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Volume 17, Number 4,
Issue of February 15, 1997
pp. 1519-1528
Copyright ©1997 Society for Neuroscience
The Role of Internal Models in Motion Planning and Control:
Evidence from Grip Force Adjustments during Movements of Hand-Held
Loads
J. Randall Flanagan1 and
Alan M. Wing2
1 Department of Psychology, Queen's University,
Kingston, Ontario, Canada K7L 3N6, and 2 Medical Research
Council Applied Psychology Unit, Cambridge CB2 2EF, United Kingdom
ABSTRACT
- INTRODUCTION
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- FOOTNOTES
- REFERENCES
ABSTRACT 
We investigated the issue of whether or not the CNS makes use of an
internal model of the motor apparatus in planning and controlling arm
movements. In particular, we tested the ability of subjects to predict
different hand-held loads by examining grip force adjustments used to
stabilize the load in the hand during arm movements.
Subjects grasped a manipulandum using a precision grip with the tips of
the thumb and index finger on either side. The grip force (normal to
the contact surfaces) and the load force (tangential to the surfaces)
were measured, along with the trajectory of the hand. The manipulandum
was attached to two servo-controlled linear motors used to create
inertial and viscous loads as well as a composite load, including
inertial, viscous, and elastic components.
The form of the hand trajectory was independent of load for some
subjects but varied systematically across load conditions in others.
Nevertheless, under all load conditions and in all subjects, grip force
was modulated in parallel with, and thus anticipated, fluctuations in
load force despite the marked variation in the form of the load
function. This indicates that the CNS is able to predict the load force
and the kinematics of hand movement on which the load depends. We
suggest this prediction is based on an internal model of the motor
apparatus and external load and is used to determine the grip forces
required to stabilize the load.
Key words:
internal model;
feedforward control;
reaching movement;
dynamics;
grip force;
load force;
hand trajectory
INTRODUCTION
A current controversy in motor control is whether
the CNS makes use of an internal model of the motor apparatus in
planning and executing goal-directed movements. A number of
investigators have suggested that an internal model is used either to
predict the movement consequences of motor commands (forward model)
(Jordan and Rumelhart, 1992
; Miall et al., 1993; Jordan et al., 1994; Wolpert et al., 1995) or to determine the commands needed to achieve a
desired movement trajectory (inverse model) (Saltzman, 1979; Atkeson,
1989; Uno et al., 1989; Hollerbach, 1990). However, other workers have
proposed control theories that explicitly reject the notion of an
internal model (Bizzi et al., 1984; Flash, 1987; Bullock and Grossberg,
1988; Feldman et al., 1990; Flanagan et al., 1993a). We tested the
hypothesis that an internal model is used to predict movement-dependent
loads by examining grip force adjustments during arm movements with
hand-held loads. In particular, we investigated whether changes in grip
force anticipate, or predict, fluctuations in load force under
different load conditions.
When an object is held with the tips of the thumb and index finger at
the sides, grip (or normal) force allows the development of frictional
force to counteract the load (or tangential) force. In a series of
elegant studies, Johansson and colleagues (Johansson and Westling,
1984; Johansson et al., 1992) have shown that, when lifting objects or
pulling on fixed loads, grip force (GF) is adjusted in parallel with
changes in load force (LF) such that it is always slightly greater than
the minimum required to prevent slip.
Recently, we have examined GF adjustments during rapid arm movements
with hand-held objects. We have shown that GF is modulated in parallel
with fluctuations in the acceleration-dependent inertial load (Flanagan
et al., 1993b; Flanagan and Wing, 1993, 1995; Flanagan and Tresilian,
1994). This finding indicates that the CNS is able to predict precisely
the movement-induced load, and it seems reasonable to suggest that this
prediction is based on an internal model of the motor apparatus and
external load.
However, to date we have examined only inertial loads and cannot rule
out the possibility that the precise anticipatory modulation of GF with
fluctuations in LF is restricted to these loads, perhaps reflecting a
relatively fixed relation between motor commands for arm movement to
those governing GF. The relation between arm movement motor commands
and the load experienced at the hand will depend on the type of load
being moved. Thus, to adjust GF precisely for fluctuations in LF under
different load conditions, it is necessary to alter the mapping between
arm movement and GF commands. In this paper, we examine the
coordination of GF and LF during movements of inertial, viscous, and
elastic loads. Should GF and LF be coupled precisely under all three
load conditions, we would have evidence that the commands for grip
force are not rigidly linked to the commands for arm movement but,
instead, are based on an internal model of the motor apparatus and
external load.
MATERIALS AND METHODS
Subjects. Fifteen subjects, including members of the
subject panel and staff of the MRC Applied Psychology Unit,
participated in this study with informed consent. The panel subjects
were paid for their participation. The subjects included eight men and
seven women between the ages of 24 and 40. Ten of the subjects
completed all three experiments described below and, thus, the present
analyses will focus on their data.
