基于弹道逃逸和小推力捕获的地月转移轨道设计
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摘要
针对地月空间货运任务和环月轨道空间设施建设任务,提出一种弹道逃逸和小推力捕获相结合的新型地月轨道转移模式,并建立了一整套该类型轨道设计方法。首先,在三体模型假设下分别建立地心弹道逃逸轨道和月心小推力捕获轨道的二维极坐标动力学模型。对于弹道逃逸轨道,将地心旋转系对准角和地月转移加速速度增量作为控制变量,提出初值估计解析公式,并应用序列二次规划算法进行快速求解。对于小推力捕获轨道,以月心距为参考量设置与弹道逃逸轨道的拼接点约束,提出能量匹配方法预估飞行时间,采用最优螺旋轨道的初始伴随状态解析式预估近月点伴随变量初值。基于混合法和轨道逆推思想,采用人工免疫算法进行小推力捕获轨道求解。仿真结果表明,基于弹道逃逸和小推力捕获的地月轨道转移方式大幅降低了近月制动燃料消耗,能快速穿越地球辐射带,且飞行时间适中;同时,提出的轨道设计方法能快速搜索到基于弹道逃逸和小推力捕获的地月转移轨道,验证了该方法的有效性。
Considering the mission of cargo delivery in the cislunar space and the mission of space facility construction in the circumlunar orbit,a new Earth-Moon orbit transfer mode based on ballistic escape and low-thrust capture is proposed,and a complete set of design method for this type of trajectory is established.First,the two-dimensional polar coordinate dynamics models for the geocentric ballistic escape trajectory and the selenocentric low-thrust capture trajectory are established respectively based on the hypothesis of three-body model.For the ballistic escape trajectory,the alignment angle in the geocentric rotating frame and the velocity increment of trans-lunar injection are selected as control variables,analytic formulas for initial value estimation are proposed,and the sequential quadratic programming algorithm is applied to quickly search this trajectory.For the low-thrust capture trajectory,selenocentric distance is considered as reference quantity to set the splicing point constraints with ballistic escape trajectory,an energy matching method is proposed to estimate the flight time,and the initial values of adjoint variables in perilune are estimated by using analytic formulas of initial adjoint states for optimal spiral trajectory.Based on the hybrid method and backward orbit propagate,the artificial immune algorithm is used to solve the low-thrust capture trajectory.Simulation results show that the Earth-Moon orbit transfer based on ballistic escape and lowthrust capture can significantly reduce fuel consumption of lunar orbit insertion,and can fly through the radiation belts of Earth quickly with moderate flight time.The trajectory design method proposed in this paper can rapidly search the trans-lunar trajectory with ballistic escape and low-thrust capture,validating the effectiveness of this method.
Considering the mission of cargo delivery in the cislunar space and the mission of space facility construction in the circumlunar orbit,a new Earth-Moon orbit transfer mode based on ballistic escape and low-thrust capture is proposed,and a complete set of design method for this type of trajectory is established.First,the two-dimensional polar coordinate dynamics models for the geocentric ballistic escape trajectory and the selenocentric low-thrust capture trajectory are established respectively based on the hypothesis of three-body model.For the ballistic escape trajectory,the alignment angle in the geocentric rotating frame and the velocity increment of trans-lunar injection are selected as control variables,analytic formulas for initial value estimation are proposed,and the sequential quadratic programming algorithm is applied to quickly search this trajectory.For the low-thrust capture trajectory,selenocentric distance is considered as reference quantity to set the splicing point constraints with ballistic escape trajectory,an energy matching method is proposed to estimate the flight time,and the initial values of adjoint variables in perilune are estimated by using analytic formulas of initial adjoint states for optimal spiral trajectory.Based on the hybrid method and backward orbit propagate,the artificial immune algorithm is used to solve the low-thrust capture trajectory.Simulation results show that the Earth-Moon orbit transfer based on ballistic escape and lowthrust capture can significantly reduce fuel consumption of lunar orbit insertion,and can fly through the radiation belts of Earth quickly with moderate flight time.The trajectory design method proposed in this paper can rapidly search the trans-lunar trajectory with ballistic escape and low-thrust capture,validating the effectiveness of this method.
引文
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[2]CODERRE K,RICHEY D,PRATT W,et al.International,scientific,and commercial opportunities enabled by the deep space gateway[C]∥68th International Astronautical Congress,2017:IAC-17-A5.1.5.
