초록 ▼

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 Jaco

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.

대표청구항 ▼

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; anda computer apparatus comprising a processing component communicatively coupled to said at least th

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; anda 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; andoutputting 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. 2. The method of claim 1, said method further comprising: generating said corrective torque vector μ based on a difference between a desired attitude and an actual attitude. 3. The method of claim 1, wherein said calculating a gimbal rate {dot over (δ)} using said singularity avoidance steering law equation comprises: utilizing a constrained singularity-robust inverse wherein a rate of change of said determinant D of said Jacobian matrix is constrained such that said determinant D quickly transients through zero. 4. The method of claim 3, wherein when said CMG array includes at least four gimbals, said method further comprising: iteratively generating said Jacobian matrix A until said determinant D is not zero, wherein a different set of three gimbals are selected from said at least four gimbals for each iteration. 5. The method of claim 1, wherein said calculating a gimbal rate {dot over (δ)} using said singularity avoidance steering law equation comprises: utilizing a singularity penetration using a unit-delay, wherein said utilizing a singularity penetration using said unit-delay comprises:holding said gimbal rate {dot over (δ)} to a last valid, non-singular value, {dot over (δ)}SW. 6. 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; andoutputting said gimbal rate {dot over (δ)} from said processing component to each of said at least three gimbals within said CMG array; andoutputting said gimbal rate {dot over (δ)} from said processing component; and correcting the attitude of the spacecraft. 7. The computer based apparatus of claim 6, said method further comprising: wherein said calculating a gimbal rate {dot over (δ)} using a singularity avoidance steering law equation comprises: utilizing a constrained singularity-robust inverse inverse, wherein a rate of change of said determinant D of said Jacobian matrix is constrained such that said determinant D quickly transients through zero. 8. The computer based apparatus of claim 7, said method further comprising: wherein when said CMG array includes at least four gimbals, said method further comprising: iteratively generating said Jacobian matrix A until said determinant D is not zero, wherein a different set of three gimbals are selected from said at least four gimbals for each iteration. 9. The computer based apparatus of claim 6, said method further comprising: wherein said calculating a gimbal rate {dot over (δ)} using a singularity avoidance steering law equation comprises: utilizing a singularity penetration using a unit-delay, wherein said utilizing a singularity penetration using said unit-delay comprises:holding said gimbal rate {dot over (δ)} to a last valid, non-singular value, {dot over (δ)}SW. 10. The computer based apparatus of claim 6, said method further comprising: generating said corrective torque vector μ based on a difference between a desired attitude and an actual attitude. 11. 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; andoutputting said gimbal rate {dot over (δ)}; and correcting the attitude of the spacecraft. 12. The non-transitory computer program storage component of claim 11, said method further comprising: wherein said calculating a gimbal rate {dot over (δ)} using a singularity avoidance steering law equation comprises: utilizing a constrained singularity-robust inverse, wherein a rate of change of said determinant D of said Jacobian matrix A is constrained such that said determinant D quickly transients through zero. 13. The non-transitory computer program storage component of claim 12, wherein when said CMG array includes at least four gimbals, said method further comprising: repeating generating said Jacobian matrix A until said determinant D is not zero, wherein a different set of three gimbals are selected from said at least four gimbals for each repetition. 14. The non-transitory computer program storage component of claim 11, said method further comprising: wherein said calculating a gimbal rate {dot over (δ)} using a singularity avoidance steering law equation comprises: utilizing a singularity penetration using a unit-delay, wherein said utilizing a singularity penetration using a unit-delay comprises: holding said gimbal rate {dot over (δ)} to a last valid, non-singular value, {dot over (δ)}SW. 15. The non-transitory computer program storage component of claim 11, said method further comprising: generating said corrective torque vector μ based on a difference between a desired attitude and an actual attitude.