Experimental setup. Subjects grasped a manipulandum
instrumented with a three-dimensional force transducer (Novatech, model F233) that recorded the grip force, normal to the grip surface, and the
horizontal and vertical load forces tangential to the surface. A
one-dimensional accelerometer (Entran, model EGB-125-10D) was taped to
the manipulandum to measure acceleration in the direction of movement.
The manipulandum was attached to a two-dimensional force transducer
(Novatech, model F232) that recorded forces in the horizontal plane.
The two-dimensional transducer was fixed to two force-served linear
motors coupled at right angles to give motion in the horizontal plane
(see Fig. 1). Position was provided by an optical
encoder attached to the motor.
Fig. 1.
A, Top view of the experimental
setup. Subjects grasp a manipulandum attached to two force-served
linear motors mounted at right angles to give motion in the horizontal
plane. B, Side view of the manipulandum instrumented
with force sensors to measure grip force normal to the contact surface
and load forces tangential to the surface.
[View Larger Version of this Image (20K GIF file)]
A Macintosh IIfx computer with a 16 bit A-D board (National
Instruments, model NBMI016X) was used to sample the position and acceleration of the manipulandum and the five forces measured by the
two-dimensional and three-dimensional force transducers at 500 Hz. The
computer also was used to control the load force, resisting the
movement on the basis of the acceleration, velocity (integrated from
acceleration), or position of the manipulandum. The force servo rate
(i.e., the speed of the control loop) was 80 Hz.
In the inertial and viscous load conditions, we were able to generate
nearly pure inertial and viscous loads. However, we were unable to
achieve a pure elastic load and thus will refer to this load as a
composite load to reflect the fact that it also contained inertial and
viscous components. Regression analysis, in which the measured load
force was regressed against position, velocity, and acceleration, was
used to estimate the mass (m), viscosity (b), and
elasticity (k) for each trial. Then these estimates were
averaged across trials to obtain single estimates for each of the 10 subjects; the latter then were averaged across subjects to obtain a
single estimate for each load condition. In the inertial condition, the
load was primarily inertial (m = 1.41 kg), but there
was a small viscous component (b = 2.55 kg/sec). In the viscous condition, the load was predominantly viscous
(b = 18.80 kg/sec), but there was a small inertial
component (m = 0.70 kg). In the complex load condition,
there was a large elastic component (k = 31.32 N/m) as
well as substantial inertial (m = 1.09 kg) and viscous
(b = 7.84 kg/sec) components. Matched-samples
t tests (using subject means) revealed that there were no
significant differences in these estimates as a function of movement
direction (push vs pull; see below). It is important to note that the
fact that we used a composite load rather than a pure elastic load has
no bearing on the logic of the experiment. We simply wished to generate
three markedly different loads to assess whether the coupling between
GF and LF is independent of the type of load.
Experimental procedure. Each subject performed 40 trials in
each of the three load conditions. All subjects first completed the
inertial load trials, followed by the viscous and then the composite
load trials. Each set of 40 trials consisted of alternating movements
away from (pushes) and toward (pulls) the body, moving the manipulandum
a distance of 26 cm between movement end points (marked with strips of
bright tape). Subjects were instructed to make each movement a single
action and were told not to be too concerned about the accuracy of end
point positioning. The subjects also were asked to move the
manipulandum in a straight line. Because the manipulandum was free to
move laterally (the lateral load force was servo-controlled to zero),
the subjects received visual feedback if they erroneously pushed the
manipulandum sideways. All subjects were able to produce straight line
movements consistently. Because of the position of the subject in
relation to the apparatus (see Fig. 1), movements involved shoulder and elbow rotations with relatively little wrist motion. However, no
specific instructions regarding joint motions were provided to the
subject.
Data analysis. The raw force and kinematic data were
smoothed digitally with a Butterworth fourth-order, zero-phase lag,
low-pass filter. A cutoff frequency of 6 Hz was used for the position
signal; a cutoff of 8 Hz was used for remaining signals. Velocity was obtained by digitally integrating the acceleration signal. The LF was
computed as the resultant of the horizontal and vertical forces
(measured from the three-dimensional force transducer) tangential to
the grasp surface. The ratio of GF to LF also was computed and will be
referred to as the force ratio. The start time of the movement was
defined as the point at which the absolute acceleration of the
manipulandum first exceeded 10 cm/sec2, and the end time
was defined as the point at which the absolute acceleration dropped
below 10 cm/sec2 for the last time. ANOVA and linear
regression analysis were used to test various experimental effects. A
p value of 0.05 was considered statistically
significant.
