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Designing Complex Interplanetary Trajectories for the Global Trajectory Optimization Competitions

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 114))

Abstract

The design of interplanetary trajectories often involves a preliminary search for options later refined/assembled into one final trajectory. It is this broad search that, often being intractable, inspires the international event called Global Trajectory Optimization Competition. In the first part of this chapter, we introduce some fundamental problems of space flight mechanics, building blocks of any attempt to participate successfully in these competitions, and we describe the use of the open source software PyKEP to solve them. In the second part, we formulate an instance of a multiple asteroid rendezvous problem, related to the 7th edition of the competition, and we show step by step how to build a possible solution strategy. In doing so, we introduce two new techniques useful in the design of this particular mission type: the use of an asteroid phasing value and its surrogates and the efficient computation of asteroid clusters. We show how the basic building blocks, sided to these innovative ideas, allow designing an effective global search for possible trajectories.

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Notes

  1. 1.

    http://sophia.estec.esa.int/gtoc_portal/.

  2. 2.

    https://github.com/esa/pykep/.

References

  1. Bäck, T., Hoffmeister, F., Schwefel, H.: A survey of evolution strategies. In: Proceedings of the 4th International Conference on Genetic Algorithms, pp. 2–9 (1991)

    Google Scholar 

  2. Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics and Astronautics, Reston (1999)

    MATH  Google Scholar 

  3. Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18 (9), 509–517 (1975)

    Article  MATH  Google Scholar 

  4. Büskens, C., Wassel, D.: The ESA NLP solver WORHP. In: Modeling and Optimization in Space Engineering, pp. 85–110. Springer, New York (2013)

    Google Scholar 

  5. Casalino, L., Colasurdo, G.: Problem Description for the 7th Global Trajectory Optimisation Competition. http://areeweb.polito.it/gtoc/gtoc7_problem.pdf (2014). [Online. Accessed 10 Mar 2016]

  6. Chaslot, G., Saito, J.T., Bouzy, B., Uiterwijk, J., Van Den Herik, H.J.: Monte-carlo strategies for computer go. In: Proceedings of the 18th BeNeLux Conference on Artificial Intelligence, Namur, pp. 83–91. Citeseer (2006)

    Google Scholar 

  7. Conway, B.A.: Spacecraft Trajectory Optimization, vol. 29. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  8. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, vol. 5(3), p. 55. MIT Press, London (2001)

    Google Scholar 

  9. D’Arrigo, P., Santandrea, S.: The APIES mission to explore the asteroid belt. Adv. Space Res. 38 (9), 2060–2067 (2006)

    Article  Google Scholar 

  10. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6 (2), 182–197 (2002)

    Article  Google Scholar 

  11. Ester, M., Kriegel, H.P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: KDD, vol. 96, pp. 226–231 (1996)

    Google Scholar 

  12. Gill, P.E., Murray, W., Saunders, M.A.: Snopt: an SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12 (4), 979–1006 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Grabmeier, J., Rudolph, A.: Techniques of cluster algorithms in data mining. Data Min. Knowl. Disc. 6 (4), 303–360 (2002)

    Article  MathSciNet  Google Scholar 

  14. Hennes, D., Izzo, D.: Interplanetary trajectory planning with monte carlo tree search. In: Proceedings of the 24th International Conference on Artificial Intelligence, pp. 769–775. AAAI Press, Palo Alto, California, USA (2015)

    Google Scholar 

  15. Izzo, D.: PyGMO and PyKEP: open source tools for massively parallel optimization in astrodynamics (the case of interplanetary trajectory optimization). In: Proceedings of the Fifth International Conference on Astrodynamics Tools and Techniques, ICATT (2012)

    Google Scholar 

  16. Izzo, D.: Revisiting lambert’s problem. Celest. Mech. Dyn. Astron. 121 (1), 1–15 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  17. Izzo, D., Simões, L.F., Märtens, M., de Croon, G.C.H.E., Heritier, A., Yam, C.H.: Search for a grand tour of the jupiter galilean moons. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation (GECCO 2013), pp. 1301–1308. ACM Press, New York (2013)

    Google Scholar 

  18. Izzo, D., Simões, L.F., Yam, C.H., Biscani, F., Di Lorenzo, D., Addis, B., Cassioli, A.: GTOC5: results from the European Space Agency and University of Florence. Acta Futura 8, 45–55 (2014). doi:10.2420/AF08.2014.45

    Article  Google Scholar 

  19. Jorba, À., Zou, M.: A software package for the numerical integration of odes by means of high-order taylor methods. Exp. Math. 14 (1), 99–117 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kuhn, H.W.: Nonlinear programming: a historical view. In: Traces and Emergence of Nonlinear Programming, pp. 393–414. Springer, Basel (2014)

    Google Scholar 

  21. McAdams, J.V., Dunham, D.W., Farquhar, R.W., Taylor, A.H., Williams, B.G.: Trajectory design and maneuver strategy for the messenger mission to mercury. J. Spacecr. Rocket. 43 (5), 1054–1064 (2006)

    Article  Google Scholar 

  22. Petropoulos, A.E., Bonfiglio, E.P., Grebow, D.J., Lam, T., Parker, J.S., Arrieta, J., Landau, D.F., Anderson, R.L., Gustafson, E.D., Whiffen, G.J., Finlayson, P.A., Sims, J.A.: GTOC5: results from the Jet Propulsion Laboratory. Acta Futura 8, 21–27 (2014). doi:10.2420/AF08.2014.21

    Article  Google Scholar 

  23. Racca, G., Marini, A., Stagnaro, L., Van Dooren, J., Di Napoli, L., Foing, B., Lumb, R., Volp, J., Brinkmann, J., Grünagel, R., et al.: Smart-1 mission description and development status. Planet. Space Sci. 50 (14), 1323–1337 (2002)

    Article  Google Scholar 

  24. Sims, J.A., Flanagan, S.N.: Preliminary design of low-thrust interplanetary missions. In: AAS/AIAA Astrodynamics Specialist Conference, AAS Paper, pp. 99–338 (1999)

    Google Scholar 

  25. Vallado, D.A., McClain, W.D.: Fundamentals of Astrodynamics and Applications, vol. 12. Springer Science and Business Media, Berlin (2001)

    Google Scholar 

  26. Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106 (1), 25–57 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Wolf, A.A.: Touring the saturnian system. Space Sci. Rev. 104 (1–4), 101–128 (2002)

    Article  Google Scholar 

  28. Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11 (6), 712–731 (2007)

    Article  Google Scholar 

  29. Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - a comparative case study. In: Parallel Problem Solving from Nature–PPSN V, pp. 292–301. Springer, New York (1998)

    Google Scholar 

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Acknowledgement

Luís F. Simões was supported by FCT (Ministério da Ciência e Tecnologia) Fellowship SFRH/BD/84381/2012.

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Correspondence to Dario Izzo .

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Izzo, D., Hennes, D., Simões, L.F., Märtens, M. (2016). Designing Complex Interplanetary Trajectories for the Global Trajectory Optimization Competitions. In: Fasano, G., Pintér, J.D. (eds) Space Engineering. Springer Optimization and Its Applications, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-41508-6_6

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