Parallelly generating halo orbit and its transfer trajectory in the full ephemeris model

  • Tao Wu
  • Xiao Pan
  • Ming XuEmail author
  • Qingyu Qu
  • Qianhui Xia
  • Shengli Liu
Original Article


This paper employs a parallelized genetic algorithm in generating long-term bounded halo orbit and optimizing transfer trajectory from earth to it in the full ephemeris model. While the conventional gradient methods are lacking in precision as well as time-consuming, the parallel genetic algorithm (PGA) offers an access to large-scale computing based on the advanced hardware capability. A bounded halo orbit without any stationkeeping maneuver in five periods is obtained inside a defined pipe region in the ephemeris model. Transfer trajectory from earth to the obtained halo orbit is also investigated in this paper. By optimizing insertion impulses in the backward propagation and midcourse in the forward propagation, a transfer trajectory from earth to halo with least fuel consumption is generated. Furthermore, launch window is investigated based on the periodic variation about inclination of the injection point on the parking orbit. A mapping method from spatial space to \(i-\varOmega \) subspace is introduced for solving the time delay and position deviation problem. The numerical method employed in this paper is of high accuracy based on large-scale computing capability as well as efficient without any analytical initial guess, which makes it extensive in designing these unstable libration point orbits.


Full ephemeris model parallel genetic algorithm Halo orbit Transfer trajectory 



This work was supported by the National Natural Science Foundation of China (11432001 and 11172024), the Fundamental Research Funds for the Central Universities, and the Foundation of Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technologies, Ministry of Education of China.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Beihang UniversityBeijingChina
  2. 2.Beijing University of Civil Engineering and ArchitectureBeijingChina
  3. 3.DFH Satellite Co., Ltd.BeijingChina

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