Menashe Dornay and Terence D. Sanger
Equilibrium Point Control of a Monkey
Arm Simulator by a Fast Learning
Artificial Neural Network
Abstract:A planar 17 muscle model of the monkey's arm based on realistic biomechanical
measurements was simulated on a Symbolics Lisp Machine. The simulator implements the
equilibrium point hypothesis for the control of arm movements. Given initial and final
desired positions, it generates a minimum-jerk desired trajectory of the hand and uses the
backdriving algorithm to determine an appropriate sequence of motor commands to the
muscles (Flash 1987; Mussa-Ivaldi et al. 1990; Dornay 1991b). These motor commands
specify a temporal sequence of stable (attractive) equilibrium positions which lead to the
desired hand movement.
A strong disadvantage of the simulator is that it has no memory of previous computations.
Determining the desired trajectory using the minimum-jerk model is instantaneous, but the
laborious backdriving algorithm is slow, and can take up to one hour for some trajectories.
In order to overcome this problem, a fast learning, tree-structured network (Sanger 1991c)
was trained to remember the knowledge obtained by the backdriving algorithm. The neural
network learned the nonlinear mapping from a 2-dimensional cartesian planar hand position {x, y}
to a 17-dimensional motor command space {u1, ... , u17}. Learning 20 training trajectories,
each composed of 26 sample points {{x,y},{u1, ... ,u17}} took only 20 minutes on a
Sun-4 Sparc workstation. After the learning stage, new, untrained test trajectories as well as
the original training trajectories of the hand were given to the neural network as input. The
network calculated the required motor commands for these movements. The resulting
movements were close to the desired ones for both the training and test cases.