A lie group variational integrator for rigid body motion in SE(3) with applications to underwater vehicle dynamics

Nikolaj Nordkvist, Amit K. Sanyal

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

52 Scopus citations

Abstract

The topic of variational integrators for mechanical systems whose dynamics evolve on nonlinear spaces has seen strong growth recently. Within this class of variational integrators is the subclass of Lie group variational integrators that can be used for mechanical systems whose dynamics evolve on Lie groups. This class of mechanical systems includes all systems that can be modeled as rigid bodies or connections of rigid bodies. In this paper, we present a Lie group variational integrator for the full (translation and orientation) motion of a rigid body under the possible influence of nonconservative forces and torques. We use a discretization scheme for such systems which is based on the discrete Lagrange-d'Alembert principle to obtain the Lie group variational integrator. We apply the composition of the Lie group variational integrator with its adjoint and a Crouch-Grossman method to the example of a conservative underwater system. We show numerically that with respect to energy these manifold methods, as expected, behave as a symplectic integrator and a nonsymplectic integrator, respectively.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages5414-5419
Number of pages6
DOIs
StatePublished - 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

ASJC Scopus subject areas

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

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