Small Time Local Controllability and Stabilizability of Spacecraft Attitude Dynamics using Control Moment Gyroscopes

Momentum exchange devices such as reaction wheels and control moment gyroscopes (CMGs) form an important class of torque actuators for spacecraft attitude control. A single gimbal CMG comprises of a rapidly spinning rotor mounted on a gimbal. The orientation of the rotor can be changed by applying torque to the gimbal, and the reaction torque thus generated serves to control the spacecraft attitude. The magnitude of torque produced by the CMG is a function of the constant rotor speed and gimbal rotation rate, while the direction is tangential to the circle along which the CMG rotor is constrained to rotate. Clearly, a single CMG cannot produce torques in all directions. In order to obtain torques along three independent directions, as well as for redundancy, CMGs are used in arrays consisting of multiple CMGs. Unfortunately, every CMG array possesses singular configurations