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The Journal of Neuroscience, September 15, 1998, 18(18):7511-7518
Predicting the Consequences of Our Own Actions: The Role of
Sensorimotor Context Estimation
Sarah J.
Blakemore,
Susan J.
Goodbody, and
Daniel M.
Wolpert
Sobell Department of Neurophysiology, Institute of Neurology,
University College London, London WC1N 3BG, United Kingdom
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ABSTRACT |
During self-generated movement it is postulated that an efference
copy of the descending motor command, in conjunction with an internal
model of both the motor system and environment, enables us to predict
the consequences of our own actions (von Helmholtz, 1867 ; Sperry, 1950;
von Holst, 1954; Wolpert, 1997). Such a prediction is evident in the
precise anticipatory modulation of grip force seen when one hand pushes
on an object gripped in the other hand (Johansson and Westling, 1984;
Flanagan and Wing, 1993). Here we show that self-generation is not in
itself sufficient for such a prediction. We used two robots to simulate
virtual objects held in one hand and acted on by the other. Precise
predictive grip force modulation of the restraining hand was highly
dependent on the sensory feedback to the hand producing the load. The
results show that predictive modulation requires not only that the
movement is self-generated, but also that the efference copy and
sensory feedback are consistent with a specific context; in this case, the manipulation of a single object. We propose a novel computational mechanism whereby the CNS uses multiple internal models, each corresponding to a different sensorimotor context, to estimate the
probability that the motor system is acting within each context.
Key words:
internal model; forward models; prediction; grip force; virtual reality; bimanual coordination
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INTRODUCTION |
The ability to predict the
consequences of our own actions using an internal model of both the
motor system and the external world has emerged as an important
theoretical concept in motor control (Kawato et al., 1987; Jordan and
Rumelhart, 1992; Jordan, 1995; Wolpert et al., 1995; Miall and Wolpert,
1996; Wolpert, 1997). Such models are known as forward models because
they capture the forward or causal relationship between actions, as
signaled by efference copy (Sperry, 1950; von Holst, 1954; Jeannerod et al., 1979), and outcomes. Such forward models may play a fundamental role in coordinative behavior. For example, to prevent an object held
in a precision grip from slipping, sufficient grip force must be
generated to counteract the load force exerted by the object. Despite
sensory feedback delays associated with the detection of load force by
the fingertips (Johansson and Westling, 1984), under both discrete
(Johansson and Westling, 1984; Flanagan and Wing, 1993) and continuous
(Flanagan and Wing, 1993, 1995) self-generated movement and when
pulling on fixed objects (Johansson et al., 1992b), grip force is
modulated in parallel with load force. Conversely, when the motion of
the object is generated externally, grip force lags behind load force
(Cole and Abbs, 1988; Johansson et al., 1992b). This suggests that for
self-produced movements the CNS may use the motor command, in
conjunction with internal models of both the arm and the object, to
anticipate the resulting load force and thereby adjust grip force
appropriately (Flanagan and Wing, 1997).
To assess the generality of such a predictive mechanism, we have
examined the relationship between grip and load force when a sinusoidal
load is applied to an object held in a fixed location by the right
hand. The first experiment was designed to test the hypothesis that
predictive grip force modulation will be observed provided the load
force is self-generated. We examined conditions in which the load force
was generated by motion of either the right or left hand. When the left
hand generated the motion, it did so either directly on the object or
indirectly by causing a robot, under joystick control, to exert the
force on the object. We also examined a condition in which the
sinusoidal load force was externally generated by a robot. Precise
predictive grip force modulation was seen when either the right or left
hand generated the load force directly. However, when the left hand
produced the load force indirectly, via the joystick, there was no
prediction. A significant lag between grip and load force was seen,
similar to when the load was generated externally.
