Manifold path selection steering law for pyramid-type single-gimbal control moment gyros

The properties of singularities for pyramid-type single-gimbal control moment gyro (SGCMG) configuration are investigated in this paper. Manifold theory is applied to the SGCMG system and singular surfaces are classified by passability and directionality. A terminal domain is introduced as a small angular momentum space wrapped by internal elliptic singular surfaces and intersected hyperbolic singular surfaces. The hyperbolic singular surfaces in a terminal domain can provide the SGCMG system with a chance to select a manifold path containing no internal elliptic singularity. Thereafter, a manifold path selection (MPS) steering law based on a modified gradient method is proposed, which can achieve internal elliptic singularity avoidance without introducing torque errors. Compared with the other two steering laws, the effectiveness of the proposed method is demonstrated using attitude maneuver examples.