RESEARCH ARTICLE

Pierre Wydoodt Æ Edouard Gentaz Æ Arlette Streri

Role of force cues in the haptic estimations of a virtual length

Received: 8 February 2005 / Accepted: 28 October 2005 / Published online: 21 December 2005� Springer-Verlag 2005

Abstract This study investigated whether and how theforce cues play a role in the haptic perception of length.We assumed that the introduction of a dynamic dis-ruption during haptic exploration generated by a hapticdisplay would lead to a systematic bias in the estimationof a virtual length. Two types of ‘‘opposition’’ disrup-tion (‘‘elastic’’ and ‘‘viscous’’) were proposed in Exper-iments 1 and 2, and two types of ‘‘traction’’ disruption(‘‘fluid’’ and ‘‘full’’) in Experiments 3 and 4. In allexperiments, blindfolded adults were asked to comparetwo lengths of virtual rods explored with the right index.Results revealed an underestimation of the length withelastic and viscous opposition disruptions and an over-estimation of this length with fluid and full-tractiondisruptions. No systematic bias in the estimation wasobserved in the ‘‘control’’ sessions in which the activeexploration of the segment was ‘‘normal’’ (i.e. not dis-rupted). These results suggest that the forces producedduring exploratory movements are used as a relevant cuein the haptic length estimation.

Keywords Touch Æ Movement Æ Dynamicdisruption Æ Perception

Introduction

In most cases, to perceive by hand the spatial propertiesof a stimulus, voluntary movements must be made tocompensate for the smallness of the tactile perceptualfield. The kinaesthetic perceptions resulting from thesemovements are necessarily linked to the purely cutane-

ous perceptions generated by skin contact, and theyform an undividable whole-labelled ‘‘haptic’’ (or tactile-kinaesthetic, or active touch) perception (Gibson 1962;Millar 1994; Revesz 1950).

Haptic perception of spatial properties, such asshape, relies on geometrical and force cues that arecorrelated (Robles-De-La-Torre and Hayward 2001).However, it has been commonly assumed that hapticspatial perception depends on stimulus geometry alone(Hatwell et al. 2003). Studies have shown that the hapticperception of length mainly depends on the physicallength of a segment (geometrical cues; cf. Gentaz andHatwell 2003). The question is to examine whether andhow the force cues play a role in the haptic perception ofa length. In a length estimation task, we introduced aforce which acts during the exploration movement andwe tried to determine whether the additional force in (orin opposition to) the way of movement can play a role inthe accuracy of length estimation. We have chosen fourdifferent forces, called dynamic disruption, of differentintensity and orientation relative to the movement (cf.details about each disruption will follow).

In haptics, some studies examined the psychophysicalfunction linking the physical length of a stimulus (asegment) and its estimated size. Results showed that thispsychophysical function was influenced by the responsemode. Thus, the function is linear with a slope of 1 whenthe estimation is given via the space between the twoindex fingers actively placed at each end of the stimulusby the participant (Teghtsoonian and Teghtsoonian1965) or via the movement along the stimulus of just oneindex finger or the whole hand (Hermelin and O’Connor1975; Stanley 1966). In these cases, an increase in thephysical value of the stimulus produces a proportionalincrease in the size perceived by the hand. However,when the estimation is given by the space between theindex finger and the thumb in a pincer posture, the slopeis 1.2 (Teghtsoonian and Teghtsoonian 1965): anincrease in the physical value of the stimulus produces amore rapid increase in the perceived size. By contrast,when the estimation is given by a reproduction of the

P. Wydoodt Æ E. Gentaz (&)Laboratoire Psychologie et Neurocognition, Universite PierreMendes France, 38040 Grenoble Cedex 9, FranceE-mail: Edouard.Gentaz@upmf-grenoble.frFax: +33-4-76827834

A. StreriCognition and Developpement Laboratory,Rene Descartes University, Paris, France

Exp Brain Res (2006) 171: 481–489DOI 10.1007/s00221-005-0295-4

stimulus length with the same index finger, the powerpsychophysical function exponent is 0.885 (Lanca andBryant 1995).

