Copy of letter to science (and Kawato)

Letter to Editor
NOTE: E-mail copy send to Kawato and Gomi.

                     Equilibrium-point control

The equilibrium-point hypothesis of limb-movement control has
been partially refuted by the experimental work of Gomi and
Kawato (1). A control-system simulation of pointing control
agrees with these experiments, and shows how the known
contractile-spring properties of muscles can be integrated into a
control-system model using continuous feedback as found in spinal
reflexes. In this control-system model, realistic trajectories of
very fast movements can be reproduced (agreeing with the velocity
and stiffness profiles found by Gomi and Kawato) by applying
step-changes in position reference signals, while slow movements
from one configuration to another are produced simply by varying
the same reference signals more slowly. This model does not use
any inverse kinematic or dynamic calculations. It does
incorporate the physical dynamics of the arm in the forward

I developed this arm model some five years ago for some
experimental work that a colleague was to carry out with
paraplegics and spine-injured patients. The project, however, was
a victim of funding cuts and shifts of priorities, and is
essentially abandoned. As I am retired and unlikely to carry on
this development alone, I have decided to put the model in the
public domain in the hope that others interested in this approach
will carry it forward from where my developments ended.

The C source, executable code, and writeups for the first two
versions of this model (for IBM compatibles) are available from
http::/ (final slash required). Follow the links
for "Computer programs", "MSDOS," and "PCTdemos". The programs
and source code may be freely downloaded, reproduced, modified,
or incorporated into any more advanced models, with suitable
credits. I hope that the result will be a step toward resolving
the current disputes over motor control in human beings.

William T. Powers
73 Ridge Place, CR 510
Durango, CO 81301

(970) 247-7986


1. H. Gomi, M. Kawato; _Science_ 272,117 (1996)