An asymmetry in force perception contingent on motion reversal
Yon Visell∗1,2

Vincent Hayward†2

1 Drexel University, Electrical and Computer Engineering Dept.

2 Institut des Systèmes Intelligents et de RobotiquePhiladelphia, USA

UPMC Univ Paris 06, Paris, France

A BSTRACT
We investigated the perception of differences between directiondependent, movement-opposing forces. The magnitude of theseforces changed in whenever the direction of motion reversed. They
were felt by participants during an experiment that required themto scan a virtual surface, represented by a planar haptic interface,
via left-right motions of the index finger. We found that individuals
are surprisingly insensitive to changes in opposing force magnitude
that are contingent on reversals in direction of motion, despite large
contrasts in force magnitude. Forces of 1 N failed consistently to bediscriminated from forces of 0 N during sequential presentation at
the highest speeds. As the mean scanning speed of the digit was reduced, the effect progressively vanished. The effect we observed issimple and robust enough to be demonstrated on virtually any haptic force-feedback interface. We suggest possible interpretations
based on temporal information processing in the nervous system,on physiology and biomechanics, and through inferences that thenervous system may rely on to relate motor commands to sensory
input during dynamic haptic interaction. The results obtained raisefundamental questions about the perceptual interpretation of kinesthetic stimuli involving rapid movement, and may also suggest areconsideration of requirements for haptic interfaces.
Index Terms: H.1.2 [User/Machine Systems]: Human Factors—
Human information processing; H.5.2 [Information Interfaces andPresentation]: User Interfaces—Haptic I/O
1 I NTRODUCTION
Forces and displacements vary in complex, time-dependent ways
during normal haptic exploration of objects and surfaces with thehand or a tool. They can arise due to spatial variations in object properties, object geometry, tool geometry and dynamics, exploratory movements, or other factors. A major task for the nervous
system is to analyze the resultant time-varying sensory-motor signals in order to extract stable percepts corresponding to invariant
features of the world. However, when individuals are asked to attend to and report on the sensory signals themselves, rather than
to the environmental interactions that they reflect (e.g., forces felt
during exploration of a surface instead of physical surface properties), perceptual results can conflict with the impression of stability
that is formed via the senses. In this contribution, we report on one
situation of this kind, involving basic asymmetries in individuals’
abilities to detect changes in the magnitude of movement-opposing
forces felt during the scanning of a surface with a finger.
Some unusual haptic effects have been identified that depend on
directional asymmetries in force perception, including the “Leadme” effect of Amemiya et al. [1], which uses asymmetrically oscillating ungrounded forces to give the impression that its user is being
tugged in a particular direction. However, a general explanation for
how such asymmetries may arise is lacking.
∗ e-mail:yonvisell@gmail.com† e-mail:hayward@isir.upmc.fr

