J Neurophysiol 113: 3736 –3743, 2015.
First published April 22, 2015; doi:10.1152/jn.00313.2015.
Motor control hierarchy in joint action that involves bimanual
force production
Junya Masumoto1 and Nobuyuki Inui2
1
The Joint Graduate School in Science of School Education, Hyogo University of Teacher Education, Kato, Japan;
and 2Laboratory of Human Motor Control, Naruto University of Education, Naruto, Japan
Submitted 1 April 2015; accepted in final form 16 April 2015
joint action; bimanual action; hierarchy; complementary force production; synchronization
between the hierarchical structure of human motor control (Bernstein 1967; Gelfand and
Tsetlin 1966) and motor redundancy (Latash 2012; Turvey
1990). The concept of hierarchical motor control has been
viewed as a means of progressively decreasing the number of
variables manipulated by each higher-control level of a hierarchy, alleviating the problem of motor redundancy. For example, Gorniak et al. (2007b) suggested how the central
nervous system can organize force-stabilizing synergies simultaneously at two levels of a motor control hierarchy in a
bimanual action that involves two-finger movements within a
hand: the upper level distributes the action between the hands,
and the lower level distributes each hand’s action between the
involved fingers. They examined force-stabilizing synergies
that required negative covariation of finger or hand forces in a
task of constant force production by two hands. The result
THERE IS AN INTIMATE RELATION
Address for reprint requests and other correspondence: N. Inui, Laboratory
of Human Motor Control, Naruto Univ. of Education, Takashima, Naruto-cho,
Naruto-shi 772-8502, Japan (e-mail: [email protected]).
3736
showed that negative covariation of the two finger forces
within a hand during the bimanual task was weaker than that in
a unimanual task [also see Gorniak et al. (2007a) and Kang et
al. (2004)].
Coordination that may occur intentionally between individuals with a common goal in a motor task has recently been
studied using the term “joint action” [defined by Ganesh et al.
(2014); Masumoto and Inui (2014b); Newman-Norlund et al.
(2008); Sebanz et al. (2006); and Skewes et al. (2015)]. For
example, Bosga and Meulenbroek (2007) asked pairs of participants to perform a virtual lifting task using constant uni- or
bimanual isometric force, although they did not examine the
hierarchical relation between bimanual and joint actions. The
forces produced by the two participants were negatively correlated when visual feedback of their forces was available,
indicating the use of complementary forces to control a virtual
bar. Masumoto and Inui (2013b) asked 10 pairs of participants
to produce periodic unimanual isometric forces, such that the
sum of forces that they produced matched a target force that
cycled between 5% and 10% of maximum voluntary contraction (MVC) with an interval of 1,000 ms. When the total force
was visible, the correlation between the forces produced by the
two participants was highly negative, and the coherence between the force-time series produced by the two participants
was highest at the target interval. These findings indicate that
the two participants simultaneously adopted both complementary and temporal synchronous strategies.
There are data on the control of force production in intrapersonal unimanual (Masumoto and Inui 2010) and bimanual
actions (Diedrichsen et al. 2003; Masumoto and Inui 2012,
2013a; Ranganathan and Newell 2008) and in an interpersonal
(joint) unimanual action (Bosga and Meulenbroek 2007; Masumoto and Inui 2013b, 2014b). However, to study the hierarchical organization of the motor control system in intra- and
interpersonal actions, it is necessary to obtain data on force
control in a joint bimanual action. It is predicted that the finger
forces of the two hands are combined into a single collective
unit (i.e., a decrease in the number of variables) to enable
complementary force production between participants. Thus
we hypothesized that turning a bimanual force-production task
into a joint force-production action would lead to positive
correlation between forces produced by the two hands and
negative correlation between forces produced by two participants. In the present study, we examined how the central
nervous system controls force production and timing simultaneously at three levels of a motor control hierarchy in a joint
action that involves bimanual force production: a top level that
controls the total force produced by the two participants, a
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Masumoto J, Inui N. Motor control hierarchy in joint action that
involves bimanual force production. J Neurophysiol 113: 3736 –3743,
2015. First published April 22, 2015; doi:10.1152/jn.00313.2015.—
The concept of hierarchical motor control has been viewed as a means
of progressively decreasing the number of variables manipulated by
each higher control level. We tested the hypothesis that turning an
individual bimanual force-production task into a joint (two-participant) force-production task would lead to positive correlation between
forces produced by the two hands of the individual participant (symmetric strategy) to enable negative correlation between forces produced by two participants (complementary strategy). The present
study consisted of individual and joint tasks that involved both
unimanual and bimanual conditions. In the joint task, 10 pairs of
participants produced periodic isometric forces, such that the sum of
forces that they produced matched a target force cycling between 5%
and 10% of maximum voluntary contraction at 1 Hz. In the individual
task, individuals attempted to match the same target force. In the joint
bimanual condition, the two hands of each participant adopted a
symmetric strategy of force, whereas the two participants adopted a
complementary strategy of force, highlighting that the bimanual
action behaved as a low level of a hierarchy, whereas the joint action
behaved as an upper level. The complementary force production was
greater interpersonally than intrapersonally. However, whereas the
coherence was highest at 1 Hz in all conditions, the frequency
synchrony was stronger intrapersonally than interpersonally. Moreover, whereas the bimanual action exhibited a smaller error and
variability of force than the unimanual action, the joint action exhibited a less-variable interval and force than the individual action.
MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
Table 1. A matrix to show 4 experimental conditions
3737
Procedure
Apparatus and Measurements
middle level that distributes the force between the two participants, and a bottom level that distributes the force generated
by the two hands of each participant.
MATERIALS AND METHODS
Participants
The present study consisted of an individual task, performed by one
participant, and a joint task, performed by two participants paired
randomly. Both tasks consisted of unimanual and bimanual conditions, giving a total of four conditions in this study: the individualunimanual, individual-bimanual, joint-uinmanual, and joint-bimanual
conditions (Table 1). The individual task was conducted using onehalf of the setup shown in Fig. 1A. In the individual-unimanual
condition, the participants were seated facing the load cell with their
palms resting on a support surface, 6 cm above the table (see Fig. 1A).
In this posture, the participants made periodic isometric pressing
movements with the right or left index finger at the metacarpophalangeal joint with a target peak force of 10% MVC, a target valley
force of 5% MVC, and a target peak-to-peak interval (PPI) or
valley-to-valley interval (VVI) of 1,000 ms (Fig. 1B). The target force
and the force output of the load cell were displayed on a monitor so
that the participant could see the difference between the actual force
and target force. In the individual-bimanual condition, the participant
was required to produce force using both index fingers, and the sum
of the two finger forces was required to match the target force, which
was for both hands, and the sum of the forces produced by the two
fingers was displayed on the monitor.
In the joint-bimanual condition, two participants were seated on
chairs at opposite ends of a table facing the load cell and monitor (Fig.
1A). They produced the target force, such that the sum of the forces
produced by both index fingers of the two participants was the target
peak force of 10% MVC or the target valley force of 5% MVC with
the target interval. The force generated was thus summed across
participants, rather than two hands. In the joint-unimanual condition,
each participant was required to produce force using his right index
finger, and the sum of the forces produced by the right index fingers
of the two participants was required to match the target. In the joint
task, the target force for the pair and the sum of the forces produced
by the two participants were displayed on the monitor. The participants were instructed to synchronize the timing of production of
forces with the partner’s timing. The participants could not see the
other’s action because of the two monitors between them, and they
were instructed not to verbally communicate with each other.
At the start of the experimental session, each participant performed
a maximal isometric contraction three times, and the force generated
at the finger tip of each index finger was recorded as MVC. The
participant was instructed to place the distal pad of the index finger in
contact with the load cell and then to apply as much pressure as
possible to the load cell and maintain that force output for 3 s without
The output of the load cell (Model LUB-5KB; Kyowa Electronic
Instruments, Tokyo, Japan; rated 5 kg), pressed by participants, was
amplified (Model MCC-8A; Kyowa Electronic Instruments), converted from analog to digital (PowerLab/8sp; ADInstruments, Dunedin, New Zealand), and recorded on a personal computer (Vostro
200; Dell, Round Rock, TX). The force output was also displayed on
a 20-inch computer monitor (1440 ⫻ 900 pixel resolution), located
⬃60 cm in front of the participant. Data were sampled at a frequency
of 1,000 Hz by a 16-bit analog-to-digital converter with a low-pass
filter at 100 Hz. Figure 1C shows data collected from two participants
in the bimanual condition of the joint task. Peak force, valley force,
PPI, and VVI were measured using software (Emile Soft, Tokushima,
Japan) for analysis of force and interval.
A
B
Peak-to-peak
interval
Peak force
Force
Joint-unimanual
Joint-bimanual
Valley force
C
Force (% MVC)
Individual-unimanual
Individual-bimanual
Load cell
Valley-to-valley
interval
Time
Total force
Sum of two hand forces
12
Left hand force
Right hand force
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
Time (s)
Fig. 1. Experimental setup, dependent variables, and example data showing the
forces produced by the 2 hands of each of 2 participants in the joint-bimanual
condition and the total force. A: the individual task was performed by 1
participant using ½ of the setup shown in the drawing, and the joint task was
conducted by 2 participants using the setup shown in the drawing. B: definition
and measurement of dependent variables. C: the black line represents the total
force, i.e., the sum of the forces produced by both hands of both participants.
The 2 black, dashed lines represent the sums of the forces produced by each
participant. The 2 gray, solid lines represent the left-hand force produced by
each participant, and the 2 gray, dashed lines represent right-hand force
produced by each participant. MVC, maximum voluntary contraction.
