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Multiple Space Debris Collecting Mission—Debris Selection and Trajectory Optimization

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Abstract

This paper investigates the cost requirement for a space debris collecting mission aimed at removing heavy debris from low Earth orbits. The problem mixes combinatorial optimization to select the debris among a list of candidates and functional optimization to define the orbital manoeuvres. The solving methodology proceeds in two steps: Firstly, a specific transfer strategy with impulsive manoeuvres is defined so that the problem becomes of finite dimension; secondly the problem is linearized around an initial reference solution. A Branch and Bound algorithm is then applied iteratively to optimize simultaneously the debris selection and the orbital manoeuvres, yielding a new reference solution. The optimal solutions found are close to the initial guess despite a very complicated design space. The method is exemplified on a representative application case.

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References

  1. Klinkrad, K.: Space Debris Models and Risks Analysis. Springer, Berlin and Heidelberg (2006). ISBN: 3-540-25448-X

    Google Scholar 

  2. Liou, J.: An assessment of the current LEO debris environment and what needs to be done to preserve it for future generations. In: International Conference on Orbital Debris Removal, Brazil, Chantilly, Virginia (2008)

    Google Scholar 

  3. Position paper on space debris mitigation. In: International Academy of Astronautics (2005)

  4. Walker, R., Martin, C.E., Stokes, P.H., Wilkinson, J.E.: Studies of space debris mitigation options using the debris environment long term analysis (DELTA) model. In: 51st International Astronautical Congress, Brazil, Rio de Janeiro, pp. IAA-00_IAA.6.6.07 (2000)

    Google Scholar 

  5. Bastida Virgili, B., Krag, H.: Strategies for active removal in LEO. In: 5th European Conference on Space Debris, Germany. ESOC, Darmstadt (2009)

    Google Scholar 

  6. Leitmann, G.: Optimization techniques. Math. Sci. Eng. 5 (1962)

  7. Trélat, E.: Contrôle Optimal—Théorie et Applications. Vuibert, Paris (2005)

    MATH  Google Scholar 

  8. Lacomme, P., Prins, C., Sevaux, M.: Algorithmes de Graphes, 2ème edn. Eyrolles, Paris (2003)

    Google Scholar 

  9. Schneider, J.J., Kirkpatrick, S.: Stochastic Optimization. Springer, Berlin (2006)

    MATH  Google Scholar 

  10. Nemhauser, G.L., Rinnooy Kan, A.H.G., Todd, M.J.: Optimization. Handbooks in Operations Research and Management Science, vol. 1. Elsevier, Amsterdam (1989)

    MATH  Google Scholar 

  11. Minoux, M.: Programmation Mathématique—Théorie et Algorithmes, 2ème edn. Editions Tec&Doc, Lavoisier, Paris (2008)

    MATH  Google Scholar 

  12. Dréo, J., Pétrowski, A., Siarry, P., Taillard, E.: Métaheuristiques Pour L’optimisation Difficile. Eyrolles, Paris (2003)

    Google Scholar 

  13. Oberle, H.J., Taubert, K.: Existence and multiple solutions of the minimum-fuel orbit transfer problem. J. Optim. Theory Appl. 95, 243–262 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gergaud, J., Haberkorn, T.: Orbital transfer: some links between the low-thrust and the impulse cases. Acta Astronaut. 60(6–9), 649–657 (2007)

    Article  Google Scholar 

  15. Minieka, E.: On computing sets of shortest paths in a graph. Manag. Sci. Oper. Res. 17(6) (1974)

  16. Eppstein, D.: Finding the k shortest paths. In: 35th IEEE Symp. Foundations of Comp. Sci., Santa Fe, 1994, pp. 154–165 (1997). Tech. Rep. 94-26

    Google Scholar 

  17. Hershberger, J., Maxel, M., Suri, S.: Finding the k shortest simple paths: a new algorithm and its implementation. ACM Trans. Algorithms 3(4) (2007)

  18. Sedeno-Noda, A., Gonzalez-Martin, C.: On the k shortest path trees problem. Eur. J. Oper. Res. 202, 628–635 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Billionnet, A.: Optimisation Discrète. Dunod, Paris (2007)

    Google Scholar 

  20. Chao, C.: Applied Orbit Perturbation and Maintenance. The Aerospace Press, Reston (2005)

    Google Scholar 

  21. Chobotov, V.: Orbital Mechanics, 3rd edn. AIAA Education Series. AIAA, Washington (2002)

    Book  Google Scholar 

  22. Murakami, J., Hokamoto, S.: Approach for optimal multi-rendezvous trajectory design for active debris removal. In: 61th International Astronautical Congress, Prague, CZ, pp. IAC-10.C1.5.8 (2010)

    Google Scholar 

  23. Chapman, S.J.: Fortran 90/95 for Scientists and Engineers, 2nd edn. McGraw-Hill, New York (2004)

    Google Scholar 

  24. Guéret, C., Prins, C., Sevaux, M.: Programmation Linéaire, 2ème edn. Eyrolles, Paris (2003)

    Google Scholar 

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Acknowledgements

This work was carried out at EADS Astrium Space Transportation in 2010–2011 in the frame of the internal R&D. I am very grateful to Emmanuel Trélat (UPMC, Paris) and Thomas Haberkorn (MAPMO, University of Orléans) for their support and advices in order to write down a comprehensive paper.

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  1. EADS Astrium Space Transportation, Les Mureaux, France

    M. Cerf

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  1. M. Cerf
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Correspondence to M. Cerf.

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Communicated by Ryan P. Russell.

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Cerf, M. Multiple Space Debris Collecting Mission—Debris Selection and Trajectory Optimization. J Optim Theory Appl 156, 761–796 (2013). https://doi.org/10.1007/s10957-012-0130-6

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  • DOI: https://doi.org/10.1007/s10957-012-0130-6

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