Sensorimotor Mapping for Anticipatory Grip Force Modulation
Frédéric Crevecoeur,1,2Jean-Louis Thonnard,2and Philippe Lefèvre1,2
1Center for Systems Engineering and Applied Mechanics and2Institute of Neuroscience, Université catholique de Louvain,
Submitted 26 January 2010; accepted in final form 21 June 2010
Crevecoeur F, Thonnard J-L, Lefèvre P. Sensorimotor mapping for
anticipatory grip force modulation. J Neurophysiol 104: 1401–1408,
2010. First published June 23, 2010; doi:10.1152/jn.00114.2010.
During object manipulation, predictive grip force modulation allows
compensation for inertial forces induced by the object’s acceleration.
This coupling between grip force (GF) and load force (LF) during
voluntary movements has demonstrated high levels of complexity,
adaptability, and flexibility under many loading conditions in a broad
range of experimental studies. The association between GF and LF
indicates the presence of internal models underlying predictive GF
control. The present experiment sought to identify the variables taken
into account during GF modulation at the initiation of a movement.
Twenty subjects performed discrete point-to-point movements under
normal and hypergravity conditions induced by parabolic flights. Two
control experiments performed under normal gravitational conditions
compared the observed effect of the increase in gravity with the
effects of a change in movement kinematics and a change in mass. In
hypergravity, subjects responded accurately to the increase in weight
during stationary holding but overestimated inertial loads. During
dynamic phases, the relationship between GF and LF under hyper-
gravity varied in a manner similar to the control test in which object
mass was increased, whereas a change in movement kinematics could
not reproduce this result. We suggest that the subjects’ strategy for
anticipatory GF modulation is based on sensorimotor mapping that
combines the perception of the weight encoded during stationary
holding with an internal representation of the movement kinematics.
In particular, such a combination reflects a prior knowledge of the
unequivocal relationship linking mass, weight, and loads under the
invariant gravitational context experienced on Earth.
I N T R O D U C T I O N
The ability to predict and anticipate the consequences of
one’s actions is a robust and general component of the pro-
cesses involved in motor control (Wolpert and Flanagan 2001).
Motor predictions and anticipatory control are evidenced in
various contexts, such as the remapping of the visual field prior
to a saccade completion (Duhamel et al. 1992), the compen-
sation of self-generated Coriolis acceleration in pointing during
active trunk rotation (Pigeon et al. 2003), and the synchronized
modulation of grasping forces with inertial loads during object
manipulation (Flanagan and Wing 1993). In the latter context,
the grip force (GF) normal to the surface of the manipulated
object is modulated with self-induced variations of the load
force (LF) resulting from inertial and gravitational constraints
between the fingertips and the object.
GF depends on many variables, including the object’s
weight, the mechanical properties of the skin–object interface
(André et al. 2010; Johansson and Westling 1984), the sensory
feedback provided by cutaneous afferents (Augurelle et al.
2003b; Monzee et al. 2003; Nowak et al. 2001a; Witney et al.
2004), and the manipulated object’s internal model of dynam-
ics (Flanagan and Wing 1997).
The coupling between GF and LF exhibits high levels of
complexity and flexibility relative to distinct loading condi-
tions. For instance, Flanagan and Wing (1995) demonstrated
that the slope and intercept of the GF/LF relationship were
independently adjusted in response to increased frequency of
movement during rhythmic cycles. A similar result was re-
ported in the context of multidigit grasp with distinct condi-
tions of movement acceleration and object mass (Zatsiorsky et
al. 2005), yielding the hypothesis that gravitational and inertial
constraints could be treated separately. Moreover, the flexibil-
ity of the coupling between GF and LF allows adaptation to
changes in load profiles induced by changes in gravity, for both
rhythmic and discrete types of movements (Augurelle et al.
2003a; Nowak et al. 2001b).
The possible dissociation between gravitational and inertial
constraints encouraged us to decompose GF into static and
dynamic components to investigate the adaptation of GF in
zero-gravity conditions (Crevecoeur et al. 2009a). This ap-
proach revealed a distinct timescale of adaptation for each
component, giving further support to the hypothesis that each
outcome could adapt and evolve independently.
The dissociation of static from dynamic components yields
the hypothesis that gravitational and inertial constraints may be
independently controlled. Under this assumption, the internal
representation of the manipulated object’s weight should be the
primary factor influencing the adjustment of GF during sta-
tionary holding, whereas the GF modulation should be primar-
ily based on the prediction of inertial loads. It is therefore
necessary to estimate weight and inertial load to produce
adequate GF levels. To date, however, the physical variables
taken into account during these estimations and the sensori-
motor strategies underlying the prediction of inertial loads have
not been thoroughly investigated.
To this purpose, this study used a hypergravity environment
to induce changes in weight without changing the mass of the
manipulated object. We show that the factors underlying the
GF modulation are based on a combination of the object weight
encoded during stationary holding and an internal representa-
tion of the intended movement. In particular, this combination
reflects a sensorimotor mapping between the object weight and
a prior knowledge of the life-long experienced physical laws
linking mass, weight, and loads on Earth.
