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

A computer based apparatus for avoiding gyroscopic singularities during attitude correction, comprising:

• a processing component configured to perform a method for avoiding gyroscopic singularities during attitude correction, said method comprising:
• receiving a corrective torque vector μ;
• receiving gimbal angle values δ for each of at least three gimbals within a control moment gyroscope (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, wherein said direct modification of singular values comprises:
• 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
• outputting said gimbal rate {dot over (δ)} from said processing component;
• and correcting the attitude of the spacecraft.

A non-transitory computer program storage component, said computer program storage component having stored therein program instructions executable by a computer processing component to perform a method for avoiding gyroscopic singularities during attitude correction, said method comprising:

• receiving a corrective torque vector μ;
• receiving gimbal angle values δ for each of at least three gimbals within a 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, wherein said direct modification of singular values comprises:
• 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)};
• and correcting the attitude of the spacecraft.