Mixed integer (non)linear approaches for the satellite constellation design problem

In this paper, we propose mathematical optimization models to solve the satellite constellation design problem for discontinuous coverage. In such a design problem, the aim is to determine the minimal number of satellites (and, incidentally, their 3D placements) in order to observe a fixed Earth reg...

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Veröffentlicht in:	Optimization and engineering Jg. 24; H. 4; S. 2299 - 2320
Hauptverfasser:	Mencarelli, Luca, Floquet, Julien, Georges, Frédéric, Grenier, Dominique
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.12.2023 Springer Verlag
Schlagworte:	Computer Science Control Engineering Environmental Management Financial Engineering Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Research Article Systems Theory Discontinuous coverage Satellite constellation design Revisiting time Mixed integer nonlinear and linear programming DISCONTINUOUS COVERAGE SATELLITE CONSTELLATION DESIGN REVISITING TIME MIXED INTEGER NONLINEAR AND LINEAR PROGRAMMING
ISSN:	1389-4420, 1573-2924
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Abstract	In this paper, we propose mathematical optimization models to solve the satellite constellation design problem for discontinuous coverage. In such a design problem, the aim is to determine the minimal number of satellites (and, incidentally, their 3D placements) in order to observe a fixed Earth region within a given revisiting time. Two Mixed Integer Nonlinear formulations are introduced. The first one is a feasibility problem based on the direct mathematical definition of pixel observability. The second one consists in introducing a set of indicator variables which specify if a satellite observes a pixel at a given time-stamp. In order to obtain a linear problem, the possible positions of the satellites are discretized. Finally, computational results show the potential and limitations of the proposed approaches.
AbstractList	In this paper, we propose mathematical optimization models to solve the satellite constellation design problem for discontinuous coverage. In such a design problem, the aim is to determine the minimal number of satellites (and, incidentally, their 3D placements) in order to observe a fixed Earth region within a given revisiting time. Two Mixed Integer Nonlinear formulations are introduced. The first one is a feasibility problem based on the direct mathematical definition of pixel observability. The second one consists in introducing a set of indicator variables which specify if a satellite observes a pixel at a given time-stamp. In order to obtain a linear problem, the possible positions of the satellites are discretized. Finally, computational results show the potential and limitations of the proposed approaches. In this paper, we propose mathematical optimization models to solve the satellite constellation design problem for discontinuous coverage. In such a design problem, the aim is to determine the minimal number of satellites (and, incidentally, their 3D placements) in order to observe a fixed Earth region within a given revisiting time. Two Mixed Integer Nonlinear formulations are introduced. The first one is a feasibility problem based on the direct mathematical definition of pixel observability. The second one consists in introducing a set of indicator variables which specify if a satellite observes a pixel at a given time-stamp. In order to obtain a linear problem, the possible positions of the satellites are discretized. Finally, computational results show the potential and limitations of the proposed approaches.
Author	Floquet, Julien Georges, Frédéric Grenier, Dominique Mencarelli, Luca
Author_xml	– sequence: 1 givenname: Luca surname: Mencarelli fullname: Mencarelli, Luca email: luca.mencarelli@ensta-paris.fr organization: UMA, ENSTA Paris, Institut Polytechnique de Paris – sequence: 2 givenname: Julien surname: Floquet fullname: Floquet, Julien organization: DTIS, ONERA, Université Paris Saclay – sequence: 3 givenname: Frédéric surname: Georges fullname: Georges, Frédéric organization: DTIS, ONERA, Université Paris Saclay – sequence: 4 givenname: Dominique surname: Grenier fullname: Grenier, Dominique organization: DTIS, ONERA, Université Paris Saclay
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Keywords	Discontinuous coverage Satellite constellation design Revisiting time Mixed integer nonlinear and linear programming DISCONTINUOUS COVERAGE SATELLITE CONSTELLATION DESIGN REVISITING TIME MIXED INTEGER NONLINEAR AND LINEAR PROGRAMMING
