Amir Karniel, and Gideon F. Inbar
Biol. Cybern. Volume 77 Issue 3 (1997) pp 173-183
Abstract - 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 the human arm during ballistic reaching
movements is presented. The model 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 is modeled as an adjustable pattern generator that creates the control
signals to the muscles. The control signals in this model are rectangular
pulses activated at various amplitudes and timings, that are determined
according to the given target. These amplitudes and timings are the parameters
that should be related to each target and initial conditions in the workspace.
The model of the nervous system consists of an artificial neural net that maps
any given target to the parameter space of the pattern generator. In order to
train this net, the nervous system model includes a sensitivity model that
transforms the error from the arm end-point coordinates to the parameter
coordinates. The error is assessed only at the termination of the movement from
knowledge of the results.
The role of the non-linearity in the muscle model and the performance of the
learning scheme are analysed, illustrated in simulations and discussed. The
results of the present study demonstrate the 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 this scheme, which is based on the adjustment of
only a few parameters instead 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
conclusion agrees with the general concept that motor control is the result of
an interaction between the nervous system and the musculoskeletal dynamics.