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Multi-objective transfer to libration-point orbits via the mixed low-thrust and invariant-manifold approach

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Abstract

The multi-objective optimization of transfer trajectories from an orbit near Earth to a periodic libration-point orbit in the Sun–Earth system using the mixed low-thrust and invariant-manifold approach is investigated in this paper. A two-objective optimization model is proposed based on the mixed low-thrust and invariant-manifold approach. The circular restricted three-body model (CRTBP) is utilized to represent the motion of a spacecraft in the gravitational field of the Sun and Earth. The transfer trajectory is broken down into several segments; both low-thrust propulsion and stable manifolds are utilized based on the CRTBP in different segments. The fuel cost, which is generated only by the low-thrust trajectory for transferring the spacecraft from an orbit near Earth to a stable manifold, is minimized. The total flight time, which includes the time during which the spacecraft is controlled by the low-thrust trajectory and the time during which the spacecraft is moving on the stable manifold, is also minimized. Using the nondominated sorting genetic algorithm for the resulting multi-objective optimization problem, highly promising Pareto-optimal solutions for the transfer of the spacecraft are found. Via numerical simulations, it is shown that tradeoffs between time of flight and fuel cost can be quickly evaluated using this approach. Furthermore, for the same time of flight, transfer trajectories based on the mixed-transfer method can save a larger amount of fuel than the low-thrust method alone.

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Acknowledgments

The authors are grateful to the financial supports of the National Science Foundation of China (11102031), the Fundamental Research Funds for the Central Universities (DUT13LK25), Program Funded by Liaoning Province Education Administration (L2013015) and the State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0114G02).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

    Haijun Peng & Biaosong Chen

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, 116024, China

    Zhigang Wu

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  1. Haijun Peng
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  2. Biaosong Chen
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  3. Zhigang Wu
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Correspondence to Haijun Peng.

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Peng, H., Chen, B. & Wu, Z. Multi-objective transfer to libration-point orbits via the mixed low-thrust and invariant-manifold approach. Nonlinear Dyn 77, 321–338 (2014). https://doi.org/10.1007/s11071-014-1296-2

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  • DOI: https://doi.org/10.1007/s11071-014-1296-2

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