-produced actions(Fig. 2A), and this prediction is compared with the sensoryinflow (Blakemore et al. 1998). A violation of the prediction,as would occur when the force on the postural hand is main-tained, may be misperceived as an increase in force. In theunloading task, this sensorimotor prediction is directly observ-able: it results in a reduction in the upward force generated bythe postural hand at the time of unloading, an anticipatoryresponse that allows the postural hand to remain stable (Hugonet al. 1982). This anticipatory response is not generated whenthe object is lifted by an external agent, even if this event ishighly predictable, and extensive training is provided(Diedrichsen et al. 2003). Thus following this hypothesis, themisperception of force should only be present when the objectis lifted with a self-generated action. Furthermore, we haveshown that the postural response is modified immediately aftera catch trial (Diedrichsen et al. 2005b). If this adaptationchanges the predictive forward model that also influences forceperception, the illusion should also be modulated in a similartrial-by-trial fashion.

*J. Diedrichsen and T. Verstynen contributed equally to this work.Address for reprint requests and other correspondence: J. Diedrichsen,

School of Psychology, Univ. of Wales, Bangor, Adeilad Brigantia, Bangor,Gwynedd LL57 2AS, UK (E-mail: [email protected]).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

J Neurophysiol 97: 3305–3313, 2007.First published March 7, 2007; doi:10.1152/jn.01076.2006.

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Second, the unintended movement of the hand itself, themotor error, may lead to the illusion. A displacement of thepostural hand during unloading occurs when the postural re-sponse is not correctly matched to the actual force change onthe hand (Fig. 2B). A downward perturbation accompanied bythe stretch of the muscles may be interpreted as an increase inthe force acting on that hand. This hypothesis would predictthat the illusion would only be present when motor errors arepresent.

Third, the illusion may arise because the brain attempts tomake sense of the sensory input, attributing sensations topossible causes based on conceptual knowledge and the visualcontext (Fig. 2C). From experience, we know that supported

objects exert load forces. When the attributed cause of theforce is removed (e.g., the object is lifted), a persistent force onthe postural hand may be perceived to become heavier becausethat force has no known source (for a similar argument of howcausal attributions influence perception, see Haggard et al.2002). In contrast to sensorimotor predictions, this interpreta-tion may influence the percept after the fact, because visualinformation about the lifted object arrives at the brain later thanproprioceptive information. This hypothesis would predict thatthe visual presence or absence of an object on the handdetermines the size of the force illusion. Therefore the illusionshould be just as strong when an object is lifted by an externalforce as when it is lifted by the person’s other hand (Fig. 1C),and the illusion should be absent when the object is visuallyperceived to remain on the hand (Fig. 1, D–F).

Here, we evaluate the contribution of these three possiblecauses to the force illusion in the unloading task. In experiment1, we compared the perception of force when the object waslifted by the other hand (i.e., volitional action) to a condition inwhich the object was lifted externally. If sensorimotor predic-tions are at least partly responsible for the illusion, the forceshould be perceived to increase more strongly in the self-liftingthan in the external lifting condition. Also, to determinewhether the occurrence of motor errors alters force perception,we compared conditions in which the postural hand was eitherunsupported or rested on a supporting surface. The lattercondition eliminates the anticipatory response of the posturalhand and the occurrence of motor errors.

In experiment 2, we evaluated the influence of visual infor-mation of the object on force perception using two manipula-tions. First, we only used trials in which the force was sus-tained on the postural hand, leading to a rapid adaptation ofsensorimotor predictions. In this manner, we effectively elim-inated the influence of sensorimotor predictions on force per-ception. A similar strategy was used by Flanagan and Beltzner(2000) in the context of the size-weight illusion. In their

FIG. 1. Force illusion during unloadingtask. A: participants hold an object with thepostural hand. B: object is lifted by the par-ticipant using the other, lifting hand. A vir-tual environment was used to simulate forcesto hands. When load force of object remainson the postural hand, even after object islifted, a sudden increase in force is perceived.Participants could not see their hand duringthe task, but small spheres symbolized loca-tion of their index fingers. C: during externallifting, a simulated force lifts object frompostural hand. D–F: to manipulate the visualinformation about object, a part of the objectremains on the postural hand during 2-objectcondition (experiment 2).