1.1 Perception of unexpected force changes
Prior assumptions about the physical origin of forces and displacements that are felt during haptic interaction are arguably requiredfor haptic sensory signals to be interpreted in ways that are consistent with the physical interactions through which they originate. In
the simplest cases, assumptions such as continuity or object constancy are involved. When they are violated, sensory stimuli canmeet with unexpected interpretations. The ways in which component signals of haptic experiences may be perceived likely depend
on factors like the instantaneous state of the limb (e.g., arm stiffness), the perceptual or motor task being executed at the time ofstimulation, and prior expectations or models for the dynamics of
the interaction involved. Consider the following simple, yet illustrative, scenarios:• A constant force field unexpectedly changes in magnitude.
Such a force can be regarded as a basic disturbance applied
to the (nonlinear) haptic perceptual-motor system. The “unexpected” nature of the stimulus may lead to important inferences (e.g., contact with a previously undetected object).
• A change in force magnitude when the speed of the finger ortool is constant but the direction of motion is changed. This
could be the case when the friction coefficient of a scanned
surface depends on the direction of exploration – perhaps
due to asymmetric microstructure (e.g., fine hairs or asperities aligned along one direction).
Occurrences like these can be thought of as “disturbing” in a few
different ways. For example, they may violate basic presumptions
such as temporal or spatial continuity. Alternately, they may conflict prior expectations for the relation between motor actions andsensory input during physical interaction – i.e., an “internal model”
of the interaction scenario (Sec. 1.2). Either result may lead to a
reinterpretation of the felt forces involved. The latter could be perceived as unchanged, or might be felt more prominently if the impression they give conflicts with prior expectations (e.g., the expectation that the same surface scanned identically in two directions
should feel the same).
1.2 Force adaptation: movement and perception
While perceptual adaptation to unexpected force changes has received some attention in the haptics literature, the adaptation of
movement strategies to modified sensory input has been a topic ofextensive investigation in motor control. Numerous studies suggest that individuals compensate for forces that arise during interaction with the environment by forming an internal model of the
dynamics of interaction, relating motor commands to sensory input[9, 7, 6, 5, 12]. If the sensory input that is felt during interaction
conflicts with what is expected, online error correction and model
adaptation may ensue. Such an internal model is instrumental tocontrolling the musculature so as to reproduce a desired kinematic
trajectory (i.e., that of the hand or tool). Studies have also suggested that internal dynamical models play a role in adapting limb
impedance to best suit the dynamics of the environment and task
– in particular, in compensating for external disturbances during
movement [2]. The resulting changes changes in limb impedance

or forces could also be expected to have important effects on how
haptic stimuli are perceived during interaction; For example, theperception of an unexpected force change might be masked by its
own tendency to modulate arm impedance. Although there seems
to have been limited prior research on this topic, a study of Watson
et al. demonstrated that if the limb is required to compensate foran externally-imposed force field during a position-matching task
involving pointing with the forearm, both the force exerted by thelimb and the position influenced perceived direction, as reflected in
the pointing arm [10].
1.3Perceived changes in movement-opposing forces
accompanying motion reversal

In the experiment described below, we explored one situation of thistype, using novel stimuli that consist of movement-opposing forces,
similar to Coulomb-friction, whose magnitude changes upon eachreversal of the direction of motion. We designed the force stimuli such that, over the course of several motion reversals, the force
magnitude changes grew from zero to a maximum of 100% of theinitial force value. We independently manipulated the speed of exploration. Based on our informal testing, and some of the reasoning outlined above, we expected the perception of these forces toresemble that shown in
Fig. 1. After-EffectWe assessed individuals’ abilities
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2

E XPERIMENT

We conducted an experiment to assess the perception of changes
in movement-opposing force magnitude coincident with changes
in the direction of exploration during a simple bilateral (left-right)
exploratory task with the finger, and the dependence of individuals’
abilities to detect such force changes upon the speed of exploration.
We hypothesized that the force magnitude changes would be mosteasily detected at very low exploration speeds, since that regime
most resembles one of static force perception. Thus, by varying
exploration speed, we aimed to manipulate participants’ sensitivity
to motion-reversal coincident force magnitude changes.

2.1

MethodBecause of the evanescent nature of the effect, the experiment was
based on a variation of the psychophysical method of limits. Participants were presented with one-dimensional (left-right) force fields
that changed in magnitude when the direction of movement reversed. The forces were explored based on a repeating left-rightmotion of the finger on the manipulandum. The forces during leftward and rightward motion were initially equal in magnitude, andthe difference between them grew on successive reversals. In our
procedure, both force values were simultaneously incremented withthe difference between values held constant (see “Stimuli”). Participants judged when the magnitudes differed. We selected thepsychophysical method of limits for this experiment due to its efficiency, suitability for the exploration mode and stimuli used, andbecause we expected it to require less cognitive effort on the partof users, who were already taxed with performing simultaneous velocity matching and force comparison tasks, than would be neededwith other methods.
2.2

Participants

Seven participants (6 of them male), ranging in age between 20 and
30, volunteered for this study. All of them were research staff at theauthors’ institution and reported normal touch sensation. All participants were naive with respect to the purpose of the experiment.
2.3

