Motion Control for Nonholonomic Systems on Matrix Lie Groups

Title of Dissertation: Motion Control for Nonholonomic Systems on Matrix Lie Groups Herbert Karl Struemper, Doctor of Philosophy, 1997 Dissertation directed by: Professor P. S. Krishnaprasad Department of Electrical Engineering In this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coordinates and other mathematical tools provided by the Lie group setting. An approximate tracking control law is derived for so-called chained form systems which arise as local representations of systems on a certain nilpotent matrix group. After studying the technique of nilpotentization in the setting of systems on matrix Lie groups we show how motion control laws derived for nilpotent systems can be extended to nilpotentizable systems using feedback and state transformations. The proposed control laws exhibit highly oscillatory components both for tracking and feedback stabilization of local representations of nonholonomic systems on Lie groups. Applications to the control and analysis of the kinematics of mechanical systems are discussed and numerical simulations are presented. Motion Control for Nonholonomic Systems on Matrix Lie Groups by Herbert Karl Struemper Dissertation submitted to the Faculty of the Graduate School of The University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1997 Advisory Committee: Professor P. S. Krishnaprasad, Chairman/Advisor Professor John J. Benedetto Professor Steven I. Marcus Professor Shihab A. Shamma Professor Andre L. Tits c © Copyright by Herbert Karl Struemper 1997