Dynamic control of human eye on head system

In this paper we study the human eye movement, when the eye shifts its gaze between two possible gaze directions, as a simple mechanical control system. When the head is restrained to remain fixed, eye movements obey Listing's constraint, which states that the allowed orientations of the eye are obtained by rotating a fixed `primary gaze direction' by a subclass of rotation matrices. These rotation matrices have their axes of rotation restricted to a fixed plane perpendicular to the primary gaze direction. Under head fixed restriction, eye movement satisfies the Listing's constraint throughout its entire trajectory. On the other hand, when the head is allowed to move, the eye orientations satisfy the Listing's constraint only at the beginning and at the end of a trajectory. Intermediate points of the trajectory, do not satisfy the Listing's constraint. In this paper, we study the dynamic control of eye movement with or without satisfaction of the Listing's constraint. The control has been synthesized by a suitable choice of a potential function and an externally added damping term.