Apparatus

The apparatus consisted of a planar haptic force-feedback device,
the Pantograph mkII, that has been extensively characterized in aprior paper [3]. The maximum force the device can exert is approximately 2 N, and the sampling frequency of the computer-inthe-loop control system was 5 kHz. The device has a wide usable
frequency bandwidth, from 0 to 400 Hz.
During each trial, participants explored a one-dimensional (leftright) force by using the index finger of their dominant hand to operate the manipulandum of this device; see Fig. 2. They were seatedat a desk in a quiet environment with their arm at a comfortable angle. They received instructions and entered responses via the video
screen and keyboard of a personal computer (operated using theiropposite hand). Participants wore noise-isolating headphones during the experiment in order to aid their concentration. A computer
graphic provided a real-time indication of the speed and phase of
the exploratory movement for each trial, and an audio metronome
also provided a synchronous, auditory indication of the required
movement speed (see “Stimuli”).
2.4

Stimuli

The stimuli consisted of one-dimensional (left-right) force fields
presented via the Pantograph device. The force stimuli werepiecewise-constant in each direction, were opposite to the velocity
of movement, and could also change magnitude when the direction of motion was reversed, as the manipulandum reached the faredge of the workspace (i.e., after the rightward traversal). A stimulus trial consisted of a sequence of repeated left-right explorationsof the workspace. For each stimulus trial, participants began at
the left side of the workspace and made a rightward-leftward scanning motion that repeatedly traversed the width of the workspace,thus encountering forces fA = −| fA | (during rightward motion) andfB = | fB | (leftward). Changes were effected in the forces between
consecutive scans according to the psychophysical procedure thatwas implemented (see Procedure). The tempo of the motion, andhence average speed, was specified by the experimenters, and enforced via an auditory metronome that indicated when the manipulandum should reach each side of the workspace, and a real-timegraphic display that showed the left-right movement trajectory to
be followed via a left-right moving ball whose motion was imitated. Each rightward or leftward traversal was specified to occur

right scan; See Fig. 3. The change ∆ f was randomly selected to
be positive or negative for each trial (i.e., for each limit procedure), with half the trials in the experiment selected to be increasing(with probability 0.5) and the other half decreasing. After a number
N = n + n0 left-right scans, the force values were fA = f0 + σ n|∆ f |and fB = − f0 + σ n|∆ f |, where σ = +1 or −1 for an increasingor decreasing trial, respectively. The speed for each trial was randomly selected from one of five values, v = 50, 100, 150, 200, or
300 mm/s.

𝜏 = d/v
d

x

0
A

f0
Figure 2: The apparatus consisted of the Pantograph planar haptic interface and the personal computer used to operate and control
it. [3]. Stimuli were explored, and forces rendered, in the left-right
direction as indicated by the red arrow.

in a time τ = d/v, where d = 100 mm was the workspace widthand v the mean speed of exploration. Thus, the force and velocity
trajectories, F(t) and V (t), were as follows:−| fA |, v > 0
F(t) =(1)| fB |, v < 0+v,
2kτ < t < (2k + 1)τ
V (t) =−v, (2k + 1)τ < t < (2k + 2)τ
(2)
τ = d/v, k = 0, 1, 2, . . .
Here, V (t) represents an idealized velocity trajectory following theindicated tempo. We anticipated that participants would, instead,
perform a motion that was non-constant in velocity but that followed the designated mean velocity in each direction, since instantaneous motion reversals are not possible.
A smooth transition from fA to fB was insured by switching theforce value only when a zero-value of the velocity was detected
within a threshold distance from the extremum of motion. (We detected v = 0 using a sign detector applied to the adaptive windowing
velocity estimator described in [4].)For each stimulus, participants began at the left side of theworkspace and made a rightward-leftward exploratory scanningmotion, which they repeated without pause until they responded
that the two forces, fA and fB felt different (see “Procedure”).
2.5 Procedure
At the beginning of each trial, the initial values of movementopposing forces fA and fB were equal and opposite with magnitudes of f0 = 0.5 N. The forces were initially held at these values for a random number n0 of right-left scans, where n0 was
randomly distributed between 1 and 10 with uniform probability.
After the initial, held, portion of the trial, the values of both fA
and fB were changed by an amount ∆ f = ±0.025 N after eachleft-right scan of the workspace. Thus, the difference | fA − fB |was held constant, equal to 1.0 N, while the difference in magnitudes, ∆F = | | fA | − | fB | | grew by an amount 2∆ f on each left-

