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Application of a genetic algorithm in orbital maneuvers

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Abstract

This paper has the goal of calculating transfer trajectories between two coplanar orbits using several impulses, trying to find solutions that reduce the costs related to the fuel consumption required to apply these impulses. The number of impulses is given a priori, and a genetic algorithm is used to find the maneuvers that spent less fuel to be completed. Several types of maneuvers are simulated, including constrained maneuvers, where the spacecraft is forced to pass by intermediate orbits, and maneuvers that transfer a spacecraft from one body back to the same body. The method worked in all the situations and the maneuvers were found in all the situations.

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References

  • Betts JT, Erb SO (2003) Optimal low thrust trajectories to the Moon. SIAM J Appl Dyn Systems 2(2):144–171

    Article  MATH  MathSciNet  Google Scholar 

  • Cacciatore F, Toglia C (2008) Optimization of orbital trajectories using genetic algorithms. J Aerosp Eng Sci Appl 1(1):58–69

    Google Scholar 

  • D’Amario LA, Byrnes DV, Stanford RH (1982) Interplanetary trajectory optimization with application to galileo. J Guid Control Dyn 5(5):465–471

    Article  Google Scholar 

  • Davis LD (1991) Handbook of genetic algorithms. [S.l.]: Van Nostrand Reinhold

  • De Felipe G, Prado AFBA (1999) Classification of out-of-plane swing-by trajectories. J Guid Control Dyn 22(5):643–649

    Article  Google Scholar 

  • Dunham D, Davis S (1985) Optimization of a multiple lunar-swingby trajectory sequence. J Astronaut Sci 33(3):275–288

    Google Scholar 

  • Fazelzadeh SA, Varzandian GA (2010) Minimum-time earth–moon and moon–earth orbital maneuvers using time domain finite element method. Acta Astronaut 66(3):528–538

    Article  Google Scholar 

  • Fernandes SS, Carvalho FC (2008) A first-order analytical theory for optimal low-thrust limited-power transfers between arbitrary elliptical coplanar orbits. Math Probl Eng 1–31:2008

    Google Scholar 

  • Fernandes SS (2009a) Hori method for generalized canonical systems. Acta Astronaut 64:95–108

    Article  Google Scholar 

  • Fernandes SS, Marinho CMP (2012) Optimal two-impulse trajectories with moderate flight time for earth–moon missions. Math Probl Eng (Print) 2012:1–34

    Google Scholar 

  • Fernandes SS, Marinho CMP (2012b) Sun influence on two-impulsive Earth-to-Moon transfers. J Aerosp Eng Sci Appl 4:82–91

    Google Scholar 

  • Fernandes SS (2009) Optimization of low-thrust limited-power trajectories in a noncentral gravity field transfers between orbits with small eccentricities. Math Probl Eng (Print) 2009:1–36

    Article  Google Scholar 

  • Gobetz FW, Doll JR (1969) A survey of impulsive trajectories. AIAA J 7:801–834

    Article  Google Scholar 

  • Goddard RH (1919) A method of reaching extreme altitudes. Smithsonian Institute Public Miscellanea Collect. v. 71. n. 2

  • Goldberg David E (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, EUA

    MATH  Google Scholar 

  • Golfetto WA, Fernandes SS (2012) A review of gradient algorithms for numerical computation of optimal trajectories. J Aerosp Technol Manage 4:131–143

    Article  Google Scholar 

  • Gomes VM, Prado AFBA (2010) A study of the impact of the initial energy in a close approach of a cloud of particles. WSEAS Trans Math 9:811–820

    Google Scholar 

  • Hitzl DL, Hénon M (1977a) Critical generating orbits for second species periodic solutions of the restricted problem. Celest Mech 15: 421–452

  • Hitzl DL, Henon M (1977b) The stability of second periodic orbits in the restricted problem (\(\mu =\) 0). Acta Astronaut 4:1019–1039

  • Hoelker RF, Silber R (1959) The bi-elliptic transfer between circular co-planar orbits. Tech Memo 2–59, Army Ballistic Missile Agency, Redstone Arsenal, Alabama, USA

  • Hohmann W (1925) Die Erreichbarkeit der Himmelskorper. Oldenbourg, Munique

    Google Scholar 

  • Ivashkin VV, Skorokhodov AP (1981) Definition and analysis of properties of optimal three-impulse point-to-orbit transfers under time constraint. Acta Astronaut 8(1):11–23

    Article  MATH  Google Scholar 

  • Longuski JM, Williams SN (1991) The last grand tour opportunity to Pluto. J Astronaut Sci 39:359–365

    Google Scholar 

  • Jezewski DJ, Mittleman D (1982) An analytic approach to two-fixed-impulse transfers between Keplerian orbits. J Guid Control Dyn 5(5):458–464

