Optimal control problems in binocular vision

Human eye movement can be looked at, as a rotational dynamics on the space SO(3) with constraints that have to do with the axis of rotation. A typical eye movement can be decomposed into two components, that go by the name 'version' and 'vergence'. The version component produces identical eye movement in both the eyes, and is used to follow a target located far away by taking the general direction of the target. In order to focus on a closer target, the eyes rotate in opposite directions, using the vergence component. A typical eye movement can be regarded as a concatenation of version followed by vergence. These two eye movements are modeled in this paper assuming that the eyes are perfect spheres with their mass distributed uniformly and that the eyes rotate about their own centers. An optimal control problem is considered where the goal is to rotate an eye pair from an initial 'parallel gaze direction' to a final 'gaze focusing on a target'. The eye pairs are to be actuated optimally using an external torque vector of minimum energy.