Method and apparatus for singularity avoidance for control moment gyroscope (CMG) systems without using null motion

Abstract

A method is described for avoiding gyrocopic singularities during attitude correction to a sytem, such as a spacecraft having a CMG array. The method receives a corrective torque vector µ and gimbal angle values δ for each of at least three gimbal within the CMG array. The method a a Jacobian matrix A as a function of gimbal angle value δ. A. lf the determinant is not equal to zero, it is not singular, and the method calculate a gimbal rate δ using a using a pseudo-inverse steering law equation. lf the determinant is equal to zero, it is singular, and the method calculate a gimbal rate δ using a singularity avoidance steering law equation. The gimbal rate δ is output and can be applied to a CMG array resulting in applied torque to a spacecraft and attitude correction.