Binocular eye tracking control satisfying Hering's law

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'. Hering's law proposes that the version component of the eye movement is identical in both the eyes, and versional eye movement is used to follow a target located far away. In order to focus on a closer target, the eyes rotate in opposite directions, using the vergence component. A typical eye movement would be regarded as a concatenation of version followed by vergence. In this paper, we shall represent such eye movements using unit quaternion, with constraints. Assuming that the eyes are perfect spheres with their mass distributed uniformly and rotating about their own centers, eye movement models are constructed using classical mechanics. For targets moving in near field, for which both version and vergence eye movements are required, optimal eye movement trajectories are simulated, where the goal is to minimize a quadratic cost function on the energy of the applied control torques.