RESULTS
The results consist of two main sections. The first focuses
on the coordination of grip force (GF) and load force (LF) under the
three load conditions. In the second section, the form of the hand
velocity profiles is considered. In this paper, we have focused on the
kinematic and kinetic patterns observed during steady-state performance
after subjects completed initial trials under each load condition. A
report examining the performance during the initial trials under the
different load conditions is forthcoming.
Coordination of grip force and load force
The main result of this paper is that, in each load condition, GF
is adapted to the LF such that the two forces fluctuate in parallel.
This finding is illustrated in Figure 2, which shows kinematic and kinetic records from a single push trial under each of
the three load conditions for one subject (S5). In each panel the
shaded trace in the top part of the figure indicates the (primary) kinematic variable determining the component of load force in the
direction of movement (HF). Under the inertial load,
GF has two peaks that correspond in time to the peaks in LF. Moreover, GF tracks LF throughout the movement. The initial rise in GF allows the
hand to accelerate the object without slip; the second GF rise permits
the hand to decelerate the object without slip. Under the viscous load,
the GF function exhibits a single peak that coincides with the peak LF.
The GF and LF peaks occur near the middle of the movement when
acceleration is close to zero and velocity is close to its maximum.
Thus, peak GF occurs at a different point in the movement than either
of the GF peaks observed under the inertial load. Finally, in the
composite load condition, GF again is modulated in parallel with the
LF, which primarily reflects changes in position but also exhibits some
covariation with acceleration and velocity.
Fig. 2.
Single kinematic and force records from one
subject under the three load conditions. Shaded regions
indicate the horizontal load force (HF) resisting
the movement and the primary kinematic variable on which this component
of the load depended. Under all three load conditions, grip force
(GF) is adjusted in parallel with fluctuations in
load force (LF), the resultant load tangential to
the grasp surface. All calibration bars start at zero. Dashed vertical lines indicate movement onset.
[View Larger Version of this Image (19K GIF file)]
In Figures 3-5 we present superimposed traces for pulls
and pushes under each load condition for two subjects (S8, S10). These traces were selected from the last 10 push and last 10 pull trials, by
which time the subjects had adapted to the load. The panels in these
figures show kinematics (above) and kinetics (below) as well as the
ratio of GF to LF, or force ratio. Under the inertial load condition,
all subjects exhibited velocity profiles that were unimodal and
approximately symmetric. Similar velocity profiles have been described
previously for movements under inertial loading (Ruitenbeek, 1984;
Atkeson and Hollerbach, 1985; Stein et al., 1988; Bock, 1990). In the
viscous and composite load conditions, the form of the velocity profile
varied across subjects. Approximately one-half of the subjects,
including S8, exhibited nearly symmetric velocity profiles, regardless
of the load. However, other subjects, S10 among them, exhibited
positively skewed velocity profiles under the viscous and/or complex
load conditions. One subject, S6, produced velocity profiles that were
skewed negatively in the viscous condition.
Fig. 3.
Overlaid kinematic and kinetic records taken from
the last 20 trials under the inertial load condition (after adaptation
to the load). Five push and five pull trials are shown for two
subjects. Calibration values for bars are given in the bottom
left panel. All bars start at zero.
[View Larger Version of this Image (29K GIF file)]
As illustrated in Figures 3, 4, 5, the form of the GF
function varies systematically across the three load conditions.
However, under all load conditions, GF fluctuates in parallel with LF. Right from the beginning of the movement, GF increases and decreases in
phase with LF. If GF were adjusted in reaction to changes in LF, we
would expect modulations in GF to lag behind changes in LF. The fact
that the two forces vary in phase indicates that GF anticipates LF. We
have previously reported parallel changes in GF and LF during vertical
arm movements with hand-held objects in which the load acting on the
object included gravitational and acceleration-dependent inertial
components (Flanagan and Wing, 1993, 1995). The present results
indicate that the tight coupling between GF and LF extends to other
loads. Because LF depends on both the trajectory of the hand and the
load properties, the precise anticipatory GF adjustments evident in
Figures 3, 4, 5 indicate that the motor system is able to
predict both the trajectory and the load.
Fig. 4.
Overlaid kinematic and kinetic records taken from
the last 20 trials under the viscous load condition (after adaptation
to the load). Five push and five pull trials are shown for two
subjects. Calibration values for bars are given in the bottom
left panel. All bars start at zero.
[View Larger Version of this Image (29K GIF file)]
Fig. 5.
Overlaid kinematic and kinetic records taken from
the last 20 trials under the composite load condition (after adaptation to the load). Five push and five pull trials are shown for two subjects. Calibrations for bars are given in the bottom left
panel. All bars start at zero.
