Singular direction avoidance steering for control-moment gyros

A new form of the equations of motion for a spacecraft with single gimbal c ontrol 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 c ontrol law. Specifically, the attempt to avoid singular gimbal configuratio ns is abandoned in favor of simply avoiding movement in the singular direct ion. The singular value decomposition is used to compute a pseudoinverse th at prevents large gimbal rate commands near or at actual singularities.