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, we demonstrate 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 controllable under the restriction that the total angular momentum vector of the system is zero. The spacecraft dynamics under such a restriction cannot be asymptotically stabilized to any equilibrium attitude using a timeinvariant continuous feedback control law, but discontinuous feedback control strategies are constructed that stabilize any equilibrium attitude of the spacecraft in finite time. Consequently, reorientation of the spacecraft can be accomplished using discontinuous feedback control.