M E T H O D S
Twenty healthy subjects (11 males and 9 females) without neuro-
logical disorders participated in this experiment. All subjects gave
Address for reprint requests and other correspondence: P. Lefèvre, 4 Avenue
Georges Lemaître, 1348 Louvain-la-Neuve, Belgium (E-mail: philippe.lefevre
J Neurophysiol 104: 1401–1408, 2010.
First published June 23, 2010; doi:10.1152/jn.00114.2010.
14010022-3077/10 Copyright © 2010 The American Physiological Society www.jn.org
informed consent and the experimental protocol complied with the
ethical requirements observed by the Medical Board of the European
Space Agency (ESA) and the French Committee for the Protection of
Persons. The latter organization is responsible for life-science exper-
iments performed in France.
Each subject was seated in front of three vertically aligned visual
targets (green light-emitting diodes) placed 18 cm apart, with the
central target at shoulder height. Subjects were asked to grasp a
manipulandum (4.5 cm grip aperture; 250 g mass) with a precision
grip and to align it in front of the central target. Each subject’s arm
was thus in a horizontal position. A random sequence of targets was
then generated and the subject was asked to align the manipulandum
with the current target by means of outstretched-arm rotation around
the shoulder in the sagittal plane. After each upward or downward
movement (from center to the top or bottom target, respectively), the
subject returned the arm to central alignment prior to the next
Each subject performed the experiment in a training session under
laboratory conditions (normal gravity, 1 g) to learn the task and
become familiarized with the experimental protocol. The training
session was composed of 10 blocks of 16 to 20 movements. The first
group of subjects (n ? 10) then performed the experiment under the
hypergravity conditions induced in parabolic flights. We used the 47th
and 48th ESA Parabolic Flight Campaigns. One parabolic flight was
composed of a sequence of 31 parabolic maneuvers. The gravity was
increased to 1.8 g over a period of about 20 s during the first phase of
each parabola. The second phase consisted of roughly 22 s of zero
gravity, followed by another 20 s phase of hypergravity. The subjects
performed the experimental task during the second hypergravity phase
of each parabola. Two subjects were evaluated per flight and each
subject performed the task during ?14 consecutive parabolas.
The 10 remaining subjects were involved in two control experi-
ments. After the training session, the first control group (n ? 5)
performed another series of eight blocks under normal laboratory
conditions. This control experiment allowed only 1 s to complete each
movement, instead of the 1.25 s allowed in the training session. In
addition, the subjects were explicitly requested to perform faster
movements. The second control group (n ? 5) performed a second
series of eight blocks without changes in movement timing or instruc-
tions regarding the velocity of the movement, but the manipulandum
was loaded with an additional mass of 220 g (470 g in total). The
increase in weight for this control group was similar to that experi-
enced by the group tested under hypergravity conditions. For each
control session performed under 1 g conditions, the data from the first
block were systematically removed from the sample to avoid transient
effects due to learning the task. Based on visual inspection, the second
block was removed for three of the control subjects for similar
The manipulandum was equipped with force and torque sensors
located under each finger (Mini 40 F/T Transducers; ATI Industrial
Automation, Apex, NC), and with a low-g accelerometer sensitive to
acceleration changes in a range of ?3 g (ADXL330; Analog Devices,
Cambridge, MA). Another accelerometer of the same type was used
during the flights to sample the gravity inside the aircraft and to verify
that the movements were performed during stable gravitational
phases. Trials performed during unstable gravitational phases were
discarded. The three-dimensional position of the manipulandum was
sampled at 200 Hz with a motion-tracking device (Codamotion;
Charnwood Dynamics, Leicestershire, UK) to measure the movement
accuracy across the different gravitational conditions. Given that the
movement amplitude depended on subjects’ arm length, the analysis
of movement variance was based on the amplitude coefficient of
variation (CV; the SD was normalized to the mean amplitude).
The data collected from the sensors and accelerometers were
digitally low-pass filtered with a fourth-order zero-lag Butterworth
filter and a cutoff frequency of 50 Hz. Position data of the manipu-
landum were low-pass filtered at 20 Hz. GF was defined as the mean
of the absolute force components normal to the sensor surfaces.
Variation in LF was collected from the accelerometer signal and
multiplied by the object’s mass.
Representative trials performed under both gravitational conditions
are shown in Fig. 1, with the variables for the hypergravity trials
illustrated (Fig. 1, right column). GF was decomposed into a static
component (GFS, dashed horizontal line), measured prior to move-
ment when the arm was stable, and a dynamic component (GFI, gray
arrow), measured as an increment of GF at the peaks of LF relative to
the static component. The increment of LF (LFI, black arrow) is the
difference between maximum LF and the weight of the object. During
hypergravitational conditions, weight was computed using the actual
gravity measured during each trial. The decomposition was computed
for each trial at maximum LF, corresponding to the acceleration phase
(for upward movements) or the deceleration phase (for downward
movements). This decomposition of GF is similar to the method that
we used previously (Crevecoeur et al. 2009a). It is a convenient
approach to examine the combined estimation of object mass during
static phases and dynamic modulation during dynamic phases that
produce the grip motor command. By measuring the increments of
grip force at the load force peaks, we address the capability of subjects
to anticipate the actual variation of load force, taking into account the
trial-to-trial variability. The temporal coupling between the GF and
LF was measured as the time lag between the GF peak and the LF
peak for each individual trial.
