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Homotopy method for optimization of variable-specific-impulse low-thrust trajectories

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Abstract

The homotopy method has been used as a useful tool in solving fuel-optimal trajectories with constant-specific-impulse low thrust. However, the specific impulse is often variable for many practical solar electric power-limited thrusters. This paper investigates the application of the homotopy method for optimization of variable-specific-impulse low-thrust trajectories. Difficulties arise when the two commonly-used homotopy functions are employed for trajectory optimization. The optimal power throttle level and the optimal specific impulse are coupled with the commonly-used quadratic and logarithmic homotopy functions. To overcome these difficulties, a modified logarithmic homotopy function is proposed to serve as a gateway for trajectory optimization, leading to decoupled expressions of both the optimal power throttle level and the optimal specific impulse. The homotopy method based on this homotopy function is proposed. Numerical simulations validate the feasibility and high efficiency of the proposed method.

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Notes

  1. Data available online at http://ssd.jpl.nasa.gov/horizons.cgi [retrieval date: March 1st, 2017].

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Acknowledgements

This work is supported by the National Natural Science Fund of China (Grant Nos. 11672146 and 11572166). The authors would like to thank Haiyang Li, from Tsinghua University, for the many discussions on low-thrust trajectory optimization.

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Authors and Affiliations

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

    Zhemin Chi, Shiyu Chen & Junfeng Li

  2. Department of Astronautics Engineering, College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Hongwei Yang

  3. Department of Astronautics Engineering, Space New Technology Laboratory, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Hongwei Yang

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  1. Zhemin Chi
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  2. Hongwei Yang
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  3. Shiyu Chen
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  4. Junfeng Li
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Correspondence to Hongwei Yang.

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Chi, Z., Yang, H., Chen, S. et al. Homotopy method for optimization of variable-specific-impulse low-thrust trajectories. Astrophys Space Sci 362, 216 (2017). https://doi.org/10.1007/s10509-017-3196-7

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  • DOI: https://doi.org/10.1007/s10509-017-3196-7

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