Control of stratified systems with robotic applications

Author: Goodwine, John William

Year: 1998

Degree: Dissertation (Ph.D.)

Advisor: Burdick, Joel Wakeman

Committee Members: Burdick, Joel Wakeman; Antonsson, Erik K.; Marsden, Jerrold E.; Murray, Richard M.; Caughey, Thomas Kirk

Option: Applied Mechanics

DOI: 10.7907/49h9-q898

Abstract

Many interesting and important control systems evolve on stratified configuration spaces. Roughly speaking, a configuration manifold is called "stratified" if it contains subspaces (submanifolds) upon which the system had different equations of motion. Robotic systems, in particular, are of this nature. For example, a legged robot has discontinuous equations of motion near points in the configuration space where each of its "feet" comes into contact with the ground. In such a case, when the system moves from one submanifold to another, the equations of motion change in a non-smooth, or even discontinuous manner. In such cases, traditional nonlinear control methodologies are inapplicable because they generally rely upon some form of differentiation. Yet, it is precisely the discontinuous nature of such systems that is often their most important characteristic.

This dissertation presents methods which consider the intrinsic physical geometric structure present in such problems to address nonlinear controllability and motion planning for stratified systems. For both problems, by exploiting this geometric structure of stratified systems, we can extend standard nonlinear control results and methodologies to the stratified case. A related problem addressed by this dissertation is that of controllability of systems where some control inputs are constrained to be non-negative. This problem arises in stratified systems which arise by way of physical contact because the normal force between contacting systems must be nonnegative. For all the results, a basic goal is to generate results which are general. For example, for robotics applications, these results are independent of a particular robot's number of legs, fingers or morphology.

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