Optimal Attitude Control for a Rigid Body with Symmetry
  Optimal control problems are formulated and efficient computational procedures are proposed for attitude dynamics of a rigid body with symmetry. The rigid body is assumed to act under a gravitational potential and under a structured control moment that respects the symmetry. The symmetry in the attitude dynamics system yields a conserved quantity, and it causes a fundamental singularity in the optimal control problem. The key feature of this paper is its use of computational procedures that are guaranteed to avoid the numerical ill-conditioning that originates from this symmetry. It also preserves the geometry of the attitude dynamics. The theoretical basis for the computational procedures is summarized, and examples of optimal attitude maneuvers for a 3D pendulum are presented. 
Taeyoung Lee, N. Harris McClamroch, Melvin Leok