FIG. 2. Possible causes for force illusion. A: efference copy of motorcommands in self-lifting condition is used by a forward model to generate asensorimotor prediction. This prediction is directly compared with sensoryinput, and discrepancy influences perceived force. B: the sensorimotor predic-tion is also used by a postural controller to issue an anticipatory posturalresponse. This can lead to a motor error, a downward perturbation of thepostural hand on sustained trials. This, in turn, changes the proprioceptiveinput and may be perceived as an increase in force. C: visual information aboutthe object may alter the perceived force.

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experiment, participants repetitively lifted small and largeobjects of the same weight. Initially, small objects were liftedwith less grip force than large objects. However, the sensori-motor prediction adapted quickly: after a few lifts, participantsproduced identical grip forces for small and large objects.Nonetheless, the size-weight illusion persisted, indicating thatvisual information about the object rather than sensorimotorpredictions caused the illusion.

Second, we manipulated the visual information directly. Inone condition, the whole object was lifted, creating the expec-tation that the load should disappear. In a second condition, theobject consisted of two parts, one of which remained on thepostural hand (Fig. 1, D–F), creating the expectation that theforce should remain constant. To the degree to which theinterpretation of visual information leads to an illusory percept,the force should be perceived to increase more in the one-object than in the two-object condition, even in the absence oferroneous sensorimotor predictions.

M E T H O D S

Participants

Ten participants were recruited for experiment 1 (4 male; meanage � 22.8 yr; 1 left handed) and 24 participants (15 male; meanage � 19.2 yr; 3 left handed) were recruited for experiment 2. Allparticipants were recruited from the University of California Berkeleycommunity. Participants were naıve to the purpose of the study andeither received course credit or monetary compensation for theirparticipation. The experimental protocol was approved by the Insti-tutional Review Board of UC Berkeley.

Apparatus and stimuli

A virtual three-dimensional (3D) environment was created in whichparticipants could interact with objects. Participants viewed a virtualscene that was presented on a 22-in computer monitor and reflectedthrough a mirror such that it appeared to be in the natural manualworkspace directly in front of the participant’s chest. Within the 40 �26 � 35-cm workspace (width, height, depth), a virtual object,consisting of a platform (20 � 2 � 10 cm) and stand (3.5 � 7 � 3.5cm), was visible (Fig. 1, A–C). Although the participants could not seetheir hands, the position of each hand was indicated by a 1-cm-diameter sphere. By calibrating the visual display to robotic deviceslinked to each hand, the 3D location of the spheres reflected thevertical position of the index fingers. Index and middle finger of eachhand were yoked together and linked to the end of a robotic arm(PHANToM 3.0 System, SensAble Technologies). The robotic systemallowed us to simulate forces that would be experienced as the personinteracted with a 400g object, creating the convincing impression ofan interaction with a real object.

Experiment 1 procedure

Participants in experiment 1 underwent two testing sessions, con-ducted on separate days. In one session, the postural hand wasunsupported. Participants began each trial by holding their hands,palms facing upward, below the object. When cued, they lifted theobject with the postural hand and held it at a visually specified height,4–7 cm above the floor of the workspace (Fig. 1A). In self-liftingtrials, a sound was played after 500 ms instructing participants to liftthe object with their other hand (Fig. 1B). Participants were trained tolift the object with a smooth motion, bringing it to a height �13 cmabove the workspace floor, and to hold the object in this new position.In external lifting trials, the object was lifted by a computer-generated

force, while the lifting hand rested in the lap of the participant. Thetiming of this force was fixed and approximated the time-course ofunloading in the self-lifting trials (Fig. 1C). For both self- and externallifting trials, the participant judged whether the force on the posturalhand had increased or decreased during the lifting of the object. Thisjudgment was made relative to external lifting trials that were pre-sented as standards at the beginning of each block (see Perceptualjudgments). The response was made as soon as the object had beenmoved to its final position. The instructions emphasized that theresponses were to be only based on the change in the force acting onthe postural hand. Participants were instructed not to judge the weightof the object or the force exerted on the lifting hand.

In the other session, the postural arm was supported by a woodenplatform positioned 4–7 cm over the floor of the workspace. Partic-ipants were instructed to keep the arm relaxed for the entire trial, withthe object passively resting on the supported postural hand at the startof each trial. All other aspects of the supported trials were the same asfor the unsupported trials. The object was lifted, either by the partic-ipant’s other hand or by the computer, and a judgment was madeabout the force acting on the postural hand after the object was lifted.

