Steering law for two parallel variable-speed double-gimbal control moment gyros

A control moment gyro (CMG) is a representative torque producing actuator for the spacecraft attitude control. It generates control torques by changing the momentum direction of a reaction wheel (RW). The most serious difficulty while designing CMG steering laws is the existence of singular configurations, for which CMGs cannot produce torques in a certain direction. The wheel of a variable-speed DGCMG can either rotate about the inner and outer gimbal axes with arbitrary gimbal rates or rotate about the spin axis with variable angular speeds. Each rotation can generate a control torque through changing the direction of the angular momentum of the wheel. Generally, a variable-speed DGCMG has three degrees of freedom, including the time-varying orientations of the inner and outer gimbals and the variation of the wheel speed, and so it can generate a 3-D torque independently.