A one-way ANOVA was used to test the presence of a main effect
on the tested variables across the parabolas. The comparisons between
the hypergravity and normal gravity conditions, and between the
normal and fast or loaded conditions for the control experiments, were
in the 2 gravitational conditions (1 g, left; 1.8 g, right) and in the
2 movement directions (upward, up; downward, down). The
variables are represented on the examples selected from hyper-
gravity: the static grip force measured during stationary holding
prior to the movement (GFS), the increment of GF (GFI)
measured at the time of load force peak (tM) relative to GFS, and
the increment of LF (LFI) measured at the difference between
the peak of LF and the weight of the held load.
Typical traces of grip force (GF) and load force (LF)
1402 F. CREVECOEUR, J.-.L. THONNARD, AND P. LEFÈVRE
J Neurophysiol • VOL 104 • SEPTEMBER 2010 • www.jn.org
realized with Wilcoxon rank-sum test. The relationship between GFI
and LFIwas addressed by means of classical least-square linear
regressions and the R2statistics reported in the following text indicate
the square of the linear correlation coefficient estimated from the
R E S U L T S
The accuracy of movements was generally similar across the
two gravitational conditions. For the upward movements, there
was no significant effect of gravity on the endpoint variance
(Wilcoxon rank-sum test, P ? 0.1): the CV of the movement
amplitude ranged between 0.07 ? 0.016 and 0.085 ? 0.024 in
normal and hypergravity conditions, respectively (mean ? SD
across subjects). For the downward movements, however, the
movement CV was significantly greater in hypergravity (P ?
0.01): we measured 0.068 ? 0.01 in normal gravity, against 0.1 ?
0.02 in hypergravity. In this gravitational condition, there was
no significant evolution of the CV across the parabolas (one-
way ANOVA, F ?1.3, P ? 0.2). A detailed analysis of the
movement kinematics was reported in our previous study
(Crevecoeur et al. 2009b).
The temporal coupling between GF and LF was similar
under hyper- and normal gravity conditions. The time lag
between the GF and LF peaks did not show a significant
tendency across the parabolas for both upward and downward
movements (one-way ANOVA, F ?1.4, P ? 0.16). The time
lag in hypergravity was 17 ? 9 ms (average ? SD across
subjects). These values are similar to the time lag measured
under normal gravity for these subjects, where the average was
19 ? 17 ms. There was no effect of the change in gravity on
the time lag (Wilcoxon rank-sum test, P ? 0.5).
Under normal gravity conditions, GFSvaried across sub-
jects. The individual means during the training session ranged
between 2.5 and 9.6 N (with a mass of 250 g). Under 1.8 g
conditions, GFSincreased in response to the weight increase
induced by the change in gravity: the individual means ranged
between 4.87 and 9.83 N. Figure 2A shows the mean GFS,
normalized for each subject to his/her normal gravity mean,
and the time course of GFSacross the parabolas. There was no
significant evolution of GFSacross the parabolas (one-way
ANOVA, F ? 0.22, P ? 0.9). Despite some variability, the
relative increase in GFSunder hypergravity corresponded to
the relative increase in object weight, as evidenced by the
increase in gravity shown on the same plot (gray line). Both
GFSand gravity data were averaged across subjects in each
block (one block corresponds to one parabola). The low vari-
ability in the gravity data (Fig. 2A) confirms the stability and
reproducibility of experimental conditions across parabolas.
The absolute ratio between GF and maximum LF during
upward and downward movements (measured at LF peaks)
significantly increased under hypergravity (Wilcoxon rank-
sum test, P ? 0.001). This effect was significant for seven
subjects (individual P ? 0.005). The dynamic phase was
analyzed to address the origin of the increase. Figure 2B shows
that increments of GF increased under hypergravity for a given
variation of LF, as evidenced by a greater ratio between the
two variables than that observed under normal gravity condi-
tions (Fig. 2B, left). There was no significant main effect of the
parabola number on the GFI/LFIratio for both upward and
downward movements (one-way ANOVA, F ?0.44, P ? 0.9).
The ratio between increments of GF and LF increased an
average of 0.44 for upward movement and 0.62 for downward
The origin of this effect was investigated using the following
linear model for increments of GF (GFI) as a function of the
variation of LF (LFI)
GFI? a0? a1LFI
As shown in Fig. 3, A and B, GFIwas significantly correlated
with LFIin both gravitational conditions among all subjects
(all subjects pooled, F ?174, P ? 0.001, R2range 0.289–
0.621 for each regression). The upward and downward move-
ment data were separated since the linear regression parameters
were distinct. This difference in parameters between the two
movement types was consistent under both gravitational con-
ditions. The linear regressions were significant for all individ-
ual subjects (individual F ?5.71, P ? 0.05), except for the
downward movements of one subject in hypergravity (P ?
normalized to the individual means measured under the 1 g condition. The
average gravity during the measurement of GFSis shown on the same plot
(gray trace). B: ratio between GFIand LFIin 1 g and in hypergravity across
the parabolas in each movement direction. Data from up and down trials are
represented in gray and black, respectively. In A and B, the vertical bars
indicate the SE computed across subjects.