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Participants were 20 healthy men without any apparent neurological disorders (mean age ⫽ 23.8 yr; SD of age ⫽ 2.4 yr). Handedness
was tested using the Edinburgh Handedness Inventory (Oldfield
1971). All 20 participants were right-hand dominant, and the mean
laterality quotient score was ⫹96.01 (SD ⫽ 7.34). All participants
gave informed consent, and the Ethical Committee of Naruto University of Education approved the procedures. The work conformed to
the principles of the Declaration of Helsinki.
lifting the hand or forearm. His wrist was fixed to the rest on which
the load cell was mounted by Velcro straps (Magic Tape; Kuraray,
Tokyo, Japan). The MVC (mean ⫽ 43.3; SD ⫽ 10.9 N) was determined as the average of three trials. The target force is the sum of 10%
or 5% MVCs produced by the left and right finger in the bimanual
condition and the sum of 10% or 5% MVCs produced by the two
participants in the joint task.
The order of the conditions performed by the participants was
varied randomly. The participants practiced each condition separately,
with the corresponding test trial following immediately after the
practice trials. They pressed their fingers against the load cell for 60
cycles in five practice trials for each condition. During practice trials,
the pressing rate was prescribed by means of an audible metronome
(Model SQ100-88; Seiko Holdings, Tokyo, Japan) at a 500-ms interval. Although the target interval (PPI and VVI) was 1,000 ms, the
participants were instructed to synchronize peak and valley forces on
the load cell with the metronome at a 500-ms interval. The visual
information provided to the participant was the same in the practice
trials and the test trials, but the participant was instructed to produce
the force without the metronome pulse in the test trials.
3738
MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
Statistical Analysis
The test trials were analyzed. The initial and final five cycles of the
force-time series were removed to avoid the effects of the initial
stabilization period and any premature cessation of force production,
and the values were calculated from the middle 50 cycles in each trial.
Complementary strategy, frequency synchrony, phase synchrony, accuracy of force production and interval, and variability of force and
interval were calculated as dependent variables, as described below.
To quantify the complementary strategy of force production in the
individual-bimanual condition (Table 2), correlation coefficients were
calculated between the peak forces produced by the two hands and
between the valley forces produced by the two hands. To quantify the
complementary strategy of force production in the joint-bimanual
condition, correlation coefficients were calculated for each participant
between the peak forces produced by the two hands and the valley forces
produced by the two hands (the intrapersonal joint-bimanual condition).
Correlation coefficients were also calculated for each pair of participants
between the total peak forces produced by the two participants and
between the total valley forces produced by the two participants (the
interpersonal joint-bimanual condition). In the joint-unimanual condition,
correlation coefficients were calculated for each pair of participants
between the peak forces produced by the two participants and between
the valley forces produced by the two participants.
The cross-spectral coherence was calculated to quantify the frequency synchrony between the forces produced by the two hands in
the individual-bimanual condition. The coherence evaluated the correlation of the two force-time series at different frequencies. In the
intrapersonal joint-bimanual condition, the coherence was calculated
to evaluate the frequency synchrony between the forces produced by
the two hands. In the interpersonal joint-bimanual condition, the
coherence was calculated to evaluate the frequency synchrony between the sum of the forces produced by the two hands of each
participant. In the joint-unimanual condition, the coherence was
calculated to evaluate the frequency synchrony between forces produced by the two participants. The coherence was calculated over all
force-time series (100 samples/s), with a window length of 200 points
(frequency resolution of 0.5 Hz) using the mscohere command in
GNU Octave Forge, version 3.6.1 (freeware; John W. Eaton). Thus
the peak coherence over all frequencies was used as an estimate of the
frequency synchrony between forces produced by the two hands or
participants.
The distribution of relative phase angles between the force-time
series produced by the two hands or participants was used to quantify
the phase synchrony between their force outputs. The continuous
relative phase was first computed using the Hilbert transform (Rosenblum and Kurths 1998), which was calculated by using the Hilbert
command in GNU Octave Forge. The distribution of relative phase
angles examined the concentration of relative phase angles between
forces produced by two hands or participants across nine 20° regions
of relative phase (0 –20°, 21– 40°, 41– 60°, 61– 80°, 81–100°, 101–
120°, 121–140°, 141–160°, 161–180°). The phase synchrony was
indicated by a high concentration of relative phase angles near 0°,
whereas an even distribution indicated no phase synchrony.
Absolute error (AE) was calculated to assess the accuracy of force
and interval. AE was calculated by averaging the size of the error (i.e.,
the difference between the produced and the target forces or intervals),
regardless of sign, over the 50 cycles. SD of peak force, valley force,
PPI, and VVI was calculated to evaluate the variability of force and
interval.
In the unimanual condition, the difference for AE and SD of force
and interval between the left and right hands was analyzed using a 2 ⫻
2 ANOVA of hand (left hand, right hand) ⫻ force (peak force, valley
force) or interval (PPI, VVI). Because there was no significant
difference for the AE and SD of force and interval between the left
and right hands, the forces and intervals produced by the left or right
hands were treated as a single level under factor condition: AE of
force [hand, F(1, 76) ⫽ 0.22; force, F(1, 76) ⫽ 1.69], SD of force
[hand, F(1, 76) ⫽ 0.02; force, F(1, 76) ⫽ 3.87], AE of interval [hand,
F(1, 76) ⫽ 2.36; force, F(1, 76) ⫽ 1.55], and SD of interval [hand,
F(1, 76) ⫽ 1.98; force, F(1, 76) ⫽ 0.55].