To examine the reasons for this lack of prediction, a second experiment
was performed in which we examined the conditions necessary for
prediction when the left hand generated the load force on the right
hand by acting through a virtual object. Using the virtual object,
simulated by two robots, we could dissociate the forces acting on each
hand. The force acting on the active left hand relative to the right
hand was parametrically varied. This allowed us to test the hypothesis
that to use the motion of the left hand to generate precise predictive
grip force modulation in the right hand, the hands must act through a
physically realizable object. At one level of the force feedback
parameter, the force feedback to each hand was equal and opposite,
thereby simulating a normal physical object between the hands. Precise
prediction was seen under this condition but smoothly deteriorated as
the force feedback deviated from that consistent with a real, rigid object held between the hands.
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MATERIALS AND METHODS |
A total of 14 right-handed subjects (age range, 21-30 years),
who were naive to the issues involved in the research, gave their
informed consent and participated in the study. Nine subjects (six
male, three female) participated in the first experiment. Nine subjects
(six male, three female) participated in the second experiment,
including four of the subjects who had participated in the first
experiment. The experiments were performed 1 month apart.
Apparatus. Subjects sat at a table and gripped a cylindrical
object (radius, 1 cm; width, 4 cm) with the tips of their right thumb
and index finger (Fig. 1). The forearm
was supported on the table and stabilized using velcro straps. The hand
was further stabilized by requiring subjects to grasp a vertically
oriented aluminum rod (diameter, 2 cm) with their three ulnar fingers. The mass of the gripped object (50 gm) was centered midway between the
two grip surfaces, which were covered with sandpaper (No. 240). A
six-axis force transducer (Nano ATI) embedded within the object allowed
the translational forces (and torques) to be recorded with an accuracy
of 0.05 N, including cross-talk. The forces and torques were sampled at
250 Hz by a CED 1401plus data acquisition system. The data were stored
for later analysis and were also used on-line during the experiments.
Grip force was measured perpendicular to the plane of the grip surface
and load force tangential to this plane.
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Figure 1.
Schematic diagram of the apparatus used in
each condition of Experiment 1 and in Experiment 2. Experiment 1:
In all conditions subjects held a cylindrical object in their right
hand. In condition 1 (Robot), the object was attached to
the robot, which produced the load force on the object. In condition 2 (self-produced; right hand), subjects were required to pull down on the
object, which was fixed in a clamp, to track the target load waveform.
In condition 3 (self-produced; left hand), subjects were required
to push the object upward from underneath with their left index
finger to match the target load waveform. In condition 4 (self-produced; joystick), the object was attached to the robot
and the forces produced by the robot were determined by the position of
a joystick moved by the left hand. Experiment 2: An object attached to
a second robotic device was held in the left hand. The motion of the
left hand determined the load force on the object in the right hand.
The relationship between the force acting on the left and right objects
was parametrically varied between trials. See text for details.
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Procedure. In all experiments the target and actual load
force acting on the right hand were displayed to the subject as a continuous scrolling trace on an oscilloscope. The target load force
acted as a guide to the subjects' movements; the subject was
instructed to produce a load force that corresponded to the frequency
and amplitude of the sinusoidal target waveform. For clarity, the load
force produced by the subject was displayed on the oscilloscope below
the target waveform. Two horizontal lines indicated the desired load
amplitude.
In conditions 1 and 4 of Experiment 1 and in Experiment 2 the object
was attached at its midpoint to the end of a lightweight, robotic
manipulator (Phantom Haptic Interface, Sensable Devices, Cambridge,
MA). The robot could generate vertical forces up to 10 N.
Experiment 1. Subjects performed trials of 14 sec in which
they were required to produce a load force that matched the target load
force. The target load force was a sinusoid with offset of 3.5 N and
amplitude of 3 N. The target load force, therefore, varied between
0.5 and 6.5 N, and always acted in an upward direction on the
subjects' right hand. In all conditions, subjects were instructed to
hold onto the object with their right hand and maintain it in a
constant position. For each trial the target frequency was fixed. Six
different target frequencies equally spaced between 0.5 and 3.5 Hz were
each repeated five times in pseudorandom order. To prevent the analysis
of initial transients, 10 sec of data were recorded after the first 4 sec of each trial. Subjects practiced each condition until they could
perform the task adequately. This took between 30 and 60 sec.