A: evolution of the GFSacross the parabolas. The data were
1403SENSORIMOTOR MAPPING FOR ANTICIPATORY GRIP FORCE MODULATION
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0.69). Individual R2values in both movement directions ranged
between 0.08 and 0.53 under normal gravity and between 0.1
and 0.63 under hypergravity conditions. Figure 3C shows the
effect of the increase in gravity on the parameters of the linear
regression computed for each subject. The offsets (a0) and
slopes (a1) were averaged across subjects for each movement
direction and gravitational condition. The offsets significantly
increased in hypergravity for both the upward and downward
movements (Wilcoxon rank-sum test, P ? 0.05). The esti-
mated offsets increased an average of 0.31 and 0.7 N for the
upward and downward movements, respectively. It can be
observed that the slope of the linear regressions for the upward
movements tended to increase in hypergravity, although this
tendency did not reach the level of statistical significance (P ?
0.1). Thus the default increment of GF (a0) increased under
hypergravity for both movement directions to compensate for
the increase in LF. The two control experiments presented in
the following text aimed to reproduce this increase in a0by
changing the movement kinematics (first control experiment)
or the object’s mass (second control experiment).
Several factors could underlie the above-described effect on
anticipatory GF modulation. The first control experiment tested
whether the change in GF adjustment could be induced by a
change in movement kinematics (Crevecoeur et al. 2009b).
Indeed, the movements were faster in both directions under
hypergravity conditions. The average peak inertial load in the
training session performed under normal gravity was 1.61 N
for the 10 subjects who performed the hypergravity experiment
and 1.34 N for the control group. The control group showed a
significant increase in LF peaks between the training session
(first eight blocks) and the session in which they were re-
quested to perform faster movements (eight subsequent blocks;
Wilcoxon rank-sum test, P ? 0.001). The average increase in
LFIbetween the two sessions was 1.2 N, reflecting greater
variation in the kinematics profile than that observed for the
hypergravity group (average 0.05 N increase in LFI). When the
control subjects performed rapid movements, there was a
significant increase in the ratio between GFIand LFIin both
movement directions (Wilcoxon rank-sum test, P ? 0.01). The
average increase in the ratio was 0.05 for upward movements
and 0.31 for downward movements.
The increments of GF correlated with the increments of LF
in both movement directions and movement speed conditions
in 18 of 20 computed regressions for the first control group (2
directions ? 2 speed conditions ? 5 subjects, F ?4.26, P ?
0.05). The remaining nonsignificant regressions were for
downward movements in the training session of one subject
and upward movements in the rapid session of another subject
(P ? 0.25). Individual R2values ranged between 0.06 and
0.69. Figure 4A shows the mean effect of the increase in peak
acceleration (and therefore LF) on the parameters of the linear
regressions. Indeed, there was no strong effect of the change in
under the 1 g condition. The regressions were computed on up
(gray) and down (black) data separately. The data from all
subjects were pooled for the illustration. B: same plot as in A
with the data collected in hypergravity. C: effect of the change
in gravity on the regression parameters. The vertical bars
indicate the intersubject SE on the estimation of the regression
slope and offset in each direction and gravitational condition.
A: linear regressions of GFIas a function of LFI
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movement kinematics on the offset of the linear regressions
(Wilcoxon rank-sum test on the offsets of upward and down-
ward movements pooled, P ? 0.9), which suggests that a
change in movement kinematics cannot account for the in-
crease in a0measured under hypergravity for both movement
The second control group revealed that the subjects’ strategy
during exposure to hypergravity could be attributed to the
effect of the change in weight on anticipatory GF modulation.
The average peak inertial load during the first eight blocks
performed by the second control group was 1.6 N, similar to
the average of 1.61 N observed during training sessions for the
group that performed the task in hypergravity. The peak
inertial loads were logically greater due to the change in the
object’s mass but the peak acceleration was reduced in the
session performed with the heavier manipulandum (Wilcoxon
rank-sum test, P ? 0.001). The average decrease in peak
acceleration for both directions in this session was 0.57 ms?2
and the average increase in peak inertial loads was 1.14 N.
Thus the increase in inertial loads represented 81% of the
increase in loads that would correspond to movements realized
with identical peak acceleration across the two sessions. This
suggests that the change in movement kinematics for this
control group had a limited effect relative to the variation in
inertial loads induced by the change in mass. This control
experiment also produced a significant increase in the ratio
between GFIand LFIfor upward (0.12) and downward (0.13)
movements (Wilcoxon rank-sum test, P ? 0.001).