F

fA

B
Δf

Δf

0

-f0

f0
F

fB

Trial 1 forces

Δf

fA

-Δf
Trial 2 forces

0

-f0

fB

-Δf

t
Figure 3: Illustration of two experimental trials, respectively following
the “increasing” (red lines, middle plot) and “decreasing” (blue lines,
bottom) conditions. Idealized exploratory trajectories for a sequenceof four rightward-leftward movements (whose mean velocities were
enforced via metronome) are shown in the top plot, with the corresponding displayed forces at middle and bottom. With each left-rightmovement, the difference magnitude ∆F = | | fA | − | fB | | decreases,
while the individual forces fA and fB grow (shrink) in the “increasing” (“decreasing”) condition. The complete trial would continue withfurther rightward-leftward movements until the participant judged themagnitudes of fA and fB to be different. See text for details.

Participants were instructed to respond via keyboard entry assoon as they were sure that the forces felt on successive rightward
and leftward scans were unequal. Participants were instructed to
avoid guessing. After entering their response, a new trial was begun. If no response was entered after n = f0 /∆ f = 20 scans, thetrial was terminated and this event was recorded. n=20 scans wererequired for one of the two forces to cross the zero-magnitude line,
and this is also the point at which the difference in force magnitudes, ∆F = | | fA | − | fB | |, was maximal, reaching ∆F = 2 f0 = 1 N(i.e., the magnitudes were 0 N and 1 N). Terminating at this point
thus ensured that ∆F was increasing throughout the trial and alsothat all displayed forces were of sufficiently small magnitude thatthey could be reproduced accurately within device limitations. In
order to assess that participants were aware of the forces, the experi-

Results

For those trials where the magnitudes of the forces fA and fB were,after n + n0 trials, judged to be different, the data consist of theminimum change in force, ∆F = n|∆ f |, that was detected by participants at each given speed value v. Recall that at the end of atrial, the difference in force magnitudes was | | fA | − | fB | | = ∆F.
Trials such that fA and fB were not judged to be different in magnitude after n = 20 scans (see “Procedure”) were marked as such;in the latter case, the magnitude difference ∆F = n|∆ f | = 1 N wasused to provide a lower bound on the required force magnitude difference for that trial. This manifestly underestimated the required
force magnitude difference for the affected trials. Since more than
75% of these “not different” trials occurred at the highest two velocities (Fig. 6), our measurement can be regarded as a conservative
estimate of the differential force threshold at those velocities, and aconservative evaluation of the effect we report on here.
Each participant was also presented with 5 “no force” catch trials
during the course of the experiment, and reported when one of thesetrials was encountered. These trials were detected at a mean rate of
87%, indicating that participants were mostly, but not always, alert
to and aware of the displayed forces.
We analyzed the mean differential threshold in force, ∆F, at eachvelocity level as a function of speed using a polynomial regression
analysis. A linear least-squares fit yields ∆F = p0 + p1 v = 0.35 +0.0018v and an R-squared value of 0.94. Here, v is measured in
mm/s. The fitted curve is shown in Fig. 4. The 95% confidence
intervals for p1 = 0.0018 are (1.0e-2, 2.6e-2), which confirms asignificant dependence of ∆F on v. A further quadratic term was
rejected in the fit, since it yielded a coefficient that did not exclude
zero with 95% confidence.
On many of the higher speed trials, participants did not reportany difference between the magnitudes of fA and fB before the trial
was terminated – recall that this occurred when one force magnitude was 0 N and the other 1 N, which maximized the force magnitude difference for our procedure. The proportions of times thiscondition was reached without participants reporting any differenceat each value of v are shown in Fig. 6. A logistic regression analysis indicated that this “no-difference” response frequency increased
with velocity at a significant level (p < 0.001). The fitted logit isz(v) = −2.22v + 0.082, where v is expressed in mm/s (with t-values> 8.0). The model correctly predicts 79.5% of the data.
3

