A MODEL FOR LEARNING HUMAN REACHING MOVEMENTS

Reaching movement is a fast movement towards a given target. The main characteristics of such a movement are straight path and a bell-shaped speed profile. In this work a mathematical model for the control of t he human arm during ballistic reaching movements is presented. The mod el of the arm contains a 2 degrees of freedom planar manipulator, and a Hill-type, non-linear mechanical model of six muscles. The arm model is taken from the literature with minor changes. The nervous system i s modeled as an adjustable pattern generator that creates the control signals to the muscles. The control signals in this model are rectangu lar pulses activated at various amplitudes and timings, that are deter mined according to the given target. These amplitudes and timings are the parameters that should be related to each target and initial condi tions in the workspace. The model of the nervous system consists of an artificial neural net that maps any given target to the parameter spa ce of the pattern generator. In order to train this net, the nervous s ystem model includes a sensitivity model that transforms the error fro m the arm end-point coordinates to the parameter coordinates. The erro r is assessed only at the termination of the movement from knowledge o f the results. The role of the non-linearity in the muscle model and t he performance of the learning scheme are analysed, illustrated in sim ulations and discussed. The results of the present study demonstrate t he central nervous system's (CNS) ability to generate typical reaching movements with a simple feedforward controller that controls only the timing and amplitude of rectangular excitation pulses to the muscles and adjusts these parameters based on knowledge of the results. In thi s scheme, which is based on the adjustment of only a few parameters in stead of the whole trajectory, the dimension of the control problem is reduced significantly. It is shown that the non-linear properties of the muscles are essential to achieve this simple control. This conclus ion agrees with the general concept that motor control is the result o f an interaction between the nervous system and the musculoskeletal dy namics.