# US 9,038,958 B1 · Method and apparatus for contingency guidance of a CMG-actuated spacecraft > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,038,958 B1 - Document ID: US9038958B1 - Status: Granted - Kind: B1 - Application number: 13/901,444 - Filed: 2013-05-23 - Granted: 2015-05-26 - Earliest claimed: 2012-05-29 - Assignees: The United States of America as represented by the Secretary of the Navy - Applicants: Isaac Michael Ross; Donghun Lee; Mark Karpenko - Inventors: Isaac Michael Ross; Donghun Lee; Mark Karpenko - Web page: https://patentgrep.com/patent/US9038958B1 ## CPC - B64G 1/286: {using control momentum gyroscopes (CMGs)} - B64G 1/245: {Attitude control algorithms for spacecraft attitude control} - B64G: COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR ## Abstract Methods and apparatus are presented for spacecraft operation using non-Eigen axis attitude transitions via control momentum gyroscopes (CMGs) to avoid or mitigate singularities by providing a time-varying attitude command vector including a plurality of time-varying attitude command signals or values representing a plurality of spacecraft states and control trajectories as a guidance command input to an attitude controller of the spacecraft without modifying the spacecraft feedback control law. ## Claims ### Claim 1 A method for guiding a spacecraft from an initial state to a final state using a plurality of control momentum gyroscopes (CMGs), the method comprising: receiving input data including: an initial spacecraft state defining an initial spacecraft attitude vector, an initial spacecraft motion vector, an initial CMG angle vector, and an initial CMG angle rate vector, a desired final spacecraft state defining a desired final spacecraft attitude vector, a desired final spacecraft motion vector, a desired final CMG angle vector, and a desired final CMG angle rate vector, and at least one constraint defining one or more desired limitations with respect to at least one of spacecraft attitude, spacecraft motion, and CMG operation; formulating a control problem based at least partially on the input data; solving the control problem to provide a feasible time-varying attitude command vector comprising a plurality of time-varying attitude command signals or values representing a plurality of spacecraft states and control trajectories with respect to one of spacecraft angles, spacecraft angle rates, and spacecraft angle accelerations; and providing the feasible time-varying attitude command vector as a guidance command input to an attitude controller of the spacecraft. ### Claim 2 (depends on 1) The method of claim 1: wherein formulating the control problem comprises constructing an objective function or cost function including: a spacecraft system state defined by a spacecraft attitude vector, a spacecraft motion vector, a CMG angle vector, and a CMG angle rate vector, and a control variable vector representing CMG gimbal accelerations. ### Claim 3 (depends on 2) The method of claim 2, wherein formulating the control problem comprises constructing an objective function or cost function in terms of overall maneuver time, and wherein solving the control problem comprises minimizing the overall maneuver time. ### Claim 4 (depends on 3) The method of claim 3, wherein formulating the control problem comprises providing a model of spacecraft dynamics with arbitrary fidelity. ### Claim 5 (depends on 4) The method of claim 4, wherein the at least one constraint includes at least one box constraint defining a limit on an absolute value of spacecraft angle rates of the spacecraft motion vector. ### Claim 6 (depends on 5) The method of claim 5, wherein the at least one constraint includes at least one of a box constraint defining a limit on an absolute value of gimbal rates of the CMG angle rate vector and a box constraint defining a limit on an absolute value of gimbal accelerations. ### Claim 7 (depends on 2) The method of claim 2, wherein formulating the control problem comprises providing a model of spacecraft dynamics with arbitrary fidelity. ### Claim 8 (depends on 2) The method of claim 2, wherein the at least one constraint includes at least one box constraint defining a limit on an absolute value of spacecraft angle rates of the spacecraft motion vector. ### Claim 9 (depends on 2) The method of claim 2, wherein the at least one constraint includes at least one of a box constraint defining a limit on an absolute value of gimbal rates of the CMG angle rate vector and a box constraint defining a limit on an absolute value of gimbal accelerations. ### Claim 10 (depends on 1) The method of claim 1, wherein the at least one constraint includes at least one path constraint defining a maximum limit on a norm of the