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Design and optimization of low-energy transfer orbit to Mars with multi-body environment

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Abstract

This paper discusses the problem of design and optimization of low-energy transfer orbit with multi-body environment. A new integrative method is proposed to effectively solve the problem, in which the parameterized patched manifolds in CR3BP (circular restricted three-body problems), the shape-based method with multi-body environment, the homotopic method with multi- body environment, and the low-thrust capturing and descending algorithm with multi-body environment are all included. Firstly, the parameters describing the patched manifolds in CR3BP are optimized until the least total absolute velocity increment has been got, including the employment of the shape-based method with multi-body environment. Secondly, the low-thrust control laws of the transfer orbit are optimized employing the homotopic method with multi-body environment that transfers the fuel optimization problem to an easier energy optimization problem. Thirdly, the low-thrust descending orbit around Mars is computed using the laws proposed in this paper. As a typical example, the Earth-Mars transfer orbit design is discussed. The results showed that the parameters describing the patched manifolds could be optimized by the DE (differential evolution) algorithm effectively; the homotopic method with multi-body environment could get the optimal value that meets the first order optimality conditions; and the low-thrust descending orbit could effectively be captured by Mars and finally become a circular parking orbit around it by the hypothesis control laws proposed in this paper. It shows that the final fuel cost is much less than the optimal transfer in the patched two-body problems. In conclusion, the method proposed in this paper could effectively solve the low-energy low-thrust optimal control problem in multi-body environment for the future deep space explorations.

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References

  1. Gomez G, Koon W S, Lo M W, et al. Invariant manifolds, the spatial three-body problem and space mission design. In: Astro-dynamics Specialist Meeting, Quebec City: AIAA/AAS, Canada, 2001

    Google Scholar 

  2. Xu M, Tan T, Xu S J. Research on the transfers to Halo orbits from the view of invariant manifolds. Sci China Tech Sci, 2012, 55: 671–683

    Google Scholar 

  3. Wang S, Shang H B, Wu W R, Interplanetary transfers employing invariant manifolds and gravity assist between periodic orbits. Sci China Tech Sci, 2013; 56: 786–794

    Article  Google Scholar 

  4. Gomez G, Koon W S, Lo M W, et al. Connecting orbits and invariant manifolds in the spatial restricted three-body problem. Nonlinearity, 2004; 17: 157–1606

    MathSciNet  Google Scholar 

  5. Koon W S, Lo M W, Marsden J E, et al. Constructing a low energy transfer between jovian moons. Contem Math, 2002. 292: 129–145

    Article  MathSciNet  Google Scholar 

  6. Lo M W. The interplanetary superhighway and the origins program. In: IEEE Aerospace Conference, MT: Big Sky, 2002

    Google Scholar 

  7. Yamato H, Spencer D B. Orbit transfer via tube jum** in planar restricted problems of four bodies. J Spacecraft Rockets, 2005. 42: 321–328

    Article  Google Scholar 

  8. Gomez G, Koon W S, Lo M W, et al. Invariant manifolds, the spatial three-body problem and space mission design. In: Astrodynamics Specialist Meeting, Quebec City, Canada, 2001

    Google Scholar 

  9. Wang Y M, Cui P Y, Qiao D. Opportunities search of transfer between interplanetary halo orbits in ephemeris model. Sci China Tech Sci, 2014; 56: 188–193

    Article  Google Scholar 

  10. Anil V R, David A B, Christopher D, et al. GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method. ACM T Math Software, 2010; 37: 22–39

    Google Scholar 

  11. Lin K P, Luo Y Z, Zhang J, et al. Planning for space station long-duration orbital mission under multi-constraints. Sci China Tech Sci, 2014; 56: 1075–1085

    Article  Google Scholar 

  12. Li H N, Gao Z Z, Li J S, et al. Mathematical prototypes for collocating geostationary satellites. Sci China Tech Sci, 2014; 56: 1086–1092

    Article  Google Scholar 

  13. Betts J T, Huffman W P. Mesh refinement in direct transcription methods for optimal control. Optim Control Appl Methods, 1998; 19: 1–21

    Article  MathSciNet  Google Scholar 

  14. Christopher L D, William W H, Anil V R. An hp-adaptive pseudospectral method for solving optimal control problem. Optim Control Appl Methods, 2011; 32: 476–502

    Article  MATH  Google Scholar 

  15. Huang G Q, Liu Y P, Nan Y, et al. Multi-goals global optimization for low-thrust deep space probe orbit. J Syst Eng Electron, 2008; 34: 1653–1659

    Google Scholar 

  16. Jiang F H, Chen Y, Liu Y C, et al. The solutions of tsinghua university for the global trajectory optimization competition in 2010 (in Chinese). Mech Pr, 2010; 3: 103–105

    Google Scholar 

  17. Kluever C A. Optimal low-thrust interplanetary trajectories by direct method techniques. J Astronaut Sci, 1997; 45: 247–262