[3]LOW G M.Apollo 11 mission report:MSC-00171[R].Washington,D.C.:NASA,1969.
[4]周文艳,杨维廉.嫦娥二号卫星轨道设计[J].航天器工程,2010,19(5):24-28.ZHOU W Y,YANG W L.Orbit design for Chang’e-2lunar orbiter[J].Spacecraft Engineering,2010,19(5):24-28(in Chinese).
[5]BETTS J T,ERB S O.Optimal low thrust trajectories to the Moon[J].SIAM Journal of Applied Dynamical Systems,2003,2(2):144-170.
[6]PENG Q B,SHEN H X,LI H Y.Free return orbit design and characteristics analysis for manned lunar mission[J].Science China,Technological Sciences,2011,54(12):3243-3250.
[7]JESICK M,OCAMPO C.Automated generation of symmetric lunar free-return trajectories[J].Journal of Guidance,Control,and Dynamics,2011,34(1):98-106.
[8]HOU X Y,ZHAO Y H,LIU L.Free return trajectories in lunar mission[J].Chinese Astronomy and Astrophysics,2013,37:183-194.
[9]李立涛,张振民,杨涤.奔月转移轨道的快速设计方法研究[J].航空学报,2003,24(2):152-156.LI L T,ZHANG Z M,YANG D.Study of rapid design method for cislunar transfer trajectory[J].Acta Aeronautica et Astronautica Sinica,2003,24(2):152-156(in Chinese).
[10]LUO Q Q,YIN J F,HAN C.Design of Earth-Moon freereturn trajectories[J].Journal of Guidance,Control,and Dynamics,2013,36(1):263-271.
[11]高玉东,郗晓宁,王威.地月空间飞行轨道分层搜索设计[J].宇航学报,2006,27(6):1157-1161.GAO Y D,XI X N,WANG W.Cislunar trajectory design using searching step by step method[J].Journal of Astronautics,2006,27(6):1157-1161(in Chinese).
[12]PENG K,YIM S Y,ZHANG B N,et al.Fast search algorithm of high-precision Earth-Moon free-return trajectory[C]∥AAS/AIAA Astrodynamics Specialist Conference and Exhibit,2015.
[13]贺波勇,沈红新,李海阳.地月转移轨道设计的改进微分校正方法[J].国防科技大学学报,2014,36(6):60-64.HE B Y,SHEN H X,LI H Y.An improved differential correction method for trans-lunar orbit design[J].Journal of National University of Defense Technology,2014,36(6):60-64(in Chinese).
[14]RANIERI C L,OCAMPO C A.Indirect optimization of low Earth orbit to low Lunar orbit transfers[C]∥AIAA/AAS Astrodynamics Specialist Conference and Exhibit.Reston,VA:AIAA,2018.
[15]LEE D,BANG H.Optimal Earth-Moon trajectory design using new initial costate estimation method[J].Journal of Guidance,Control,and Dynamics,2012,35(5):1671-1675.
[16]PIERSON B L,KLUEVER C A.Three-stage approach to optimal low-thrust Earth-Moon trajectories[J].Journal of Guidance,Control,and Dynamics,1994,17(6):1275-1282.
[17]GAO Y.Earth-Moon trajectory optimization using solar electric propulsion[J].Chinese Journal of Aeronautics,2007,20(5):452-463.
[18]徐明,徐世杰.小推力航天器的地月低能转移轨道[J].航空学报,2008,29(4):781-787.XU M,XU S J.Low-energy trajectory from Earth to Moon for low-thrust spacecraft[J].Acta Aeronautica et Astronautica Sinica,2008,29(4):781-787(in Chinese).
[19]贺波勇.载人登月转移轨道偏差传播分析与中途修正方法研究[D].长沙:国防科技大学,2006:49-53.HE B Y.Analysis of transfer orbit deviation propagation and mid-course correction for manned lunar landing[D].Changsha:National University of Defense Technology,2006:49-53(in Chinese).
[20]GILL P E,MURRAY W,SAUNDERS M A.SNOPT:An SQP algorithm for large-scale constrained optimization[J].SIAM Review,2005,47(1):99-131.
[21]彭坤,徐世杰,果琳丽,等.基于人工免疫算法的地球-火星小推力转移轨道优化[J].中国空间科学技术,2012,32(5):61-68.PENG K,XU S J,GUO L L,et al.Optimization of Earth-Mars low-thrust trajectory based on artificial immune algorithm[J].Chinese Space Science and Technology,2012,32(5):61-68(in Chinese).