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 LiEmail author
  • Lin Hu
  • Zhao-quan Cai
Methodologies and Application


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.


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



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.


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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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