Time-optimal three-axis reorientation of asymmetric rigid spacecraft via homotopic approach

This paper investigates the time-optimal rest-to-rest three-axis reorientation of asymmetric rigid spacecraft. First, time-optimal solutions for the inertially symmetric rigid spacecraft (ISRS) three-axis reorientation are briefly reviewed. By utilizing initial costates and reorientation time of the ISRS time-optimal solution, the homotopic approach is introduced to solve the asymmetric rigid spacecraft time-optimal three-axis reorientation problem. The main merit is that the homotopic approach can start automatically and reliably, which would facilitate the real-time generation of open-loop time-optimal solutions for attitude slewing maneuvers. Finally, numerical examples are given to illustrate the performance of the proposed method. For principle axis reorientation, numerical results and analytical derivations show that, multiple time-optimal solutions exist and relations between them are given. For generic reorientation problem, though mathematical rigorous proof is not available to date, numerical results also indicated the existing of multiple time-optimal solutions.