In a connected field, numerous kinaesthetic studiesinvestigated the accuracy of spatial location reachingand/or movement length reproducing. Two main resultsemerged: a range effect and a length–location interfer-ence effect. Regarding the range effect, the results oftenshowed that small lengths are generally overestimated,and large lengths are generally underestimated (e.g.Adams and Dijkstra 1966; Faineteau et al. 2003a, b;Hall and Wilberg 1977; Keele and Elis 1972; Kelso1977b; however, see Stelmach and Kelso 1973).

Regarding the length–location interference effect, theresults revealed a stereotyped pattern. In the spatiallocation task, the end is undershot when the startingpoint of the reproduction movement is modified so thatthe length to be travelled is longer with respect to thecriterion movement, and is overshot when the length isshorter. Conversely, in the length task the criterion ex-tent is underestimated when the starting point is movedtowards the end location, and overestimated when it ismoved away from the end location (Imanaka andAbernethy 2000; Walsh and Russel 1979; Walsh et al.1979). In order to avoid these two potential effects frominterfering with those of force cues, one 10 cm lengthreference segment positioned in different spatial loca-tions was proposed in the present study.

The role of force cues in the haptic perception oflength has not been investigated directly yet. However,several types of research indirectly studied the role offorces on the haptic perception in varying the conditionof manual exploration. The first type concerned thestudies which compare passive versus active movements.It has been argued (Paillard and Brouchon 1968) thatactive displacements afford a more faithful representa-tion of the spatial properties of the layout than passivedisplacements, because motor commands enhance theeffectiveness of the kinaesthetic inputs. Thus, bothlength and location of active movements are reproducedmore accurately than passive movements (Roy 1977,1978; Roy and Diewert 1978; Stelmach et al. 1976,1975).

The second type concerns the studies which modifythe spatial plane of exploration (horizontal, sagittal andfrontal planes). Thus, performing the task in the frontalplane induces a break in the radial symmetry amongmovements with different directions. When the plane isoriented vertically, the encoding movements involve ahigher level of muscle activation to oppose gravity thanthose in the reverse direction. Thus, the asymmetry al-lows one to address the question of the role that motoreffort has in perceiving the spatial properties of thedisplacements. In haptics, previous studies have shownthat both the perception of lengths and the horizontal–vertical (V–H) illusion are significantly modified by theplane orientation (Day and Avery 1970; Deregowski andEllis 1972). The vertical segment of an L figure is over-estimated as compared with the same segment in a

horizontal orientation. The V–H illusion occurs whenthe movements are executed in the horizontal plane, butdisappears in the frontal plane. The variation of planeexploration also affects the perception of other spatialproperties, such as orientation (e.g. Gentaz and Hatwell1995, 1996, 1998) and parallelity (e.g. Kappers 2002).

Two studies directly investigated the role of forcecues in the haptic perception of curvature and shape.First, Drewing and Ernst (2003) showed that the intro-duction of orthogonal forces in a surface can create anillusion of curvature when the force field is divergent (orconvergent). Moreover, a convex surface can be per-ceived as a plane when conflict forces (convergent field)are generated at the surface. Second, Robles-De-La-Torre and Hayward (2001) revealed that force cuesovercome object geometry in the haptic perception ofshape. Regardless of surface geometry, participantsidentified and located shape features on the basis offorce cues or their correlates. Using paradoxical stimulicombining the force cues of a bump with the geometryof a hole, the authors found that participants perceived abump. Conversely, when combining the force cues of ahole with the geometry of a bump, participants per-ceived a hole. Taken together, these results suggestedthat force cues may also play a role in the haptic per-ception of length.