[View Larger Version of this Image (27K GIF file)]
To assess the phase relation between GF and LF quantitatively, we
computed cross-correlations between GF rate and LF rate, the first time
derivatives of GF and LF. (Force rates were used to obtain a more
sensitive measure of the phase relation.) The phase lag at which the
maximum correlation occurred was computed for each of the last 20 trials from each load condition. For each subject we computed mean
scores for each load and movement direction (push, pull). When further
averaged across subjects, the phase lags for the six load-by-direction
combinations ranged from 
3 to 21 msec with an overall mean of 14 msec
a positive lag indicating that GF rate led LF rate. A repeated
measures ANOVA failed to reveal reliable effects of load
(F(2,18) = 3.04; p = 0.07) or direction (F(1,9) = 0.04; p = 0.84) on phase lag. [In contrast, the maximum correlation coefficient
did vary significantly with load (F(2,18) = 11.3; p = 0.001) but not direction
(F(1,9) = 1.4; p = 0.27). The
mean coefficients for the inertial, viscous, and composite loads were
0.76, 0.90, and 0.76, respectively.] Finally, no reliable
correlations between phase lag and trial number were observed
(p > 0.10 in all six loads by direction
conditions). These results are consistent with the observation that GF
is modulated in parallel with, and thus anticipates, fluctuations in
LF.
The parallel modulation of GF and LF also is reflected in the force
ratio traces shown in Figures 3, 4, 5. The force ratio provides an index
of grasp stability; if the ratio drops below a critical value, slip
occurs. Johansson and Westling (1984) observed that the force ratio
tends toward a stable minimum value in manipulation tasks and suggested
that the ratio is a controlled parameter. The minimum ratios are
approximately similar across loads despite differences in the form of
the force ratio curve because of differences in the load function.
(Note that the ratio increases rapidly when the load force approaches
zero.)
To provide a summary across subjects, we computed a number of
descriptive statistics on the basis of the last 30 trials (i.e., excluding the first 10 trials) from each load condition. For each subject we computed a mean score for each combination of load and
direction (push, pull), yielding six scores per subject. We then
averaged these mean scores across subjects. Table 1
presents means and SD for the following variables: movement time (MT)
and peak velocity; times to peak velocity, the initial LF peak, and the
initial GF peak (all expressed as a percentage of MT); the amplitudes
of the initial LF peak and the initial GF peak; and the median force
ratio during the movement. Repeated measures ANOVA was used to assess
the effects of load condition and movement direction on these
variables.
Table 1.
|
Inertial
load
|
Viscous load
|
Composite
load
|
| Pushes |
Pulls |
Pushes |
Pulls |
Pushes |
Pulls |
|
| Movement
time (MT)
(sec) |
0.72 |
0.72 |
0.82 |
0.78 |
0.87 |
0.84 |
|
(0.05) |
(0.06) |
(0.08) |
(0.13) |
(0.08) |
(0.09) |
| Peak
velocity
(cm/sec) |
71.6 |
71.4 |
68.5 |
66.7 |
56.6 |
55.6 |
|
(7.4) |
(8.8) |
(9.1) |
(10.3) |
(7.0) |
(8.7) |
| Time
to peak velocity (% MT) |
46.1 |
46.9 |
42.6 |
44.0 |
45.6 |
46.2 |
|
(4.2) |
(3.3) |
(6.6) |
(8.3) |
(5.7) |
(4.3) |
| Peak
load force (LF)
(N) |
7.1 |
7.1 |
13.4 |
13.8 |
9.79 |
9.14 |
|
(2.1) |
(1.2) |
(3.1) |
(2.4) |
(2.4) |
(1.1) |
| Peak
grip force (GF)
(N) |
15.7 |
18.1 |
23.6 |
28.8 |
20.6 |
21.9 |
|
(5.4) |
(4.7) |
(5.7) |
(4.7) |
(3.9) |
(4.7) |
| Time
to peak LF (% MT) |
28.3 |
26.0 |
38.5 |
38.0 |
|
|
|
(6.3) |
(3.7) |
(6.3) |
(9.4) |
|
|
| Time
to peak GF (% MT) |
27.3 |
26.1 |
36.6 |
35.1 |
|
|
|
(5.3) |
(4.3) |
(9.7) |
(9.6) |
|
|
| Median
force
ratio |
2.95 |
3.07 |
2.25 |
2.63 |
2.41 |
2.76 |
|
(1.05) |
(0.58) |
(0.46) |
(0.55) |
(0.83) |
(0.95) |
|
|
Means and SD (in parentheses) of the mean scores of 10 subjects.
