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空间小推力轨道最优Bang-Bang控制的两类延拓解法综述

朱政帆 高扬

朱政帆, 高扬. 空间小推力轨道最优Bang-Bang控制的两类延拓解法综述[J]. 深空探测学报(中英文), 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
引用本文: 朱政帆, 高扬. 空间小推力轨道最优Bang-Bang控制的两类延拓解法综述[J]. 深空探测学报(中英文), 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
ZHU Zhengfan, GAO Yang. Survey of Two Classes of Continuation Methods for Solving Optimal Bang-Bang Control of Low-Thrust Space Trajectories[J]. Journal of Deep Space Exploration, 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
Citation: ZHU Zhengfan, GAO Yang. Survey of Two Classes of Continuation Methods for Solving Optimal Bang-Bang Control of Low-Thrust Space Trajectories[J]. Journal of Deep Space Exploration, 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001

空间小推力轨道最优Bang-Bang控制的两类延拓解法综述

doi: 10.15982/j.issn.2095-7777.2017.02.001
基金项目: 国家自然科学基金项目(11372311);中国科学院空间科学研究院培育项目;中国科学院国防科技创新基金项目(CXJJ-15M016)

Survey of Two Classes of Continuation Methods for Solving Optimal Bang-Bang Control of Low-Thrust Space Trajectories

