Eye and Head Rotation Control Via Feedback Linearization

In this paper, recently studied rigid body rotation control problems are summarized as a constrained dynamics on SO(3) from the point of view of a nonlinear multi input multi output system. Our specific interests are in the rotation of human head and eye, where the control objective is to direct the pointing direction towards a stationary or mobile point target in space. Eye and head rotation control problems were studied in the mid-nineteenth century by Listing, Donders, Helmholtz and others. In these studies, it was observed by Donders that, for rotations away from the primary direction, the rotation vectors are restricted to lie on a surface, called the Donders' surface. Additionally, for eye movements under head-fixed condition, it was observed by Listing that the Donders' surface is actually a plane, called the Listing's plane. The input signals to the eye and head are provided by a triplet of external torques generated by muscles. Three output signals from the eye and head are chosen as follows. Two of the signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders' surface (respectively Listing's plane). Thus we have a 3 × 3 square system and the claim is that the proposed square system is locally feedback linearizable on a suitable neighborhood N of the state space.