Singularity avoidance in single gimbal CMG using the theory of potential functions

The control moment gyro (CMG) actuators used in attitude control of spacecraft suffer from the singularity problem where they fail to generate the output torque in some particular direction called the singular direction. In connection to the avoidance of the singularity, the notion of the potential function is discussed and shown to behave as an avoidance potential. Using the theory of the superquadric isopotential contours around the singular point, a suitable algorithm is developed to avoid a small region enclosing the singular point. The isopotential contour, where the avoidance potential exceeds some pre-fixed value can be avoided. The stability of the CMG system using the potential function is discussed. Simulation is run to show the gimbal angle and output torque profiles. Comparative studies using PID and PD controllers are done.