D ISCUSSION

The results of this experiment demonstrate a basic asymmetry in
the perception of force magnitudes contingent on a reversal of thedirection of motion. We have demonstrated that this effect manifests at force magnitudes and differences on the order of 1 N, far

0.8

0.6

0.4

0.2
50

100

150

200

300

Velocity, mm/s
Figure 4: Mean measured differential force thresholds between
forces fA and fB as a function of speed v for all trials. The value∆F = 1.0 N, corresponds to a situation in which one of the force magnitudes was zero and the other equal to 1.0 N. The line corresponds
to the fit described in the text. Error bars: ±1 standard error of themean (SEM).

1.0
Force difference threshold (N)

2.6

1.0
Force difference threshold (N)ment also included catch trials, in which the velocity was randomly
selected and no force was displayed. When participants encountered one of these trials, they were required to report that no force
was displayed.
Participants completed an instructional phase at the outset of theexperiment, during which they practiced with several stimuli in trials that did not produce recorded data. The training period wascontinued (typically for fewer than 10 test trials) until participants
could reliably track the specified trajectory with the specified speed
v. During the subsequent, main, experiment, stimuli were presented
in block-randomized order, with all five speed values presented ineach direction (increasing or decreasing). There were a total often stimuli together with one zero-force catch trial in each randomized block of eleven stimuli. The experiment consisted of five suchblocks, for a total of 50 stimulus-trials (i.e., 50 limit procedures).
Participants were required to pause and rest their hand between
blocks of trials. The entire experiment lasted between 20 and 30
minutes.

0.8

0.6

0.4

0.2
50

100

150

200

300

Velocity, mm/s
Figure 5: Results from one participant in the study, with linear leastsquares fit to the data (Error bars: ±1 SEM).

• Tactile afference suppression: Prior research has indicatedthat tactile sensations in the hand are suppressed during somemovement tasks (e.g., [8, 11]). However, the demonstrated
suppression effects involve weak stimuli near sensory thresholds, thus do not seem significant enough to explain the results
reported here, which involve signals that are far above previously reported force detection thresholds.

% of trials "no difference"

60

45

30

15

0
50

100

150

200

300

Velocity, mm/s

Figure 6: Percent of trials (among all participants) at each velocity such that fA and fB were not discriminated at any values tested.
Dashed line: logistic regression fit.

above perceptual thresholds, and equalling half of the maximum
force that our apparatus is capable of exerting. At low speeds, thethreshold for detection of force changes increased monotonicallyover the range of speeds studied. In addition, participants were significantly less likely to detect a change in force magnitude at highspeeds than at low speeds. The speeds tested were, nonetheless,within a range that is relevant to many everyday manual tasks.
While participants had little difficulty in following the specified
tempo, and therefore mean velocity, one limiting factor in this experiment was related to the fact that, consistent with basic considerations of motor control, it is not generally possible for subjects to
reproduce constant-speed motion trajectories while freely controlling their own motion, as we desired for them to do.
A number of potential explanations for the effect observed heresuggest themselves, including the following, not necessarily mutually exclusive, possibilities:• Temporal adaptation to the mean force magnitude: As in the
hypothesis represented in Fig. 1, this could, in the simplest
case, constitute a high pass filter that would emphasize transient aspects of the felt signals. Here, “transient” could refer
to either the force magnitude, or to its consistency with priorexpectations. However, the effect observed here seems to depend crucially on the coincidence between directional change
and force magnitude change. Indeed, in informal testing, we
failed to elicit an effect when the force transition was not coincident with the motion reversal (we will attempt to demonstrate this in future work).
• Open-loop control of position. Participants may have ignored
sensory input, hence force information, at higher speeds, if
they switched to an open-loop movement control model that
focused on following a high-speed movement trajectory withspecified times for motion reversal at its extrema.
• Arm impedance modulation: At higher speeds, the periodic
changes in force direction provided a strong disturbance capable of destabilizing the motor program. As a result, the limb
seems to have stiffened (through muscular co-contraction),
perhaps limiting undesired deflections of the phalangeal orother joints. This could have led to decreased proprioceptive
input or other sensory input yielding lower force estimates.