The main goal of the present study was to investigatewhether and how the force involved during manualexploration of stimulus plays a fundamental role in thehaptic perception of length. If it is the case, the intro-duction of a dynamic disruption (disruption here meansany force acting on the manipulandum during the handmovement in any direction) during haptic exploration ofa segment should lead to a systematic bias in the esti-mation The possible natures of disruption are innu-merable; however, these disruptions may be classified intwo symmetric categories having different effects:opposition or traction disruptions (Fig. 1). As for thenature of this systematic bias, an opposite patternshould be observed with these two types of disruption.Indeed, traction force (acting in the direction of manualexploration) should have an opposite role in lengthestimation as compared to the opposition force (actingin a direction opposed to the manual exploration). Thus,if an underestimation (or an overestimation) of a lengthwas observed with opposition disruption, an overesti-mation (or an underestimation) should be observed withtraction disruption. No systematic bias in the estimationwould be expected in the ‘‘control’’ condition in whichthe active exploration of the segment was ‘‘normal’’, i.e.not disrupted.

To examine these hypotheses, two types of oppo-sition disruption were generated: one, labelled ‘‘elas-tic’’, acting as an extended spring, was proposed inExperiment 1, and a second opposition disruption,labelled ‘‘viscous’’, acting as a move in a liquid, wasproposed in Experiment 2. Two types of tractiondisruption were also generated: one, labelled ‘‘fluid’’,which in fact is a negative viscosity, was proposed in

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Experiment 3, and a second traction disruption, la-belled ‘‘full-traction’’, which drags the manipulandumalong the segment by applying the relevant force, wasproposed in Experiment 4 (cf. General method). In allexperiments, we have chosen a classical paradigm ofpsychophysics based on the comparison of differentlengths. Asking participants to compare successivesegments provided an estimation of a point of sub-jective equalization (PSE) between normal segmentsand dynamically modified segments.

General method

Participants

In the four experiments, participants were all exempt ofany neurological disease history. Informed consent wasobtained from all participants who remained naıve;however, as to the expected effects of the experimentalmanipulation, their volunteer participation was paid.The experimental protocol was approved by the localEthical Committee of the University and was in accor-dance with the ethical standards laid down in the Dec-laration of Helsinki.

Apparatus and experimental procedure

Blindfolded participants sat in front of a table on whichlay the force feedback apparatus (PHANToM 1.5).Each participant put the right index into a thimble thatwas mounted at the extremity of the device. At thebeginning of each trial, the device produced a force thatguided the participant’s finger to one extremity of thehaptic virtual segment consisting in a cylindrical sym-metry force field which constrains movements inside athin cylinder as long as the segment and about 1 mm

wide. The virtual segment was positioned in the fronto-parallel plane (Fig. 1). The start spatial location of eachsegment was randomly spread on a 3 cm radius circlecentred on a middle sagittal point. The probability P ofa point, determined by the angle h to appear on thecircle, was uniform in the interval [0; 2p], and wasP(h)dh=1/2p. The parts of arm involved in the explor-atory movement were not imposed and not measured.However, a subjective observation revealed that most ofthe motions relied on a forearm movement coupled witha shoulder rotation (and sometimes with a contributionof wrist ad/abduction).

A beep indicated the beginning of the exploration ofthe segment. During this phase, the device allowed theparticipant to move the fingertip along a 10 cm lengthreference segment (LR) from left to right and vice versa(one time). Then, a second beep informed the participantthat he could explore in the same way the second testlength (LT) which varied in length from {�20, �10, �5,0, 5, 10, 20} mm relative to LR. It should be noted that�30 and +30 mm length values used in the pre-test arealso mentioned in Fig. 2. For each pair, segments LTand LR appeared one after the other with the samestarting position (left extremity). The participants wereasked to estimate whether the LT was longer or shorterthan the LR by pressing one of two buttons with theirleft hand. Each participant performed both experimentaland control sessions in counterbalanced order. Inexperimental session, an elastic dynamical disruptionwas introduced during the exploration of the LT. Incontrol session, no disruption was introduced during theactive exploration of the LT. Each session was com-posed of 140 length comparisons between LR and LT (7LT · 20 trials). In total, each participant performed 280length comparisons. Before the beginning, all partici-pants performed a practice session composed of six trials(where LT differed from LR by 30 mm) in a not dis-rupted (control) condition.

