Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups

Author

Nordkvist, Nikolaj ; Bullo, Francesco

Author_Institution

Tech. Univ. of Denmark, Lyngby

fYear

2007

fDate

12-14 Dec. 2007

Firstpage

6232

Lastpage

6237

Abstract

We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation analysis and the design of inversion primitives and composition methods. We illustrate the algorithms on an underactuated planar rigid body and on a satellite with two thrusters.

Keywords

Lie algebras; Lie groups; acceleration control; motion control; multivariable control systems; perturbation theory; stability; Lie groups; invariant systems; iterative small-amplitude control forces; motion control algorithm design; perturbation analysis; relative equilibrium; stabilization; underactuated Lagrangian systems; underactuated mechanical systems; underactuated planar rigid body; Actuators; Automatic control; Control systems; Force control; Iterative algorithms; Lagrangian functions; Mechanical systems; Satellites; USA Councils; Velocity control;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2007 46th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

978-1-4244-1497-0

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2007.4434093

Filename

4434093