Robust gimbal reorientation singularity-avoidance steering strategy for regular pentagonal pyramid configuration with two control moment gyroscopes failed

The failure configuration which consists of four single-gimbal control moment gyroscopes (SGCMGs) of the widely-used regular pentagonal pyramid SGCMG system, i.e. failure 4-SGCMG configuration, is investigated in this paper. On account of the symmetry of regular pentagonal pyramid configuration, a conversion method which could transform any failure 4-SGCMG configuration to the chosen failure system is introduced. Then, the zero-momentum gimbal angle of the chosen failure system is derived and its distribution in gimbal angle space is analyzed. In order to avoid internal singularity, preferred initial gimbal angles are calculated basing on derivation of zero-momentum gimbal angles and the corresponding terminal singular surfaces are obtained through numerical simulations. Furthermore, a constraint about maneuver direction is introduced and a robust gimbal reorientation steering strategy is proposed. Finally, simulations on a non-chosen failure configuration with inertia matrix uncertainty demonstrate the effectiveness of the conversion method and robustness of the proposed steering law.