Synchronisation and Differentiation: Two Stages of Coordinative Structure



skills.

Now recall our results. In the kneading, differentia-
tion is highly ordered. We saw temporally hierarchy of
phase difference in the experts’ movements. There was a
major phase delay between arm and torso and torso was
divided into two groups pivoted around the hip. While
experienced person’s trajectories were similar to the ex-
pert’s and coordination was established, differentiation
was lacking. Adding modulation without breaking cycle
may require long term self learning.

In samba shaking, modulation was also observed. One
of the hip joints desynchronised to the torso although
it was synchronised to the whole body to maintain the
balance. This is why the samba dancer’s upper body
looks stable. We may thus conclude that differentiation
observed in skill is also hierarchically ordered although
differentiated movement of hip was not regular. We need
yet to analyse time series of joint angles carefully, but we
expect a qualitative difference of desynchronisation to
be found between experienced persons and experts (or
novices).

Our study may be applied to training or teaching
method of skills. We think that controlling points can
be found by investigating dynamics, the control points
at which modulation is effective.

A promising candidates for controlling points are the
zeros of angular momentum or joint torque. The former
corresponds to the turning point of joints (i.e., starting
point of a stroke) and it has dynamical significance since
the direction of momentum changes. The latter has sig-
nificance for muscular control because some of muscles
generate strong torque instantaneously (i.e., pulse-like).
This point is also suitable for adding force in any direc-
tion since there is no force is added or balancing to the
external force. It is important to note that above zeros
exist discretely in time. This feature agrees with our
hypothesis described above.

Finally, let us discuss the significance of our result in
the context of epigenetic robotics. Basic level can be
achieved easily, either by machine learning or exploita-
tion of limit cycles. We then discuss further step, differ-
entiation by adding control input.

The learning process should be essentially the same
as that for human. However, one possible merit for the
robot is that its sensory system is faster and more ac-
curate than that of human. To find controlling points,
global stability analysis of body dynamics is helpful, but
if we had hints discussed above (i.e., zero of some vari-
ables), on-line learning might be possible.

We do not expect real time learning to be easily re-
alised because once stability is broken, there is no way to
recover (e.g., falling down in walking). However, by “re-
view” process, learning can be possible. Review process
is a data mining process in which causal chain between
sensory input and resulting movement (or, simply fit-
ness) to find correct control inputs and there points to
apply. What we expect to be most important factor is
timing, not strength of control input. Although human
muscle is not precision device, highly skillful movement
is realised. Timing is also not based on physical time
but depends on the phase within each cycle. If we find
an appropriate rhythm and feed it to the robot, its body
should follow the rhythm.

Acknowledgment

We are grateful to Ms. Mamiko Abe, who initiated this
research of skills. We are also thankful to Dr. Gen-
taro Taga for his inspiring discussion with us. We are
helped a lot for our experiments by Mr. Yutaka Andou,
Mr. Akihiko Kamimura, Mr. Sou Tunetugu, and Mr.
Tsuyoshi Miwa. We finally express our gratitude to peo-
ple who took part in our experiments: Mr. Mogami, Mr.
Nakashima, and Mr. Suguru Endou.

References

Abe, M., Yamamoto, T., and Fujinami, T. (2003). A
dynamical analysis of kneading using a motion cap-
ture device. In
proceedings of second international
workshop on Epigenetic Robotics 2003
, pages 41-48.

Bernstein, N. (1967). The co-ordination and regulation
of movements
. Pergamon.

Bernstein, N. (1996). On dexterity and its development.
Lawrence Erlbaum Associates.

Haken, H., Kelso, J. A. S., and Bunz, H. (1985). A the-
oretical model of phase transitions in human hand
movements.
J. Biological Cybernetics, 51:347 - 356.

Panter, P. (1965). Modulation, Noise and Spectral Anal-
ysis
. McGraw Hill, New York.

Pikovsky, A., Rosenblum, M., and Kurths, J. (2001).
Synchronization - a universal concept in nonlinear
sciences
. Cambridge University Press.

Taga, G. (1995). A model of the neuro-musculo-skeletal
system for human locomotion i. emergence of basic
gait.
Biological Cybernetics, 73:97-111.

Taga, G. (1998). A model of the neuro-musclo-skeletal
system for anticipatory adjustment of human loco-
motion during obstacle avoidance.
Biological Cyber-
netics
, 78:9-17.

Yamamoto, T. and Kuniyoshi, Y. (2002). Stability and
controllability in a rising motion: a global dynamics
approach. In
proceedings of IROS2002, pages 2467-
2472.

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