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Soft Computing

, Volume 22, Issue 9, pp 2921–2934 | Cite as

Optimal solution to orbital three-player defense problems using impulsive transfer

  • Yifang Liu
  • Renfu Li
  • Lin Hu
  • Zhao-quan Cai
Methodologies and Application
  • 122 Downloads

Abstract

This paper investigates three-dimensional orbital three-spacecraft-player defense problems. An attacker is about to strike a non-maneuverable asset, while a defender attempts to prevent this attacking in order to protect the asset. It is assumed that both the attacker and the defender have only one chance to maneuver using impulsive thrust. The attacker is not aware of the defender’s participation, while the latter has full information about the former. A hybrid method combined particle swarm optimization with a Newton-Interpolation algorithm is proposed to solve presented orbital defense problems. Numerical results show that the proposed methodology can solve orbital three-player defense problems effectively. Energy consumption of defender is analyzed in detail to tell whether the specified upper bound of defender’s energy is justified. The interesting discovery is the valid departure window of defender in lurk orbit which have important significance for design defender’s strategy in orbital three-player defense problems.

Keywords

Orbital three-player defense problem Impulsive thrust Newton-Interpolation algorithm Particle swarm optimization 

Notes

Acknowledgements

This study was funded by the Ministry of Science and Technology Fund Project (Grant No. 2015DFA81640), Aeronautical Science Foundation of China (Grant No. 20130179002) at the Huazhong University of Science and Technology, National Natural Science Foundation of China (Grant No. 61370185), Natural Science Foundation of Guangdong Province (Grant Nos. S2013010013432, S2013010015940), Science and Technology Planning Project of Huizhou (Grant Nos. 2014B050013016, 2014B020004023).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflicts of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Abdelkhalik O, Gad A (2012) Dynamic-size multiple populations genetic algorithm for multigravity-assist trajectory optimization. J Guid Control Dyn 35(2):520–529. doi: 10.2514/1.54330 CrossRefGoogle Scholar
  2. Anderson GM, Grazier VW (1976) Barrier in pursuit-evasion problems between two low-thrust orbital spacecraft. AIAA J 14(2):158–163. doi: 10.2514/3.61350 MathSciNetCrossRefGoogle Scholar
  3. Bai Q (2010) Analysis of particle swarm optimization algorithm. Comput Inf Sci 3(1):180–184. doi: 10.5539/cis.v3n1p180 Google Scholar
  4. Battin RH (1999) An introduction to the mathematics and methods of astrodynamics. AIAA Education Series, RestonMATHGoogle Scholar
  5. Blasch EP, Pham K, Shen D (2012) Orbital satellite pursuit-evasion game-theoretical control. In: Information science, signal processing and their applications (ISSPA), 2012 11th international conference on, IEEE, pp 1007–1012Google Scholar
  6. Boyell RL (1976) Defending a moving target against missile or torpedo attack. IEEE Trans Aerosp Electron Syst AES–12(4):522–526. doi: 10.1109/TAES.1976.308338 CrossRefGoogle Scholar
  7. Burk RC, Widhalm JW (1989) Minimum impulse orbital evasive maneuvers. J Guid Control Dyn 12(1):121–123. doi: 10.2514/3.20378 CrossRefGoogle Scholar
  8. Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, Nagoya, pp 39–43Google Scholar
  9. Gandomi AH, Yun GJ, Yang X-S, Talatahari S (2013) Chaos-enhanced accelerated particle swarm optimization. Commun Nonlinear Sci Numer Simul 18(2):327–340. doi: 10.1016/j.cnsns.2012.07.017 MathSciNetCrossRefMATHGoogle Scholar
  10. Goel T, Stander N (2009) Adaptive simulated annealing for global optimization in ls-opt. In: Proceedings of the 7th European LS-DYNA conference, LSTC, California, pp 1–8Google Scholar
  11. Hafer WT, Reed HL (2015) Orbital pursuit-evasion hybrid spacecraft controllers. In: AIAA guidance, navigation, and control conference, Kissimmee, Florida, AIAA Paper 2015–2000. doi: 10.2514/6.2015-2000
  12. Hu X, Shi Y, Eberhart RC (2004) Recent advances in particle swarm. In: Proceedings of IEEE congress on evolutionary computation, vol 1, pp 90–97Google Scholar
  13. Isaacs R (1965) Differential games. Wiley, New YorkMATHGoogle Scholar
  14. Islam SM, Das S, Ghosh S, Roy S, Suganthan PN (2012) An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Trans Syst Man Cybern Part B Cybern 42(2):482–500. doi: 10.1109/TSMCB.2011.2167966 CrossRefGoogle Scholar