For a given trial, force feedback on the postural hand eithersimulated natural unloading or a sustained force. For unloading trials,the load force of the object reduced to zero, corresponding to theupward movement of the object. The force was calculated based onthe contact of the hand with the object, using a stiff spring (580 N/m)as a model for the object surface. For sustained trials, the forcepresented to the unloading hand was a scaled version of the force thatwould have been experienced on an unloading trial. Therefore thesetrials showed the same time-course of force change as natural unload-ing trials, only the amount of force changed varied between �20%and �20%, with natural unloading trials showing a force change of�100%. For example, if the lifting action would have reduced theload force on the postural hand at time t from 5 to 1 N on an unloadingtrial, the presented force on an sustained trial would be 5 N � 0.2(5N � 1 N) � 4.2 N for a �20% trial, 5 N � 0.2(5 N � 1 N) � 5.8N for a �20% trial, and 5 N for a 0% trial.

Because the sensorimotor prediction and the anticipatory responseare quickly attenuated after sustained trials (Diedrichsen et al. 2005b),we included a majority of natural unloading trials to ensure thatparticipants maintained a sensorimotor prediction. Each block wascomposed of 20 unloading trials and 10 sustained trials, randomlyintermixed.

In each session, participants completed 20 blocks, alternating be-tween self- and external lifting blocks. The postural hand switchedafter each pair of self- and external lifting blocks. No differences injudgments were observed between the two hands; thus we collapsedthe data across hands in the analyses. The sequence of trials for theunsupported and supported sessions was identical. The first fourblocks were practice blocks to allow the participants to becomefamiliar with the VR environment and unloading task. No forcejudgments were made during these blocks. One half of the participantsstarted with the unsupported session and the other half with thesupported session.

Experiment 2 procedure

One half of the participants were assigned to the one-object con-dition and the other half to the two-object condition. In the one-objectcondition, the visual display and trial procedure were identical to theunsupported condition of experiment 1. In the two-object condition,the display contained two objects, each consisting of a platform 7.5cm in width. The two objects, one on the left and one on the right side,were separated by a gap of 5 cm.

In the two-object condition, the object on the opposite side of thepostural hand was elevated 5 cm above the virtual floor at thebeginning of the trial. The participant lifted the other object with thepostural hand to the same height (Fig. 1D). During both external and

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self-lifting trials, the supported object remained on the postural hand,whereas the other one was lifted (Fig. 1, E and F). Thus the participantsaw that the object remained on the postural hand while experiencingthe same forces (including the force change) as in the one-objectcondition.

Participants completed 16 blocks of 21 trials each, all involvingsustained load force. No unloading trials were presented in thisexperiment. As in experiment 1, participants judged whether the forceon the postural hand increased or decreased relative to that perceivedbefore the object was lifted. The weight of each object was set to350 g, and the simulated force changes ranged from �30% to �30%in steps of 10%. The first four blocks were practice blocks and did notinvolve force judgments.

Perceptual judgments

Participants responded verbally whether they perceived the sus-tained force on the postural hand as “heavier” or “lighter” relative tothe load force generated by the object before lifting. They were alsoallowed to report that they perceived no sustained force, the correctresponse on normal unloading trials. The participants’ verbal forcejudgments were entered into the computer by the experimenter. Forthe sustained trials, these responses were modeled separately for eachparticipant and condition using a logistic regression model

log� p�increased�

1 � p�increased�� 0 � �1x1

where p(increased) is the probability for each trial that the participantjudges the force to have increased, x1 is the actual force change, and�i is the regression coefficient. The point of subjective equality (PSE)

can be calculated as PSE � ��0

�1

. To study the influence of the

sensorimotor prediction onto force perception on a trial-by-trial basis,we re-estimated the model after adding the additional regression term�2zn, where zn represents the size of the sensorimotor prediction onthat trial (see RESULTS for details).

For the mixture of natural unloading trials and sustained trials inexperiment 1, pilot data showed that participants were inclined to

judge any sustained force as an increase over that experienced beforeunloading. This bias presumably arose because of the significantacross-trial contrast between unloading and sustained trials. To over-come this bias, we presented two reference trials, labeling one “adecrease ” and the other “an increase ” at the start of each block oftrials, using external lifting conditions with a force change of �20%or �20%, respectively. We indicated to participants that they shouldjudge the force change with these standards in mind. Therefore theperceptual judgments were made relative to the external lifting con-dition. Thus only the difference between psychometric curves, but nottheir absolute values, could be interpreted in experiment 1.

