Structured linearization of discrete mechanical systems on Lie groups: A synthesis of analysis and control

Taosha Fan, Todd Murphey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Lie group variational integrators have the advantages of both variational and Lie group integrators, which preserve the momentum, symplectic form, holonomic constraints and the Lie group structure. In addition, their long-time energy stable behaviour and coordinate-independent nature make it quite suitable to simulate a variety of mechanical systems. The structure-preservation of a Lie group variational integrator implies its linearization is structure-preserving as well, thus we call such a linearization structured linearization. However, due to the implicit nature of variational integrators and the non-trivial differential structure of Lie groups, the structured linearization of Lie group variational integrators is much more complicated than that in generalized coordinates. In this paper, we formulate the structured linearization of Lie group variational integrators to synthesize existing analysis and control tools. To illustrate the utility of the paper, LQR controllers are constructed directly on constrained Lie groups for the asymmetric 3D pendulum and quadrotor with a suspended load, simulation results show that both controllers have a large basin of attraction.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1092-1099
Number of pages8
ISBN (Electronic)9781479978861
DOIs
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
Country/TerritoryJapan
CityOsaka
Period12/15/1512/18/15

Keywords

  • LQR
  • Lie groups
  • structured linearization
  • variational integrators

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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