深空机动对运载火箭发射火星探测轨道研究
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摘要
为解决长征(LM)运载火箭发射火星探测器转移轨道时,因低温入轨级最长允许滑行时间及测控限制,有效发射日期窗口亟需拓展的问题,采用主矢量理论结合序列二次规划算法(SQP),研究了探测器深空机动(DSM)对优化运载火箭发射火星转移轨道的作用。在发射直接转移火星探测轨道算法基础上,重点研究了包含引力影响球(SOI)内近地及近火飞行段后,采用主矢量获取深空机动最优猜测初值的分析算法,通过直接使用探测器近火点目标轨道参数优化运载火箭发射轨道,研究对比不同优化目标及设计约束下深空机动的分析结果,证实深空机动对降低转移轨道总发射能量需求、拓展发射日期窗口的高效性;该算法已应用于工程设计。
In order to resolve the problems of extending the effective launch periods, resulting from the Earth-to-Mars trajectory design of a Long March(LM) launch vehicle constrained by the longest coasting phase and tracking & telecommunication, the primer vector theory and sequence quadratic program(SQP) are used to study the influence of the deep space maneuver(DSM) of a Mars probe on the optimization of the launch vehicle's Earth-to-Mars trajectory. A brief analysis on the direct Earth-to-Mars trajectory design is given firstly, then details of the algorithm on how to get the optimal initial guess values on DSM through the primer vector theory are studied, including the flight phases inside each gravitational sphere of influence(SOI). Furthermore, with SQP, the launch trajectories via DSM are optimized using the final orbital parameters of the Mars probe directly. The research based on different optimal aims including the design constraints shows that DSM is highly effective to lower the overall launch energy of the Earth-to-Mars transfer trajectory, and to extend the launch periods under the restriction of the longest coasting phase during the parking orbit of the LM launch vehicle. The algorithm has been used in engineering.
In order to resolve the problems of extending the effective launch periods, resulting from the Earth-to-Mars trajectory design of a Long March(LM) launch vehicle constrained by the longest coasting phase and tracking & telecommunication, the primer vector theory and sequence quadratic program(SQP) are used to study the influence of the deep space maneuver(DSM) of a Mars probe on the optimization of the launch vehicle's Earth-to-Mars trajectory. A brief analysis on the direct Earth-to-Mars trajectory design is given firstly, then details of the algorithm on how to get the optimal initial guess values on DSM through the primer vector theory are studied, including the flight phases inside each gravitational sphere of influence(SOI). Furthermore, with SQP, the launch trajectories via DSM are optimized using the final orbital parameters of the Mars probe directly. The research based on different optimal aims including the design constraints shows that DSM is highly effective to lower the overall launch energy of the Earth-to-Mars transfer trajectory, and to extend the launch periods under the restriction of the longest coasting phase during the parking orbit of the LM launch vehicle. The algorithm has been used in engineering.
引文
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[21] 耿光有,李东.运载火箭一级飞行段底部力的机理分析[J].导弹与航天运载技术,2015(2):67-71.[Geng Guang-you,Li Dong.Mechanism analysis of rocket’s base-force during the 1st stage flight phase[J].Missiles and Space Vehicles,2015(2):67-71.]
[22] Hu W D.Fundamental spacecraft dynamics and control[M].Singapore:Wiley,2015.
[23] 刘林,侯锡云.深空探测器轨道力学[M].北京:电子工业出版社,2015.
[24] Vallado D A.Fundamentals of astrodynamics and applications [M].New York:Microcosm Press,2013.
[25] Vavrina M A,Englander J A,Ellison D H.Global optimization of n-maneuver,high-thrust trajectories using direct multiple shooting[EB/OL].2016[2019].https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20160001644.pdf.
[26] Bryson A E,Ho Y.Applied optimal control,optimization,estimation,and control [M].London:Taylor & Francis,1975.
[27] George L E,Kos L D.Interplanetary mission design handbook:Earth-to-Mars mission opportunities and Mars-to-Earth return opportunities 2009-2024[R].Maryland,United States:NASA Center for AeroSpace Information,July 1998.
[2] 褚桂敏.低温上面级滑行段的推进剂管理续[J].导弹与航天运载技术,2007(2):24-29.[Chu Gui-min.Propellant management of cryogenic upper stage during coast(Continue)[J].Missiles and Space Vehicles,2007(2):24-29.]
