Singular direction avoidance steering for control-moment gyros

A new form of the equations of motion for a spacecraft with single gimbal control moment gyros (CMG) is developed using a momentum approach. This set of four vector equations describing the rotational motion of the system is of order 2N + 7, where N is the number of CMGs. The central input is an N X 1 column vector of torques applied to the gimbal axes. A modification to a singularity robust Lyapunov control law is examined and compared to that control law. Specifically, the attempt to avoid singular gimbal configurations is abandoned in favor of simply avoiding movement in the singular direction. The singular value decomposition is used to compute a pseudoinverse that prevents large gimbal rate commands near or at actual singularities.