In condition 1 (externally produced; robot, Fig. 1), the object was
attached to the robot, which was programmed to produce the target
waveform. Subjects gripped the object with their right hand and were
required to restrain the object, and the target and actual load force
were displayed on the oscilloscope. In this condition the subject did
not need to track the load force because this was generated
automatically by the robot. In condition 2 (self-produced; right hand),
subjects gripped the object, which was fixed in a clamp, with their
right hand. They were required to pull down on the object to track the
target load waveform so that the force acting on their right hand was
in an upward direction. In condition 3 (self-produced; left hand),
subjects were required to push the object upward from underneath with
their left index finger to match the target load waveform. Subjects
were specifically instructed to use their right hand to restrain the
object only, and to avoid using it to push down on the object to match
the target waveform. In condition 4 (selfproduced; joystick), the object was attached to the robot, and the forces produced by the robot
were determined by the position of a low-friction joystick held in the
left hand. The force generated by the robot was linearly related to the
angular position of the joystick with a movement of 4° (4 mm)
producing 1 N. Subjects were required to move the joystick in the
sagittal plane to match the target waveform and were informed that
movements of the joystick caused the force exerted on their right hand.
The order of the conditions was counterbalanced between subjects.
Experiment 2: virtual objects. The object in the right hand
was attached to the robot, and subjects held a second object in a
precision grip with the thumb and index finger of their left hand. This
object was held directly above the first and was attached to a second
robotic device (Fig. 1). Subjects were required to move the object held
in their left hand vertically to produce the load force on the object
held in their right hand. The load force acting on the right hand was
the same for all trials.
Vertical forces at time t into the trial were generated
independently on both the right hand
Ftr and the left hand
Ftl. For all trials the relationship
between movement of the left hand and the force generated on the right
object was simulated, by the robot, as a stiff spring between the
objects. The force was given by Ftr = K (Lt  Rt D), where Lt and
Rt were the vertical positions of the left and
right object, respectively, at time t, K was a fixed spring
constant of 20 N cm 1, and D was the
initial vertical distance between the objects at the start of the
trial. Hence, at the start of each trial there was no force acting on
the right hand (as L0 R0 D = 0), and an upward
movement of the left hand caused an upward force on the object in the
right hand. The force acting on the left hand depended on a feedback
gain parameter g, which could be varied between trials such
that Ftl = gK
(Lt Rt D). When g = 0, the left hand received no
force feedback, whereas when g = 1, the force feedback
to the left hand was equal and opposite to that exerted on the right.
These conditions are similar, in terms of haptic feedback to the left
hand, to conditions 4 (self-produced; joystick) and 3 (self-produced;
left hand) of Experiment 1, respectively.
For each block of trials, the value of the feedback gain parameter
g was fixed at one of seven values equally spaced between 0 and 1.5. Within each block, for gains of 0 and 1, six different target
frequencies equally spaced between 0.5 and 3.5 Hz were used as in
Experiment 1. For each of the other gain values (0.25, 0.5, 0.75, 1.25, and 1.5), three different target frequencies (1.1, 2.3, and 3.5 Hz)
were used. Each frequency was presented for 10 sec and repeated five
times in pseudorandom order; data were recorded after 2 sec in each
trial. Subjects were told that load on the object held in their right
hand was produced by the movements of their left hand. They were
instructed to move the object in their left hand to match the target
waveform whose amplitude was 2 N with offset 2.3 N. The load force
therefore varied between 0.3 and 4.3 N and was always in an upward
direction. Subjects practiced the task until they could perform it
adequately. This took between 1 and 2 min.
Data analysis. Load and grip force were filtered using a
Butterworth 5th order, zero phase lag, low-pass filter with a 10 Hz
cut-off. To analyze the relationship between these two time series,
cross-spectral analysis was performed using Welch's averaged periodogram method (window width, 512 points with a 50% overlap; Matlab signal analysis toolbox).
