Singularity avoidance by cooperative game theory for control moment gyros

Abstract

To obtain rapid rotational maneuver ability or agility, the device generating torque command continuously is needed. The two most common such devices are the reaction wheels(RWs) and the control moment gyroscopes(CMGs). Unlike RW, as a CMG contains a spinning rotor whose angular momentum vector can be changed with respect to the spacecraft, it can produce a large effective torque output. The drawback of CMGs is that such CMG systems encounter certain singular gimbal angle configurations. Therefore, the best scenario to deal with CMG singularities is to avoid them altogether. In this study, to solve the singularity problem inherent in a system of pyramid-type CMGs, two singularity avoidance strategies based upon the game theory are introduced. First, in a method using the cooperative game theory, we can get a parameter optimization problem with inequality constraints to minimize the square sum of gimbal angular rates. While, in a method using the TU multi-player game theory, we can get a real-time solution to minimize the cost function about gimbal angular rates. Also, the approach based on the generalized singularity robust inverse and the gradient method with null motion are presented, and we compare the results by the proposed methods in this study.