on different timings. The differentiation is achieved by
increasing the degree of freedom without loss of control
and leads to flexibility and adaptability.
Our findings are consistent with the theory of dexter-
ity as proposed by Bernstein (Bernstein, 1996). Dexter-
ity means manual or manipulative skill and addresses
neat-handedness in the use of the limbs and in move-
ments in general. Bernstein proposed to classify devel-
opmental stage of the skill into four levels: A, B, C, and
D, each of which is related to some part of the brain func-
tionally. The lowest level A controls the balance. The
second level B controls the basic movements. The third
level C controls movements performed in the space with
a target. The control in the level B only concerns with
the body, not with the space surrounding the body. The
level D includes other fascinating skills requiring higher
brain functions such as reasoning or planning.
The synchronisation we observed in some subjects’
trajectories indicates that their movements are con-
trolled in the level of B. The trajectories in the level of B
are simple, cyclic and repetitive movements and are per-
formed without a target. The various parts of the body
are thus synchronised to produce a force most effectively.
The differentiation we observed in the experts’ trajecto-
ries indicates that their movements are controlled in the
level of C. According to Bernstein, the lower level B be-
comes the background and is adjusted by the higher level
C. What we observed in the experts’ trajectories as dif-
ferent timings at which some section moves jointly, are
the points in which the level C intervenes in the move-
ments controlled in the level of B.
Our interpretation is supported by our inner observa-
tion, too. As Bernstein pointed out, we are only aware
of the foreground level of control, that is, we do not
pay much attention to the background level, letting it to
work automatically. For the case of shaking, each sub ject
was aware of beating the samba rhythm in a particular
part of his body, i.e., hip or knee, both of which were
observed to move at different timings from other parts
synchronised.
How is the hierarchical development achieved? Our
hypothesis is that in higher levels (level C or above), con-
trolling point is discretised in the phase space of body
dynamics. While the lower levels maintain the balance
and coordination in shorter time scales, the higher levels
activate control input instantly in longer time scales (i.e.,
intermittently). This hypothesis is based on the concept,
“Global Dynamics” (Yamamoto and Kuniyoshi, 2002).
One of the authors proposed that higher control input
only works on the branching point of stable sets of tra-
jectories within the phase space. The results obtained
in this work agree with the concept above and temporal
differentiation of controlling point can be investigated as
an expansion.
We have seen differentiation of phase in skillful per-
sons’ trajectories. Since this feature requires multiple
control input per cycle, one might think the brain be-
comes busy. However, if control signal is preprogrammed
as a sequence, a single signal input can describe com-
plex movement with temporal differentiation. It may
be helpful to note that due to the delay in neural sig-
nal transmission, feedback control is impossible for quick
movements.
Using discretising feature described above, we think
that the representation of higher level of motor control
can be written as a “score”. Temporal discretisation
of controlling points may be easily understood through
analogy to music score. Spatial discretisation is not one-
dimensional. We think minimal information consists of
the pattern of coordinating joints, the coupling strength
within them, and the initial acceleration or momentum
for the joints at the boundaries between groups.
Although the background level must be trained in ad-
vance, once mastered, differentiation within coordina-
tion of DOFs can be written as modulation of control
input sequences. Still we do not have proof of this hy-
pothesis, but our results are consistent with it.
One might think cyclic movement is realised by adopt-
ing Central Pattern Generator(CPG) (Taga, 1995). Our
hypothesis, however, focuses on the fine tuning of move-
ment after the motion is mastered. Let us describe a
hypothesis about the acquisition process of the differ-
entiation phenomenon for CPG based theory. In CPG
based studies, the coordinated movement is regarded to
be acquired by exploiting entrainment. The phenomenon
may be regarded as a synchronising process to a single
oscillator. Differentiation within coordination, however,
requires a temporal differentiation of oscillators. As long
as we are concerned with exploiting entrainment to a
limit cycle, differentiation of it means a partial braking
of cycles within the limit cycle. It is, however, a non-
trivial process since stability (i.e. attraction to a limit
cycle) is not expected within the limit cycle.
We think that the differentiation is obtained through
trials, in which modulation signals are added to CPG,
e.g., (Taga, 1998). Modulation signals can be generated
by taking a hint from the sensory input. After skill is
acquired, the modulation signals are integrated to CPG
by changing parameters of neural network.
It is important to note that the search for control-
ling point is nontrivial. Like double support phase in
walking, trajectories of skillful movements may go across
unstable regions in the phase space to switch stable dy-
namical modes. For such cases, the control input must
be adopted in correct timing and state. Also, even for
the stable dynamical modes, the possible trajectories oc-
cupy only a small volume in the phase space. Small er-
rors then may pull the state out of it and the skill might
be not acquired. Only after synchronisation is highly or-
ganised, modulation plays a significant role in improving
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