Because the time series were predominantly sinusoidal, we calculated
five measures at the dominant load frequency. To quantify amplitude
relationships between the two signals, independent of the phase
relationship, two measures were used. The baseline gain was
taken as the ratio of the mean grip and load force
( / ). The relative
degree of modulation was quantified by the amplitude gain
taken as the ratio between the amplitude of the grip and load force
modulation. To quantify the relative temporal relationships between the
grip and load force series, three measures were made. The first two,
phase and lag, quantify the temporal shift
required to align the two series. Phase is expressed in degrees and was taken to lie between 270 and +90°, with negative values
corresponding to grip lagging behind load. This split was chosen at a
point where there were very few data points; based on all the data, only 0.9% lay within a 45° band of +90°. The lag represents the same shift in milliseconds (and should not be confused with phase lag
that is used to measure phase delays in degrees), and again a negative
value indicates grip lagging behind load. Finally, the
coherence of the two signals was used as a measure of the variability of the phase relationship between grip and load force. Coherence values always lie between 0 and 1. If the phase difference is
constant over the entire trial, coherence is 1, whereas
fluctuations in the phase difference results in coherence values
lower than 1.
For each condition in Experiment 1 and for the g = 0 and g = 1 conditions of Experiment 2, the five measures
were averaged across all trials and subjects, binned by frequency, and
plotted with SE bars. Actual rather than target frequency of tracking was used when calculating statistics and plotting graphs.
In Experiment 1, average values across frequencies and linear
regression as a function of load force frequency were used to test the
influence of frequency and condition on the five measures. To test the
influence of frequency on a particular measure and condition, separate
linear regressions were performed for each of the nine subjects, and
paired t tests were performed across the slope estimates. To
compare the parameters between conditions, paired t tests,
by subject, were performed on these parameters. To test the mean levels
across all frequencies, paired t tests were performed for
each subject mean within a condition and between conditions.
In Experiment 2, a repeated-measures ANOVA was performed on each
measure as a function of the gain g (as categorical
variables). A polynomial contrast was used to determine whether there
were significant linear, quadratic, or higher order trends across the gains g. The highest order polynomial for which this was
true was used to fit the ensemble data for individual and combined frequencies. For all plots for which a quadratic regression
significantly fitted the data, the g value at which the
quadratic peaked was calculated and t tests were performed
to test whether this point differed significantly from 1 across the
subjects. The value of the peak of the quadratic was also
calculated.
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RESULTS |
After practice each subject was able to track the desired load
waveform with reasonable accuracy and produced load forces that were
predominately sinusoidal with narrow power spectra around their
dominant frequency. The grip forces were also predominantly sinusoidal.
In particular, the modulation was smooth and showed little evidence of
catch-up responses, which have been reported to occur to unpredictable
onsets of load force (Johansson et al., 1992b).
Experiment 1
Typical raw data for the four conditions are shown in Figure
2. These traces show that when the load
force was generated externally by the robot, the mean grip force level
was high, showed low modulation, and lagged behind the load force (Fig.
2, Condition 1). In contrast, when the load force was
self-generated by the right hand, the mean grip force level was lower,
showed a large degree of modulation, and appeared in phase with the
load force (Fig. 2, Condition 2). When the left hand was
used to generate the load, a predictive modulation was seen similar to
that in the right hand condition, but with a smaller amplitude of
modulation (Fig. 2, Condition 3). However, when the left
hand generated the load force indirectly through the joystick, the
pattern of grip force modulation was similar to that of the externally
generated condition (Fig. 2, Condition 4).
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Figure 2.
Typical example of grip force (dashed
line) and load force (solid line) traces for the four
conditions of Experiment 1 taken from a single subject tracking a
frequency of 3.5 Hz. The data are taken from the same 4 sec time period
in each trial and have been low pass-filtered.
