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

摘要

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 μ and gimbal angle values δ 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 δ. 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 (δ)} 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 (δ)} using a singularity avoidance steering law equation. The gimbal rate {dot over (δ)} is output and can be applied to a CMG array resulting in applied torque to a spacecraft and attitude correction.

主权项

1. A method for avoiding gyroscopic singularities during attitude correction of a spacecraft, comprising:
at least three gimbals within a control moment gyroscope (CMG) array; an attitude controller; and a computer apparatus comprising a processing component communicatively coupled to said at least three gimbals and to said attitude controller, said processing component performing a method for avoiding gyroscopic singularities during attitude correction, said method comprising:
receiving a corrective torque vector μ from said attitude controller;receiving gimbal angle values δ from each of at least three gimbals within said CMG array;generating a Jacobian matrix A as a function of said gimbal angle values δ, said Jacobian matrix A including singular values;calculating a determinant D of said Jacobian matrix A;determining whether said determinant D is equal to zero;wherein when said determinant D is not equal to zero, calculating a gimbal rate {dot over (δ)} using a pseudo-inverse steering law equation; otherwise, wherein when said determinant D is equal to zero, calculating a gimbal rate {dot over (δ)} using a singularity avoidance steering law equation, wherein said calculating a gimbal rate {dot over (δ)} using a singularity avoidance steering law equation comprises:
utilizing a direct modification of singular values, comprising:
modifying singular values of said Jacobian matrix A by directly modifying a value of σr, where σr is a smallest singular value; and outputting said gimbal rate {dot over (δ)} from said processing component to each of said at least three gimbals within said CMG array; and correcting the attitude of the spacecraft.