In experiment 2, only sustained trials were presented, makingreference trials at the start of each block unnecessary. This also meantthat both the difference in the psychometric functions and the absolutevalues of these functions (PSE) were interpretable.

Kinematic data

To assess the size of the anticipatory response of the postural hand,we recorded the position of the postural hand and the forces producedby the robotic device at 200 Hz. Acceleration was computed bydouble numerical differentiation of position data and smoothed with a12-ms FWHM (full width at half maximum) Gaussian kernel.

R E S U L T S

Experiment 1

Experiment 1 was designed to dissociate the influence ofsensorimotor predictions and motor errors on force judgment.Participants either lifted the object using the hand that was notsupporting the object (self lifting) or the object was removed atan unpredictable time by the computer (external lifting). Sen-sorimotor predictions should only be present during self-lift-ing. To manipulate motor errors, we compared the unsupportedand supported condition. The visual information concerningthe object during both conditions was essentially identical.

ANTICIPATORY POSTURAL RESPONSE. Figure 3 shows the aver-age load force and velocity for the postural hand in the self-

FIG. 3. Behavior of postural hand duringself- and external lifting. A: time-course offorce acting on postural hand, averaged overall participants. Data are combined acrosstrials in which the left or right hand was usedto support object. Negative numbers indicatedownward forces. Force either disappearedcompletely (�100%, natural unloading;dashed line) or changed by an amount be-tween �20% and �20%. All traces arealigned to beginning of unloading (0 ms)—time-point when force begins to be applied tothe object by the lifting hand or externalforce. B: velocity (positive number indicatesupward movement) of postural hand. Re-duced upward movement in unsupportedself-lifting condition indicates anticipatoryresponse.



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and external lifting conditions for the unsupported and sup-ported session. The load force was removed very rapidlyduring self-lifting (median, 44 ms) and during external lifting(35 ms). The difference between the self- and external liftingconditions was reliable [t(9) � 4.486, P � 0.002]. There wereno significant differences between the supported and unsup-ported trials in the speed of unloading.

The velocity traces (Fig. 3B) of the postural hand indicate ananticipatory postural response in the unsupported condition.During trials in which the weight was completely removed, thehand showed an upward perturbation during external lifting.This perturbation was substantially reduced during self-lifting.Here, the postural hand showed an anticipatory downwardmovement, beginning �50 ms before the start of lifting,indicative of an anticipatory reduction of the upward force(Diedrichsen et al. 2005b).

The results of the sustained trials provide further evidencefor an anticipatory response: during external lifting, the pos-tural hand moved upward when the load force decreased anddownward when the load force increased (Fig. 3B). Duringself-lifting, all sustained trials showed a downward perturba-tion, with the magnitude related to the size of the force change.

On supported trials, the postural hand did not move. Theresidual velocity on unloading trials is an artifact caused by thefact that the link between the hand and robotic device was notperfectly stiff. Therefore when the load force on the handreduced, the robot arm moved slightly upward, stretching thelink between robot arm and human hand. However, mostimportantly, the velocity of the robot arm did not differbetween the self- and external lifting conditions, indicating theabsence of an anticipatory postural response.

To obtain a measurement of the size of the anticipatoryresponse, we plotted the average acceleration of the posturalhand against the force imposed on that hand (Fig. 4A). Thiscalculation was averaged over the time interval from �25 msbefore until 50 ms after the start of lifting to exclude feedback-based adjustments. During external lifting, the hand behavedlike a passive object; the acceleration was linearly related to theforce acting on the hand in that period. The slope of this lineprovides an estimate of the effective inertia of the hand (Fig.2B, dashed line; see also Diedrichsen et al. 2005b). Duringself-lifting, acceleration was systematically more negative thanfor the same level of force during external lifting. Thus theupward force produced by the postural hand must have beenreduced during self-lifting, a manifestation of an anticipatoryresponse. The size of this reduction can be estimated by taking

the horizontal distance from the self-lifting force to the externallifting regression line, i.e., the force that resulted in the sameacceleration during external lifting. This distance provides ameasure of the anticipatory response for individual trials.