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Analysis of the group data is shown in Figures
3 and 4. In
all conditions, subjects showed a grip force that modulated, to some
extent, with load force. As expected, when the subjects generated the
load force with their right hand they showed a large degree of grip
force modulation (Fig. 3b), and this modulation showed a
small significant (p < 0.01) average phase
advance of +10.6 msec across the frequencies tested (Fig.
4b). However, when the same load force was produced
externally by the robot, the modulation was significantly smaller
(p < 0.01) and showed a significant (p < 0.001) average phase lag of 100.4
msec.
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Figure 3.
Average baseline (a) and amplitude gain
(b) of grip force modulation against frequency for the four
conditions of Experiment 1.
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Figure 4.
Average phase (a), lag (b),
and coherence (c) between load force and grip force against
frequency for the four conditions of Experiment 1.
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When subjects used their left hand to generate the load force directly,
there was a small average phase lag of 12 msec that was not
significantly different from 0. However, when the left hand generated
the same load force through the joystick-controlled robot, and subjects
were explicitly informed of this relation, performance was markedly
different. In this condition the baseline gain, amplitude gain, phase,
and lag were not significantly different from these values in the
externally generated condition. In particular, in the joystick
condition, the grip force modulation had a significant phase lag of
104.2 msec with respect to load (p < 0.01).
Analysis of coherence (Fig. 4c) showed that it was
significantly higher when the movements were self-generated by the
right hand compared with the other three conditions
(p < 0.01).
Experiment 2
Typical raw data for four of the levels of feedback gains,
g to the left hand, are shown in Figure
5. This shows that modulation of grip
force grip was small for g = 0 and increased as the
feedback gain to the left hand increased. Analysis of the group data
for feedback parameter g = 1 (solid lines) and
g = 0 (dashed line) are shown in Figures
6 and 7. At
a value g = 1, the effect should be qualitatively
similar to the left hand direct condition of Experiment 1 because the
robots simulate a single object between the two hands. Correspondingly,
when g = 0 the effect should be similar to left hand
operating indirectly through the joystick. When the feedback gain
parameter g was 1, the average phase advance was
significantly higher (p < 0.01) at +11.4 msec
compared with a lag of 57.7 msec when g = 0. The grip
force modulation amplitude was significantly greater for
g = 1 compared with g = 0 (p < 0.05) (Fig. 6b). Modulation of
grip decreased in amplitude with increasing frequencies in both
conditions (p < 0.05). Coherence (Fig.
7c) was significantly higher when g = 1 compared with 0 (p < 0.01). Therefore the
differences between the g = 0 and g = 1 conditions are qualitatively similar to the joystick and left-hand
conditions of Experiment 1.
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Figure 5.
Typical example of grip force (thin
line) and load force (thick line) traces for four
feedback gains, g, of Experiment 2 taken from a single
subject tracking a frequency of 2.3 Hz. The data are taken from the
same time period in each trial and have been low pass-filtered.
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Figure 6.
Baseline gain (a) and amplitude gain
(b) of grip force modulation against frequency at feedback
gains 1 (solid lines) and 0 (dashed lines).
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Figure 7.
Phase, lag, and coherence at different frequencies
at feedback gains 1 (solid lines) and 0 (dashed
lines). Average phase (a), average lag (b),
average coherence (c) between load force and grip
force.
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Figures 8 and
9 compare the grip force responses to
different frequency load forces applied to the object by the left hand via a second robot with different levels of force feedback gain (g varied between 0 and 1.5). The ANOVA performed on
the measures as a function of gain showed that a significant difference
between the seven levels of gain for lag (p < 0.01), phase (p < 0.05), coherence
(p < 0.01), and amplitude gain
(p < 0.05). There was no significant difference
between the seven levels of gain for baseline gain
(p = 0.67). A polynomial contrast on the gains
showed a significant fit for the quadratic term for lag
(p < 0.01), phase (p < 0.01), and coherence (p < 0.05), and for the
linear term for amplitude gain (p < 0.05). A
comparison of the extremal values of gain (g = 0 and g = 1.5) with g = 1 showed a
significant difference for phase (p < 0.01 for
g = 0; p < 0.05 for g = 1.5), lag (p < 0.01 for g = 0; p < 0.05 for g = 1.5), and
coherence (p < 0.01 for g = 0;
p < 0.05 for g = 1.5). For the
combined frequencies, therefore, the highest significant term for the
amplitude gain was linear, and for the phase, lag, and coherence it was
quadratic. For baseline gain a linear fit was not significant.