[3] Geng G Y,Wang J,Song Q,et al.Analysis of typical Earth-Mars launch trajectory on mission profiles and launch window extension[J].Missiles and Space Vehicles,2018(1):18-23,31.
[4] Fimple W R.Optimal midcourse plane changes for ballistic interplanetary trajectories[J].AIAA Journal,1971,1(2):430-434.
[5] 耿长福.航天动力学[M].北京:中国科学技术出版社,2006.
[6] 戴光明.行星际脉冲转移轨道设计与优化算法[M].武汉:中国地质大学出版社,2012.
[7] Lawden D F.Optimal trajectories for space navigation [M].London:Butterworths,1963.
[8] Lion P M,Handelsman M.Primer vector on fixed-time impulsive trajectories[J].AIAA Journal,1968,6(1):127-132.
[9] Jezewski D J,Rozendaal H L.An efficient method for calculating optimal free-space n-impulse trajectories[J].AIAA Journal,1968,6(11):2160-2165.
[10] Jezewski D J.Primer vector theory and applications[R].Washington D C,USA:NASA,November 1975.
[11] Conway B A.Spacecraft trajectory optimization[M].Cambridge:Cambridge University Press,2010.
[12] Iorfida E,Palmer P L,Roberts M.AHamiltonian approach to the planar optimization of mid-course corrections[J].Celest.Mech.Dyn.Astr.,2016(124):367-383.
[13] Glandorf D R.Primer vector theory for matched-conic trajectories[J].AIAA Journal,1970,8(1):155-156.
[14] Battin R.H.An introduction to the mathematics and methods of astrodynamics revised[M].New York:AIAA,1999.
[15] Navagh J.Optimizing interplanetary trajectories with deep space maneuvers[R].Washington D C,USA:George Washington University,1993.
[16] Olympio J T,Marmorat JP.Global trajectory optimization:can we prune the solution space when considering deep space maneuvers?[EB/OL].2008[2018].https://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-MAD-ARI-06-4101-CanWePrune-Ecole-des-Mines.pdf.
[17] 乔栋,崔平远,尚海滨.星际探测多脉冲转移发射机会搜索方法研究[J].北京理工大学学报,2010,30(3):275-278,347.[Qiao Dong,Cui Ping-yuan,Shang Hai-bin.Searching launch opportunity of multiple impulsive transfer for interplanetary mission[J].Transactions of Beijing Institute of Technology,2010,30(3):275-278,347.]
[18] 沈红新.脉冲推力最优轨迹的Hamilton边值问题[J].宇航学报,2017,38(7):686-693.[Shen Hong-xin.Hamilton boundary value problem for optimal impulsive trajectory[J].Journal of Astronautics,2017,38(7):686-693.]
[19] 潘迅,杨瑞,泮斌峰,等.平动点双脉冲转移轨道的快速计算方法[J].宇航学报,2017,38(6):574-582.[Pan Xun,Yang Rui,Pan Bin-feng,et al.An efficient calculation method for two-impulse transfers to libration point[J].Journal of Astronautics,2017,38(6):574-582.]
[20] 赵瑞安.深空探测轨道设计和分析[M].北京:中国宇航出版社,2018.
[21] 耿光有,李东.运载火箭一级飞行段底部力的机理分析[J].导弹与航天运载技术,2015(2):67-71.[Geng Guang-you,Li Dong.Mechanism analysis of rocket’s base-force during the 1st stage flight phase[J].Missiles and Space Vehicles,2015(2):67-71.]
[22] Hu W D.Fundamental spacecraft dynamics and control[M].Singapore:Wiley,2015.
[23] 刘林,侯锡云.深空探测器轨道力学[M].北京:电子工业出版社,2015.
[24] Vallado D A.Fundamentals of astrodynamics and applications [M].New York:Microcosm Press,2013.
[25] Vavrina M A,Englander J A,Ellison D H.Global optimization of n-maneuver,high-thrust trajectories using direct multiple shooting[EB/OL].2016[2019].https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20160001644.pdf.
[26] Bryson A E,Ho Y.Applied optimal control,optimization,estimation,and control [M].London:Taylor & Francis,1975.
[27] George L E,Kos L D.Interplanetary mission design handbook:Earth-to-Mars mission opportunities and Mars-to-Earth return opportunities 2009-2024[R].Maryland,United States:NASA Center for AeroSpace Information,July 1998.