The size of the anticipatory response varied from trial totrial. This is because the sensorimotor system rapidly adaptedto errors in the prediction on the previous trial (Diedrichsen etal. 2005b). Figure 4B shows the average size of the anticipatoryresponse plotted as a function of whether it preceded orfollowed a sustained trial. After a sustained trial, the anticipa-tory response was significantly reduced and returned to base-line only after a number of natural unloading trials.

This fast adaptation can be modeled using a state-spacemodel of sensory motor learning (Donchin et al. 2003). Thisallows us to estimate the sensorimotor prediction on each trialgiven the history of actual force changes, a result that will beuseful in our analysis on the influence of sensorimotor predic-tions on perceptual judgments. In this model, the size of theanticipatory response on each trial n, yn, depends on thesensorimotor prediction, i.e., the predicted change in force, onthat trial, zn. Over the course of the experiment, the participantexperienced a series of actual force changes, u1. . .uN. Wereasoned that the participant would predict on average theaverage force change, i.e., z� � u. We further assumed thatwhen an individual predicted no force change, i.e., z � 0, theywould not show any anticipatory response, from which follows

yn � y� �y�

u�zn � u�

We proposed that the sensorimotor prediction on the next trial(zn�1) is a combination of the last sensorimotor prediction andthe prediction error on the last trial (un � zn)

zn�1 � u� � A�zn � u�� B�un � zn�

The parameter B expresses how fast the prediction adapts tonew sensory experiences; the parameter A determines how fastthe prediction drifts back to the average prediction if no errorsare present. We estimated the model parameters A and B byminimizing the sums-of-squares between predicted and actualanticipatory response. The average A was 0.958 � 0.056 (SE)and the average B was 0.379 � 0.037, which was highlysignificantly different from zero [t(9) � 9.744, P 0.001].Thus the participants showed significant trial-by-trial adapta-tion of the anticipatory response.

FIG. 4. Anticipatory postural adjust-ments in experiment 1. A: acceleration ofpostural hand plotted as a function of forceacting on postural hand for a representativeparticipant. Large right cluster shows resultsfor natural unloading, whereas the 5 smallerclusters show results for 5 levels of forcechange during sustained trials. Difference inforce between self- and external lifting trialsgiving rise to the same acceleration (hori-zontal line) can be taken as a measure of sizeof anticipatory response. B: average size ofanticipatory response as a function ofwhether trial occurred before or after sus-tained trial. Unless otherwise stated, errorbars represent SE across participants.



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PERCEPTUAL JUDGMENTS. Participants correctly judged thatthere was no sustained force on unloading trials and rarelyresponded “no force” on sustained trials (0.54%). Psychomet-ric functions were constructed for the remaining sustainedtrials, indicating the proportion of trials in which participantsreported a force increase for each level of force change (Fig.5A). Participants were more likely to report force increases onself-lifting trials compared with external lifting trials. For theunsupported trials, the average point of subjective equality(PSE; Fig. 5B) was 17.6 � 4.4% lower for self-lifting and thanfor external lifting. Thus when a sensorimotor prediction ispresent, a 17% reduction in the sustained force applied to thepostural hand was needed for the participants to judge that theforce did not change from that perceived before unloading.

Interestingly, this illusion was not influenced by the antici-patory response itself or by motor errors. For the supportedtrials, the illusion was unchanged in size, with a difference inPSE of �23.5 � 6.4% between self-lifting and external lifting.In a 2 � 2 ANOVA of the PSEs, the effect of self- versusexternal lifting was highly significant [F(1,9) � 20.27, P 0.001], whereas the effect of support [F(1,9) � 2.59, P �0.142] and the interaction [F(1,9) � 0.95, P � 0.355] were notsignificant.

Although the participants seemed to judge the force cor-rectly in the external lifting trials, it is important to rememberthat the judgments were made relative to external trials asstandards, thereby forcing the PSE in the external condition tozero. We will show in experiment 2, in which the absolute PSEcould be interpreted, that the external lifting trials were alsosomewhat biased.

We asked whether the trial-by-trial variations in the senso-rimotor prediction influenced the perceptual judgments. In Fig.5C, we split the judgments in the unsupported self-liftingcondition by the fitted sensorimotor prediction (zn). As can be

seen, the illusion became larger when the expected change wascloser to the natural change of �100%.

