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Control of stratified systems with robotic applications


Goodwine, John William (1998) Control of stratified systems with robotic applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/49h9-q898.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Burdick, Joel Wakeman
Thesis Committee:
  • Burdick, Joel Wakeman (chair)
  • Antonsson, Erik K.
  • Marsden, Jerrold E.
  • Murray, Richard M.
  • Caughey, Thomas Kirk
Defense Date:18 November 1997
Record Number:CaltechETD:etd-01232008-144001
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:306
Deposited By: Imported from ETD-db
Deposited On:15 Feb 2008
Last Modified:16 Apr 2021 23:04

Thesis Files

PDF (Goodwine_jw_1998.pdf) - Final Version
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