Mitsuo Kawato, Hiroaki Gomi, Masazumi Katayama, Yasuharu Koike
Supervised Learning
for Coordinative Motor Control
Abstract:Fast, smooth and coordinated movements in humans and animals cannot be realized
by pure feedback control only because delays associated with feedback loops are long
(about 200 ms for visual feedback and 100 ms for somatosensory feedback) and feedback
gains are low in biological motor control systems [23]. Additionally, feedback
controllers such as the commonly used PID (proportional, integral and derivative) controllers
do not incorporate predictive dynamic and/or kinematic knowledge of controlled
objects or environments. Feedforward control, however, explicitly incorporates
such predictive internal models, and appears to be essential at least for relatively
fast movements. Two different approaches have been proposed for feedforward motor
control: learning of internal models of the controlled object [3, 36, 6, 31], and the
virtual trajectory control hypothesis [12, 22]. The second approach is quite attractive
if some simple virtual trajectory can realize observed trajectories that are roughly
straight [51, 1], because it implies that complicated calculation of torque (in other
words, the inverse dynamics problem) need not be addressed.
In this chapter, we ask two fundamental questions about the computational study
of motor control. The first one is: does the brain use internal models of motor
apparatus and the environment for motor control? We propose that the answer is yes.
Then we ask, if the brain uses internal models, where are they stored and how are
they acquired? We propose that at least some of the internal models are stored in the
cerebellar cortex and that they are acquired by supervised motor learning based on
long term depression.
We first show some invariant features of multi-joint arm movements that suggest
feedforward control is operative. Then, we examine the virtual trajectory control
hypothesis, in which internal models of motor apparatus are usually assumed to be
unnecessary. We critically examine a virtual trajectory control hypothesis based on recently measured, low mechanical stiffness values during human movement, and
showed that internal models of the motor apparatus are necessary even for this virtual
trajectory control hypothesis. We then compare several computational schemes for
acquiring internal neural models through supervised motor learning. We explain,
in detail, the feedback-error-learning scheme that we proposed and applied to robot
trajectory control. Convergence of synaptic weights and trajectories in this scheme are
mathematically examined based on an averaging of the stochastic differential equation
and Lyapunov method. Finally, based on this feedback-error-learning scheme, we
propose computationally coherent models of different regions of the cerebellum.