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Figure 8.
Baseline gain and amplitude gain of grip force
modulation at different frequencies with different force feedback
coupling, g, between the robots held in each hand. Graphs
show the baseline gain (solid line shows the mean) and the
amplitude of grip force modulation (solid line shows linear
regression fit) at different feedback gains at three different
frequencies and the average over all six frequencies.
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Figure 9.
Phase, lag, and coherence at different frequencies
with different force feedback coupling between the robots held in each
hand. Graphs show phase, lag, and coherence at different feedback gains
at three different frequencies and the average over all six
frequencies. The solid line shows the quadratic fits to the
data.
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An analysis of the location of the maxima of the quadratic fits for lag
and phase (Fig. 9) showed that they occurred at a feedback gain value
not significantly different from 1 at each frequency. For lag this
value was 1.10 ± 0.22 (SE) at 1.1 Hz, 0.92 ± 0.07 at 2.3 Hz, 0.87 ± 0.11 at 3.5 Hz, and on average (combining all six
frequencies) 1.05 ± 0.09. The mean lag value at which the peaks
occurred was 0.3 ± 12.0 msec. Therefore with feedback gains of
less or more than one, grip significantly lagged behind load.
Similarly, coherence significantly decreased at feedback gains of less
or more than one. The mean location of the peak (combining frequencies)
in coherence was at a feedback gain of 0.81 ± 0.06. As the
feedback gain g increased, the amplitude of modulation
increased significantly for the ensemble data (p < 0.05).
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DISCUSSION |
Although previous studies have demonstrated predictive modulation
of grip force to self-generated load forces, we have shown that this
self-generation in itself is not sufficient to produce precise
predictive grip force modulation. Precise prediction was seen only when
the left hand experienced force feedback that was equal and opposite to
the force exerted on the right hand, a situation consistent with the
presence of a real, rigid object between the hands. However, when the
force feedback to the left hand was either greater or less than the
force experienced by the right hand, grip lagged behind load force.
To prevent a gripped object from slipping during movement without
maintaining an excess safety margin, grip force must change with load
force. In line with previous findings (Johansson and Westling, 1984;
Johansson et al., 1992b; Flanagan and Wing, 1995, 1997), we have
demonstrated that when load force is generated by the hand holding the
object, grip force is modulated in parallel with load force. Grip force
anticipated load force even at frequencies as high as 3.5 Hz (Fig.
4b), and as demonstrated by the high coherence (Fig.
4c), the phase relationship showed minimal variability
within each trial. The large amplitude and parallel nature of the grip force modulation allows a small safety margin to be achieved while preventing the object from slipping and may be important in economizing muscular effort (Johansson and Westling, 1984). However, when the load
force was externally produced by the robot, the grip force modulation
lagged ~100 msec behind load force. This lag is similar to that seen
in response to unpredictable load force perturbations (Cole and Abbs,
1988; Johansson et al., 1992a,b), showing that even for a repetitive
sinusoid there is no predictive modulation. If in the presence of such
a large delay the amplitude of modulation and the baseline force were
similar to that in the self-produced condition, the object would slip.
Therefore, when little grip force prediction is seen, there is a
concomitant increase in the baseline grip force (Fig. 3a,
Robot) and a reduction in grip force modulation amplitude (Fig.
