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Optimal Attitude Control of a Rigid Body Using Geometrically Exact Computations on SO(3)

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Abstract

An efficient and accurate computational approach is proposed for a nonconvex optimal attitude control for a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete time necessary conditions for optimality are derived, and an efficient computational approach is proposed to solve the resulting two-point boundary-value problem. This formulation wherein the optimal control problem is solved based on discretization of the attitude dynamics and derivation of discrete time necessary conditions, rather than development and discretization of continuous time necessary conditions, is shown to have significant advantages. In particular, the use of geometrically exact computations on SO(3) guarantees that this optimal control approach has excellent convergence properties even for highly nonlinear large angle attitude maneuvers.

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Authors and Affiliations

  1. Department of Aerospace Engineering, University of Michigan, 2008 FXB, 1320 Beal Ave., Ann Arbor, MI, 48109, USA

    T. Lee & N. H. McClamroch

  2. Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, IN, 47907, USA

    M. Leok

Authors
  1. T. Lee
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  2. M. Leok
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  3. N. H. McClamroch
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Correspondence to T. Lee.

Additional information

The first and second authors have been partially supported by NSF (project Nos. DMS-0504747 and DMS-0726263). The first and third authors have been partially supported by NSF (project Nos. ECS-0244977 and CMS-0555797.

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Lee, T., Leok, M. & McClamroch, N.H. Optimal Attitude Control of a Rigid Body Using Geometrically Exact Computations on SO(3). J Dyn Control Syst 14, 465–487 (2008). https://doi.org/10.1007/s10883-008-9047-7

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  • DOI: https://doi.org/10.1007/s10883-008-9047-7

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