Spacecraft constrained attitude control using positively invariant constraint admissible sets on SO(3) × ℝ3

This paper presents a constrained attitude control approach for performing spacecraft reorientation maneuvers that maintain specified body vectors within inclusion zones and out of exclusion zones, while respecting control authority limits. The controller uses a supervisory switching strategy with an inner-loop Lyapunov SO(3)-based controller and an outer-loop set-point guidance. A virtual net of orientation equilibria covering SO(3) is introduced, and positively invariant constraint admissible sets on SO(3) × ℝ³ of the inner loop controller are constructed to determine if equilibria are connected by a feasible trajectory. Optimization procedures to maximize the size of the positively-invariant sets are discussed. Graph search is used in the outer-loop to compute the set-point sequence leading from an initial orientation to a final orientation that rigorously enforces constraints. The proposed methodology reduces the search space of possible attitude maneuver solutions, and has computational and implementation simplicity. Numerical simulation results are reported to illustrate the performance of the proposed constrained attitude control methodology.