Analysis of complementary strategy. Correlation coefficients were
standardized using a Fisher z-transformation for averaging across
pairs and then analyzed using a 4 ⫻ 2 ANOVA of condition (individual-bimanual, intrapersonal joint-bimanual, joint-unimanual, interpersonal joint-bimanual) ⫻ force. Masumoto and Inui (2010, 2012)
found that the valley force was markedly more variable than the peak
force in an isometric force-production task. The present study also
showed the same result in the SD of force in the individual task (see
Fig. 7A). The present study thus analyzed peak and valley forces
separately.
Analysis of coherence. Cross-spectral coherence was analyzed
using a one-way ANOVA to examine the main effects between forces
produced by two hands or participants.
Analysis of distribution of relative phase angles. Analysis of the
distribution of relative phase angles: a 4 (condition) ⫻ 9 (phase
region: 0 –20°, 21– 40°, 41– 60°, 61– 80°, 81–100°, 101–120°, 121–
140°, 141–160°, 161–180°) ANOVA was performed to examine the
main effects on phase region. When an interaction of condition and
phase was found, separate analyses on phase region were performed.
Analysis of accuracy and variability in force and interval. AE of
force and interval and SD of force and interval were analyzed using a
2 ⫻ 2 ⫻ 2 ANOVA of task (individual, joint) ⫻ condition (unimanual, bimanual) ⫻ force or interval. When a significant main effect
of condition was found, post hoc multiple comparisons were performed using Tukey’s honestly significant difference test to detect
differences between conditions. Statistical significance was defined at
P ⬍ 0.05.
Table 2. A matrix to show analysis levels (intra- vs. interpersonal)
for the analyses of correlation, cross-spectral coherence, and relative
phase angle
Intrapersonal individual-bimanual
Intrapersonal joint-bimanual
Interpersonal joint-unimanual
Interpersonal joint-bimanual
RESULTS
The novel findings of the present study are that in the
joint-bimanual condition, the correlation between forces produced by the two hands of each participant was strongly
positive, whereas that between forces produced by the two
participants was negative. The coherence between force-time
series produced by two hands or two participants was highest
at 1 Hz in all conditions. The complementary force production
was greater interpersonally than intrapersonally, but the synchronization of performance to each other’s timing was higher
intrapersonally than interpersonally.
Complementary Strategy
Figure 2 shows the forces produced by two hands or two
participants in each of four conditions (also see Tables 3 and
4). The correlation between the forces produced by the two
hands (Fig. 2A) or the two participants (Fig. 2, C and D) was
negative in the individual-bimanual, joint-unimanual, and interpersonal joint-bimanual conditions, whereas the correlation
between the forces produced by the two hands (Fig. 2B) was
positive in the intrapersonal joint-bimanual condition.
Table 3 shows correlation coefficients calculated for each
participant between the peak forces produced by the two hands
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Data Analysis
MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
Intra-personal
B
Individual-bimanual
Left hand force (% MVC)
Left hand force (% MVC)
A 10
5
0
5
0
10
Joint-bimanual
10
5
0
Right hand force (% MVC)
0
5
10
Right hand force (% MVC)
Inter-personal
D
Force of participant B (% MVC)
Joint-unimanual
10
5
0
5
0
10
Force of participant A
(% MVC)
Joint-bimanual
10
Figure 3 shows the mean correlation coefficients in each of
the four conditions. The correlation differed across conditions
[F(3, 112) ⫽ 64.01, P ⬍ 0.0001] but did not differ across
force. The correlation between hands was more positive in the
intrapersonal joint-bimanual condition than in the other three
conditions. The correlation between participants in the jointunimanual (P ⬍ 0.05) and interpersonal joint-bimanual (P ⬍
0.005) conditions was more negative than the correlation
between hands in the individual-bimanual condition. In the
joint task, the two participants in a pair thus adopted a complementary strategy, whereby one person compensated for
force errors of the other person. The most important result is
that the correlation between the forces produced by two hands
was strongly positive in the intrapersonal joint-bimanual condition (Figs. 2B and 3A). Two hands adopted a symmetric
strategy of force production, whereas two participants adopted
a complementary one.
Temporal Synchronous Strategy
5
0
5
0
10
Force of participant A
(% MVC)
Fig. 2. Distribution of forces produced by 10 participants or pairs. A: distribution of forces produced by both hands in the individual-bimanual condition.
B: distribution of forces produced by both hands in the intrapersonal jointbimanual condition. C: distribution of forces produced by 1 hand of 2
participants in the joint-unimanual condition. D: distribution of the sum of
force produced by both hands of 2 participants in the interpersonal jointbimanual condition. A: dashed lines represent the target force (left finger
force ⫹ right finger force ⫽ 5% or 10% of MVC). C and D: dashed lines
represent the target force (the force produced by participant A ⫹ the force
produced by participant B ⫽ 5% or 10% of MVC). The data points represent
the force produced by both hands (A and B) and the force produced by the pair
of participants (C and D). The gray points represent peak forces, and the black
points represent valley forces.
and the valley forces produced by the two hands under the
individual-bimanual and intrapersonal joint-bimanual conditions.
