Quasivelocities and stabilization of relative equilibria of underactuated nonholonomic systems

Author

Bloch, Anthony M. ; Marsden, Jerrold E. ; Zenkov, Dmitry V.

Author_Institution

Dept. of Math., Univ. of Michigan, Ann Arbor, MI, USA

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

3335

Lastpage

3340

Abstract

This paper is concerned with the theory of quasivelocities and its applications to control. The equations of motion of a mechanical system are derived using the Lagrange-d´Alembert principle written in an arbitrary configuration-dependent frame. The structure of the equations of motion written in quasivelocities is utilized in the design of a nonlinear feedback stabilizing controller for an example of a nonholonomically constrained underactuated system.

Keywords

control system synthesis; feedback; nonlinear control systems; stability; Lagrange-d´Alembert principle; mechanical system; motion equations; nonholonomically constrained underactuated system; nonlinear feedback stabilizing controller design; relative equilibria; underactuated nonholonomic systems; Angular velocity; Control systems; Feedback; Lagrangian functions; Mathematics; Mechanical systems; Motion control; Nonlinear control systems; Nonlinear equations; Potential energy;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5399479

Filename

5399479