Construction and Automated Deployment of Local Potential Functions for Global Robot Control and Navigation

Abstract

This report presents a method for addressing integrated navigation and control tasks for constrained dynamical systems. Specifically, we focus on solving this problem for an idealized point robot subject to bounds on velocity and acceleration. The basic approach divides the overall task into discrete sub-tasks, and achieves those sub-tasks using feedback control policies. The method is based on sequential composition of safe, reliable, and robust feedback control policies. This report presents an extension to the method of sequential composition that allows a new class of feedback control policies with goal sets, not just goal points. Where previous work only allowed for goal sets that were completely contained in the domain of another control policy, this extension allows the deployment of policies whose goal intersects the domains of multiple policies. This extension allows for a larger class of policies to be deployed, making it easier to build near globally convergent overall control policies. This report also details the new local control policies, defined over cells in the configuration space. The policies cause a large subset of initial states to exit the cell in a specified manner. The resulting composition of local control policies induces a global control strategy that brings any initial condition contained in the union of the domains of the control policies the goal, provided that there is a single connected component of free space containing both the start and goal configurations. The underlying control policies are designed to respect environmental constraints such as obstacles, velocity bounds, and acceleration bounds. Control policies for fully actuated kinematic and dynamical systems are developed.