Abstract
We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Myatt, D.R., Becerra, V.M., Nasuto, S.J., Bishop, J.M.: Advanced global optimisation for analysis and design. Final Report. Ariadna id: 03/4101. Contract Number: 18138/04/NL/MV, 2004. Available: http://www.esa.int/gsp/ACT/doc/ACT-RPT-03-4101-ARIADNA-GlobalOptimisationReading.pdf
Di Lizia, P., Radice, G.: Advanced global optimisation for mission analysis and Design. Final Report. Ariadna id: 03/4101. Contract Number: 18139/04/NL/MV, 2004. http:// www.esa.int/gsp/ACT/doc/ACT-RPT-03-4101-ARIADNA-GlobalOptimisationGlasgow. pdf
Bryson A.E., Ho Y. (1989). Applied Optimal Control. Taylor & Francis, New York, pp. 1–89
Brown, C.D.: Spacecraft Mission Design, ch. 6, AIAA, Reston (1998)
Yokoyama N., Suzuki S. (2005) Modified genetic algorithm for constrained trajectory optimization. J. Guidance Control Dyn. 28(1): 139–144
Vasile M., Summerer L., De Pascale P. (2005) Design of earth–mars transfer trajectories using evolutionary-branching technique. Acta Astronautica 56(8): 705–720
Battin H.B. An Introduction to the Mathematics and Methods of Astrodynamics, ch. 7, AIAA, Reston (1999)
Prussing J.E. (2000) A class of optimal two-impulse rendezvous using multiple-revolution Lambert solutions. J. Astronaut. Sci. 48(2–4): 131–148
Gobetz F.B. Optimal transfer between hyperbolic asymptotes. AIAA J. 1(9), (1963)
Storn R., Price K., (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359
Kennedy, J., Eberhart, R.: Particle swarm optimization. Proc. IEEE Int. Conf. on Neural Networks, 1942–1948, (1995)
Blackwell, T.M., Branke, J.: Multi-swarm optimisation of the moving peaks function. Proc. Appl. Evolut. Comp. EuroWorkshops 2004, pp. 489–500, Springer-Verlag (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially funded under the Ariadna scheme of the European Space Agency, contract number 18138/04/NL/MV.
Rights and permissions
About this article
Cite this article
Izzo, D., Becerra, V.M., Myatt, D.R. et al. Search space pruning and global optimisation of multiple gravity assist spacecraft trajectories. J Glob Optim 38, 283–296 (2007). https://doi.org/10.1007/s10898-006-9106-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9106-0