Subject means were based on the last 30 trials in each load condition.
|
|
There were significant effects of load
(F(2,18) = 18.4; p < 0.001) and
direction (F(1,9) = 5.22; p = 0.048) on MT, but the interaction between load and direction was not
reliable (F(2,18) = 2.74; p = 0.092). MT was less in the inertial load condition than in the other
load conditions. On average, the pulls were slightly shorter than the
pushes. There was a reliable effect of load on peak velocity
(F(2,18) = 17.3; p < 0.001),
but neither the effect of direction (F(1,9) = 1.23; p = 0.295) nor the interaction between direction
and load (F(2,18) < 1) was significant. The percentage time to peak velocity, a measure of the skewness of the
velocity profile, did not vary significantly with load
(F(2,18) = 3.40; p = 0.056) or
direction (F(1,9) = 2.04; p = 0.187), and the interaction between load and direction
(F(2,18) < 1) was also not significant.
In the inertial load condition, the initial peaks in GF and LF both
occurred approximately a quarter of the way through the movement. In
the viscous load condition, the two force peaks closely coincided in
time but occurred later in the movement (35-40% of MT). Under the
composite load condition, the timing of the GF and LF peaks was quite
variable, often occurring at the end of the movement. The percentage
time to peak GF was reliably different in the inertial and viscous load
conditions (F(1,9) = 218; p < 0.001), as was the percentage time to peak LF
(F(1,9) = 270; p < 0.001). In
neither case was there a reliable effect of direction (F(1,9) < 1 in both instances).
Finally, there was a reliable effect of load condition on median
force ratio (F(2,18) = 5.1; p = 0.018). The ratio was lowest for the viscous load and highest for the
inertial load. No reliable effects were found for direction
(F(1,9) = 1.40; p = 0.27) or the
interaction between load and direction (F(2,18) < 1).
There is evident trial-to-trial variation in Figures 3, 4, 5, and to
assess the coordination between GF and LF, we examined the relation
between the time to peak GF and the time to the peak LF using linear
regression analysis. For the inertial load trials, which exhibit two
force peaks, we took the first GF peak and the first LF peak. (The
composite load trials were not analyzed because of the difficulty of
obtaining clearly defined peaks.) Separate analyses were performed for
each subject and load condition (inertial, viscous), collapsing across
pushes and pulls. For 18 of the 20 subject-by-load combinations, the
slope of the relation between time to peak GF and time to peak LF was
significant (r = 0.38-0.93; p < 0.05 in all 18 cases). These results indicate that, on a trial-by-trial basis, there is a close temporal coupling between GF and LF for both
the inertial and viscous load conditions. To assess the extent to which
the two force peaks coincided in time, we computed the time lag between
peak GF and peak LF (a positive lag indicating that GF leads LF) on a
trial-by-trial basis and then obtained average scores for each subject
for each of the two load conditions (inertial and viscous). The
mean ± SD of these scores was 3 ± 14 msec for the inertial
load and 19 ± 26 msec for the viscous load. A repeated measures
ANOVA indicated that there was no effect of load condition on the time
lag between peak forces (F(1,9) = 3.53;
p = 0.09). These results are in agreement with the
cross-correlation phase lags reported above and indicate that GF tends
to lead LF by a small margin (11 msec on average, overall). The
findings further support the notion that modulations in GF anticipate
fluctuations in LF.
Hand velocity profiles
As noted above, the form of the hand velocity
profile was relatively invariant across loads for some subjects but not
for others. This is illustrated in Figure 6, which shows
normalized velocity profiles for four subjects taken from the last ten
pull trials. These profiles were normalized with respect to area (i.e., displacement) and peak velocity (see Atkeson and Hollerbach, 1985) and
then aligned to peak velocity. The figure shows data from two subjects
(S6 and S8) whose velocity profiles were similar across loads and from
two other subjects (S3 and S10) whose profiles under the different load
conditions were visibly different. In particular, the velocity profiles
under the viscous load were skewed more positively than those observed
under the inertial and composite loads. This observation was confirmed
quantitatively by using percentage time to peak velocity, a
measure of the skew of the velocity profile. Although the overall
effect of load on percentage time to peak velocity was not significant
across subjects (see above), when the data from each subject were
analyzed separately, differences in percentage time to peak velocity
across load conditions were observed in six of the ten subjects
(p < 0.05 in all 6 cases). In five of these six
subjects, the velocity profiles under the viscous load condition were
skewed more positively than in the other two load conditions. (One
subject, S7, showed the opposite result.) Thus, in one-half of the
subjects, the velocity profiles were skewed more positively under
viscous loading than under inertial or composite loading.
Fig. 6.
Five hand velocity profiles from the last 10 pull
trials in each of the three load conditions for four subjects. Velocity profiles were normalized with respect to area and peak velocity and
aligned with respect to peak velocity. Whereas one-half of the subjects
produced profiles that were invariant across loads (illustrated by
S8 and S6), the others did not
(illustrated by S10 and S3).
