Computational Geometric Optimal Control of Rigid Bodies

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dc.creatorLee, Taeyoung
dc.creatorLeok, Melvin
dc.creatorMcClamroch, N. Harris
dc.date2008-05-06
dc.date.accessioned2026-07-07T09:37:14Z
dc.date.available2026-07-07T09:37:14Z
dc.descriptionThis 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.
dc.description29 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0805.0639
dc.identifierhttp://arxiv.org/abs/0805.0639
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160386
dc.subjectOptimization and Control
dc.titleComputational Geometric Optimal Control of Rigid Bodies
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