Attitude stabilization of a spacecraft with two parallel control moment gyroscopes

The attitude stabilization of a spacecraft carrying two parallel control moment was approached in the zero-momentum mode. The conflicting requirements between precise attitude stabilization and singularity escape were discussed and accommodated by developing a modified direct-inverse steering law. Then, a novel saturated singular quaternion control law, which allowed small control gains to secure closed-loop stability, was constructed to stabilize the spacecraft attitude. Finally, the proposed stabilization law and the modified direct-inverse (MDI) steering law could be used to stabilize the spacecraft attitude by means of two parallel control moment gyroscopes (CMGs), yielding an ultimately bounded attitude error. It was shown that, by tuning a damping parameter for escaping the internal singularities of the two CMGs, the MDI steering law could make a tradeoff between the attitude pointing accuracy and gimbal rate oscillations in the steady state.