GFIcorrelated with LFIfor all subjects (F ?6.02, P ? 0.05),
excepting upward movements in the loaded condition of one
subject. The relationship approached significance in this case
(P ? 0.06). Individual R2values ranged between 0.08 and
0.71. In this control experiment (Fig. 4B), the change in mass
produced a significant increase in the regressions offset (Wil-
coxon rank-sum test on the offsets of upward and downward
movements pooled, P ? 0.05), consistent with the effect of
hypergravity on these parameters (Fig. 3C). The offsets of the
linear regressions increased an average 0.61 and 0.84 N for the
upward and downward movements, respectively. Thus quali-
tatively the effect of the change in mass on the regressions
offsets was similar to the effect of hypergravity, although the
average increases were greater in this second control experi-
The results of the second control experiment suggest that the
increase in a0could be due to the change in the object’s weight.
However, although the two control experiments reproduced the
increase in the ratio between GFIand LFI, neither was in
quantitative agreement with the increase in this ratio measured
under hypergravity conditions. This suggests that inertial loads
may be overestimated in hypergravity. In the following text we
show that such overestimation is consistent with the applica-
tion in hypergravity of the strategy revealed by the second
Under normal gravity conditions, a change in weight is
necessarily due to a change in mass. However, the 10 subjects
who performed the experiment in hypergravity faced an in-
crease in weight that was due to gravity rather than to mass. By
erroneously attributing the increase in weight to mass under
hypergravity conditions, the subjects would expect an inertial
load equal to
where ? is the increase in gravity, m is the mass of the
manipulated object, and a(tM) is the peak acceleration of the
intended movement. Based on the static GF developed under
hypergravity (Fig. 2A), we can hypothesize that the subjects
had a good internal estimate of ?. However, the actual inertial
load for this movement would be equal to ma(tM). Conse-
quently, if the predicted inertial load is equal to ? times the
actual inertial load, then we expect that Eq. 1 becomes
GFI? a0? a1?LFI
where a1corresponds to the gain of modulation applied to the
internal estimate of the upcoming LFIwhen manipulating an
object of mass ?m.
The second control experiment provided us with an estimate
of a1applied by the subjects who experienced a change in
weight due to mass. By multiplying this value (average a1in
the heavy condition of the second control experiment) by ?
(average increase in gravity), we estimated the slopes of the
modulation in hypergravity that corresponded to a strategy
based on estimation of weight combined with an internal
representation of movement kinematics. Figure 4C shows the
slopes obtained in this situation for upward (solid circle) and
downward (open circle) movements. The increase of GF mod-
ulation in hypergravity showed a consistent tendency toward
these values, under the assumption that the subjects who
experienced the increase in gravity used a similar strategy as
the subjects tested during the second control experiment.
kinematics on the parameters of the coupling
between GFIand LFIin the first control group
with identical mass across the 2 testing sessions.
B: effect of the change in object weight on the
parameters of the coupling between GFIand LFI
in the second control group, with an additional
mass on the held load and similar instruction
relative to the movement speed across the 2 test-
ing sessions. C: same plot as in Fig. 3C for
comparison with the results of the control exper-
iments. The open and filled circles show the re-
sults of the second control experiment in the
heavy condition multiplied by the average rela-
olas in each movement direction.
A: effect of the change in movement
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D I S C U S S I O N
Our results describe the GF adjustments to LF variation
during voluntary movements realized under hypergravity con-
ditions. First, the increase in weight was properly compensated
for by an increase in the level of GF developed during station-
ary holding. Second, the increase in the ratio between the
increments of GF and LF revealed that the magnitude of the
predicted inertial loads could be overestimated. The control
experiments determined that such changes were likely due to
the increase in weight that could be treated as an increase in
mass in agreement with the invariant relationship between
mass and weight on Earth.
These results reflect a coherent sensorimotor strategy under
the hypotheses of optimal feedback control (Izawa et al. 2008;
Liu and Todorov 2007; Todorov and Jordan 2002) and Bayes-
ian integration of state and parameter estimation in motor
control (Kording and Wolpert 2004). Optimal feedback control
posits that the state estimate is mapped into motor commands
in a way that optimizes a performance index. In the present
study, the observed increase in GF modulation following an
increase in object weight is fully compatible with the presence
of a sensorimotor loop in which the anticipatory control of GF
is modulated by the sensory inflow that conveys information
about the object’s weight. Under these assumptions, the per-
sistent overestimation of the inertial loads may reflect that the
on-line state estimate of the load force based on internal
models and sensory feedback is biased by the internal prior that
changes in weight are usually due to changes in mass. This
could explain the overproduction of grip force since, by erro-
neously attributing the increase in weight to the mass, subjects
would predict greater inertial loads for a given movement
acceleration. Such persistent overestimation of inertial loads
mapped into grip motor commands possibly generated the
overproduction of grip force under hypergravity. Although it is
not in itself an optimal behavior, the overproduction of grip
force increments is compatible with the assumption that inter-
nal prior and sensory feedback are integrated in a Bayesian
way and continuously mapped into motor commands.
A possible mechanism for such modulation is that the neural
structures controlling the grip force receive proprioceptive
input from the fingers, in addition to the arm, and that the
encoding of weight is based on the force developed to maintain
a stable grip. This proposed mechanism is based on the over-
lapping of sensory and motor representations of a given body
part. This local sensorimotor association forms the basis for the
default strategy or prior estimate used by the CNS during
motor learning (Asanuma 1981; Singh and Scott 2003).
