Journal of Dynamical and Control Systems

, Volume 14, Issue 4, pp 465–487 | Cite as

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

  • T. LeeEmail author
  • M. Leok
  • N. H. McClamroch


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.

Key words and phrases

Optimal control symplectic integrator 

2000 Mathematics Subject Classification

49J15 37M15 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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