Singularity Robust Steering Logic for Redundant Single-Gimbal Control Moment Gyros

Abstract

In this paper we investigate a problem inherent in a system of redundant single-gimbal control moment gyros (CMGs). In particular, we present a simple yet effective way of passing through, and also escaping from, any internal singularities. The proposed approach is based on the so-called singularity robust inverse, but it utilizes a nondiagonal weighting matrix in the mixed, two-norm and weighted least-squares minimization problem. The proposed steering logic effectively generates deterministic dither signals when the CMG system becomes near singular. Because the proposed CMG steering logic is based on the simple minimum two-norm, pseudoinverse solution, it does not explicitly avoid encounters but it rather approaches and rapidly transits unavoidable singularities whenever needed. However, the proposed steering logic is not intended for special missions in which prescribed attitude trajectories are to be exactly tracked in the presence of internal singularities.