Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos
Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity an...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Russell, Ryan P. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© American Astronautical Society 2014 |
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| Übergeordnetes Werk: |
Enthalten in: The Journal of the Astronautical Sciences - Springer-Verlag, 2006, 59(2012), 1-2 vom: Juni, Seite 193-215 |
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| Übergeordnetes Werk: |
volume:59 ; year:2012 ; number:1-2 ; month:06 ; pages:193-215 |
| Links: |
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| DOI / URN: |
10.1007/s40295-013-0013-6 |
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SPR036446076 |
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| 520 | |a Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. | ||
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10.1007/s40295-013-0013-6 doi (DE-627)SPR036446076 (SPR)s40295-013-0013-6-e DE-627 ger DE-627 rakwb eng Russell, Ryan P. verfasserin aut Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society 2014 Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. Relative Motion (dpeaa)DE-He213 Optimal Control Problem (dpeaa)DE-He213 Solar Radiation Pressure (dpeaa)DE-He213 Halo Orbit (dpeaa)DE-He213 Model Fidelity (dpeaa)DE-He213 Lantoine, Gregory aut Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 59(2012), 1-2 vom: Juni, Seite 193-215 (DE-627)SPR036426385 nnns volume:59 year:2012 number:1-2 month:06 pages:193-215 https://dx.doi.org/10.1007/s40295-013-0013-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 59 2012 1-2 06 193-215 |
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10.1007/s40295-013-0013-6 doi (DE-627)SPR036446076 (SPR)s40295-013-0013-6-e DE-627 ger DE-627 rakwb eng Russell, Ryan P. verfasserin aut Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society 2014 Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. Relative Motion (dpeaa)DE-He213 Optimal Control Problem (dpeaa)DE-He213 Solar Radiation Pressure (dpeaa)DE-He213 Halo Orbit (dpeaa)DE-He213 Model Fidelity (dpeaa)DE-He213 Lantoine, Gregory aut Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 59(2012), 1-2 vom: Juni, Seite 193-215 (DE-627)SPR036426385 nnns volume:59 year:2012 number:1-2 month:06 pages:193-215 https://dx.doi.org/10.1007/s40295-013-0013-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 59 2012 1-2 06 193-215 |
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10.1007/s40295-013-0013-6 doi (DE-627)SPR036446076 (SPR)s40295-013-0013-6-e DE-627 ger DE-627 rakwb eng Russell, Ryan P. verfasserin aut Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society 2014 Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. Relative Motion (dpeaa)DE-He213 Optimal Control Problem (dpeaa)DE-He213 Solar Radiation Pressure (dpeaa)DE-He213 Halo Orbit (dpeaa)DE-He213 Model Fidelity (dpeaa)DE-He213 Lantoine, Gregory aut Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 59(2012), 1-2 vom: Juni, Seite 193-215 (DE-627)SPR036426385 nnns volume:59 year:2012 number:1-2 month:06 pages:193-215 https://dx.doi.org/10.1007/s40295-013-0013-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 59 2012 1-2 06 193-215 |
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10.1007/s40295-013-0013-6 doi (DE-627)SPR036446076 (SPR)s40295-013-0013-6-e DE-627 ger DE-627 rakwb eng Russell, Ryan P. verfasserin aut Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society 2014 Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. Relative Motion (dpeaa)DE-He213 Optimal Control Problem (dpeaa)DE-He213 Solar Radiation Pressure (dpeaa)DE-He213 Halo Orbit (dpeaa)DE-He213 Model Fidelity (dpeaa)DE-He213 Lantoine, Gregory aut Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 59(2012), 1-2 vom: Juni, Seite 193-215 (DE-627)SPR036426385 nnns volume:59 year:2012 number:1-2 month:06 pages:193-215 https://dx.doi.org/10.1007/s40295-013-0013-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 59 2012 1-2 06 193-215 |
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10.1007/s40295-013-0013-6 doi (DE-627)SPR036446076 (SPR)s40295-013-0013-6-e DE-627 ger DE-627 rakwb eng Russell, Ryan P. verfasserin aut Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society 2014 Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. Relative Motion (dpeaa)DE-He213 Optimal Control Problem (dpeaa)DE-He213 Solar Radiation Pressure (dpeaa)DE-He213 Halo Orbit (dpeaa)DE-He213 Model Fidelity (dpeaa)DE-He213 Lantoine, Gregory aut Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 59(2012), 1-2 vom: Juni, Seite 193-215 (DE-627)SPR036426385 nnns volume:59 year:2012 number:1-2 month:06 pages:193-215 https://dx.doi.org/10.1007/s40295-013-0013-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 59 2012 1-2 06 193-215 |
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Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos |
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Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. © American Astronautical Society 2014 |
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Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. © American Astronautical Society 2014 |
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Abstract A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials. © American Astronautical Society 2014 |
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Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos |
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Lantoine, Gregory |
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