Mitsuo KAWATO, Yoshiharu MAEDA*, Yoji UNO** and Ryoji SUZUKI**
Trajectory Formation of Arm Movement by
Cascade Neural Network Model Based on
Minimum Torque-change Criterion
Abstract:We proposed that the trajectory followed by human subject arms tended
to minimize the time integral of the square of the rate of change of torque
(Uno, Kawato, Suzuki, 1987). This minimum torque-change model predicted
and reproduced human multi-joint movement data quite well (Uno,
Kawato, Suzuki, 1989). Here, we propose a neural network model for trajectory
formation based on the minimum torque-change criterion. Basic ideas
of information representation and algorithm are (i) spatial representation
of time, (ii) learning of forward dynamics and kinematics model and (iii)
relaxation computation based on the acquired model. Operations of this
network are divided into the learning phase and the pattern-generating
phase. In the learning phase, this network acquires a forward model of
the multi-degrees-of-freedom controlled object while monitoring the actual
trajectory as a teaching signal. In particular, it learns a vector field of
the ordinary differential equation which describes the dynamics of the controlled
object. Correspondingly, the network structure is a cascade of many
identical network units, each of which approximates the vector field. In the
pattern-generating phase, electrical coupling between neurons representing
motor commands at neighboring times is activated to guarantee the minimum
torque-change criterion. The network changes its state autonomously
by forward calculation through the cascade structure, and by error backpropagation
based on the acquired model. At the stable equilibrium state
with minimum energy, the network outputs the torque which realizes the
minimum torque-change trajectory. The model can resolve ill-posed inverse
kinematics and inverse dynamics problems for redundant controlled
objects as well as ill-posed trajectory formation problems. By computer
simulation, we show that the model can produce a multi-joint arm trajectory
while avoiding obstacles or passing through via-points.