3b, Robot). In addition, the phase relationship, as
indicated by the low coherence, is more variable in this externally
produced condition compared with the self-generated condition. When the
load force was generated by the left hand pushing directly on the
object, grip force modulation was predictive but of a smaller amplitude
than when the load force was generated by the right hand. This parallel
modulation suggests that the motor command sent to the left hand can be
used to produce precise predictive modulation by the right hand. The
phase relationship was strikingly similar to the relationship when the
right hand produced the load.
Previous studies have shown anticipatory responses to discrete events
such as loading the limb by dropping a ball (Johansson and Westling,
1988; Lacquaniti et al., 1992) or unloading the limb using the opposite
hand (Lum et al., 1992). For example, when subjects are required to
remove an object held in one hand with the other, anticipatory
deactivation of the forearm muscles occurs before the unloading, and
therefore the position of the loaded hand remains unchanged (for
review, see Massion, 1992). However, when the subjects were required to
press a button that caused the load to be removed from their other
hand, no anticipatory behavior was seen (Dufosse et al., 1985). These
two conditions can be thought of as analogous to our self-produced left
hand and joystick conditions. When the load force was indirectly
generated by the left hand controlling the robot via a low-friction
joystick, grip force lagged significantly behind load force by over 100 msec. This is comparable to the externally produced condition. Therefore, although the load force was self-generated by the left hand
in both the direct and indirect (joystick) conditions, only the former
elicited precise predictive grip force modulation. The present study
extends this work by examining the reasons behind such a discrepancy in
anticipatory responses.
Two possible reasons were hypothesized to account for the lack of
precise prediction in our indirect (joystick) condition when compared
with the direct action of the left hand on the object. The first was
that the coordinate transformation between joystick action, which was
both remote to the right hand and in the sagittal direction, prevented
precise prediction. Alternatively, the difference in sensory feedback
received by the left hand in the two conditions produced the
differential results. In the direct condition, the left hand received
force feedback that was equal and opposite to that experienced by the
right hand, whereas in the joystick case the left hand received minimal
force feedback. To investigate this issue we examined grip force
modulation when the force feedback to the left hand was parametrically
varied. This was achieved by simulating a virtual object between the
two hands, whose properties did not necessarily conform to normal
physical laws. The first hypothesis was rejected as precise prediction
was not observed in the condition g = 0, although both
hands acted in the same coordinate system. However, we found that the
lag between load and grip force was minimal (0.3 msec) when the
feedback gain to the left hand simulated a normal physical object
(g = 1), and the lag increased in a systematic
way as the virtual object deviated from normal physical laws,
supporting the second hypothesis.
The present results can be interpreted within a new computational
framework of multiple forward models. One problem the CNS must face
when both hands are in contact with objects is determining whether the
hands are manipulating a single object or are acting on separate
objects and thereby select the appropriate control strategy. Only in
the former case should the motor commands to each limb be used in a
predictive manner to modulate the grip force of the other hand. For
example, when holding a cup in one hand and a saucer in the other,
there is no reason why one hand should take account of what the other
is doing in terms of grip force modulation. However, if the cup and
saucer were rigidly joined, then it would be desirable for each hand to
take account of the other's actions.
One computational solution to this problem is to use multiple internal
forward models, each predicting the sensory consequences of acting
within different sensorimotor contexts (Fig.
10). For example, one internal model
could capture the relation between the motor commands and subsequent
sensory feedback when the hands manipulate a single object (Fig. 10,
left) while another model captures the condition in which
the hands act on separate objects (Fig. 10, right). Each
forward model predicts the sensory consequences, based on its
particular model of the context and the motor command, and these
predictions are then compared with the actual sensory feedback. The
errors in these predictions are then used to estimate the probability
that each model captures the current behavior. In the present study,
for example, when the feedback is equal and opposite to both hands
(g = 1), the internal model of a single object
between the hands would have a small error compared with the separate
models. This would give rise to a high probability that the hands are
manipulating a single object, thereby allowing the efference copy of
the command to the left hand to modulate predictively, as was observed,
the grip force in the right hand. As the sensory feedback deviates from
the prediction of the model (g more than 1 or
g less than 1), the probability of this model capturing the
behavior would fall, leading, as observed, to an increase in the lag
between grip and load force. Our results therefore suggest that an
internal model exists that captures the normal physical properties of
an object and is used to determine the extent to which the two hands
are manipulating this object. Although it is probably not possible to
have a model for every context that we are likely to experience, we
propose that by selectively combining the outputs of multiple simple
forward models we could construct predictions suitable for many
different contexts.
