Avoid ability of singular states in redundant single gimbal control moment gyroscope systems

Single Gimbal Control Moment Gyroscope (SGCMG) is kind of inertial actuator applied to the spacecraft. Generally, three or more SGCMGs are often used in order to meet the need of the 3-axis attitude control. However, singularity often arises when several SGCMGs work coordinately. Therefore, avoidability of singular states should be studied so as to make the system escape from the singularity. In this paper, a new detecting method of avoidability for singular states is proposed on the basis of the definition and analysis of a kind of null-motion differential dynamical systems. Thus, the problem of detecting avoidability/unavoidability is transformed to a stability study on a set of nonlinear ordinary differential equations. Several examples indicate that the method presented above is feasible.