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.