Whereas more than one-half coefficients (24/40) were negative
under the individual-bimanual condition, the majority of the
coefficients (38/40) was positive under the intrapersonal jointbimanual condition. Table 4 shows correlation coefficients calculated for each pair of participants between the total peak forces
produced by the two participants and between the total valley
forces produced by the two participants under the joint-unimanual
and interpersonal joint-bimanual conditions. All coefficients except one (39/40) were negative in both conditions.
Analysis of frequency. Figure 4 shows the mean crossspectral coherence between force-time series produced by two
hands (Fig. 4, A and B) or participants (Fig. 4, C and D). The
coherence was highest at 1 Hz in all conditions, indicating that
each hand or participant synchronized the time-force series
with the other hand or participant at the target interval. An
analysis of the peak coherence [F(3, 56) ⫽ 10.78, P ⬍ 0.0001]
indicated that the peak coherence of the force produced by two
hands (Fig. 4, A and B) was higher than that of the force
produced by two participants [Fig. 4, C (P ⬍ 0.0001) and D
(P ⬍ 0.05)]. Thus although the complementary force production was greater interpersonally than intrapersonally, the synchronization of their performance to each other’s timing was
higher intrapersonally than interpersonally.
Analysis of phase. To examine the phase synchrony between
force-time series produced by two hands or participants, Fig. 5
shows the distribution of relative phase angles for four conditions. An analysis of the relative phase angles showed a main
effect on phase region [F(8, 504) ⫽ 190.88, P ⬍ 0.0001], and
an interaction of condition and phase region was significant
[F(24, 504) ⫽ 11.09, P ⬍ 0.0001]. Separate analyses on phase
region showed that whereas the percentage of occurrence for
the 0 –20° phase region [F(3, 56) ⫽ 12.19, P ⬍ 0.0001] was
markedly higher in the individual-bimanual and intrapersonal
joint-bimanual conditions than in the joint-unimanual (P ⬍
0.0001) and interpersonal joint-bimanual conditions (P ⬍ 0.005),
the percentage for the 21– 40° phase region [F(3, 56) ⫽ 4.99, P ⬍
0.005] was lower in the intrapersonal joint-bimanual condition
than in the joint-unimanual (P ⬍ 0.05) and interpersonal jointbimanual conditions (P ⬍ 0.01). Whereas the percentage for the
Table 3. Correlation coefficients calculated for each participant between the peak forces produced by the 2 hands and between the
valley forces produced by the 2 hands under the individual-bimanual and intrapersonal joint-bimanual conditions
Pair
Participant
Individual-bimanual
Peak force
Valley force
Joint-bimanual
Peak force
Valley force
1
A
2
B
A
3
B
A
4
B
A
5
B
A
6
B
A
7
B
A
8
B
A
9
B
A
10
B
A
B
0.19 ⫺0.18 ⫺0.20 ⫺0.12
0.06 ⫺0.12 ⫺0.37 ⫺0.53
0.01 ⫺0.65 0.19 ⫺0.39 ⫺0.84
0.22 0.55 ⫺0.19
0.03 0.16 ⫺0.13 0.02
0.08 ⫺0.17 ⫺0.21
0.08 ⫺0.03 ⫺0.04 ⫺0.59 ⫺0.11 ⫺0.04 ⫺0.61 0.12
0.03 ⫺0.03 ⫺0.15 0.58 ⫺0.16 ⫺0.20 0.40 ⫺0.12 0.08
0.47
0.33
0.43
0.52
0.51
0.79
0.73
0.79
0.76
0.51
0.55 ⫺0.41
0.72 ⫺0.25
0.77
0.75
0.11
0.53
0.28 0.67
0.32 0.79
0.48
0.72
0.67
0.60
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0.75 0.36
0.90 0.34
0.98
0.96
0.51 0.78
0.37 0.82
0.15 0.50
0.38 0.47
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Force of participant B (% MVC)
C
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MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
Table 4. Correlation coefficients calculated for each pair of participants between the total peak forces produced by the 2 participants (A
and B) and between the total valley forces produced by the 2 participants under the joint-unimanual and interpersonal joint-bimanual
conditions
2
3
4
5
6
7
8
9
10
⫺0.53
⫺0.38
⫺0.43
⫺0.31
⫺0.39
⫺0.38
⫺0.43
⫺0.34
0.02
⫺0.31
⫺0.28
⫺0.48
⫺0.17
⫺0.16
⫺0.45
⫺0.23
⫺0.35
⫺0.12
⫺0.56
⫺0.63
⫺0.57
⫺0.52
⫺0.33
⫺0.23
⫺0.51
⫺0.26
⫺0.81
⫺0.44
⫺0.40
⫺0.24
⫺0.37
⫺0.53
⫺0.36
⫺0.52
⫺0.64
⫺0.63
⫺0.47
⫺0.40
⫺0.41
⫺0.02
Accuracy of Force Production and Movement Interval
Figure 6A shows AE of force production in the individual
task, and Fig. 6B shows AE of force production in the joint
task. AE of force production differed across tasks [F(1, 152) ⫽
8.02, P ⬍ 0.01] and conditions [F(1, 152) ⫽ 6.79, P ⬍ 0.05]
but did not differ across forces. There was no interaction of
task and condition. Post hoc tests indicated that AE of force
was smaller in the bimanual condition than in the unimanual
condition and smaller in the joint task than in the individual
task. Figure 6 shows AE of interval in the individual task, and
Fig. 6D shows AE of interval in the joint task. AE of interval
did not differ across conditions, tasks, or forces.