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|
Figure 10.
A model for determining the extent to which two
hands are acting through a single object. For simplicity only two
internal models are shown. On the left is an internal
forward model that captures the relationship between the motor commands
sent to the left (ML) and right
(MR) hands and expected sensory feedback
when the two hands act on a single object. On the right is
shown the two internal forward models that capture the behavior when
the hands are manipulating separate objects. Both models make
predictions of the sensory feedback from both the left
(SL) and right
(SR) hands based on the motor commands.
These predictions are then compared with the actual sensory
feedback to produce the sensory prediction errors (E). The
errors from each model, Ê and  , are
then used to determine the probability P that each
model captures the current behavior. This probability determines the
extent to which the motor command to one hand can be used in predictive
grip force modulation of the other hand.
|
|
The observed relationship between lag and feedback gain, g,
constrains the way in which sensory prediction errors could be used
to select between the internal models (Fig. 10). Our results rule out a
model selector producing a hard classification in which grip force
modulation corresponds to the hands acting on either a single object or
separate objects. Such a relationship would have led to a binary
distribution of the lags consistent either with predictive modulation
(lag of zero) or no prediction (lag  100 msec). However, our
results show that the lag was minimal when the feedback gain to the
left hand was 1 and increased smoothly when the feedback gain was
either greater or less than 1. Prediction is therefore graded by the
similarity between the force feedback expected for a real, rigid object
and the feedback actually received.
Burstedt et al. (1997) recently demonstrated that grip force is
modulated in parallel with load force when subjects lifted an object
between the index finger of their left and right hands, and
cooperatively with another subject using the right index finger. Performance was similar in both these conditions and was comparable to
that when subjects lifted the object between the thumb and index finger
of their right hand. The authors suggest that this result demonstrates
that the forward model can be adjusted to account for various
situations. In our study we have shown that the context of the
movement, as coded by the haptic feedback to each hand, critically
modulates the nature of the grip force response.
Anticipatory grip force modulation has been shown to depend on several
contextual cues such as object weight (Johansson and Westling, 1988),
experience from previous lifts (Gordon et al., 1993), type of load
(Flanagan and Wing, 1997), and friction of the object's surface
(Johansson and Westling, 1984). Knowledge of the mechanical properties
of objects is probably also learned by handling and manipulating
objects (Gordon et al., 1993), as is demonstrated by prediction
improving throughout development (Eliasson et al., 1995), suggesting a
continual refinement of the internal models. Our results support the
hypothesis that predictive mechanisms rely on there being sensory
feedback to the two hands that obey the physical laws encountered in
normal objects.
In conclusion, the present results suggest that efference copy in
itself is not sufficient to allow generalized prediction. Precise
prediction is seen when the feedback to both hands is consistent with a
single object and declines smoothly as the feedback becomes
inconsistent with this context. We propose that multiple internal
forward models can be used to estimate the context of the movement and
thereby determine whether it is appropriate to use such a predictive
mechanism.
| |
FOOTNOTES |
Received Feb. 18, 1998; revised June 29, 1998; accepted June 29, 1998.
This research was supported by the Wellcome Trust and Royal Society.
S.J.B. is funded by the Wellcome four-year Ph.D. Program in
Neuroscience at University College London.
Correspondence should be addressed to Dr. Daniel M. Wolpert, Sobell
Department of Neurophysiology, Institute of Neurology, Queen Square,
London WC1N 3BG, UK.
| |
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Top
Abstract
Introduction
