Attitude control of underactuated spacecraft

In this paper we consider the problem of maneuvering an axisymmetric spacecraft in the case that no torques about the symmetry axis can be exerted, for example due to a thruster failure. Explicit control laws are derived which steer such a spacecraft between states of pure spin between prescribed attitudes. These laws are found by minimizing a cost functional measuring the suitably weighted overall angular velocity during the maneuver. In arriving at the solution, differential geometric techniques in the theory of optimal control are used.