  15. Leeghim H (2013) Spacecraft intercept using minimum control energy and wait time. Celest Mech Dyn Astron 115(1):1–19. doi: 10.1007/s10569-012-9448-5 MathSciNetCrossRefMATHGoogle Scholar
  16. Li D, Cruz JB (2011) Defending an asset: a linear quadratic game approach. IEEE Trans Aerosp Electron Syst 47(2):1026–1044. doi: 10.1109/TAES.2011.5751240 CrossRefGoogle Scholar
  17. Liu Y, Li R, Wang S (2016a) Orbital three-player differential game using semi-direct collocation with nonlinear programming. In: 2016 2nd international conference on control science and systems engineering (ICCSSE), pp 217–222. doi: 10.1109/CCSSE.2016.7784385
  18. Liu Y, Li R, Wang S (2016b) Particle swarm optimization applied to orbital three-player conflict. In: 2016 8th international conference on intelligent human-machine systems and cybernetics (IHMSC), vol 02, pp 513–517. doi: 10.1109/IHMSC.2016.171
  19. Liu Y, Li R, Wang S (2017) Optimal anti-interception orbit design based on genetic algorithm. Int J Comput Sci Eng (in press)Google Scholar
  20. Menon PKA, Calise AJ, Leung SKM (1988) Guidance laws for spacecraft pursuit-evasion and rendezvous. In: AIAA guidance navigation and control conference, Minneapolis, pp 688–697Google Scholar
  21. Mohan BC, Baskaran R (2012) A survey: ant colony optimization based recent research and implementation on several engineering domain. Expert Syst Appl 39(4):4618–4627. doi: 10.1016/j.eswa.2011.09.076 CrossRefGoogle Scholar
  22. Morgan JA (2011) Interception in differential pursuit/evasion games. arXiv preprint arXiv:1109.4059
  23. Perelman A, Shima T, Rusnak I (2011) Cooperative differential games strategies for active aircraft protection from a homing missile. J Guid Control Dyn 34(3):761–773. doi: 10.2514/1.51611
  24. Pontani M, Conway BA (2009) Numerical solution of the three-dimensional orbital pursuit-evasion game. J Guid Control Dyn 32(2):474–487. doi: 10.2514/1.37962 CrossRefGoogle Scholar
  25. Pontani M, Conway BA (2012) Particle swarm optimization applied to impulsive orbital transfers. Acta Astronaut 74:141–155. doi: 10.1016/j.actaastro.2011.09.007 CrossRefGoogle Scholar
  26. Pontani M, Ghosh P, Conway BA (2012) Particle swarm optimization of multiple-burn rendezvous trajectories. J Guid Control Dyn 35(4):1192–1207. doi: 10.2514/1.55592 CrossRefGoogle Scholar
  27. Prussing JE, Clifton RS (1994) Optimal multiple-impulse satellite evasive maneuvers. J Guid Control Dyn 17(3):599–606. doi: 10.2514/3.21239 CrossRefMATHGoogle Scholar
  28. Rahimi A, Kumar KD, Alighanbari H (2013) Particle swarm optimization applied to spacecraft reentry trajectory. J Guid Control Dyn 36(1):307–310. doi: 10.2514/1.56387 CrossRefGoogle Scholar
  29. Rusnak I (2008) Guidance laws in defense against missile attack. In: IEEE 25th convention of electrical and electronics engineers in Israel, pp 90–94. doi: 10.1109/EEEI.2008.4736664
  30. Shen D, Pham K, Blasch E, Chen H, Chen G (2011) Pursuit-evasion orbital game for satellite interception and collision avoidance. In: Proceedings of SPIE, vol 8044. doi: 10.1117/12.882903
  31. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, pp 69–73. doi: 10.1109/ICEC.1998.699146
  32. Shneydor NA (1977) Comments on ”defending a moving target against missile or topedo attack”. IEEE Trans Aerosp Electron Syst AES–13(3):321. doi: 10.1109/TAES.1977.308401 MathSciNetCrossRefGoogle Scholar
  33. Showalter DJ, Black JT (2014) Responsive theater maneuvers via particle swarm optimization. J Spacecr Rockets 51(6):1976–1985. doi: 10.2514/1.A32989 CrossRefGoogle Scholar
  34. Stratemeier D (2002) Optimum two-impulse orbital transfer solved using evolutionary programming. In: AIAA/AAS astrodynamics specialist conference and exhibit, Monterey, CA, AIAA Paper 2002–4908. doi: 10.2514/6.2002-4908
  35. Subbarao K, Shippey BM (2009) Hybrid genetic algorithm collocation method for trajectory optimization. J Guid Control Dyn 32(4):1396–1403. doi: 10.2514/1.41449 CrossRefGoogle Scholar
  36. Venter G, Sobieski JS (2003) Particle swarm optimization. AIAA J 41(8):1583–1589. doi: 10.2514/2.2111 CrossRefGoogle Scholar
  37. Widhalm JW, Heise SA (1991) Optimal in-plane orbital evasive maneuvers using continuous thrust propulsion. J Guid Control Dyn 14(6):1323–1326. doi: 10.2514/3.20793 CrossRefGoogle Scholar
  38. Wong RE (1967) Some aerospace differential games. J Spacecr Rockets 4(11):1460–1465. doi: 10.2514/3.29114 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Aerospace EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanChina
  3. 3.Department of Computer ScienceHuizhou UniversityHuizhouChina

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