spacecraft attitude vector. ### Claim 11 (depends on 1) The method of claim 1, wherein formulating the control problem comprises providing a model of spacecraft dynamics with arbitrary fidelity. ### Claim 12 (depends on 1) The method of claim 1, wherein the at least one constraint includes at least one box constraint defining a limit on an absolute value of spacecraft angle rates of the spacecraft motion vector. ### Claim 13 (depends on 1) The method of claim 1, wherein the at least one constraint includes at least one of a box constraint defining a limit on an absolute value of gimbal rates of the CMG angle rate vector and a box constraint defining a limit on an absolute value of gimbal accelerations. ### Claim 14 A non-transitory computer readable medium with computer executable instructions for guiding a spacecraft from an initial state to a final state using a plurality of control momentum gyroscopes (CMGs), the computer readable medium having computer executable instructions for: receiving input data including: an initial spacecraft state defining an initial spacecraft attitude vector, an initial spacecraft motion vector, an initial CMG angle vector, and an initial CMG angle rate vector, a desired final spacecraft state defining a desired final spacecraft attitude vector, a desired final spacecraft motion vector, a desired final CMG angle vector, and a desired final CMG angle rate vector, and at least one constraint defining one or more desired limitations with respect to at least one of spacecraft attitude, spacecraft motion, and CMG operation; formulating a control problem based at least partially on the input data; solving the control problem to provide a feasible time-varying attitude command vector comprising a plurality of time-varying attitude command signals or values representing a plurality of spacecraft states and control trajectories with respect to one of spacecraft angles, spacecraft angle rates, and spacecraft angle accelerations; and providing the feasible time-varying attitude command vector as a guidance command input to an attitude controller of the spacecraft. ### Claim 15 A spacecraft guidance system, comprising: at least one processor programmed to: receive input data including: an initial spacecraft state defining an initial spacecraft attitude vector, an initial spacecraft motion vector, an initial CMG angle vector, and an initial CMG angle rate vector, a desired final spacecraft state defining a desired final spacecraft attitude vector, a desired final spacecraft motion vector, a desired final CMG angle vector, and a desired final CMG angle rate vector, and at least one constraint defining one or more desired limitations with respect to at least one of spacecraft attitude, spacecraft motion, and CMG operation; formulate a control problem based at least partially on the input data; solve the control problem to provide a feasible time-varying attitude command vector comprising a plurality of time-varying attitude command signals or values representing a plurality of spacecraft states and control trajectories with respect to one of spacecraft angles, spacecraft angle rates, and spacecraft angle accelerations; and provide the feasible time-varying attitude command vector as a guidance command input to an attitude controller of the spacecraft. ### Claim 16 (depends on 15) The spacecraft guidance system of claim 15, wherein the at least one processor is programmed to formulate the control problem with an objective function or cost function including: a spacecraft system state defined by a spacecraft attitude vector, a spacecraft motion vector, a CMG angle vector, and a CMG angle rate vector, and a control variable vector representing CMG gimbal accelerations. ### Claim 17 (depends on 16) The spacecraft guidance system of claim 16, wherein the at least one processor is programmed to formulate the control problem with an objective function or cost function in terms of overall maneuver time, and to solve the control problem by minimizing the overall maneuver time. ### Claim 18 (depends on 15) The spacecraft guidance system of claim 15, wherein the control problem comprises a model of spacecraft dynamics with arbitrary fidelity. ### Claim 19 (depends on 15) The spacecraft guidance system of claim 15, wherein the at least one constraint includes at least one box constraint defining a limit on an absolute value of spacecraft angle rates of the spacecraft motion vector. ### Claim 20 (depends on 15) The spacecraft guidance system of claim 15, wherein the at least one constraint includes at least one of a box constraint defining a limit on an absolute value of gimbal rates of the CMG angle rate vector and a box constraint defining a limit on an absolute value of gimbal accelerations.