The exchange of modulation gain for a constant offset under
an increased load is compatible with the motor system’s
tendency to minimize motor output variability in the presence
of signal-dependent noise (Harris and Wolpert 1998; Todorov
2002). Higher loads are necessarily associated with higher arm
or grip motor commands. Thus the internal prediction of
inertial loads suffers from greater uncertainty in these situa-
tions, which is compensated for by applying a constant incre-
ment of grip force and a lower modulation gain based on
prediction. We suggest that this strategy minimizes the vari-
ability in grip modulation when the magnitude of the inertial
Several factors could influence grip force outcome and
produce the increase in the ratio between the grip force and
load force increments. For instance, variability in the gravity
level during the task execution potentially disrupted subjects’
estimates of the object mass. However, these variations were
rather limited and the possibility that this produced consistent
overestimation is not straightforward.
A change in muscular cocontraction and grip stiffness con-
trol is another possible origin of excessive grip force modula-
tion under hypergravity. In the present experiment, such an
effect could be due to stiffness adjustment while subjects
learned to move in a novel force field (Franklin et al. 2003,
2008), given that the greater variability observed for the
downward movement could indicate that the acquisition of
internal models adapted to hypergravity was not totally com-
pleted. However, this possibility fails to explain the persistent
overestimation of load force variation observed for upward
movements, for which movement accuracy was comparable in
hyper- and normal gravity conditions and movement kinemat-
ics were stable across parabolas (Crevecoeur et al. 2009b).
Changes in grip stiffness can also be due to the amplification
of muscle spindle activity under hypergravity, which could
influence the motor behavior (Fisk et al. 1993). In the context
of isometric force production, Mierau and colleagues (2008)
observed in a similar experimental context that the change in
tonic input at a segmental level could not account for the
exaggerated forces produced under hypergravity and suggested
that the impairment of force estimation was a consequence of
higher neural processing. In addition, Mierau and colleagues
demonstrated that it was not due to deficient proprioceptive
feedback, in agreement with the observation that the impair-
ment of isometric force estimation found its origin in central
motor commands and partially corrected by sensory feedback
(Girgenrath et al. 2005).
In several ways, these findings are similar to the present
findings: we observe an overestimation of the self-generated
inertial loads measured at the load force peaks, precluding
the possibility that altered proprioceptive feedback misled
the estimation of load force variation. Why was the load
force overestimated at a central level? We suggest an
alternative hypothesis based on Bayesian inference for state
estimation (Kording and Wolpert 2004). Our results suggest
that the encoding of weight is combined with an internal
representation of the intended movement and that this com-
bination is based on a Bayesian prior corresponding to the
unequivocal relationship between weight, mass, and inertial
loads experienced on Earth. However, in hypergravity, the
sensory feedback must inform the CNS that the actual loads are
smaller than expected, compared with the expected load while
assuming only an increase in mass. Under the assumption of
Bayesian integration, we hypothesize that the adjustments in
grip modulation parameters are based on whether the differ-
ence between the expected and actual loads is most likely due
to a change in the body or in the environment. Indeed, such
Bayesian inference for estimating the origin of motor errors
was demonstrated to be a very powerful model for motor
adaptation and generalization (Berniker and Kording 2008).
We suggest that a similar inference was processed in hyper-
gravity and that the persistent overestimation of inertial loads
reflects the strength of our internal prior knowledge of an
environment in which gravity never changes.
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The Bayesian inference allows one to interpret the distinct
aspects of movement and force control. Indeed, a sensorimotor
map based on the arm’s weight could also yield excessive arm
motor commands for upward acceleration since the inertial
force would be overestimated. Such an effect would counter
the overestimation of actual inertial force, since acceleration
would be underestimated even when mass was overestimated.
However, this factor could not account for the effect of hyper-
gravity on the kinematics of downward movements; these
movements were faster and there was a sharp reduction in
target overshooting (Crevecoeur et al. 2009b). These results
contradict the suggestion that arm motor commands were
calibrated to overcome a force that was smaller than expected.
We may thus conclude that the internal models of arm dynam-
ics were adapted and that the internal representation of move-
ment kinematics was reliable. This is further supported by the
good correlations (similar to 1 g conditions) between incre-
ments of the grip force and the load force in hypergravity and
by the synchronization of grip force with load force that did not
change across the two gravitational conditions. These results
are also similar to the results of a previous experiment in which
isometric force production was exaggerated under hypergrav-
ity, whereas hand displacements were similar to the normal
gravity condition (Guardiera et al. 2007). In the context of
Bayesian integration, these and our results are compatible with
the fact that visual feedback—providing good estimates of the
effector’s position and velocity—comes into play in the con-
text of movement control, whereas force estimation is mostly
based on prior experience and on proprioceptive signals, the
latter being directly influenced by the force background.
Our hypothesis that gravitational forces are used to calibrate
the internal models is compatible with the observation that
under the 0 g condition, the mass discrimination threshold is
impaired (Ross et al. 1984). This suggests that the loss of
information provided by the object weight alters the internal
estimates of its mass. Similarly, we have proposed in a recent
study that the control strategy under 0 g was modulated by a
greater uncertainty affecting the internal representation of arm
and held objects dynamics (Crevecoeur et al. 2010). The
present paper gives an interpretation of this phenomenon under
0 g, there is no weight information that can be mapped onto
grip motor commands at movement initiation.
