Minimum-Time Reorientation of a Rigid Body

Recent advances in optimal control theory and computation are used to develop minimum-time solutions for the rest-to-rest reorientation of a generic rigid body. It is shown that the differences in the geometry of the inertia ellipsoid and the control space lead to counterintuitive noneigenaxis maneuvers. The optimality of the open-loop solutions are verified by an application of Pontryagin's principle as a necessary condition and not as a problem-solving tool. It is shown that the nonsmoothness of the lower Hamiltonian compounds the curse of dimensionality associated in solving the Hamilton-Jacobi-Bellman equations for feedback solutions. These difficulties are circumvented by generating Caratheodory-π trajectories, which are based on the fundamental notion that a closed loop does not necessarily imply closed-form solutions. While demonstrating the successful implementation of the proposed method for practical applications, these closed-loop results reveal yet another counterintuitive phenomenon: a suggestion that parameter uncertainties may aid the optimality of the maneuver rather than hinder it.