Composition of local potential functions for global robot control and navigation

This paper develops a method of composing simple control policies, applicable over a limited region in a dynamical system´s free space, such that the resulting composition completely solves the navigation and control problem for the given system operating in a constrained environment. The resulting control policy deployment induces a global control policy that brings the system to the goal, provided that there is a single connected component of the free space containing both the start and goal configurations. In this paper, control policies for both kinematic and simple dynamical systems are developed. This work assumes that the initial velocities are somewhat aligned with the desired velocity vector field. We conclude by offering an outline of an approach for accommodating arbitrary dynamical constraints and initial conditions.