Singularity Analysis and Visualization for Single-Gimbal Control Moment Gyro Systems

The singularity problem inherent in redundant single-gimbal control moment gyro (CMG) systems is examined. It is intended to provide a comprehensive mathematical treatment of the CMG singularity problem, expanding upon the previous work by Margulies, Aubrun, and Bedrossian. However, particular emphasis is placed on characterizing and visualizing the physical as well as mathematical nature of the singularities, singular gimbal angles, singular momentum surfaces, null motion manifolds, and degenerate null motions. The mathematical framework for characterizing the geometric property of singular surfaces is also established by applying the surface theory of differential geometry. Two and three parallel single-gimbal CMG configurations and a typical pyramid array of four single-gimbal CMGs (including a special case of 90-deg skew angle) are examined in detail to illustrate the various concepts and approaches useful for characterizing and visualizing the CMG singularities.