[View Larger Version of this Image (32K GIF file)]
DISCUSSION
We have shown that when hand-held loads are moved that depend on
different kinematic variables, GF is modulated in parallel with and
thus anticipates the LF in all cases. Because LF depends on both the
dynamics (i.e., load properties) of the object and the kinematics of
the object, the present results indicate that the CNS (1) has an
internal model of the dynamics of the object and (2) can predict the
trajectory of the object. The latter prediction is, presumably, based
on an internal model of the loaded limb. Thus, our results indicate
that not only does the CNS build an internal model of the external
load, but it also integrates the dynamics of the load into an internal
model of the motor apparatus as a whole.
The finding that the CNS is able to predict precisely the different
hand-held loads places strong constraints on theories of motor control.
Consider, first, the inverse model of reaching, which assumes that the
CNS explicitly plans the trajectory of the hand and then computes the
central commands required to realize the desired trajectory. In this
case, the planned trajectory of the hand could be sent to a grip force
controller, which also would receive information about the properties
of the object, including its dynamics and surface texture. Provided
that the internal model is accurate (so that the actual kinematics
match the planned kinematics), then the grip force should be adjusted appropriately. The inverse model predicts that, after load adaptation, the form of the hand trajectory will be invariant across loads. However, in one-half of our subjects we found that the form of the hand
trajectory changed as a function of load. Although several investigators have reported that the form of the hand velocity profile
is unaffected by inertial (Ruitenbeek, 1984; Atkeson and Hollerbach,
1985; Bock, 1990) and velocity-dependent loads (Lackner and Dizio,
1992; Shadmehr and Mussa-Ivaldi, 1994), other workers have reported
changes in the movement trajectory because of various loads (Stein et
al., 1988; Uno et al., 1989). These findings speak to the flexibility
of motion planning. Recently, Rosenbaum et al. (1993) have proposed a
model of reaching based on the idea of weighted cost functions.
According to this model, the CNS selects a trajectory by balancing
various costs associated with end point accuracy, movement amplitude,
etc. Within this framework, one might speculate that the two patterns
of results reported here might reflect differences in cost assignment
(see also Nelson, 1983). Thus, for example, the subjects who exhibited
invariance in the form of the hand velocity profile may have placed
more weight on the smoothness of the trajectory than the others.
Overall, the present results are better accounted for by an internal
forward model. A forward model of the dynamics of the motor apparatus
and external load would enable the CNS to predict the load force acting
on the hand and thus could serve as the basis of the coordination
between grip force and load force. The forward model does not make any
specific assumptions about the form of the hand trajectory and can be
incorporated into various control schemes. For example, a forward model
could be used in combination with equilibrium point (EP) control
(Flash, 1987; Feldman et al., 1990; Flanagan et al., 1993a). In this
case, movements would be generated by shifting the EP of the hand, and
the forward model would be used to estimate the load force. Then this
information would be used to control grip force, presumably by
specifying the EPs of the fingertips. In addition, a high level
controller might, under some conditions, modify the central commands
governing the EP of the hand to produce a desired trajectory. (It is
worth noting that the 
model predicts that the form of the velocity profile will be skewed more positively under the viscous load condition
than under the inertial load condition if the central commands
underlying the movement are the same under both loads.)
Grip force adjustments during object transport may be considered more
broadly as anticipatory postural adjustments (APAs) (Johansson and
Cole, 1994; Wing, 1996). There is a large body of literature on APAs,
and the focus of work in the area has been to characterize adjustments
in trunk and leg muscles (measured in terms of electromyographic
activity and/or ground reaction forces) that occur before arm movements
(Belen
kii et al., 1967; Bouisset and Zattara, 1987). These adjustments
are thought to stabilize the body in the face of potentially
destabilizing reaction forces that arise during arm movement (Friedli
et al., 1988). An internal model of the dynamics of the limb could be
used in stabilization of the body posture in addition to stabilization of the hand-held object during arm movement (Flanagan et al., 1995;
Wing et al., 1997).
Given the evidence favoring the existence of an internal model, the
question naturally arises as to the neural mechanisms involved. Miall
et al. (1993) have suggested that the cerebellum makes use of two
internal models: a forward model of the motor apparatus, which provides
a rapid prediction of the sensory consequences of motor commands, and a
second model of the time lags in the control loop because of receptor
and effector delays, conduction times, and so on. The second model
delays the predicted sensory feedback so that it can be compared
directly with the actual sensory feedback. The error signal from this
comparison may be used to modify motor commands during performance and
to update the first model. In contrast, Kawato and Gomi (1992)
suggested that the cerebellum functions as an inverse model to
translate information about the desired trajectory, provided by signals
from parietal cortex, into the required motor commands. In line with
this idea, Kalaska (1991) has proposed that superior parietal cortex
may provide a neuronal representation of kinematics for kinesthetic perception as well as for movement control.