  • 摘要: 介绍了空间小推力轨道优化问题中的最优Bang-Bang控制问题,对两类延拓解法给出了描述:第一类解法首先求解能量最优解,然后采用能量-燃耗同伦得到最优Bang-Bang控制;第二类解法引入推力开关切换准则,以双脉冲解作为初解,通过参数延拓得到最优Bang-Bang控制。对两类延拓解法进行了比较,指出了各自的优势与特点。对延拓方法应用于求解更加复杂的小推力轨道设计问题进行了展望,提出了包含初解、延拓与拼接三要素的人工智能轨道优化概念。
  • [1] Conway B A. Spacecraft trajectory optimization[M].UK:Cambridge University Press,2010.
    [2] Kemble S. Interplanetary mission analysis and design[M].Netherland:Springer Science & Business Media,2006.
    [3] Bryson A E,Ho Y. Applied optimal control:optimization,estimation and control[M]. Boca Raton:CRC Press,1975.
    [4] Gill P E,Murray W,Saunders M A,et al. User's guide for NPSOL(Version 4.0):a FORTRAN package for nonlinear programming[M]. USA:Department of Operations Research,Stanford University,1986.
    [5] Gill P E,Murray W,Saunders M A. SNOPT:an SQP algorithm for large-scale constrained optimization[J]. SIAM Review,2002,47:99-131.
    [6] Gill P E,Murray W,Saunders M A. User's guide for SNOPT version 7:software for large scale nonlinear programming[M]. Research Gate,2008.
    [7] Springer B. KNITRO:an integrated package for nonlinear optimization[J]. Large Scale Nonlinear Optimization,2010,83:35-59.
    [8] Betts J T. Survey of numerical methods for trajectory optimization[J]. Journal of Guidance,Control,and Dynamics,1998,21(2):193-207.
    [9] Rao A V. A survey of numerical methods for optimal control[J]. Advances in the Astronautical Sciences,2009,135(1):497-528.
    [10] 高扬. 电火箭星际航行:技术进展、轨道设计与综合优化[J]. 力学学报,2011,43(6):991-1019.Gao Y. Interplanetary travel with electric propulsion:technological progress,trajectory design,and comprehensive optimization[J]. Chinese Journal of Theoretical and Applied Mechanics,2011,43(6):991-1019.
    [11] 李俊峰,蒋方华. 连续小推力航天器的深空探测轨道优化方法综述[J]. 力学与实践,2011,33(3):1-6.Li J,Jiang F. Survey of low-thrust trajectory optimization methods for deep space exploration[J]. Mechanics in Engineering,2011,33(3):1-6.
    [12] Pontryagin L S,Boltyansky V G,Gamkrelidze R V,et al. The mathematical theory of optimal processes[M]. New York:Interscience Publishers,1962.
    [13] Bartholomew-Biggs M C,Dixon L C W,Hersom S E,et al. From high thrust to low thrust:an application of advanced optimisation methods to mission analysis[J]. ESA J.,1983,11:61-73.
    [14] Dixon L C W,Hersom S E,Maany Z A. Low thrust orbit optimisation for interplanetary missions[R]. The Hatfield Polytechnic:Technical Report 137,Numerical Optimisation Centre,1983.
    [15] Dixon L C W,Maany Z A. To bus and back[C]//ESA Proceedings of the Second International Symposium on Spacecraft Flight Dynamics. Darmstadt,Germany:ESA,1986.
    [16] Bartholomew-Biggs M C,Dixon L C W,Hersom S E,et al. The solution of some difficult problems in low-thrust interplanetary trajectory optimization[J]. Optimal Control Applications and Methods,1988,9:229-251.
    [17] Oberle H J,Taubert K. Existence and multiple solutions of the minimum-fuel orbit transfer problem[J]. Journal of Optimization Theory and Applications,1997,95(2):243-262.
    [18] Fowler W T,O'Neill P M. Relationship between coast arc length and switching function value during optimization[J]. Journal of Spacecraft and Rockets,1976,3(7):445-446.
    [19] Chuang C H,Goodson T,Hanson J. Fuel-optimal,low-and medium-thrust orbit transfers in large numbers of burns[C]//AIAA 94-3650,Guidance,Navigation,and Control Conference.USA:AIAA,1994.
    [20] Chuang J C H,Goodson T D,Hanson J. Multiple-burn families of optimal low-and medium-thrust orbit transfers[J]. Journal of Spacecraft and Rockets,1999,36(6):866-874.
    [21] Redding D C. Highly efficient,very low-thrust transfer to geosynchronous orbit-Exact and approximate solutions[J]. Journal of Guidance,Control,and Dynamics,1984,7(2):141-147.
    [22] Redding D,Breakwell J V. Optimal low-thrust transfers to synchronous orbit[J]. Journal of Guidance,Control,and Dynamics,1984,7(2):148-155.
    [23] Gao,Y. Near-optimal very low-thrust Earth-orbit transfers and guidance schemes[J]. Journal of Guidance,Control,and Dynamics,2007,30(2):529-539.
    [24] Zuiani F,Vasile M. Preliminary design of debris removal missions by means of simplified models for low-thrust,many-revolution transfers[J]. International Journal of Aerospace Engineering,2012.
    [25] Goodson T,Chuang J C H,Hanson J,et al. Optimal finite thrust orbit transfers with large numbers of burns[J]. Journal of Guidance,Control,and Dynamics,1999,22(1):139-148.
    [26] Bai X,Turner J D,Junkins J L. A robust homotopy method for equality constrained nonlinear optimization[C]//AIAA 2008-5845,12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Columbia:AIAA,2008.
    [27] Bai X,Turner J D,Junkins J L. Optimal thrust design of a mission to apophis based on a homotopy method[C]//AAS/AIAA Spaceflight Mechanics Meeting. Georgia:AIAA,2009.
    [28] Bai X,Turner J D,Junkins J L. Bang-Bang control design by combing pseudospectral method with a novel homotopy algorithm[C]//AIAA Guidance,Navigation,and Control Conference and Control Conference.[S.l.]:AIAA,2009.
    [29] Shan J,Ren Y. Low-thrust trajectory design with constrained particle swarm optimization[J]. Aerospace Science and Technology,2014,36:114-124.
    [30] Darby C L,Hager W W,Rao A V. Direct trajectory optimization using a variable low-order adaptive pseudospectral method[J]. Journal of Spacecraft and Rockets,2011,48(3):433-445.
    [31] Zondervan K P. Optimal low thrust,three burn orbit transfers with large plane changes[D]. California:California Institute of Technology,1983.
