A homotopy approach connecting time-optimal with fuel-optimal trajectories

Abstract

This paper describes a novel homotopy method to compute fuel-optimal trajectories starting from a time-optimal solution. The time-optimal problem is proposed to serve as a gateway for solving the minimum thrust problem. Homotopy is used to link the original low-thrust fuel-optimal problem with the minimum thrust problem. Two new variables are introduced in the dynamic model. The first is a logarithm of mass variable and the second is an acceleration magnitude variable. The analytic expression of the logarithm of mass co-state is solved. For the time-optimal problem, initial co-state of logarithm of mass can be expressed by thrust magnitude and transfer time. Then, the number of unknown initial co-states decreased. The effectiveness and optimality of the proposed method is validated through simulations of two rendezvous missions.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 11872034).

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Correspondence to Zhaokui Wang.

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Li, T., Wang, Z. & Zhang, Y. A homotopy approach connecting time-optimal with fuel-optimal trajectories. Astrophys Space Sci 366, 11 (2021). https://doi.org/10.1007/s10509-020-03890-7

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Keywords

  • Fuel optimal
  • Low thrust
  • Homotopy method
  • Time-optimal