Minimum-Time Reorientation of Axisymmetric Rigid Spacecraft Using Three Controls

A minimum-time reorientation of an axisymmetric rigid spacecraft controlled by three torques is studied. The orientation of the body is modeled such that the attitude kinematics are representative of a spin-stabilized spacecraft. The optimal control problem considered is shown to have a switching control structure. Moreover, under certain assumptions, the solutions contain segments that lie on a singular arc. A numerical optimization study is performed using a recently developed method that is designed to accurately solve bang-bang and singular optimal control problems. The optimality conditions for the resulting optimal control problem are derived and analyzed for a variety of cases. Also, the results obtained in this study are compared to a previous method existing in the literature. The key features of the optimized trajectories and controls are identified, and the aforementioned method for solving bang-bang and singular optimal control problems is shown to efficiently and accurately solve the problem under consideration.