Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups

Author

Nordkvist, N. ; Bullo, Francesco

Author_Institution

Dept. of Math., Tech. Univ. of Denmark, Copenhagen

Volume

53

Issue

11

fYear

2008

Firstpage

2651

Lastpage

2658

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; actuators; control system synthesis; force control; nonlinear control systems; Lie groups; invariant systems; iterative small-amplitude control; perturbation analysis; underactuated Lagrangian systems; underactuated mechanical systems; underactuated planar rigid body; Acceleration; Algorithm design and analysis; Control systems; Force control; Iterative algorithms; Lagrangian functions; Mechanical systems; Motion control; Satellites; Velocity control; Mechanical systems; nonlinear control; relative equilibria; underactuated systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2008.2007143

Filename

4700860