Fig. 1 Depiction of the experimental setup. The arm-robotproduces forces which can be felt when finger is fixed to itsextremity. The virtual segment is in fact a real-time computed forcefield of which vectors are oriented towards the central axe of acylinder Disruption forces (F) are colinear to the segment (and theexploratory movement) and are represented by grey arrows on the

central axis. Black arrow indicates the direction of velocity (v) ofthe movement. Left Disruption is oriented in opposition toexploratory movement along the horizontal virtual rod (Experi-ments 1 and 2). Right Disruption is in addition to exploratorymovement (Experiments 3 and 4)

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Data processing

For each participant, the point of subjective equality(PSE) was calculated from all comparisons (LR and alldifferent sizes of LT) when 50% of LT were judged longerthan the LR. The cumulative Gaussian is obtained by anexhaustive fit of psychophysical data, then PSE is theintersection of the curve with 50% axis. An increase in thePSE reveals an underestimation of disrupted lengthevaluation, whereas a decrease in the PSE indicates anoverestimation.Twovalueswere, thus, computed for eachparticipant: the PSEunder the disruption (PSEd) andPSEin the control condition (PSEc). In order to observe theindividual effect of a disruption, the displacement of PSE(DPSE) was computed for each participant: The PSEdisplacement was calculated from the individual expres-sionDPSE=PSEd�PSEc (Fig. 2). In other words,DPSEis the displacement of PSE from control condition todisruption condition. All kinematic parameters, such asexploration time, velocity and generated force, were alsocollected for each comparison movement.

As an example, Fig. 2 shows one participant’s psy-chophysical data for the ‘‘full-traction’’ disruption bothin the disruption session when the traction is on (dottedline) and in the control condition session when thetraction is off (line). The PSE (computed as the inter-section of the plotted line and the x=50% horizontalline) was higher in the disrupted condition than in thecontrol condition.

Experiment 1: effect of an ‘‘elastic’’ opposition disruption

The main purpose of the present experiment was toinvestigate the effect of an elastic disruption in the haptic

perception of a length. The elastic force is equivalent toa virtual ideal spring that would be attached at oneextremity of a segment and whose force would act in adirection opposite to the exploratory movement. Asystematic bias in estimation was expected in this elasticdisruption condition, whereas no bias was expected in acontrol condition (no disruption).

Participants

The participants were six right-handed adults (three fe-males and three males, age 21–38 years; mean=28).

Depiction of the ‘‘elastic’’ disruption

The ‘‘elastic’’ disruption was equivalent to the forceproduced by a linear spring (F= �kx) fixed on the leftextremity of LT (equilibrium point) and acting inextension. The stiffness coefficient k was adjusted so thatit provided a constant 1.5 N force on the right LT end.

Results and discussion

Table 1 shows PSE and DPSE (the distance between thePSEc and PSEd) values for each participant in eachcondition. When the PSE displacement is positive (whenPSEd is larger than PSEc), it means that, in disruptedcondition, the length test (LT) estimated as equal to thelength reference (LR) is larger than the LT estimated asequal to LR in control condition. Such difference is anunderestimation of the disrupted LT. Five participantsshowed a large positive displacement of PSE and one, anegative displacement. The mean individual PSE dis-placement of the group is + 2.9 mm (SD=2.1). Two-tailed t test comparing this value with zero showed thatthe elastic disruption leads to a significant underesti-mation of LT (P<0.05).

The mean exploration time of each participantamong session varied slightly (from 1.7 to 2.8 s). Themean values of exploration time of LR over all trials andthe six participants were similar in disrupted(M=1.6±0.6) and in control (M=1.67±0.5) sessions.

