On the Attitude Stabilization of a Rigid Spacecraft Using Two Control Torques

The attitude stabilization problem of a rigid spacecraft using only two control torques is considered. The control torques are assumed to be generated by either gas jet actuators or momentum wheel actuators. In particular, we focus on the development of a control strategy for the following two problems which have not been considered elsewhere: the attitude stabilization of an axially symmetric spacecraft using control torques supplied by two pairs of gas jet actuators about axes spanning a two dimensional plane orthogonal to the axis of symmetry; the attitude stabilization of a spacecraft using control torques supplied by two momentum wheel actuators about axes spanning a two dimensional plane orthogonal to a principal axis. The complete dynamics of the spacecraft system fails to be controllable or even accessible in these cases. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a restricted sease; but the restricted spacecraft dynamics cannot be asymptotically stabilized using any smooth C¹ feedback. A nonsmooth feedback control strategy is developed for the restricted spacecraft dynamics which achieves an arbitrary reorientation of the spacecraft.