    Article  MATH  Google Scholar 

  • Jin H, Melton RG (1991) Transfers between circular orbits using fixed impulses. AAS paper 91–161. In: AAS/AIAA Spaceflight Mechanics Meeting, Houston, TX, 11–13 Feb

  • Lion PM, Handelsman M (1968) Primer vector on fixed-time impulsive trajectories. AIAA J 6(1):127–132

    Article  MATH  Google Scholar 

  • Marec JP (1979) Optimal space trajectories. Elsevier, New York

    MATH  Google Scholar 

  • Okutsu M, Yam CH, Longuski JM (2006) Low-thrust trajectories to Jupiter via gravity assists from Venus, Earth and Mars, AIAA Paper 2006–6745

  • Prado AFBA, Broucke RA (1995) Transfer orbits in restricted problem. J Guid Control Dyn 18(3):593–598

    Article  Google Scholar 

  • Prado AFBA, Broucke RA (1995) Effects of atmospheric drag in Swing-by trajectory. Acta Astronaut 36(6):285–290

    Article  Google Scholar 

  • Prado AFBA (2005) Numerical and analytical study of the gravitational capture in the bicircular problem. Adv Space Res 36(3):578–584

    Article  MathSciNet  Google Scholar 

  • Prado AFBA (2006) Orbital control of a satellite using the gravity of the moon. J Braz Soc Mech Sci Eng 28(1):105–110

    Article  MathSciNet  Google Scholar 

  • Prado AFBA, Broucke R (1996) Transfer orbits in the Earth–Moon system using a regularized model. J Guid Control Dyn 19(4):929–933

    Article  MATH  Google Scholar 

  • Prado AFBA (1997) Close-approach trajectories in the elliptic restricted problem. J Guid Control Dyn 20(4):797–802

    Article  MATH  MathSciNet  Google Scholar 

  • Prado AFBA (1996) Powered Swing-By. J Guid Control Dyn 19(5):1142–1147

    Article  MATH  Google Scholar 

  • Prussing JE (1970) Optimal two- and three-impulse fixed-time rendezvous in the vicinity of a circular orbit. AIAA J 8(7):1221–1228

    Article  MATH  Google Scholar 

  • Prussing JE (1969) Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit. AIAA J 7(5):928–935

    Article  MATH  Google Scholar 

  • Rosa Sentinella M, Casalino L (2006) Genetic algorithm and indirect method coupling for low-thrust trajectory optimization. AIAA No. 064468

  • Roth HL (1967) Minimization of the velocity increment for a bi-elliptic transfer with plane change. Astronaut Acta 13(2):119–130

    MATH  Google Scholar 

  • Santos DPS, Prado AFBA, Teodoro ARB (2013) Rendezvous maneuvers using genetic algorithm. J Phys. Conference Series (Print), 465. pp 012005

  • Santos DPS, Prado AFBA, Rocco EM (2013) The study of the asymmetric multiple encounters problem and its application to obtain Jupiter gravity assisted maneuvers. Math Probl Eng (Print), 2013. pp 1–12

  • Santos DPS, Prado AFBA, Colasurdo G (2012) Four-impulsive rendezvous maneuvers for spacecrafts in circular orbits using genetic algorithms. Math Probl Eng 2012(493507). doi:10.1155/2012/493507

  • Song YJ, Park SY, Choi KH, Sim ES (2009) A lunar cargo mission design strategy using variable low thrust. Adv Space Res 43(9):1391–1406

    Article  Google Scholar 

  • Walton JM, Marchal C, Culp RD (1975) Synthesis of the types of optimal transfers between hyperbolic asymptotes. AIAA J 13(8):980–988

    Article  MATH  Google Scholar 

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Acknowledgments

This work was accomplished with the support of São Paulo State Science Foundation (FAPESP) under Contracts 2009/16517-7 and INPE-National Institute for Space Research, Brazil.

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Authors and Affiliations

  1. INPE-National Institute for Space Research, Mechanics and Control Division, Avenida dos Astronautas, 1758 , São José dos Campos, Brazil

    Denílson Paulo Souza dos Santos & Jorge Kennety da Silva Formiga

  2. FATEC-College of Technology, São José dos Campos, Brazil

    Jorge Kennety da Silva Formiga

Authors
  1. Denílson Paulo Souza dos Santos
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  2. Jorge Kennety da Silva Formiga
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Correspondence to Denílson Paulo Souza dos Santos.

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Communicated by José Mario Martinez.

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dos Santos, D.P.S., da Silva Formiga, J.K. Application of a genetic algorithm in orbital maneuvers. Comp. Appl. Math. 34, 437–450 (2015). https://doi.org/10.1007/s40314-014-0151-x

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  • DOI: https://doi.org/10.1007/s40314-014-0151-x

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