Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System

WU Di1, CHENG Lin2, WANG Wei1, LI Junfeng1

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PDF(2716 KB)
Journal of Deep Space Exploration ›› 2021, Vol. 8 ›› Issue (5) : 528-533. DOI: 10.15982/j.issn.2096-9287.2021.20200090
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Article

Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System

  • WU Di1, CHENG Lin2, WANG Wei1, LI Junfeng1
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Abstract

The traditional homotopy method usually transforms the low-thrust fuel-optimal control problem into the energy-optimal problem to increase the convergence rate of the indirect method. However, it is still necessary to guess the initial values of the co-states to initialize the solving algorithm. In this paper, the optimization model of the fuel-optimal problem is embedded in the switching system with the analytical initial co-states, which further improves the convergence rate with the analytical initialization. Firstly, the switching system is introduced with the embedded fuel-optimal problem. The switching function of the conventional switching system is derived from the optimal control, but in this paper, the given switching function is designed artificially to realize the switching and continuation among different systems. Secondly, based on the linearization technique, the target system is designed with analytical initial co-states, initializing the solving algorithm by a simple nominal trajectory. Finally, the numerical simulation verifies the effectiveness of the proposed method, which is more efficient than the traditional homotopy method.

Keywords

low thrust / trajectory optimization / switching system / linearization around nominal trajectory / analytical initialization of the co-states

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WU Di, CHENG Lin, WANG Wei, LI Junfeng. Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System. Journal of Deep Space Exploration, 2021, 8(5): 528‒533 https://doi.org/10.15982/j.issn.2096-9287.2021.20200090

References

[1] JIANG F,TANG G,LI J. Improving low-thrust trajectory optimization by adjoint estimation with shape-based path[J]. Journal of Guidance,Control,and Dynamics,2017,40(12):3282-3289
[2] KITAMURA K,YAMADA K,SHIMA T. Minimum energy coplanar orbit transfer of geostationary spacecraft using time-averaged Hamiltonian[J]. Acta Astronautica,2019,160:270-279
[3] WALL B J,CONWAY B A. Shape-based approach to low-thrust rendezvous trajectory design[J]. Journal of Guidance,Control,and Dynamics,2009,32(1):95-101
[4] BETTS J T. Very low-thrust trajectory optimization using a direct sqp method[J]. Journal of Computational and Applied Mathematics,2000,120(1-2):27-40
[5] 刘俊丽,高扬. 十年一剑刃锋利,苦寒方得梅花香——全国空间轨道设计竞赛发展历程回顾[J]. 力学与实践,2019,41(4):488-497
LIU J,GAO Y. With ten years’ effort the sword edge is grinded sharp,after the cold winter plum flower blossoms—a review of China Trajectory Optimization Competition[J]. Mechanics in Engineering,2019,41(4):488-497
[6] YANG H,TANG G,JIANG F. Optimization of observing sequence based on nominal trajectories of symmetric observing configuration[J]. Astrodynamics,2018,2(1):25-37
[7] BETTS J T. Survey of numerical methods for trajectory optimization[J]. Journal of guidance,control,and dynamics,1998,21(2):193-207
[8] GAO Y. Near-optimal very low-thrust earth-orbit transfers and guidance schemes[J]. Journal of guidance,control,and dynamics,2007,30(2):529-539
[9] HABERKORN T,MARTINON P,GERGAUD J. Low thrust minimum-fuel orbital transfer:a homotopic approach[J]. Journal of Guidance,Control,and Dynamics,2004,27(6):1046-1060
[10] JIANG F,BAOYIN H,LI J. Practical techniques for low-thrust trajectory optimization with homotopic approach[J]. Journal of Guidance,Control,and Dynamics,2012,35(1):245-258
[11] BENGEA S C,DECARLO R A. Optimal control of switching systems[J]. Automatica,2005,41(1):11-27
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