In the supported and external lifting conditions, there was noanticipatory response, and we therefore could not fit the modelto infer the sensorimotor prediction. However, we reasonedthat, if the sensorimotor prediction was adapted in these con-ditions, this should occur in a similar way as in the unsupportedself-lifting condition. We therefore used the parameters A andB from the unsupported self-lifting condition to infer thesensorimotor prediction on each trial, z1, . . . , zN, in the otherthree conditions. The sensorimotor prediction was then enteredfor each of the four conditions as a continuous variable in alogistic regression (see METHODS) to model the force judgments.The estimated regression coefficients indicate how much thesensorimotor prediction influenced the perceptual judgment ineach condition (Fig. 5D). The strongest influence was mea-sured in the self-lifting, unsupported condition, with the meanof the regression weights being significantly smaller than zero[t(9) � �2.69, P � 0.025]. For the self-lifting, supportedcondition, the influence was slightly weaker, but still signifi-cant [t(9) � �2.49, P � 0.034]. A direct comparison of thetwo self-lifting conditions indicated no significant difference[t(9) � 1.37, P � 0.203]. For the two external conditions, theestimated sensorimotor prediction did not influence the percep-tual judgments in either the unsupported [t(9) � �1.64, P �0.139] or supported [t(9) � 0.36, P � 0.73] conditions. Thusin the self-lifting condition, the sensorimotor prediction seemsto adapt on a trial-by-trial basis even in the absence of motorerrors, and this rapid adaptation significantly influences theperception of force.

To summarize, the results of experiment 1 show that theperception of force is closely linked to a sensorimotor predic-tion of the change in force. After self-lifting, the force remain-ing on the postural hand is perceived to be greater than that

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FIG. 5. Force judgments in experiment 1.A: proportion of heavier judgments is greaterduring self-lifting than during external liftingtrials, with no difference between supportedand unsupported trials. B: boxplot of point ofsubject equality (PSE)—force change neces-sary to be perceived as no change in force.Note that judgments were made relative toforce change in external lifting trials. Horizon-tal lines indicate median, boxes indicate rangeof middle 50%, and whiskers indicate fullrange of PSEs of individual participants. C:judgment in unsupported self-lifting conditionwas influenced by history of force changes. Aspredicted force change approached forcechange that would occur under natural condi-tions (�100%), size of illusion increased. D:size of regression coefficient for predictedforce change. More negative values indicate astronger influence of predicted force change onperceptual judgment.



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experienced after external lifting. Moreover, the persistentforce is influenced by the trial-by-trial variation of the senso-rimotor prediction. However, the actual occurrence of motorerrors does not contribute to the illusion. We did not observeany differences in the magnitude of the illusion between thesupported and unsupported trials.

There exist some other differences between the self- andexternal lifting conditions that could account for the differ-ences in perception of force. First, the difference in perceptualjudgments might be related to unloading speed given that thetime of unloading was slightly delayed during self-liftingcompared with external lifting. We conducted a secondaryanalysis restricted to the fastest half of the self-unloading trials.Here, unloading time was similar to that observed in theexternal lifting condition. With this partial data set, the differ-ence in perceptual judgments between self- and external liftingconditions remained.

Second, the timing of the force change was predictableduring self-lifting but not during external lifting. Third, in theself-lifting condition, participants felt a force with the liftinghand as they picked up the object; no forces were applied to thenonpostural hand in the external lifting condition. Althoughparticipants were explicitly instructed to make their judgmentssolely by considering the force on the postural hand, thepresence of the other force may have biased their responses. Inexperiment 2, we address these latter two concerns and assessthe influence of visual object information on the illusion.

Experiment 2

Studies of other illusions of perceived force such as thesize-weight illusion (Flanagan and Beltzner 2000) have shownthat visual object information can play a significant role in thefinal perception, independent of sensori-motor predictions. Inexperiment 1, participants saw an object leaving the posturalhand in both the self- and external lifting condition. The visualinformation (e.g., not being able to attribute the force to anobject) should therefore have influenced force judgmentsequally in both conditions. Because the judgments in experi-ment 1 were made relative to the reference of external-liftingtrials, this influence would not have been evident in exper-iment 1.

We therefore tested directly whether visual informationabout the object can influence the perception of force inexperiment 2. Here we only tested sustained trials. This shouldquickly attenuate the sensorimotor prediction (and conse-quently the anticipatory response). We also manipulated thevisual information directly by comparing two visual scenarios.The one-object condition was identical to experiment 1; anobject, either self- or externally lifted, was seen to leave thehand (Fig. 1, A–C). In the two-object condition, one objectremained on the postural hand and a second object was raisedupward during lifting (Fig. 1, D–F).

