Singularity escape/avoidance steering logic for control moment gyro systems

A singularity-robust control moment gyro (CMG) steering logic, developed previously, is a simple yet effective way of passing through, and also escaping from, any internal singularities. However, it is unable to escape the external saturation singularities of certain special CMG; configurations, even when momentum desaturation is requested. Consequently, a new steering logic based on a mixed weighted two-norm and least-squares optimization solution is developed to overcome this deficiency of being trapped: in the momentum saturation singularities. The ne steering logic also provides a simple means of avoiding troublesome, internal elliptic singularities, which are commonly encountered by most pseudoinverse-based steering logic, including the previous singularity-robust steering logic. Although a CMG is a powerful torque amplification actuator, redundant CMG systems have an inherent geometric singularity problem, and consequently, transient torque errors are inevitable while escaping or passing through elliptic singularities. However, the resulting attitude transient dynamics are often acceptable because precision pointing is not required during large-angle slew maneuvers or CMG momentum desaturation maneuvers of most imaging satellites. Such slew maneuvers are usually performed by a closed-loop attitude control system, and thus, the steady-state pointing accuracy is not affected by such a CMG singularity problem.