Directional singularity escape and avoidance for single-gimbal control moment gyroscopes

Abstract

Despite the long history of studies on the singularity problem inherent to single-gimbal control moment gyroscopes, few existing gimbal steering laws can both accurately track moments and escape or avoid every type of singularity. The most-referenced steering laws perturb the system suboptimally at every singularity to enforce escape, which creates a tradeoff between minimizing escape time and minimizing transient tracking errors and gimbal rates. It is shown that no such tradeoff is necessary by proposing new singularity measures to quantify the current and future reference moment tracking capabilities and defining explicitly how an anticipated singularity can be avoided or escaped. Using these measures to separate and prioritize the tasks of moment tracking, gimbal damping, and singularity escape and avoidance, a gimbal steering law is designed that accurately tracks moments and avoids singularities when possible while escaping them with a minimal error moment otherwise. The steering law has smaller overall tracking errors and lower peak gimbal rates, and it achieves singularity escape faster than existing methods, as demonstrated analytically and using simulations.