Pseudo-inverse control in biological systems: a learning mechanism for fixation stability.

Abstract

The problem of redundancy in motor control is common to both robotics and biology. Pseudo-inverse control has been proposed as a solution in robotics and appears to be used by the oculomotor system for eye position. Learning mechanisms for implementing pseudo-inverse control using a distributed system of ocular motor units were investigated by modelling integrator calibration for horizontal eye movements. Ocular motoneuron (OMN) input weights were adjusted with a gradient-descent learning rule, using a retinal-slip estimate as an error signal. Firing-rate threshold only became related to motor-unit strength when a noise term was added to OMN firing rates. The learning rule suppressed those units making the largest contribution to the noise-related error, causing the strongest units to have the highest thresholds (size principle). Because the size principle and pseudo-inverse control are related, the trained system approximated pseudo-inverse control over the central +/-35 degrees of the oculomotor range.