Exterior Differential Systems in Control and Robotics

Abstract

The vast majority of the mathematically oriented literature in the areas of robotics and control has been heavily influenced by a differential geometric point of view. For nonlinear systems in particular, most of the research has concentrated on the analysis of the Lie algebras associated with controllability, reachability and observability. In recent years, however, a small but influential trend has begun in the literature on the use of other methods, such as differential algebra [9, 8, 10] and exterior differential systems [13, 11] for the analysis of nonlinear control systems and nonlinear implicit systems. In this paper we survey some key results from the theory of exterior differential systems and their application to current and challenging problems in robotics and control.