Attitude stabilization of a rigid spacecraft using two momentum wheel actuators

It is well known that three momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished using smooth feedback. If failure of one of the momentum wheel actuators occurs, it is demonstrated that two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished. Although the complete spacecraft equations are not controllable, the spacecraft equations are small time locally controllable in a reduced nonlinear sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to any equilibrium attitude using a time-variant continuous feedback control law, but discontinuous feedback control strategies are constructed which stabilize any equilibrium attitude of the spacecraft in finite time. Consequently, reorientation of the spacecraft can be accomplished using discontinuous feedback control.