Optimal Steering of Nonredundant Single-Gimbal CMGs using Gauss Pseudospectral Method

This paper presents the problem of optimal steering with three single-gimbal control moment gyros (SGCMGs). Most SGCMG configurations use more than three rotors because the resulting Jacobian would always have a nontrivial nullspace. We consider the specific case of a four-CMG pyramid configuration where one CMG has failed and only three CMGs are operational. We use the Gauss pseudospectral method to find the optimal gimbal angle trajectories of the CMGs and the states of an agile spacecraft subject to mission-specific constraints while maximally avoiding the angular-momentum singularities. The proposed steering law is tested in scenarios where the gimbal angles initially start in both nonsingular and singular positions. Results are compared with the standard four-SGCMG maneuvering via the generalized singularity robust steering law in the literature.