Singularity Avoidance/Passage Steering Logic for a Variable-speed Double-gimbal Control Moment Gyro Based on Inverse Kinematics

Abstract

In this paper, we propose a novel singularity avoidance/passage logic based on inverse kinematics for steering a variable-speed double-gimbal control moment gyro (VSDGCMG). Two solutions generating the command torque are obtained using the inverse kinematics for a VSDGCMG system. The proposed method basically selects the solution close to the current wheel momentum and gimbal angles. A transition to another solution is conducted to reduce the attitude error in the vicinity of the singular state based on an evaluation function that corresponds to the approximate torque error and explicitly includes gimbal rate limitations. Its function results in a decision with small attitude error when compared with a previous method that uses just an approximate gimbal angle without the gimbal-rate limitation. Furthermore, the proposed method generates more precise torque closer to the reference torque than the previous method when avoiding the singular state. The effectiveness of the method is demonstrated through numerical simulations.