ANTICIPATORY POSTURAL RESPONSE. The kinematic results forthe postural hand were similar in the one- and two-objectconditions; thus only the combined results are shown. Theinitial force change was slightly slower in the external than inthe self-lifting condition (Fig. 6A). Because we excluded nat-ural unloading trials, the anticipatory response during self-lifting was quickly extinguished, resulting in similar velocity

profiles for self- and external lifting trials (Fig. 6B). In partic-ular, the direction of the hand velocity reverses as a function ofwhether the sustained force was increased or decreased duringself-lifting, as well as during external lifting. Thus no antici-patory response was present in the self-lifting trials.

PERCEPTUAL JUDGMENTS. In the one-object condition, the psy-chometric functions for the force judgments overlapped forself- and external lifting (Fig. 7A), resulting in nearly identicalPSEs [t(11) � �0.014, P � 0.98]. This finding providesadditional support for the hypothesis that the difference be-tween self- and external lifting trials in experiment 1 wascaused by sensorimotor predictions. Other differences betweenthe conditions, such as the predictability of the time of theforce change or the force on the lifting hand, were the same inthis experiment as in experiment 1. By eliminating the senso-rimotor prediction through the use of sustained trials only, thedifference between the self- and external lifting conditions wasabolished.

We found, however, a significant difference in the PSE (Fig.7B) between the one-object and the two-object condition[F(1,22) � 24.93, P 0.001]. The mean PSE for the one-object condition, both for self- and external lifting, was �10%,significantly different from zero [t(11) � �7.58, P 0.001].Although the mean PSE for the external lifting condition inexperiment 1 was close to zero, it should be kept in mind thatthe judgments in experiment 1 were made relative to externallifting trials as a standard, therefore clamping the externalcondition artificially to zero. In experiment 2, the absolute PSEcan be interpreted, showing that visual information regardingthe object alone can lead to a 10% shift in force judgment.

For the two-object condition, the PSE was �1.5%, a valuethat was not significantly different from zero [t(11) � �1.45,P � 0.174]. Therefore participants perceived an increase inforce only when the virtual environment created a violation ofa expectation; otherwise their judgment was unbiased. The size

FIG. 6. A: average force, across participants and hands, on the posturalhand in experiment 2. Unloading is faster in the self-lifting condition. B:average velocity profiles of postural hand are symmetric in both self- andexternal lifting conditions, indicating absence of an anticipatory response. Dataare combined for 1- and 2-object conditions because results were similar.



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of this illusion induced by visual information was one half thesize of the difference between self- and external lifting trials inexperiment 1, which was induced by a violation of a sensori-motor prediction.

D I S C U S S I O N

We report a novel force illusion, in which a constant forceacting on a hand is perceived to increase when the apparentreason for that force is removed. This illusion arises because ofa violation of an internal prediction. When an object is re-moved from a supporting hand, we expect that the load forcegenerated by the object will be eliminated. The virtual realityenvironment allowed us to (serendipitously) observe this illu-sion by creating a somatosensory experience at odds with thisexpectation. The load force remained constant on the posturalhand and participants perceived an increase in this force.

We sought to evaluate the role of three mechanisms thatmight underlie this illusion. In experiment 1, we found that theperception of the force depended on whether the load was liftedby a volitional action generated by the participant or by anexternal agent. The magnitude of this effect was substantial,with the illusion increased by �20% during self-lifting. Thisresult is congruent with previous work comparing self- andexternally produced sensory stimuli (Bays et al. 2005; Blake-more et al. 1999; Shergill et al. 2003; Weiskrantz et al. 1971),and this difference is assumed to reflect the operation ofsensorimotor predictions. A copy of the outgoing motor com-mand, the efference copy (Von Holst 1954), is used to generatea sensorimotor prediction through a forward model of themotor system (Miall and Wolpert 1996; Wolpert et al. 1995).Thus sensorimotor predictions are closely linked to self-gen-erated actions.