A
B
Correlation (between participants)
Correlation (between hands)
1.0
0.5
0.0
-0.5
-1.0
Individual
Task
Joint
1.0
Peak force
Valley force
0.5
0.0
-0.5
-1.0
Unimanual
Bimanual
Condition
Fig. 3. Mean correlation coefficient between the forces produced by the left
and right hands or by the 2 participants in a pair. Error bars show the
between-participants SE. A: mean correlation between forces produced by 2
hands in the individual-bimanual and intrapersonal joint-bimanual conditions.
B: mean correlation between forces produced by 2 participants in the jointunimanual and interpersonal joint-bimanual conditions.
Variability of Force and Movement Interval
Figure 7A shows SD of force in the individual task, and Fig.
7B shows SD of force in the joint task. SD of force differed
across tasks [F(1, 152) ⫽ 4.10, P ⬍ 0.05] and conditions [F(1,
152) ⫽ 20.70, P ⬍ 0.0001] but did not differ across forces.
There was no interaction of task and condition. Post hoc tests
indicated that SD of force was smaller in the bimanual condition than in the unimanual condition and smaller in the joint
task than in the individual task.
Figure 7C shows SD of interval in the individual task, and
Fig. 7D shows SD of interval in the joint task. SD of interval
did not differ across conditions in either force but did differ
A
Intra-personal
B1.0
Individual-bimanual
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
Joint-bimanual
0.0
0
1
2
3
4
5
6
7
0
8
1
2
3
4
5
6
7
8
7
8
Inter-personal
C
D
Joint-unimanual
1.0
Joint-bimanual
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
0
1
2
3
4
5
6
Frequency (Hz)
7
8
0
1
2
3
4
5
6
Frequency (Hz)
Fig. 4. Cross-spectral coherence between force-time series produced by 2
hands or participants. A: the coherence between force-time series produced by
the left and right hands in the individual-bimanual condition. B: the coherence
between force-time series produced by the left and right hands in the intrapersonal joint-bimanual condition. C: the coherence between force-time series
produced by 1 hand of each participant in the joint-unimanual condition. D: the
coherence between the sums of force-time series produced by both hands of
each participant in the interpersonal joint-bimanual condition. Black lines
represent the between-hands (A and B) or between-participants (C and D)
mean, and 2 gray lines represent the SE.
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41– 60° phase region [F(3, 56) ⫽ 8.65, P ⬍ 0.0001] was lower in
the individual-bimanual and intrapersonal joint-bimanual conditions than in the joint-unimanual (P ⬍ 0.005) and interpersonal
joint-bimanual conditions (P ⬍ 0.05), the percentage for the
61– 80° phase region [F(3, 56) ⫽ 6.25, P ⬍ 0.005] was lower in
the individual-bimanual (P ⬍ 0.005) and intrapersonal jointbimanual conditions (P ⬍ 0.05) than in the joint-unimanual
condition. The percentage for the 81–100° phase regions
[F(3, 56) ⫽ 2.93, P ⬍ 0.05] was lower in the individual-bimanual
condition than in the joint-unimanual condition (P ⬍ 0.05).
Whereas the relative phase occurrence increased mainly in the
0 –20° phase region under all four conditions, similar to the
frequency synchrony, the phase synchrony was higher intrapersonally than interpersonally.
Coherence (between hands)
Joint-unimanual
Peak force
Valley force
Joint-bimanual
Peak force
Valley force
1
Coherence (between participants)
Pair
Individual-bimanual
Intrapersonal joint-bimanual
Joint-unimanual
Interpersonal joint-bimanual
0.8
0.6
0.4
0.2
0
0
40
80
120
160
Phase region (°)
across tasks [F(1, 152) ⫽ 4.33, P ⬍ 0.05]. There was no
interaction of condition and task. The post hoc test indicated
that SD of interval was smaller in the joint task than in the
individual task.
DISCUSSION
Relations Between Motor Redundancy and Hierarchical
Motor Control
In the present study, the negative correlation between forces
was stronger in the joint-unimanual and interpersonal jointbimanual conditions than in the individual-bimanual condition,
indicating that the complementary force production was stron1.2
Individual
B
1.2
A
Joint
Peak force
Valley force
0.9
0.9
0.6
0.6
0.3
0.3
0
Unimanual Bimanual
C
200
AE of interval (ms)
0
150
150
100
100
50
50
0
D
Unimanual Bimanual
Condition
200
0
PPI
VVI
Unimanual Bimanual
Condition
Fig. 6. Absolute error (AE) of force and interval. Error bars show the
between-participants SE. A: AE of peak and valley forces in the individualunimanual and individual-bimanual conditions. B: AE of peak and valley
forces in the joint-unimanual and joint-bimanual conditions. C: AE of peakto-peak interval (PPI) and valley-to-valley interval (VVI) in the individualunimanual and individual-bimanual conditions. D: AE of PPI and VVI in the
joint-unimanual and joint-bimanual conditions.
