Communications in Information & Systems

Computational Geometric Optimal Control of Rigid Bodies

Taeyoung Lee, Melvin Leok, and N. Harris McClamroch

Full-text: Open access

Abstract

This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each rigid body is viewed as evolving on a configuration manifold that is a Lie group. Discrete-time dynamics of each rigid body are developed that evolve on the configuration manifold according to a discrete version of Hamilton’s principle so that the computations preserve geometric features of the dynamics and guarantee evolution on the configuration manifold; these discrete-time dynamics are referred to as Lie group variational integrators. Rigid body optimal control problems are formulated as discrete-time optimization problems for discrete Lagrangian/Hamiltonian dynamics, to which standard numerical optimization algorithms can be applied. This general approach is illustrated by presenting results for several different optimal control problems for a single rigid body and for multiple interacting rigid bodies. The computational advantages of the approach, that arise from correctly modeling the geometry, are discussed.

Article information

Source
Commun. Inf. Syst., Volume 8, Number 4 (2008), 445-472.

Dates
First available in Project Euclid: 6 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.cis/1241616528

Mathematical Reviews number (MathSciNet)
MR2495749

Zentralblatt MATH identifier
1168.49024

Citation

Lee, Taeyoung; Leok, Melvin; McClamroch, N. Harris. Computational Geometric Optimal Control of Rigid Bodies. Commun. Inf. Syst. 8 (2008), no. 4, 445--472. https://projecteuclid.org/euclid.cis/1241616528


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