-30 -20 -10 0 10 20 300

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fit /controlexp. data /controlfit /disruptedexp. data /disrupted

∆PSE

LT-LR (mm)

LT>LR

Estimation

Number (%)

Fig. 2 PSEc, PSEd and DPSE values. Data of one participant in atraction condition were processed and presented. The PSE areobtained from the fitted cumulative Gaussian corresponding topsychophysical data in control session (line) and in disruptedsession (dotted line). The PSE displacement (DPSE) was thedifference PSEd � PSEc (abscissa is in cm)

Table 1 Detailed PSE and DPSE values for each participant andtheir respective mean exploration time (MT) among session inExperiment 1

Participants PSE control(mm)

PSE elastic(mm)

DPSE(mm)

MT (s)

1 2.5 6.4 3.9 2.8±0.42 8.6 12.0 3.4 2.4±0.33 �1.3 3.6 4.9 1.8±0.94 0.0 1.3 1.3 2.2±1.95 �2.5 2.5 5.0 1.7±0.66 �6.3 �7.5 �1.2 2.1±0.6Mean 0.1±4.0 3.1±5.8 2.9±2.4

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This result was expected because the exploratorymovements of LR were not disrupted in these two ses-sions. This was not the case for the exploration of LT.However, the mean values of exploration time of LTwere similar in disrupted (M=1.57±0.6) and in control(M=1.67±0.4) sessions.

Taken together, these results revealed that the elasticforce, when introduced during haptic exploration oflength, leads to an underestimation whereas no bias isobserved in the control condition. Is this effect specific toan elastic force or is it a consequence of oppositionduring exploratory movement? In order to address thisquestion, we used another opposition force in Experi-ment 2.

Experiment 2: effect of a ‘‘viscous’’ opposition disruption

The main goal of this experiment was to examine theeffect of a viscous–friction disruption in the haptic per-ception of a length. Viscosity is a linear velocity-dependent force working in opposition to the directionof the exploratory movement of a segment. If the ‘‘vis-cous’’ disruption effect is similar to the ‘‘elastic’’ dis-ruption effect, a length underestimation is expected inthis viscous disruption condition and no bias in a controlcondition.

Participants

The six new participants were all right-handed adults(two females and four males, age 20–48; mean=38).

Depiction of the ‘‘viscous’’ disruption

The viscous disruption was a velocity-dependent oppo-sition force. The expression of the linear viscosity is gi-ven by F= �kÆv, where v is velocity of the deviceextremity (i.e. where the finger is fixed to the manipu-landum) and the viscosity value is |k|=3 N m�1 s. As anexample, the force perceived when moving with such aviscosity is approximately the same as the one perceivedwhen moving a spoon in cold water.

Results and discussion

Table 2 shows PSE and DPSE (the distance between thePSEc and PSEd) values for each participant in eachcondition. Three participants showed a large positivedisplacement of PSE, two a weak positive displacementand one a negative displacement. The mean individualPSE displacement was 4.4 mm (±4.2); this underesti-mation is significant (P=0.05)

The mean exploration time of each participantamong a session varies slightly (from 1 to 2 s). As in

Experiment 1, the mean values of the exploration time ofLR over all trials and the six participants were similar inthe disrupted (M=1.3±0.4) and in control(M=1.3±0.3) sessions. In the same way, the meanvalues of exploration time of LT were also similar in thedisrupted (M=1.23±0.3) and in control (M=1.34±0.43) sessions.

Taken together, these results revealed that the viscousforce, when introduced during haptic exploration oflength, leads to an underestimation, whereas no bias isobserved in the control condition. However, this effect isweaker in Experiment 1. It suggests that, althoughelastic and viscous forces have similar effects on thehaptic estimation of a length, these effects are not thesame strictly. This may be because the intensity ofopposing forces is not controlled to be compared.Moreover, it is possible that each nature of force gen-erates a specific effect. Further studies are necessary toexamine these hypotheses.

