Intrinsic control designs for abstract machines

Abstract

A geodesic-based formulation of geometric PD tracking control for fully actuated mechanical systems is derived from the Riemannian metric. The region of stability is determined directly from the magnitude of the system's injectivity radius and, for a restricted set of control problems, the locus of cut points about a desired reference point in the manifold. Exponential stability is proven for controlled motion along a geodesic, yielding a particularly simple, yet elegant, methodology for control design. © Springer-Verlag Berlin Heidelberg 2007.