A novel finding in this study is that both the posturalresponse and the force percept adapted on a trial-by-trial basisin a parallel manner. Similar to previous findings (Diedrichsenet al. 2005b), we found that anticipatory postural responseswere significantly attenuated after a sustained trial. A similaradaptation was also found in the perceptual judgments. Inter-estingly, this adaptation occurred even when the postural handwas supported, eliminating any overt anticipatory posturalresponse. Although our study provides no conclusive evidence,the finding of parallel trial-by-trial adaptation in action andperception is certainly in agreement with the hypothesis thatboth are caused by the adaptation of one common forwardmodel (see Fig. 2) that is used to predict the sensory result ofself-generated actions.

In contrast, we found very little evidence that the occurrenceof motor errors, the downward perturbation of the posturalhand, had any effect on the perception of the sustained force.This motor error dramatically alters the proprioceptive feed-back from the arm; however, when we prevented these motorerrors by having the arm rest on a rigid surface, the size of theillusion was unchanged. Although other studies have shownthat illusions of force can arise under similar supported con-ditions (i.e., when motor errors are likely minimized, see Bayset al. 2005, 2006; Shergill et al. 2003), our experiment allowedus to assess the influence of motor errors directly. Surprisingly,we found that there was no influence. From this, we concludethat the perceptual illusion arises solely from the internalcomparison of predicted and sensed sensory information ratherthan the perception of the hand’s perturbation. This result alsoprovides indirect evidence that, if the hand is perturbed down-ward, the nervous system correctly ascribes the perturbation tothe changed postural motor command rather than to a furtherincrease in load force. Thus the brain accurately accounts forthe consequences of its own motor actions.

A central question in studies of motor learning concerns thetypes of error signals that are used to develop and modifysensorimotor predictions (Diedrichsen et al. 2005a). The errorsignal for this adaptation process could be sensory predictionerrors, the difference between predicted and perceived sensoryoutcome, or motor errors, differences between the desired andactual movement of the limb (i.e., performance vs. predictionerror, Jordan and Rumelhart 1992). This study provides evi-dence that prediction errors are sufficient for modifying sen-sorimotor predictions. The perceived force depended on thehistory of force changes in both the unsupported and supportedconditions.

We found that contextual visual information about the ex-ternal objects provided a second, independent mechanism thatinfluenced the force illusion in this task. Participants perceivedthe sustained force to be �10% larger when they saw theobject being removed from the hand in the one-object condi-tion compared with when one object remained on the hand inthe two-object condition. Because of the delay in the visualsystem, the visual information about the displacement of theobject from the hand in the external condition is only availableafter the force change on the postural hand is perceived.Nonetheless, the magnitude of the illusion was similar in theexternal and self-lifting conditions, even though the participantcould generate a prediction of the forthcoming (visual) dis-placement in the latter condition. This suggests that, in contrast

FIG. 7. A: proportion of increased forceresponses as a function of actual forcechange in experiment 2. B: point of subjec-tive equality in the self-and external liftingconditions. Results indicate illusion in 1-ob-ject, but not 2-object, condition.



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to sensorimotor predictions, the effect of visual context informa-tion on the perception of force in this experiment is postdictiverather than predictive (Bays et al. 2006). It is likely that the effectsof visual information found in this study are similar to those foundto mediate the size-weight and material-weight illusions (Ellis andLederman 1998; Flanagan and Beltzner 2000).

Why do expectations influence our perception? Such amechanism may be advantageous for two reasons. First, itattenuates the neural response to expected stimuli and, as such,helps amplify potentially important, unexpected sensory sig-nals. Second, the bandwidth of firing rates in the nervoussystem is limited. Despite this, we can judge the weights ofboth very light and very heavy objects. By subtracting theexpected value from the raw sensory percept, the dynamicrange of a sensory channel can span a large interval of stimuli(Ross 1969). This comes at a price: the observer is no longerable to accurately judge the absolute value of a force stimulus.

In conclusion, our results provide clear evidence for a tightlinkage between sensorimotor predictions and perception,whereby sensorimotor predictions directly influence perceptualprocesses (Fig. 2B). The indirect route, through the occurrenceof motor errors (Fig. 2C), seems to have little influence on thepercept, indicating that the nervous system correctly accountsfor its own motor commands. We also showed that contextual,visual information of the workspace, even in the absence of amiscalibrated forward model, can influence force perception.This second mechanism, however, seems to act in a postdictiverather than predictive fashion.

A C K N O W L E D G M E N T S

We thank S. Tipper and P. Sabes for helpful comments on an earlier draft ofthis paper.

G R A N T S

This work was supported by National Institute of Neurological Disordersand Stroke Grants NS-30256 and NS-33504.

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