The Bayesian inference model also provides a theoretical
framework in which the variation in regressions parameters can
be explained. The first control experiment revealed that the
effect of a change in movement kinematics may contribute to
the hypergravity results because the regressions offsets tended
to increase in the fast condition. Indeed, the hypothesis that
subjects exchange gain for offset to minimize grip output
variability under higher loads also applies to faster movements.
However, this tendency was weaker than that in the heavy
condition, where the increase in regressions offsets was signif-
icant. In addition, the fast versus normal experiment produced
a change in movement kinematics that was greater than the
changes in kinematics observed under hypergravity. Thus al-
though the effect of a change in movement kinematics should
not be rejected, our data indicate that it had a limited impact on
the increase in regression offsets observed under hypergravity.
Based on the second control experiment, we interpreted that
the load force prediction was based on a combination of the
perception of the object weight and a reliable representation of
the movement kinematics. Thus the overestimation of the
inertial loads may be a consequence of the fact that inferring
inertia from weight uses a Bayesian prior assumption that the
gravity was constant. According to the hypothesis of Bayesian
integration, the prior expectation should be partially corrected
by the sensory feedback that conveys information about the
actual load variations. The partial feedback correction gives
further understanding about the fact that, in comparison with
the strategy observed in the loaded condition of the second
control experiment, the regressions parameters in hypergravity
increased by a smaller amount than that if the sensorimotor
mapping used for the anticipation of inertial loads was exclu-
sively based on the prior assumption that gravity was constant.
Despite this bias, our results demonstrate that arm and grip
motor commands are dissociated. Similar results were reported
in the context of oscillatory movements by White et al. (2005)
who showed that the grip force was adjusted to the actual load
despite the fact that the variation of load force resulted from a
distinct combination of object mass, movement acceleration,
and gravity. In the present context of discrete movements,
independent prediction must be estimated for each trial, which
presumably hardens a fine GF adjustment relative to the actual
load. In addition, our subjects were experiencing a change in
gravity for the first time, whereas the subjects tested by White
and colleagues (2005) had extensive experience with parabolic
flights (?300 parabolas). Another factor that possibly alters the
adjustment of internal prior estimate corresponding to the
hypergravity condition is the alternation of gravitational phases
to which subjects were exposed in parabolic flights. This
alternation between different gravitational phases can induce
washout between parabolas and motor variability, rendering
the process of early adaptation occurring during the first trials
quite hard to observe. Our sample did not allow observing such
an early adaptation effect and we therefore concentrated on the
main effect and the evolution across the blocks, which could be
reliably addressed. Under more stable exposure to hypergrav-
ity, the investigation of isometric force production revealed
that practice under hypergravity (3 g) improves the force
scaling (Gobel et al. 2006). Thus regarding precision grip
control, we expect that after a longer and more stable exposure,
humans are able to learn an unbiased prior mapping between
weight and loads that corresponds to a novel gravitational
A C K N O W L E D G M E N T S
We thank the subjects for kindly participating in this study.
G R A N T S
This work was supported by PROgramme for the Development of Scientific
EXperiments (PRODEX) program grants, Action de Recherche Concertée
(Belgium), and the European Space Agency of the European Union. This paper
presents research results of the Belgian Network Dynamical Systems, Control
and Optimization, funded by the Interuniversity Attraction Poles Programmes,
initiated by the Belgian State, Science Policy Office. The scientific responsi-
bility rests with its authors.
D I S C L O S U R E S
No conflicts of interest, financial or otherwise, are declared by the author(s).
R E F E R E N C E S
André T, Lefèvre P, Thonnard J-L. Fingertip moisture is optimally modu-
lated during object manipulation. J Neurophysiol 103: 402–408, 2010.
1407SENSORIMOTOR MAPPING FOR ANTICIPATORY GRIP FORCE MODULATION
J Neurophysiol • VOL 104 • SEPTEMBER 2010 • www.jn.org
Asanuma H. Functional-role of sensory inputs to the motor cortex. Prog
Neurobiol 16: 241–262, 1981.
Augurelle AS, Penta M, White O, Thonnard J-L. The effects of a change in
gravity on the dynamics of prehension. Exp Brain Res 148: 533–540, 2003a.
Augurelle AS, Smith AM, Lejeune T, Thonnard J-L. Importance of cuta-
neous feedback in maintaining a secure grip during manipulation of hand-
held objects. J Neurophysiol 89: 665–671, 2003b.
Berniker M, Kording K. Estimating the sources of motor errors for adapta-
tion and generalization. Nat Neurosci 11: 1454–1461, 2008.
Crevecoeur F, Thonnard J-L, Lefèvre P. Forward models of inertial loads in
weightlessness. Neuroscience 161: 589–598, 2009a.
