On the attitude stabilization of a rigid spacecraft using two skew control moment gyros

The attitude control of a rigid spacecraft with two skew single-gimbal control moment gyros (CMGs), which is subject to an underactuated nonholonomic constraint, is investigated. Nonlinear control theory is used to show that the combined dynamics of the spacecraft-CMG system are small-time locally controllable (STLC) from and feedback stabilizable to any equilibrium where two CMGs never encounter certain special configurations. Specially, the attitude stabilization issue is approached under the restriction that the total angular momentum of the spacecraft-CMG system is zero, which not only guarantees that the feasible equilibrium attitude can be any orientation but also renders STLC for these attitudes. In order to overcome the troublesome singular problem of two skew CMGs, a nonlinear approximation of the full attitude equations is derived for control law design by assuming that the spacecraft angular velocity is small. A novel singular quaternion stabilization law is then proposed to stabilize the spacecraft attitude with bounded angular velocities, which in turn ensures the satisfaction of the small angular velocity assumption during the entire control process. Numerical examples and experimental results validate the effectiveness of the proposed control method in stabilizing the full spacecraft-CMG system.