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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References
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)
Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics and Astronautics, Reston (1999)
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18 (9), 509–517 (1975)
Büskens, C., Wassel, D.: The ESA NLP solver WORHP. In: Modeling and Optimization in Space Engineering, pp. 85–110. Springer, New York (2013)
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]
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)
Conway, B.A.: Spacecraft Trajectory Optimization, vol. 29. Cambridge University Press, Cambridge (2010)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, vol. 5(3), p. 55. MIT Press, London (2001)
D’Arrigo, P., Santandrea, S.: The APIES mission to explore the asteroid belt. Adv. Space Res. 38 (9), 2060–2067 (2006)
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)
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)
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)
Grabmeier, J., Rudolph, A.: Techniques of cluster algorithms in data mining. Data Min. Knowl. Disc. 6 (4), 303–360 (2002)
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)
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)
Izzo, D.: Revisiting lambert’s problem. Celest. Mech. Dyn. Astron. 121 (1), 1–15 (2014)
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)
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
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)
Kuhn, H.W.: Nonlinear programming: a historical view. In: Traces and Emergence of Nonlinear Programming, pp. 393–414. Springer, Basel (2014)
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)
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
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)
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)
Vallado, D.A., McClain, W.D.: Fundamentals of Astrodynamics and Applications, vol. 12. Springer Science and Business Media, Berlin (2001)
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)
Wolf, A.A.: Touring the saturnian system. Space Sci. Rev. 104 (1–4), 101–128 (2002)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11 (6), 712–731 (2007)
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)
Acknowledgement
Luís F. Simões was supported by FCT (Ministério da Ciência e Tecnologia) Fellowship SFRH/BD/84381/2012.
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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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