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

作　　者：Jian Ma ChangxuanWen Chen Zhang 

机构地区：[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

出　　处：《Computer Modeling in Engineering & Sciences》2021年第2期617-644,共28页工程与科学中的计算机建模（英文）

基　　金：supported by the National Key Research and Development Project(Grant No.2018YFB1900605);the Key Research Program of Chinese Academy of Sciences(Grant No.ZDRW-KT-2019-1).

摘　　要：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.

关 键 词：Trajectory optimization low thrust many revolutions orbital rendezvous sun-synchronous orbits 

分 类 号：V41[航空宇航科学与技术—航空宇航推进理论与工程]