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Practical Optimization of Low-Thrust Minimum-Time Orbital Rendezvous in Sun-Synchronous Orbits

Jian Ma1,2, Changxuan Wen3, Chen Zhang2,*
1 University of Chinese Academy Sciences, Beijing, 100049, China
2 Key Laboratory of Space Utilization, Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing, 100094, China
3 School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China
* Corresponding Author: Chen Zhang. Email:

Computer Modeling in Engineering & Sciences 2021, 126(2), 617-644.

Received 30 September 2020; Accepted 12 November 2020; Issue published 21 January 2021


High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits. Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris. This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories, considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow. Firstly, a set of mean-element orbital dynamic equations of a chaser (spacecraft) and a target (debris) are derived by using the orbital averaging technique, and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem. Subsequently, the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle, and a practical optimization procedure is adopted to find the specific initial costate variables, wherein the necessary conditions of the optimal solutions are all satisfied. Afterwards, the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics. A simple correction strategy about the initialization of the mean elements, specifically the differential mean true longitude, is suggested, which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements. Finally, numerical examples are presented, and specifically, the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems, demonstrating the effectiveness of the optimization method proposed in this article.


Trajectory optimization; low thrust; many revolutions; orbital rendezvous; sun-synchronous orbits

Cite This Article

Ma, J., Wen, C., Zhang, C. (2021). Practical Optimization of Low-Thrust Minimum-Time Orbital Rendezvous in Sun-Synchronous Orbits. CMES-Computer Modeling in Engineering & Sciences, 126(2), 617–644.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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