A method is described for avoiding gyroscopic singularities during attitude correction to a system, such as a spacecraft having a CMG array. The method receives a corrective torque vector and gimbal angle values for each of at least three gimbals within the CMG array. The method generates a Jacobian matrix A as a function of gimbal angle values . The method calculates a determinant D of Jacobian matrix A. If the determinant is not equal to zero, it is not singular, and the method calculates a gimbal rate {dot over ()} using a pseudo-inverse steering law equation. If the determinant is equal to zero, it is singular, and the method calculates a gimbal rate {dot over ()} using a singularity avoidance steering law equation. The gimbal rate {dot over ()} is output and can be applied to a CMG array resulting in applied torque to a spacecraft and attitude correction.

A method is described for avoiding gyroscopic singularities during attitude correction to a system, such as a spacecraft having a CMG array. The method receives a corrective torque vector and gimbal angle values for each of at least three gimbals within the CMG array. The method generates a Jacobian matrix A as a function of gimbal angle values . The method calculates a determinant D of Jacobian matrix A. If the determinant is not equal to zero, it is not singular, and the method calculates a gimbal rate {dot over ()} using a pseudo-inverse steering law equation. If the determinant is equal to zero, it is singular, and the method calculates a gimbal rate {dot over ()} using a singularity avoidance steering law equation. The gimbal rate {dot over ()} is output and can be applied to a CMG array resulting in applied torque to a spacecraft and attitude correction.