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References	Whittecar W, Ferringer M (2014) Global coverage constellation design exploration using evolutionary algorithms. In: AIAA/AAS astrodynamics specialist conference, August 4–7, 2014, San Diego, CA, USA Wertz J (2001) Orbit and constellation design and management: spacecraft orbit and attitude systems. Microcosm Press RazoumnyYRoute satellite constellations for earth discontinuous coverage and optimal solution peculiaritiesJ Spacecr Rocket201754311010.2514/1.A33689 Wang L, Wang Y, Chen K, Zhang H (2008) Optimization of regional coverage reconnaissance satellite constellation by NSGA-II algorithm. In: 2008 International conference on intelligent computation technology and automation (ICICTA), pp 660–664 Luo Y, Shu P (2018) Optimization design of Walker constellation for multi-target rapid revisit. In: Eighth international conference on instrumentation & measurement, computer, communication and control (IMCCC), pp 483–486 ZhangTShenHLiZQieHCaoJLiHYangYRestricted constellation design for regional navigation augmentationActa Astronaut201815023123910.1016/j.actaastro.2018.04.044 RonanAFabianoLArcélioCWillerGModeling and design of a multidisciplinary simulator of the concept of operations for space mission pre-phase: a studiesConcurr Eng2019271283910.1177/1063293X18804006 Grandchamp E (2001) Quelques contributions pour l’optimisation de constellations de satellites. Ph.D. thesis, Institut National Polytechnique de Toulouse (INPT), France Hitomi N, Selva D (2018) Constellation optimization using an evolutionary algorithm with a variable-length chromosome. In: 2018 IEEE aerospace conference, pp 1–12 Baranger H, Bouchard J, Piet-Lahanier H (1991) Global optimization of GPS type satellite constellations. In: Montreal international astronautical federation congress LudersRSatellite networks for continuous zonal coverageARSJ196131217910.2514/8.5422 ZhangCJinJKuangLYanJLeo constellation design methodology for observing multi-targetsAstrodynamics2017212113110.1007/s42064-017-0015-4 Lang T, Hanson J (1984) Orbital constellations which minimize revisit time. In: Astrodynamics 1983. Proceedings of the conference, August 22–25, 1983, Lake Placid, NY, USA, pp 1071–1086 ChenXDaiGReineltGWangMA semi-analytical method for periodic earth coverage satellites optimizationIEEE Commun Lett201722353453710.1109/LCOMM.2017.2780107 Lee H, Shimizu S, Yoshikawa S, Ho K (2020) Satellite constellation pattern optimization for complex regional coverage. J Spacecr Rocket 57(6) Walker J (1970) Circular orbit patterns providing continuous whole earth coverage. Tech. rep, Royal Aircraft Establishment Farnborough, United Kingdom Walker J (1977) Continuous whole-earth coverage by circular-orbit satellite patterns. Tech. rep, Royal Aircraft Establishment Farnborough, United Kingdom Dufour F, Bertrand R, Sard J, Lasserre E, Bernussou J (1995) Constellation design optimization with a DOP based criterion. In: 14th International symposium on space flight dynamics MortariDWilkinsMBruccoleriCThe flower constellationsJ Astronaut Sci200452107127216091110.1007/BF03546424 Kim H, Jung O, Bang H (2007) A computational approach to reduce the revisit time using a genetic algorithm. In: 2007 International conference on control, automation and systems, pp 184–189 Hanson J, Evans M, Turner R (1990) Designing good partial coverage satellite constellations. In: Astrodynamics conference, August 20–22, 1990, Portland, OR, USA Vallado D, McClain W (2013) Fundamentals of astrodynamics and applications. Microcosm Press Park K, Wilkins M, Mortari D (2004) Uniformly distributed flower constellation design study for global navigation system. In: The 14th AAS/AIAA space flight mechanics meeting, Maui Savitri T, Kim Y, Jo S, Bang H (2017) Satellite constellation orbit design optimization with combined genetic algorithm and semianalytical approach. Int J Aerosp Eng. Article ID 1235692 Frayssinhes E (1996) Investigating new satellite constellation geometries with genetic algorithms,. In: Astrodynamics conference, July 29–31, 1996, San Diego, CA, USA ShtarkTGurfilPRegional positioning using a low earth orbit satellite constellationCelest Mech Dyn Astron201813021428374754010.1007/s10569-017-9811-71447.70030 Vallado D, Crawford P, Hujsak R, Kelso T (2006) Revisiting spacetrack report 3. Tech. rep, American Institute of Aeronautics and Astronautics (AIAA) ChadalavadaPDuttaARegional CubeSat constellation design to monitor hurricanesIEEE Trans Geosci Remote Sens2022601810.1109/TGRS.2021.3124473 Y Razoumny (9774_CR16) 2017; 54 D Mortari (9774_CR14) 2004; 52 T Zhang (9774_CR28) 2018; 150 T Shtark (9774_CR19) 2018; 130 X Chen (9774_CR3) 2017; 22 9774_CR8 9774_CR21 9774_CR7 9774_CR22 9774_CR9 9774_CR20 9774_CR4 A Ronan (9774_CR17) 2019; 27 9774_CR25 R Luders (9774_CR12) 1961; 31 9774_CR26 9774_CR6 9774_CR23 9774_CR5 9774_CR24 9774_CR1 P Chadalavada (9774_CR2) 2022; 60 9774_CR18 C Zhang (9774_CR27) 2017; 2 9774_CR10 9774_CR11 9774_CR15 9774_CR13