The models discussed above confer a critical role to sensory feedback
both in modifying the ongoing movement and in parameterizing the
internal model (see also Ghez et al., 1991). In this regard it is
interesting to note that patients with peripheral sensory neuropathy
produce arm movements that are uncoordinated because of failure to
allow for intersegmental dynamics (Sainburg et al., 1993). Thus,
although the cerebellum may provide predictive control, it nevertheless
depends on sensory feedback about current movement conditions. Sainburg
et al. observed that vision markedly improved performance in
deafferented patients. Thus, it seems likely that the patient's
deficits were attributable to a lack of information, such as initial
limb position, required by the cerebellar model rather than a failure
of the internal model itself. However, the results also suggest that
the default internal model, used in the absence of vision, is not
accurate.
Support for the suggestion that the cerebellum contributes to
anticipatory GF adjustments comes from a study by Müller and Dichgans (1994). These authors reported that patients with degenerative cerebellar lesions exhibited a lack of coordination of GF and LF when
performing a lifting task and using a precision grip. In these
patients, GF and LF were decoupled somewhat such that the two forces
did not always change in parallel. In contrast, when normal controls
perform this task, GF and LF are modulated in parallel (Johansson and
Westling, 1984). Moreover, over trials, the cerebellar patients did not
adapt their GF rise rates to match different loads. Although the
patients were able to adjust grip force rates to some degree, they did
so significantly less efficiently than control subjects. Müller
and Dichgans (1994) concluded that this represented a failure of
anticipatory parameterization. It is interesting to contrast the
performance of cerebellar patients with that of parkinsonian subjects
who can appropriately scale their grip force for different weights when
lifting, although they use high grip force levels (Müller and
Abbs, 1990). The deficit in Parkinson's disease may be associated with
problems with force production rather than anticipatory control.
Neurophysiological evidence that the cerebellum contributes to
anticipatory GF adjustments comes from the work of Smith and
colleagues. These researchers have reported that the discharge of
neurons in cerebellum (Espinosa and Smith, 1990), as well as primary
motor cortex (Picard and Smith, 1992), is related to object weight and
texture before movement onset.
The idea that anticipatory GF adjustments are based on an internal
model of the motor system fits well within the more general model of
precision manipulation proposed by Johansson and colleagues, referred
to as "discrete event, sensory-driven control" (Johansson and Cole,
1992, 1994; Johansson and Edin, 1993). According to this control
scheme, precision manipulation involves subtle interplay between
feedforward and feedback mechanisms. Feedforward control, based on an
internal model of the motor system and memory of object properties, is
used to specify motor commands in advance of the movement. During the
movement, sensory feedback from cutaneous mechanoreceptors and other
sources is used intermittently to inform the CNS about the completion
of various phases of the task and to trigger subsequent phases. For
example, during a task in which an object is lifted from a support
surface with a precision grip and then replaced, fast-adapting type I
(FA I) afferents reliably signal the initial contact and final release
of the digits, and FA II afferents (Pacinian corpuscles) are extremely
sensitive to the mechanical transients associated with the lift-off and touch-down of the object (Westling and Johansson, 1987). In addition, sensory feedback is used to update inappropriate motor commands that
lead to mechanical events, such as slip or the generation of excess
grip forces. Also, this information presumably is used to update the
internal model of the motor apparatus and object (Johansson and
Westling, 1987; Johansson, 1996).
FOOTNOTES
Received Oct. 31, 1996; accepted Dec. 6, 1996.
This work was supported by the Natural Sciences and Engineering Council
of Canada, the British Medical Research Council, and a Wellcome
Research Travel Grant to J.R.F.
Correspondence should be addressed to Dr. J. Randall Flanagan at the
above address.
