Newton type algorithm on Riemannian manifolds applied to robot vision, and suggestions for improvement of its performance

Abstract

In visual servo control of a robot we often encounter the structure from motion problem. To study the structure from motion problem we are led to finding a minimum of a real valued function defined on a product Riemannian manifold, e.g. special orthogonal groups and unit sphere. To take advantage of its Riemannian structure we consider the Newton algorithm on this manifold. In particular, we focus on improving the algorithm to be more robust and faster than the existing Newton algorithm on Riemannian manifolds. For this we exploit the sparseness of the Hessian matrix and suggest how to choose the step size during the optimisation procedure, which can be considered as extensions of those for vector space optimisation algorithms.