Crevecoeur F, Thonnard J-L, Lefèvre P. Optimal integration of gravity in
trajectory planning of vertical pointing movements. J Neurophysiol 102:
Crevecoeur F, McIntyre J, Thonnard J-L, Lefèvre P. Movement stability
under uncertain internal models of dynamics. J Neurophysiol 104: 1301–
Duhamel JR, Colby CL, Goldberg ME. The updating of the representation
of visual space in parietal cortex by intended eye-movements. Science 255:
Fisk J, Lackner JR, Dizio P. Gravitoinertial force level influences arm
movement control. J Neurophysiol 69: 504–511, 1993.
Flanagan JR, Wing AM. Modulation of grip force with load force during
point-to-point arm movements. Exp Brain Res 95: 131–143, 1993.
Flanagan JR, Wing AM. The stability of precision grip forces during cyclic
arm movements with a handheld load. Exp Brain Res 105: 455–464, 1995.
Flanagan JR, Wing AM. The role of internal models in motion planning and
control: evidence from grip force adjustments during movements of hand-
held loads. J Neurosci 17: 1519–1528, 1997.
Franklin DW, Burdet E, Tee KP, Osu R, Chew CM, Milner TE, Kawato
M. CNS learns stable, accurate, and efficient movements using a simple
algorithm. J Neurosci 28: 11165–11173, 2008.
Franklin DW, Osu R, Burdet E, Kawato M, Milner TE. Adaptation to
stable and unstable dynamics achieved by combined impedance control and
inverse dynamics model. J Neurophysiol 90: 3270–3282, 2003.
Girgenrath M, Gobel S, Bock O, Pongratz H. Isometric force production in
high Gz: mechanical effects, proprioception, and central motor commands.
Aviat Space Environ Med 76: 339–343, 2005.
Gobel S, Bock O, Pongratz H, Krause W. Practice ameliorates deficits of
isometric force production in ?3 Gz. Aviat Space Environ Med 77: 586–
Guardiera S, Bock O, Poncratz H, Krause W. Acceleration effects on
manual performance with isometric and displacement joysticks. Aviat Space
Environ Med 78: 990–994, 2007.
Harris CM, Wolpert DM. Signal-dependent noise determines motor plan-
ning. Nature 394: 780–784, 1998.
Izawa J, Rane T, Donchin O, Shadmehr R. Motor adaptation as a process of
reoptimization. J Neurosci 28: 2883–2891, 2008.
Johansson RS, Westling G. Roles of glabrous skin receptors and sensory
motor memory in automatic-control of precision grip when lifting rougher or
more slippery objects. Exp Brain Res 56: 550–564, 1984.
Kording KP, Wolpert DM. Bayesian integration in sensorimotor learning.
Nature 427: 244–247, 2004.
Liu D, Todorov E. Evidence for the flexible sensorimotor strategies predicted
by optimal feedback control. J Neurosci 27: 9354–9368, 2007.
Mierau A, Girgenrath M, Bock O. Isometric force production during
changed-Gz episodes of parabolic flight. Eur J Appl Physiol 102: 313–318,
Monzee J, Lamarre Y, Smith AM. The effects of digital anesthesia on force
control using a precision grip. J Neurophysiol 89: 672–683, 2003.
Nowak DA, Hermsdörfer J, Glasauer S, Philipp J, Meyer L, Mai N. The
effects of digital anaesthesia on predictive grip force adjustments during
vertical movements of a grasped object. Eur J Neurosci 14: 756–762, 2001a.
Nowak DA, Hermsdörfer L, Philipp J, Marquardt C, Glasauer S, Mai N.
Effects of changing gravity on anticipatory grip force control during point-
to-point movements of a handheld object. Motor Control 5: 231–253, 2001b.
Pigeon P, Bortolami SB, Dizio P, Lackner JR. Coordinated turn-and-reach
movements. I. Anticipatory compensation for self-generated Coriolis and
interaction torques. J Neurophysiol 89: 276–289, 2003.
Ross H, Brodie E, Benson A. Mass discrimination during prolonged weight-
lessness. Science 225: 219–221, 1984.
Singh K, Scott SH. A motor learning strategy reflects neural circuitry for limb
control. Nat Neurosci 6: 399–403, 2003.
Todorov E. Cosine tuning minimizes motor errors. Neural Comput 14:
Todorov E, Jordan MI. Optimal feedback control as a theory of motor
coordination. Nat Neurosci 5: 1226–1235, 2002.
White O, McIntyre J, Augurelle AS, Thonnard J-L. Do novel gravitational
environments alter the grip-force/load-force coupling at the fingertips? Exp
Brain Res 163: 324–334, 2005.
Witney AG, Wing A, Thonnard J-L, Smith AM. The cutaneous contribution
to adaptive precision grip. Trends Neurosci 27: 637–643, 2004.
Wolpert DM, Flanagan JR. Motor prediction. Curr Biol 11: R729–R732,
Zatsiorsky VM, Gao F, Latash ML. Motor control goes beyond physics:
differential effects of gravity and inertia on finger forces during manipula-
tion of handheld objects. Exp Brain Res 162: 300–308, 2005.
1408 F. CREVECOEUR, J.-.L. THONNARD, AND P. LEFÈVRE
J Neurophysiol • VOL 104 • SEPTEMBER 2010 • www.jn.org