    MathSciNet  Google Scholar 

  18. Li J F, Jiang F H. The review of optimization method for ccontinuous low-thrust spacecraft explorations (in Chinese). Mech Pr, 2011; 23: 1–6

    Google Scholar 

  19. Guo T D, Jiang F H, Baoyin H X, et al. Fuel optimal low thrust rendezvous with outer planets via gravity assist. Sci China Phys Mech Astron, 2011; 54: 756–769

    Article  Google Scholar 

  20. Edelbaum T N. Propulsion requirements for controllable satellites. J Am Rock Soc, 1961; 31: 1079–1089

    Google Scholar 

  21. Betts J T. Very low-thrust trajectory optimization using a direct SQP method. J Comput Appl Math, 2000; 120: 27–40

    Article  MATH  MathSciNet  Google Scholar 

  22. Gao Y. Near-optimal very-low-thrust earth-orbit transfers and guidance schemes. J Guid Control Dynam, 2007; 30: 529–539

    Article  Google Scholar 

  23. Lisa A H. Optimal transfers between libration point orbits in the elliptic restricted three-body problem. Dissertation of Doctor Degree. West Lafayette: Purdue University, 1992

    Google Scholar 

  24. Liu L, Wang X. Orbital Mechanics of the Lunar Probe. Bei**g: National Defense Industry Press, 2006. 127–139

    Google Scholar 

  25. Wang S K, Martin W L, Jerrold E M, et al. Dynamical Systems, the Three-Body Problem and Space Mission Design. Marsden Books. 2010, 151–160

    Google Scholar 

  26. Robert T, Patrick A W. The Geometry of Halo orbits in the restricted three body problem. Dissertation of Doctor Degree. Minnesota: University of Minnesota, 1996

    Google Scholar 

  27. Chen Y, Baoyin H X, Li J F. Trajectory design for the Moon departure libration point mission in full ephemeris model. Sci China Tech Sci, 2011; 54: 2924–2934

    Article  Google Scholar 

  28. Roby S W. A design tool for constructing multiple lunar swingby trajectories. Dissertation of Master Degree. West Lafayette: Purdue University, 1993. 123–136

    Google Scholar 

  29. Howard D C. Orbital Mechanics for Engineering Students. Elsevier, 2005, 163–172

    Google Scholar 

  30. Luo Y Z, Yang Z, Li H N. Robust optimization of nonlinear impulsive rendezvous with uncertainty. Sci China-Phys Mech Astron, 2014; 57: 731–740

    Article  Google Scholar 

  31. Bradley J W. Shape-based approximation method for low-thrust trajectory optimization. In: Astrodynamics Specialist Conference and Exhibit. Hawaii: AIAA, 2008. 18–21

    Google Scholar 

  32. Chen Y, Zhao G Q, Baoyin H X, et al. Orbit design for mars exploration by the accurate dynamic model (in Chinese). China Space Sci Tech, 2011; 2: 8–15

    Google Scholar 

  33. Li H N. Orbit Determination for Maneuvering Satellite. Bei**g: National Defense Industry Press, 2013. 98–99

    Google Scholar 

  34. Jiang F H, Baoyin H X, Li J F. Practical techniques for low-thrust trajectory optimization with homotopic approach. J Guid Control Dynam, 2012; 35: 245–258

    Article  Google Scholar 

  35. Frank E L, James M L. Low-thrust trajectories for human missions to Ceres. Acta Astronaut, 2014; 95: 124–132

    Article  Google Scholar 

  36. Falck R, Gefert L. A Method of efficient inclination changes for low-thrust spacecraft. In: Astrodynamics Specialist Conference and Exhibit, California: AIAA, 2002, 5–8

    Google Scholar 

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Authors and Affiliations

  1. School of Electronic and Information Engineering, **’an Jiaotong University, **’an, 710049, China

    Yi Lu, HengNian Li & JiSheng Li

  2. State Key Laboratory of Astronautic Dynamics (ADL), Affiliated to **’an Satellite Control Center, **’an, 710043, China

    Yi Lu, HengNian Li, JiSheng Li, Zheng Che & Yuan Yang

  3. College of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, 610054, China

    YiKang Yang

  4. School of Aerospace, **’an Jiaotong University, **’an, 710049, China

    Yang Sun

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  1. Yi Lu
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  2. HengNian Li
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  4. Zheng Che
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  6. Yuan Yang
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  7. Yang Sun
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Correspondence to Yi Lu.

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Lu, Y., Li, H., Li, J. et al. Design and optimization of low-energy transfer orbit to Mars with multi-body environment. Sci. China Technol. Sci. 58, 1660–1671 (2015). https://doi.org/10.1007/s11431-015-5847-7

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  • DOI: https://doi.org/10.1007/s11431-015-5847-7

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