Integrating Planning and Control for Constrained Dynamical Systems

Abstract

This thesis develops an approach to addressing the coupled navigation and control problem for wheeled mobile robots. Instead of using a top-down decoupled approach that does not respect low-level constraints, or a bottom-up approach that cannot guarantee satisfaction of high-level goals, our approach is middle-out. We develop local feedback control policies that respect the low-level constraints. The approach then uses a collection of these policies with existing formal discrete planning methods to either produce a hybrid feedback control policy that guarantees high-level goals are satisfied, or in the worst case, verifies that the high-level specification is not realizable. Our approach enables existing formal symbolic planning methods to be applied to highly constrained systems. We extend the sequential composition of local feedback control policies to wheeled mobile robots in a way that enables the automated synthesis of hybrid control policies. The thesis defines four basic ``composability'' requirements that guide our design of local policies. We develop two families of generic feedback policies that induce low-level behaviors in a way that enables their formal composition. The thesis also develops a novel approach for guaranteeing that a given control policy is collision free. By design, the policies respect multiple interacting constraints including large non-circular body shapes, nonholonomic constraints, and input bounds. Given a collection of the local policies and a task specification, our approach uses existing symbolic planning methods to automatically synthesize a switching strategy among the policies. Executing the switching strategy induces continuous motion that satisfies the high-level behavioral specification. This thesis demonstrates the approach on real mobile robots. While wheeled mobile robot navigation is the chosen domain in this thesis, our future work will develop composable policies that extend these formal methods to other constrained dynamical systems.