Communications in Information & Systems
- Commun. Inf. Syst.
- Volume 8, Number 4 (2008), 445-472.
Computational Geometric Optimal Control of Rigid Bodies
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.
Commun. Inf. Syst., Volume 8, Number 4 (2008), 445-472.
First available in Project Euclid: 6 May 2009
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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