Towards Provable Navigation and Control of Nonholonomically Constrained Convex-Bodied Systems
David C. Conner, Howie Choset, Alfred A. Rizzi · 2006
In this paper, we develop a generic class of control policies that respect nonholonomic constraints and are provably safe with respect to obstacles for a convex-bodied mobile robot. We instantiate this class of policies over local regions of configu- ration space, and compose the resulting local policies to address the global navigation and control problem for a wheeled mobile robot navigating amongst obstacles. Simulation and experimental results are given. I. INTRODUCTION We explore a general solution to the problem of simul- taneously planning and controlling the motion of a convex- bodied vehicle in a cluttered planar environment. Our approach relies on a generic class of local control policies that we instantiate over local regions of the robot's free configuration space (termed cells). The automated sequential application of the local policies effectively solves the global navigation and control problem simultaneously. The result is a global strategy, which, given the current configuration (position and orientation) of the robot determines which local policy to apply, and calculates the control inputs based on that policy. The determination of which policy to apply follows from a partial order of the cells that is determined off line, and each local policy specifies a configuration dependent velocity reference defined over its region of applicability. We guarantee that the resulting essentially global vector field respects the system constraints, and that the policies are composed in such a way that the resulting system trajectories are safe with respect to environmental obstacles. Throughout this paper, we will refer to the combination of a configuration space cell and its associated reference vector field as a policy. We explore these ideas both through a formal outline of their technical correctness, and experimentally in simulation and on a laboratory mobile robot system. Figure 1 presents some representative paths taken from two different rounds of experiments discussed in Sections IV and V.