EQUILIBRIUM POINT CONTROL OF A MONKEY ARM SIMULATOR BY A FAST LEARNING TREE-STRUCTURED ARTIFICIAL NEURAL-NETWORK

A planar 17 muscle model of the monkey's arm based on realistic biomec hanical measurements was simulated on a Symbolics Lisp Machine. The si mulator implements the equilibrium point hypothesis for the control of arm movements. Given initial and final desired positions, it generate s a minimum-jerk desired trajectory of the hand and uses the backdrivi ng algorithm to determine an appropriate sequence of motor commands to the muscles (Flash 1987; Mussa-Ivaldi et al. 1991; Dornay 1991b). The se motor commands specify a temporal sequence of stable (attractive) e quilibrium positions which lead to the desired hand movement. A strong disadvantage of the simulator is that it has no memory of previous co mputations. Determining the desired trajectory using the minimum-jerk model is instantaneous, but the laborious backdriving algorithm is slo w, and can take up to one hour for some trajectories. The complexity o f the required computations makes it a poor model for biological motor control. We propose a computationally simpler and more biologically p lausible method for control which achieves the benefits of the backdri ving algorithm. A fast learning, tree-structured network (Sanger 1991c ) was trained to remember the knowledge obtained by the backdriving al gorithm. The neural network learned the nonlinear mapping from a 2-dim ensional cartesian planar hand position {x,y} to a 17-dimensional moto r command space {u1, ..., u17}. Learning 20 training trajectories, eac h composed of 26 sample points {{x, y}, {u1, ..., u17} took only 20 mi n on a Sun-4 Sparc workstation. After the learning stage, new, untrain ed test trajectories as well as the original 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 w ere close to the desired ones for both the training and test cases.