Singularity Analysis and Avoidance of Variable-Speed Control Moment Gyros – Part I : No Power Constraint Case

Single-gimbal control moment gyros (CMGs) have several advantages over other actuators for attitude control of spacecraft. For instance, they act as torque amplifiers and, thus, are suitable for slew maneuvers. However, their use as torque actuators is hindered by the presence of singularities, which, when encountered, do not allow a CMG cluster to generate torques about arbitrary directions. A method to overcome this drawback is the use variable-speed single-gimbal control moment gyros (VSCMGs). Whereas the wheel speed of a conventional CMG is constant, VSCMGs are allowed to have variable wheel speed. Therefore, VSCMGs have extra degrees of freedom that can be used to achieve additional objectives, such as singularity avoidance and/or power tracking, in addition to attitude control. In the present article, a gradient method using null motion to avoid singularities is presented. It is proved that there exists a null motion for all singularities, if a certain number of CMG wheels operate in VSCMG mode. In addition, the analysis is adapted to the case of conventional CMGs. The result verifies the already known conditions for the existence of null motions for CMG clusters.