Bijoy Ghosh, Texas Tech University
In this talk we study the problem of optimally moving the eyes. We formulate the problem of eye movement with a suitable Riemannian Metric. Using the Euler Lagrange Equation, we write down the associated dynamics. We choose a suitable quadratic cost function and derive the state/costate equation. We find that these equations have singularities and that they can be removed if the dynamics is defined on a set of charts that cover the manifold. In effect we have a Two Point Boundary Value Problem that is now described on multiple charts. The problem is addressed when the eye movement satisfies both the Listing's constraint and when it does not. Simulations show that the optimal trajectories are highly oscillatory.