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Multi-revolution low-thrust trajectory optimization using symplectic methods

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Abstract

Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered as a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy low-thrust multi-revolution orbit transfer problem. First, the optimal orbit transfer problem is posed as a constrained nonlinear optimal control problem. Then, the constrained nonlinear optimal control problem is converted into an equivalent linear quadratic form near a reference solution. The reference solution is updated iteratively by solving a sequence of linear-quadratic optimal control sub-problems, until convergence. Each sub-problem is solved via a symplectic method in discrete form. To facilitate the convergence of the algorithm, the spacecraft dynamics are expressed via modified equinoctial elements. Interpolating the non-singular equinoctial orbital elements and the spacecraft mass between the initial point and end point is proven beneficial to accelerate the convergence process. Numerical examples reveal that the proposed method displays high accuracy and efficiency.

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Authors and Affiliations

  1. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    ZhiBo E

  2. Department of Aerospace Engineering, Auburn University, Auburn, AL, 36849, USA

    Davide Guzzetti

Authors
  1. ZhiBo E
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  2. Davide Guzzetti
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Corresponding author

Correspondence to ZhiBo E.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11672146, 11432001), and the 2015 Chinese National Postdoctoral International Exchange Program. In addition, we are grateful to Mr. Boyang Shi for his help with computational programming and the reviewers for their detailed comments that have helped improve this manuscript.

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E, Z., Guzzetti, D. Multi-revolution low-thrust trajectory optimization using symplectic methods. Sci. China Technol. Sci. 63, 506–519 (2020). https://doi.org/10.1007/s11431-019-9511-7

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  • DOI: https://doi.org/10.1007/s11431-019-9511-7

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