Experiment 3: effect of a ‘‘fluid’’ traction disruption

The main goal of this experiment was to examine theeffect of a ‘‘fluid-traction’’ disruption in the haptic per-ception of a length. The fluid force is a specific forceoriented in the same direction of the exploratorymovement of a segment (Fig. 1, right), and is a velocity-dependent force (i.e. only works when movement hasbegun). If a ‘‘fluid’’ disruption has an opposite effect tothe opposition disruption, an overestimation in estima-tion was expected in this fluid disruption condition andno bias in the control condition.

Participants

The new participants were six right-handed adults (twofemales and four males, age 24–41; mean=32).

Depiction of the ‘‘fluid’’ disruption

The fluid disruption was an artificial negative viscositydefined by the following expression Eq. 1,

Table 2 Point of subjective equality and DPSE values for eachparticipant and their respective mean exploration time (MT)among session in Experiment 2

Participants PSE control(mm)

PSE viscous(mm)

DPSE(mm)

MT (s)

7 �5.0 �2.5 2.5 1.9±0.78 �2.5 1.7 4.2 1.5±0.79 2.0 �0.5 �2.5 1.6±0.910 0.0 3.1 3.1 1.4±0.311 1.9 10.0 8.1 2.0±0.812 10.0 20.9 �10.9 1.0±0.5Mean 1.1±4.7 5.5±7.9 4.4±4.6

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F ðvÞ ¼ � jk0j v ðv� v1Þ ðv� v2Þ: ð1Þ

where k¢, v1 and v2 are constant. (k¢=16.6 (SI),v1=0.1 m s�1 and v2=0.6 m s�1).

The aim of this experiment was to introduce a purenegative viscosity, which works in addition to themovement when it has already started. The choice ofsuch a third order polynomial velocity-dependent dis-ruption is justified by the need to avoid instabilities be-fore movement start (v1 act as an inferior threshold) andto avoid a saturation of traction force when arm velocityis above 0.6 m/s (v2) (Fig. 3). This kind of disruption isnot strictly speaking a permanent traction force sincebeyond thresholds it is an opposition force. However, wehave controlled the velocity of participants movementsand have ensured that opposition, when on, was notsignificant: Velocity inferior to 0.1 m/s occurs in a veryshort time at the beginning of the movement (and cor-responds to 0.02 N max) and 0.6 m/s has never beenreached.

Results and discussion

Table 3 shows PSE and DPSE (the distance between thePSEc and PSEd) values for each participant in eachcondition. All participants showed a large negative dis-placement of PSE. The mean individual PSE displace-ment of the group is �3.3 mm (±1.7). The fluiddisruption leads to a significant overestimation of LT(P=0.005).

The mean exploration time of each participantamong session varied slightly (from 0.8 to 2.7 s). As inExperiments 1 and 2, the mean values of exploration

time of LR over all trials and the 6 participants weresimilar in the disrupted (M=0.8±0.4) and control(M=1.1±0.3) sessions. In the same way, the meanvalues of exploration time of LT were similar in thedisrupted (M=0.81±0.32) and in control(M=1.06±0.42) sessions.

Taken together, these results revealed that the fluidforce, when introduced during haptic exploration oflength, leads to an overestimation whereas no bias isobserved in the control condition. Is this effect specific toa fluid force? In order to address this question, we usedanother traction force in Experiment 4.

Experiment 4: Effect of a ‘‘full-traction’’ disruption

The main goal of this experiment was to examine theeffect of a ‘‘full-traction’’ disruption in the haptic per-ception of a length. The ‘‘full’’ force is equivalent to avirtual ideal spring, with a strong stiffness, that would befixed to the right LT extremity whereas the start ofexploratory movement begins at the left extremity of theLT. If a ‘‘full’’ disruption has a similar effect to the‘‘fluid’’ disruption, an overestimation in estimation wasexpected in this full disruption condition and no bias inthe control condition.

Participants

The new participants were six right-handed (for writing)adults (four females and two males, age 20–38;mean=32).