1.2
Individual
B
1.2
0.9
0.9
0.6
0.6
0.3
0.3
0
Unimanual Bimanual
Unimanual Bimanual
C 200
SD of interval (ms)
AE of force (%MVC)
A
0
Peak force
Valley force
Unimanual Bimanual
D 200
150
150
100
100
50
50
0
Joint
Unimanual Bimanual
Condition
0
PPI
VVI
Unimanual Bimanual
Condition
Fig. 7. SD of force and interval. Error bars show the between-participants SE.
A: SD of peak and valley forces in the individual-unimanual and individualbimanual conditions. B: SD of peak and valley forces in the joint-unimanual
and joint-bimanual conditions. C: SD of PPI and VVI in the individualunimanual and individual-bimanual conditions. D: SD of PPI and VVI in the
joint-unimanual and joint-bimanual conditions.
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Fig. 5. Distribution of relative phase angles as a function of the 9, 20° regions
of relative phase (i.e., 0 –20°, 21– 40°, 41– 60°, . . ., 161–180°) for 4 conditions.
Error bars show the between-participants SE.
3741
ger interpersonally than intrapersonally. In the joint task, the
target force was shared redundantly between two participants,
and thus each participant in the pair adopted a complementary
strategy of force so that one person compensated for force
errors of the other. However, in the intrapersonal joint-bimanual condition (Figs. 2B and 3A), the correlation between forces
produced by two hands was strongly positive. This new finding
indicates that because a symmetric strategy of the bimanual
force production decreased the number of control variables,
two participants were able to adopt a complementary strategy
with the total forces produced by the two hands. From a
hierarchical view of motor control in the joint-bimanual condition, the bottom level of the hierarchy is the force produced
by the hand, and the middle level is the control of the joint
action (see Fig. 8).
A symmetric strategy reflects a tendency to coordinate the
fingers of the two hands into a single collective unit. This
feature has been observed in several previous studies on
bimanual coordination (Kelso et al. 1979; Masumoto and Inui
2012; Ranganathan and Newell 2008), and the high stability of
this strategy may be a main reason why it is selected. Gorniak
et al. (2007b) showed that negative covariation of finger forces
within a hand during the bimanual task was weaker than in a
unimanual task. In the present study, we found a strong
positive correlation of bimanual force production in the intrapersonal joint-bimanual condition. Therefore, the present study
highlights that a motor control hierarchy within an individual
can be extended to intra- and interpersonal actions.
In addition, according to the task requirement, the time-force
series generated by one hand or participant was synchronized
SD of force (%MVC)
Occurrence of relative phase (%)
MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
to decrease the degree-of-freedom number (i.e., the number of
variables) in the bottom level. The relation between lower and
upper levels of a motor control hierarchy is required to decrease the degree-of-freedom number in the lower level.
Total force
FPA
Complementary Force Production is Stronger, and
Synchronization is Weaker Interpersonally than
Intrapersonally
Joint action
FPB
Ta
sk
-irr
ele
van
t
Ta
sk-
rel
eva
nt
3742
FLH
FRH
Fig. 8. A simplified scheme of the proposed motor control hierarchy in the
joint-bimanual condition. FPA, the force produced by participant A; FPB, the
force produced by participant B; FRH, the force produced by the right hand;
FLH, the force produced by the left hand; Task-relevant, task-relevant dimension (i.e., task error); Task-irrelevant, task-irrelevant dimension (i.e., redundancy).
with that generated by another hand or participant at the target
interval in all conditions. However, such frequency or phase
synchrony was not observed without visual feedback but only
when the image of the total or partner force was present
(Masumoto and Inui 2013b). Because the present study gave
participants the total force displayed on a monitor under all
conditions, it corroborated the result of the previous study.
Such synchronization also indicates a symmetric strategy of the
timing of force production between two hands or participants,
which can be viewed as a decrease in the number of variables
manipulated by a higher controller. After the controller decreases the number of degree of freedom of movement timing
between two hands or participants, it appears to release the
degree of freedom of force production between two hands or
participants.