• Prior expectations for movement-opposing forces: A prior expectation, possibly in the form of an internal model for resistive friction, may have led participants to assume that thedisplayed forces were equal in magnitude, as would be moreconsistent (modulo normal force variations) with a Coulombtype friction law. While this doesn’t provide a direct explanation for the velocity-dependence of the observed effect, it isconceivable that at low velocities, the parameters of such aninternal model would have had time to adapt to better reflect
the changing physical situation.
• Viscous force priors: Alternatively, one could may have aprior for viscous forces that increase in magnitude with speed.
If one assumed Weber’s law to hold, one might expect individuals to be less sensitive to force differences felt at higher
speeds, all other factors being equal. However, given the wide
range of other factors that affect movement-opposing forces(e.g., normal force, material properties, etc), it seems questionable whether a simple viscous force prior could explain
the observed dependences.
• Inertial forces: At higher speeds, inertial forces can become
significant, potentially contributing substantially to the net
force that was felt, and masking contributions due to theforces displayed by the device. A rough estimate of the orderof magnitude of such an effect can be made as follows. The
effective moving mass at the manipulandum might be taken
to be on the order of 40 grams. If we approximate the motion as sinusoidal, at the highest frequencies Newton’s second
law, F = ma, yields a force magnitude on the order of 0.2 N.
At the lowest velocity, the corresponding magnitude is just
0.03 N. While inertial forces forces of this magnitude might
be insufficient to fully explain the observed effect, this roughcalculation at least suggests that their effect can’t be entirely
neglected in this setting.
• Sensory integration: In the slower conditions, participants experienced each force level for longer, which could aid themin forming better sensory estimates. individuals with better
sensory estimates• Force neglect: A simple, alternative hypothesis to the foregoing is that higher speed motion has a tendency to impair force
perception. However, our results do not support the notionthat participants could not detect the presence of the forces,
since participants had no difficulty identifying catch trials inwhich no force was displayed. Due to the limited number ofcatch trials (just 5 per participant, or one per participant per
speed value, v), we have insufficient data to fully rule out thishypothesis in the conditions of our experiment, but are notaware of comparable results in the literature.
The experiment presented here is not able to fully distinguishbetween these potential explanations, beyond the arguments given
above. However, the effect uncovered is perceptually prominent,
relevant to normal haptic interaction, and surprising enough to suggest that further research is needed and merited. Several of thesehypotheses are aligned with the idea that the effect is mainly oneof temporal integration or adaptation, and is not dependent on thefact that there is an executed motion. Based on informal testing inwhich the effect seemed to disappear if the force change did notcoincide with motion reversal, we believe that this is not the case.
However, such a hypothesis could be ruled out in a second experiment in which we presented force stimuli to the finger pad without
motion. Certainly, this is a setting that has been studied much more
extensively, however.
From an engineering standpoint, the present study suggests thatsome unusual changes might be needed in design requirements forforce rendering and display in haptic simulation. For forces andinteraction speeds that are sufficiently large (e.g., large enoughto evoke a significant increase in the stiffness of the finger orlimb), the haptic perceptual system may be insensitive to changes inmovement-opposing forces that are contingent on motion-reversal.
This may ultimately point to perceptually-motivated compromisesthat could be made in the interest of improving future haptic display
devices.
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