Depiction of the ‘‘full-traction’’ disruption

The force generated in this experiment is more than adisruption of the exploratory movement because theparticipant’s finger is completely dragged from the leftextremity of LT to the right one. The expression of thedragging force is nothing else than a virtual extendedspring whose equilibrium point would be the LT rightextremity, whereas the exploratory movement startsfrom the left. However, to prevent sudden jerk when

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

velocity (m/s)

Assistive Force

v1 v20 -

0.4 -

Force

(N)

Fig. 3 Plot of fluid disruption as a function of the velocity inExperiment 3. When positive, the disruption is an assistive force.Beyond velocity thresholds, v1 and v2, the force produced is inopposition with the movement relatively to the velocity. However,velocity inferior to 0.1 m/s occurs in a very short time at thebeginning of the movement (and corresponds to 0.02 N max) and0.6 m/s has never been reached in any experiment)

Table 3 Point of subjective equality and DPSE values for eachparticipant and their respective mean exploration time (MT)among session in Experiment 3

Participants PSE control(mm)

PSE fluid(mm)

DPSE(mm)

MT (s)

13 0.8 �4.0 �4.8 1.7±0.914 0.0 �4.3 �4.3 2.7±1.415 �3.3 �5.0 �1.7 1.1±0.416 0.6 �5.0 �5.6 1.8±0.317 �0.6 �1.7 �1.1 0.8±0.218 2.1 0.0 �2.1 1.0±0.4Mean �0.1±1.6 �3.4±1.8 �3.3±1.9

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force is activated, a linear time-dependent coefficient f(t)is incremented by the system to thus provide a temporalwindow for g(x). The force expression is given by Eq. 2

F (x; t) = f (t) g(x) = f (t) k ( xo - x); ð2Þ

where f(t)=t for t<1 s and f(t)=1 for t>1 s;k=3 N m�1 and xo=LT.

Results and discussion

Table 4 shows PSE and DPSE (the distance between thePSEc and PSEd) values for each participant in eachcondition. All participants showed a large negative dis-placement of PSE. The mean individual PSE displace-ment of the group was �10.4 (±3.7), i.e. 10.4% of thereference segment. The full disruption leads to a signif-icant overestimation of LT (P=0.001).

The mean exploration time of each participantamong session varies slightly (from 0.4 to 0.7 s). Con-trary to the previous experiments, the mean values ofexploration time of LR over all trials and the six par-ticipants were significantly lower (P<0.05) in the dis-rupted (M=0.3±0.1) than in the control (M=1.2±0.3)sessions. In the same way, the mean values of explora-tion time of LT were lower (P<0.01) in the disruptedsession (M=0.35±0.13) than in the control(M=1.25±0.36) sessions.

The influence of the full-traction disruption on LRexploration time in the disrupted session was clearlypresent and was different from LR time in the controlsession. This may be due to the adaptation of themovement of comparison.

Taken together, these results reveal that the full forceleads to an overestimation, whereas no bias is observedin the control condition.

General discussion

In this research, we have studied the haptic perception ofa virtual length segment (Fig. 4). The main question waswhether and how force cues involved during manualexploration of the stimulus play a fundamental role in

length estimation. To examine this question, two typesof opposition disruption during haptic exploration of asegment were proposed in Experiments 1 and 2 (‘‘elas-tic’’ and ‘‘viscous’’ disruptions, respectively) and twotypes of traction disruption in Experiments 3 and 4(‘‘fluid’’ and ‘‘full’’ disruptions, respectively). In allexperiments, we used a classical paradigm of psycho-physics based on the paired comparison of normal seg-ments and dynamically modified ones.

The first result was that the different dynamic dis-ruption modified the haptic perception of a 10 cm lengthsegment in each experiment. The second result was thatopposite systematic biases in the estimation were ob-served in two symmetric—opposition or traction—dis-ruption categories. Thus, an underestimation of thislength was observed with elastic and viscous oppositiondisruptions, whereas an overestimation was obtainedwith fluid and full-traction disruptions.