References_xml	– reference: Wang L, Wang Y, Chen K, Zhang H (2008) Optimization of regional coverage reconnaissance satellite constellation by NSGA-II algorithm. In: 2008 International conference on intelligent computation technology and automation (ICICTA), pp 660–664 – reference: Hitomi N, Selva D (2018) Constellation optimization using an evolutionary algorithm with a variable-length chromosome. In: 2018 IEEE aerospace conference, pp 1–12 – reference: Frayssinhes E (1996) Investigating new satellite constellation geometries with genetic algorithms,. In: Astrodynamics conference, July 29–31, 1996, San Diego, CA, USA – reference: Walker J (1977) Continuous whole-earth coverage by circular-orbit satellite patterns. Tech. rep, Royal Aircraft Establishment Farnborough, United Kingdom – reference: ZhangTShenHLiZQieHCaoJLiHYangYRestricted constellation design for regional navigation augmentationActa Astronaut201815023123910.1016/j.actaastro.2018.04.044 – reference: LudersRSatellite networks for continuous zonal coverageARSJ196131217910.2514/8.5422 – reference: Kim H, Jung O, Bang H (2007) A computational approach to reduce the revisit time using a genetic algorithm. In: 2007 International conference on control, automation and systems, pp 184–189 – reference: MortariDWilkinsMBruccoleriCThe flower constellationsJ Astronaut Sci200452107127216091110.1007/BF03546424 – reference: Vallado D, Crawford P, Hujsak R, Kelso T (2006) Revisiting spacetrack report 3. Tech. rep, American Institute of Aeronautics and Astronautics (AIAA) – reference: Whittecar W, Ferringer M (2014) Global coverage constellation design exploration using evolutionary algorithms. In: AIAA/AAS astrodynamics specialist conference, August 4–7, 2014, San Diego, CA, USA – reference: ZhangCJinJKuangLYanJLeo constellation design methodology for observing multi-targetsAstrodynamics2017212113110.1007/s42064-017-0015-4 – reference: ShtarkTGurfilPRegional positioning using a low earth orbit satellite constellationCelest Mech Dyn Astron201813021428374754010.1007/s10569-017-9811-71447.70030 – reference: ChenXDaiGReineltGWangMA semi-analytical method for periodic earth coverage satellites optimizationIEEE Commun Lett201722353453710.1109/LCOMM.2017.2780107 – reference: Park K, Wilkins M, Mortari D (2004) Uniformly distributed flower constellation design study for global navigation system. In: The 14th AAS/AIAA space flight mechanics meeting, Maui – reference: RazoumnyYRoute satellite constellations for earth discontinuous coverage and optimal solution peculiaritiesJ Spacecr Rocket201754311010.2514/1.A33689 – reference: Lee H, Shimizu S, Yoshikawa S, Ho K (2020) Satellite constellation pattern optimization for complex regional coverage. J Spacecr Rocket 57(6) – reference: Lang T, Hanson J (1984) Orbital constellations which minimize revisit time. In: Astrodynamics 1983. Proceedings of the conference, August 22–25, 1983, Lake Placid, NY, USA, pp 1071–1086 – reference: Vallado D, McClain W (2013) Fundamentals of astrodynamics and applications. Microcosm Press – reference: Dufour F, Bertrand R, Sard J, Lasserre E, Bernussou J (1995) Constellation design optimization with a DOP based criterion. In: 14th International symposium on space flight dynamics – reference: Grandchamp E (2001) Quelques contributions pour l’optimisation de constellations de satellites. Ph.D. thesis, Institut National Polytechnique de Toulouse (INPT), France – reference: Wertz J (2001) Orbit and constellation design and management: spacecraft orbit and attitude systems. Microcosm Press – reference: Hanson J, Evans M, Turner R (1990) Designing good partial coverage satellite constellations. In: Astrodynamics conference, August 20–22, 1990, Portland, OR, USA – reference: RonanAFabianoLArcélioCWillerGModeling and design of a multidisciplinary simulator of the concept of operations for space mission pre-phase: a studiesConcurr Eng2019271283910.1177/1063293X18804006 – reference: Walker J (1970) Circular orbit patterns providing continuous whole earth coverage. Tech. rep, Royal Aircraft Establishment Farnborough, United Kingdom – reference: Baranger H, Bouchard J, Piet-Lahanier H (1991) Global optimization of GPS type satellite constellations. In: Montreal international astronautical federation congress – reference: ChadalavadaPDuttaARegional CubeSat constellation design to monitor hurricanesIEEE Trans Geosci Remote Sens2022601810.1109/TGRS.2021.3124473 – reference: Luo Y, Shu P (2018) Optimization design of Walker constellation for multi-target rapid revisit. In: Eighth international conference on instrumentation & measurement, computer, communication and control (IMCCC), pp 483–486 – reference: Savitri T, Kim Y, Jo S, Bang H (2017) Satellite constellation orbit design optimization with combined genetic algorithm and semianalytical approach. Int J Aerosp Eng. 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Title	Mixed integer (non)linear approaches for the satellite constellation design problem
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