Based on the relation between a motor control hierarchy and
the task-relevant or task-irrelevant dimension, we suggest that
the scheme depicted in Fig. 8 can account for the present
findings. To interpret the negative correlation between forces
produced by two hands or participants as a solution to the
problem of redundancy in motor control, we need to interpret
the data in terms of the uncontrolled manifold hypothesis
(Latash et al. 2002; Scholz and Schöner 1999). The hypothesis
suggests that the nervous system should minimize the variance
in the sum of the two forces (the task-relevant dimension), but
the difference between the forces (the task-irrelevant dimension) would be allowed to accumulate. The input into the
highest level comes from the task requirement (e.g., target total
force), and the output from the lowest level acts on the muscles
that control the fingers. In the individual-bimanual condition,
coordination of forces between hands is task relevant, whereas
that between fingers within the hand is task irrelevant. In the
joint-bimanual condition, however, variability of total force at
the top level may be viewed as the task-relevant dimension,
and variability of forces produced by participants (middle
level) and hands (bottom level) may be viewed as the taskirrelevant dimensions. To enable complementary force production between the two participants at the middle level of the
hierarchy, the bimanual symmetric force production is required
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FRH FLH
Bimanual action
In the present study, the complementary force production is
stronger interpersonally than intrapersonally. Reed et al. (2006)
have also found an interpersonal complementary relationship
in a joint target-acquisition task [also see Skewes et al. (2015)].
They asked pairs of participants to move a mark on a disk into
a target as quickly as possible and hold it there. Whereas one
participant contributed more to acceleration and the other to
deceleration, the participants performed faster interpersonally
than individually. In bimanual coordination, Masumoto and
Inui (2012) showed that the forces produced by both hands
were combined over all force levels without vision, whereas
the strategy for the bimanual force control changed from
force-error compensation to symmetric force production, with
an increase in force with vision [also see Hu et al. (2011) and
Ranganathan and Newell (2008)]. In addition, interhemispheric
information processing across the corpus callosum increases
with force level in a bimanual coordination task (Diedrichsen
et al. 2003). Thus a symmetric strategy of force production is
often observed in bimanual coordination, rather than forceerror compensation, and the redundancy decreases in many
cases. By contrast, communicating information between two
participants in a pair during the joint task does not depend on
neuroanatomical linkages between the control centers but
visuomotor linkages between the participants. The visuomotor
linkages appear to promote stronger complementary force
production than the interhemispheric information-processing
system.
Synchronization of their performance to each other’s timing
was stronger intrapersonally than interpersonally. The bimanual control of timing depends on interhemispheric or subcortical information processing. Previous studies on bimanual
timing control have shown that bimanual coordination of
continuous drawing of a circle depends on interhemispheric
information processing across the corpus callosum (Spencer et
al. 2003), whereas bimanual discrete tapping is controlled by
the cerebellum (Kennerley et al. 2002). Thus the periodic
bimanual action in the bimanaual condition in the present study
presumably depends on interhemispheric information processing across the corpus callosum. By contrast, in the interpersonal control of timing, the two participants in a pair were
loosely coupled via visuomotor linkages. The interhemispheric
information-processing system appears to promote stronger
synchronization of performance than visuomotor linkages.
In the present study, we further observed higher levels of
coherence for frequencies above 2 Hz intrapersonally (Fig. 4,
A and B) but not interpersonally. Whereas physiological tremor
is present at higher frequencies, between 5 and 12 Hz in force
recording (Elble and Randall 1976), processes related to slow
sensorimotor actions are located in the 0- and 4-Hz band of the
force power spectrum (Slifkin et al. 2000). Thus because the
coherence in the present study was related to visuomotor
action, the participant presumably synchronized the timing of
MOTOR CONTROL HIERARCHY IN BIMANUAL JOINT ACTION
production of forces with the partner’s timing in the fine
control of bimanual force production except attempting to
match the target interval.
Control of Force and Timing
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the authors.
AUTHOR CONTRIBUTIONS
Author contributions: J.M. and N.I. conception and design of research; J.M.
performed experiments; J.M. analyzed data; J.M. and N.I. interpreted results of
experiments; J.M. prepared figures; J.M. and N.I. drafted manuscript; J.M. and
N.I. edited and revised manuscript; J.M. and N.I. approved final version of
manuscript.
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The AE and SD of force were smaller in the bimanual action
than in the unimanual action and smaller in the joint action than
the individual action. These results indicate that force was
controlled more accurately in the bimanual action than the
unimanual action, consistent with our previous study (Masumoto and Inui 2012). These results also indicate that force was
controlled more accurately in joint action, which was performed with visuomotor linkages between participants, than in
the individual action, which involved neuroanatomical linkages between the control centers, corroborating the result of
Masumoto and Inui (2013b).
In addition, the SD of the interval was smaller in the joint
action than in the individual action, consistent with the result of
Masumoto and Inui (2013b) and suggesting that the effect was
due to visuomotor linkages between participants. Vesper et al.
(2011) have also found that the temporal variability of participants’ actions was smaller interpersonally than individually in
a two-choice reaction time task. They asked pairs of participants to press a key in synchrony in the task, indicating that the
less variable the actions were, the better the interpersonal
coordination was. They point out that reducing one’s variability may be a coordination strategy to make oneself more
predictable in joint actions. Moreover, in a joint discrete force
production (Masumoto and Inui 2014a), whereas participants
with low-force variability always produced a stronger force
than those with high-force variability, the former produced
force more complementarily than the latter. Based on such an
interpersonal coordination strategy that the variability of human actions is smaller interpersonally than individually, joint
actions exhibit larger performance gains than individual actions.
3743