These three main results suggest that force cuesinfluence the estimation of haptic perception of length.Before concluding about these observations, it is neces-sary to discuss the potential role of duration of theexploratory movement. Indeed, Armstrong and Marks(1999) noticed that the time of exploratory movementcould play a role in linear extent perception (with veryweak effect for an 11 cm length segment). The analysisof this factor in the present experiment must take intoaccount each individual difference of exploration timebetween LR and LT in one disrupted condition ascompared to the same individual difference in the con-trol condition. Then, a study on the role of time explo-ration would require a high precision of time measuresbecause the time exploration is very short as comparedto the experiment of Armstrong and Marks (1999). In-deed, if time exploration should influence length per-ception, a larger difference between LR and LT times indisrupted condition than in control condition (due to thedisruption of disrupted LT) could explain the PSE dis-placement in all experiments. The analysis of timeexploration of LR (never disrupted) and of LT in allconditions and over all experiments did not reveal anysignificant difference within and between Experiments 1,

Table 4 Point of subjective equality and DPSE values for eachparticipant and their respective mean exploration time (MT)among session in Experiment 4

Participants PSE control(mm)

PSE fluid(mm)

DPSE(mm)

MT (s)

19 1.4 �10.0 �11.4 0.6±4.220 8.3 1.0 �7.3 0.4±0.121 3.8 �7.1 �10.9 0.3±0.122 2.1 �8.3 �10.4 0.7±0.223 2.0 �3.8 –5.8 0.5±0.124 0.0 �16.7 �16.7 0.4±0.1Mean 2.9±3.6 �7.5±5.4 �10.4±3.8

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Fig. 4 Plot of DPSE mean as function of the type of disruption onthe haptic estimation of a virtual length

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2 and 3. In contrast, in Experiment 4, LR and LTexploration time was shorter in the disrupted than incontrol conditions. It is possible that time spent wouldcorrelate with the judgement in one condition but notanother. But it appears improbable and remains hard toexplain. These results showed that the time explorationfactor did not explain the systematic bias estimationobserved in Experiments 1, 2 and 3. However we cannotexclude that in Experiment 4, the exploration time dif-ference effect would increase the overestimation effect.

Taken together, these results showed that force cuesinvolved during the manual exploration of stimulusplays a fundamental role in length estimation, and per-haps, more generally in the haptic perception of space.Indeed, the disruptions proposed in the present studydiffered from earlier perception studies involving varia-tions of force cues. When using natural forces, i.e.physical consequences of contact with an object (Robles-De-La-Torre and Hayward 2001), even when a conflictexists between forces cues and position cues, the effect ofdisruption is understood as an extrapolation of theseconsequences (e.g. horizontal forces) as their theoreticalcauses (e.g. bump). The aim of disruptions proposed inthe present study was not to represent a real shape fromwhich force derives. Thus, the observed effects were notlinked to an integrated perception of an object or ashape component.

In conclusion, these results suggest that dynamicaldisruptions, which modify the energy produced to per-form exploratory movements (i.e. muscular effort) affectconsequently the spatial estimation. The hypothesis thatlength perception would be based on, or at least com-pleted, by a heuristic of produced energy involved inexploratory movement is infirmed here. Indeed, resultsshow the opposite: Resistive forces (i.e. more ‘‘physicalwork’’) lead to an underestimation and assistive forces(‘‘less work’’) lead to an overestimation. Thus, it wouldnot be the energy (work) produced that counts. If theparticipants were trying to keep work constant, wewould find the opposite pattern. Further research isneeded to examine this hypothesis and, in particular, therelevant characteristic of the force (amplitude, work,jerk) involved in movement and how these force cuesinteract with geometrical cues in haptic perception ofspace.

Acknowledgements This work was supported by Cognitique Pro-gram Grant COG 78B (French Ministry of Research) to E.G andby France Telecom Research and Development to P.W. We thankGabriel Baud-Bovy, Vincent Hayward and Gabriel Robles-De-La-Torre for their relevant comments on first version of this manu-script.

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