Exterior differential systems and nonholonomic motion planning

Abstract

This dissertation addresses the problem of motion planning for systems with velocity constraints which restrict the system velocities but do not reduce the reachable configuration space. Such constraints are nonholonomic. Traditional motion planning methods assume that a robot can move in any direction. These plans cannot be followed by nonholonomic systems, such as car-like mobile robots which cannot move sideways. The theory of exterior differential (particularly Pfaffian) systems is presented as an analysis method for nonholonomic systems. The Goursat normal form for Pfaffian systems of codimension two is shown to be equivalent to the two-input chained form for nonholonomic control systems. Since the N-trailer system satisfies the conditions for conversion in...