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Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method

Author

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  • Mauro Pontani

    (University “La Sapienza”)

  • Bruce Conway

    (University of Illinois at Urbana-Champaign)

Abstract

In the last decades, heuristic techniques have become established as suitable approaches for solving optimal control problems. Unlike deterministic methods, they do not suffer from locality of the results and do not require any starting guess to yield an optimal solution. The main disadvantages of heuristic algorithms are the lack of any convergence proof and the capability of yielding only a near optimal solution, if a particular representation for control variables is adopted. This paper describes the indirect swarming method, based on the joint use of the analytical necessary conditions for optimality, together with a simple heuristic technique, namely the particle swarm algorithm. This methodology circumvents the previously mentioned disadvantages of using heuristic approaches, while retaining their advantageous feature of not requiring any starting guess to generate an optimal solution. The particle swarm algorithm is chosen among the different available heuristic techniques, due to its apparent simplicity and the recent promising results reported in the scientific literature. Two different orbital maneuvering problems are considered and solved with great numerical accuracy, and this testifies to the effectiveness of the indirect swarming algorithm in solving low-thrust trajectory optimization problems.

Suggested Citation

  • Mauro Pontani & Bruce Conway, 2014. "Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 272-292, July.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0471-9
    DOI: 10.1007/s10957-013-0471-9
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    References listed on IDEAS

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    1. David G. Hull, 2011. "Optimal Guidance for Quasi-planar Lunar Ascent," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 353-372, November.
    2. A. Miele & T. Wang, 1997. "Optimal Trajectories for Earth-to-Mars Flight," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 467-499, December.
    3. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
    4. A. Miele & T. Wang, 2003. "Multiple-Subarc Gradient-Restoration Algorithm, Part 1: Algorithm Structure," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 1-17, January.
    5. A. Miele & T. Wang, 2003. "Multiple-Subarc Gradient-Restoration Algorithm, Part 2: Application to a Multistage Launch Vehicle Design," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 19-39, January.
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    Cited by:

    1. Mauro Pontani, 2021. "Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 545-574, December.

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