Attitude stabilization for an underactuated rigid spacecraft under non-zero angular momentum

The attitude controllability is impossible for a spacecraft actuated with two reaction wheels. However, three-axis stabilization is accessible when the total angular momentum belongs to some subset. In this paper, we first give the necessary condition for three-axis stabilization. Then we convert three-axis stabilization to pointing stabilization by means of the angular momentum conservation law. Furthermore, an expect attitude is derived on the basis of (w,z) attitude description. Further analysis shows this method is only true only for small attitude errors. Finally, a LQR control law is designed based on the linearized system. The simulation results validate the proposed law.