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2008 Computational Geometric Optimal Control of Rigid Bodies
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Commun. Inf. Syst. 8(4): 445-472 (2008).

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.

Citation

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Taeyoung Lee. Melvin Leok. N. Harris McClamroch. "Computational Geometric Optimal Control of Rigid Bodies." Commun. Inf. Syst. 8 (4) 445 - 472, 2008.

Information

Published: 2008
First available in Project Euclid: 6 May 2009

zbMATH: 1168.49024
MathSciNet: MR2495749

Rights: Copyright © 2008 International Press of Boston

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Vol.8 • No. 4 • 2008
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