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B. Mehta and S. Schaal
Forward Models in Visuomotor Control
J Neurophysiol,
August 1, 2002;
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[Abstract]
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M. B. Shapiro, G. L. Gottlieb, C. G. Moore, and D. M. Corcos
Electromyographic Responses to an Unexpected Load in Fast Voluntary Movements: Descending Regulation of Segmental Reflexes
J Neurophysiol,
August 1, 2002;
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[Abstract]
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C. Tong, D. M. Wolpert, and J. R. Flanagan
Kinematics and Dynamics Are Not Represented Independently in Motor Working Memory: Evidence from an Interference Study
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Y. Ohki, B. B. Edin, and R. S. Johansson
Predictions Specify Reactive Control of Individual Digits in Manipulation
J. Neurosci.,
January 15, 2002;
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J. Hore, S. Watts, M. Leschuk, and A. MacDougall
Control of Finger Grip Forces in Overarm Throws Made by Skilled Throwers
J Neurophysiol,
December 1, 2001;
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[Abstract]
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D. Timmann, R. Citron, S. Watts, and J. Hore
Increased Variability in Finger Position Occurs Throughout Overarm Throws Made by Cerebellar and Unskilled Subjects
J Neurophysiol,
December 1, 2001;
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I. Birznieks, P. Jenmalm, A. W. Goodwin, and R. S. Johansson
Encoding of Direction of Fingertip Forces by Human Tactile Afferents
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October 15, 2001;
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M.-J. Boudreau, T. Brochier, M. Pare, and A. M. Smith
Activity in Ventral and Dorsal Premotor Cortex in Response to Predictable Force-Pulse Perturbations in a Precision Grip Task
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September 1, 2001;
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D. M. Shiller, D. J. Ostry, P. L. Gribble, and R. Laboissiere
Compensation for the Effects of Head Acceleration on Jaw Movement in Speech
J. Neurosci.,
August 15, 2001;
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G. Bosco and R. E. Poppele
Proprioception From a Spinocerebellar Perspective
Physiol Rev,
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[Abstract]
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J. R. Flanagan and S. Lolley
The Inertial Anisotropy of the Arm Is Accurately Predicted during Movement Planning
J. Neurosci.,
February 15, 2001;
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P. Jenmalm, S. Dahlstedt, and R. S. Johansson
Visual and Tactile Information About Object-Curvature Control Fingertip Forces and Grasp Kinematics in Human Dexterous Manipulation
J Neurophysiol,
December 1, 2000;
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[Abstract]
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D Timmann, S Richter, S Bestmann, K T Kalveram, and J Konczak
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September 1, 2000;
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W. J. Kargo and S. F. Giszter
Afferent Roles in Hindlimb Wipe-Reflex Trajectories: Free-Limb Kinematics and Motor Patterns
J Neurophysiol,
March 1, 2000;
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R. A. Scheidt and W. Z. Rymer
Control Strategies for the Transition From Multijoint to Single-Joint Arm Movements Studied Using a Simple Mechanical Constraint
J Neurophysiol,
January 1, 2000;
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A. G. Witney, S. J. Goodbody, and D. M. Wolpert
Predictive Motor Learning of Temporal Delays
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November 1, 1999;
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P. L. Gribble and D. J. Ostry
Compensation for Interaction Torques During Single- and Multijoint Limb Movement
J Neurophysiol,
November 1, 1999;
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M. K. O. Burstedt, J. R. Flanagan, and R. S. Johansson
Control of Grasp Stability in Humans Under Different Frictional Conditions During Multidigit Manipulation
J Neurophysiol,
November 1, 1999;
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J. Hore, S. Watts, and D. Tweed
Prediction and Compensation by an Internal Model for Back Forces During Finger Opening in an Overarm Throw
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September 1, 1999;
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J. R. Flanagan, M. K. O. Burstedt, and R. S. Johansson
Control of Fingertip Forces in Multidigit Manipulation
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April 1, 1999;
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A. W. Goodwin, P. Jenmalm, and R. S. Johansson
Control of Grip Force When Tilting Objects: Effect of Curvature of Grasped Surfaces and Applied Tangential Torque
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December 15, 1998;
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I. Birznieks, M. K. O. Burstedt, B. B. Edin, and R. S. Johansson
Mechanisms for Force Adjustments to Unpredictable Frictional Changes at Individual Digits During Two-Fingered Manipulation
J Neurophysiol,
October 1, 1998;
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S. J. Blakemore, S. J. Goodbody, and D. M. Wolpert
Predicting the Consequences of Our Own Actions: The Role of Sensorimotor Context Estimation
J. Neurosci.,
September 15, 1998;
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J.-J. Wang, Y. Shimansky, V. Bracha, and J. R. Bloedel
Effects of Cerebellar Nuclear Inactivation on the Learning of a Complex Forelimb Movement in Cats
J Neurophysiol,
May 1, 1998;
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[Abstract]
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P. Jenmalm, A. W. Goodwin, and R. S. Johansson
Control of Grasp Stability When Humans Lift Objects With Different Surface Curvatures
J Neurophysiol,
April 1, 1998;
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[Abstract]
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P. L. Gribble, D. J. Ostry, V. Sanguineti, and R. Laboissiere
Are Complex Control Signals Required for Human Arm Movement?
J Neurophysiol,
March 1, 1998;
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[Abstract]
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R. Shadmehr and H. H. Holcomb
Neural Correlates of Motor Memory Consolidation
Science,
August 8, 1997;
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[Abstract]
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J. R. Flanagan, E. Nakano, H. Imamizu, R. Osu, T. Yoshioka, and M. Kawato
Composition and Decomposition of Internal Models in Motor Learning under Altered Kinematic and Dynamic Environments
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