    [32] Zondervan K P,Wood L J,Caughey T K. Optimal low-thrust,three-burn orbit transfers with large plane changes[J]. Journal of the Astronautical Sciences,1984,32(3):407-427.
    [33] Ilgen M R. Hybrid method for computing optimal low thrust OTV trajectories[J]. Advances in the Astronautical Sciences,1994,87(2):941-958.
    [34] Kluever C A,Pierson B L. Optimal Low-Thrust Three-Dimensional Earth-Moon trajectories[J]. Journal of Guidance,Control,and Dynamics,1995,18(4):830-837.
    [35] Gao Y,Kluever C A. Low-thrust interplanetary orbit transfers using hybrid trajectory optimization method with multiple shooting[C]//AIAA/AAS Astrodynamics Specialist Conference and Exhibit,Providence. Rhode Island:AIAA,2004.
    [36] Bertrand R.,Epenoy R. New smoothing techniques for solving bang-bang optimal control problems:numerical results and statistical interpretation[J]. Optimal Control Applications and Methods,2002,23(4):171-197.
    [37] Haberkorn T,Martinon P,Gergaud J. Low thrust minimum-fuel orbital transfer:a homotopic approach[J]. Journal of Guidance,Control,and Dynamics,2004,27(6):1046-1060.
    [38] Gergaud,J,Haberkorn T. Homotopy method for minimum consumption orbit transfer problem[J]. ESAIM:Control,Optimization,and Calculus of Variations,2006,12(2):294-310.
    [39] Gergaud J,Haberkorn T. Orbital transfer:some links between the low-thrust and the impulse cases[J]. Acta Astronautica,2007,60(8-9):649-657.
    [40] Martinon P,Gergaud J. Using switching detection and variational equations for the shooting method[J]. Optimal Control Applications and Methods,2007,28(2):95-116.
    [41] Petukhov V G. Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method[J]. Cosmic Research,2008,46(3):219-232.
    [42] Petukhov V G. Method of continuation for optimization of inth Capabilities of Indirect Methods for Impulsive Transfers[J]. The Journal of the Astronautical Sciences,2015,62(3):212-232.
    [43] Shen H X,Casalino L,Li H Y. Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem[J]. Optimal Control Applications and Methods,2015,36(4):463-474.
    [44] Shen H X,Casalino L. Indirect optimization of three-dimensional multiple-impulse Moon-to-Earth transfers[J]. The Journal of the Astronautical Sciences,2014,61(3):255-274.teroid tour missions[J]. Journal of Guidance,Control,and Dynamics,2011,34(6):1709-1720.
    [45] Guo T,Jiang F,Baoyin H,et al. Fuel optimal low thrust rendezvous with outer planets via gravity assist[J]. Science China:Physics,Mechanics and Astronomy,2011,54(4):756-769.
    [46] Guo T,Jiang F,Li J. Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization[J]. Acta Astronautica,2012,71:38-50.
    [47] Jiang F,Baoyin H,Li J. Practical Techniques for low-thrust trajectory optimization with homotopic approach[J]. Journal of Guidance,Control,and Dynamics,2012,35(1):245-258.
    [48] Li J,Xi X-N. Fuel-optimal low-thrust reconfiguration of formation-flying satellites via homotopic approach[J]. Journal of Guidance,Control,and Dynamics,2012,35(6):1709-1717.
    [49] Tarzi Z,Speyer J,Wirz R. Fuel optimum low-thrust elliptic transfer using numerical averaging[J]. Acta Astronautica,2013,86:95-118.
    [50] Zhang P,Li J,Baoyin H,Tang G. A low-thrust transfer between the Earth-Moon and Sun-Earth systems based on invariant monifolds[J]. Acta Astronautica,2013,91:77-88.
    [51] Chen Y,Baoyin H,Li J. Accessibility of main-belt asteroids via gravity assists[J]. Journal of Guidance,Control,and Dynamics,2014,37(2):623-632.
    [52] Zhang P,Li J,Gong S. Fuel-optimal trajectory design using solar electric propulsion under power constraints and performance degradation[J]. Science China Physics,Mechanics & Astronomy,2014,57(6):1090-1097.
    [53] Zhang C,Topputo F,Bernelli-Zazzera F,et al. Low-thrust minimum-fuel optimization in the circular restricted three-body problem[J]. Journal of Guidance,Control,and Dynamics,2015,38(8):1501-1510.
    [54] 张晨,赵育善. 混合推进最省燃料轨道设计方法[J]. 宇航学报,2015,36(8):869-876.Zhang C,Zhao Y. A method for hybrid propulsion minimum fuel trajectory optimization[J]. Journal of Astronautics,2015,36(8):869-876.
    [55] 陆毅,李济生,李恒年,等. 基于星历匹配法的载人小行星探测轨迹优化问题求解[J]. 力学与实践,2014,36(2):172-179.Lu Y,Li J,Li H,et al. Problem solving of the manned asteroids exploration trajectory optimization based on ephemeris matching method[J]. Mechanics in Engineering,2014,36(2):172-179.
    [56] 黄岸毅,车征,李恒年,等. 有限推力多小行星探测轨迹优化[J]. 力学与实践,2015,37(1):49-55.Huang A,Che Z,Li H,et al. Low-thrust trajectory optimization for multi-asteroid exploration[J]. Mechanics in Engineering,2015,37(1):49-55.
    [57] 朱小龙,刘迎春,高扬. 航天器最优受控绕飞轨迹推力幅值延拓设计方法[J]. 力学学报,2014,46(5):756-769.Zhu X,Liu Y,Gao Y. Thrust-amplitude continuation design approach for solving spacecraft optimal controlled fly-around trajectory[J]. Chinese Journal of Theoretical and Applied Mechanics,2014,46(5):756-769.
    [58] 朱小龙,马剑,刘强,等. 月面远程运输飞行轨迹优化设计[J]. 载人航天,2015,21(1):75-82.Zhu X,Ma J,Liu Q,Gao Y. Optimization design of long-range transport flight trajectories on lunar surface[J]. Manned Spaceflight,2015,21(1):75-82.
    [59] Battin,R.H. An introduction to the mathematics and methods of astrodynamics[M].[S.l.]:AIAA Education Series,1987.
    [60] 朱政帆,甘庆波. 第七届全国空间轨道设计竞赛乙组解法[J]. 力学与实践,2016,38(5):596-602.Zhu Z,Gan Q. 7th National space trajectory design competition:results of problem B[J]. Mechanics in Engineering,2016,38(5):596-602.
    [61] 孟雅哲. 航天器燃耗最优轨道直接/间接混合法延拓求解[J]. 航空学报,2017,38(1):259-280.Meng Y. Minimum-fuel spacecraft transfer trajectories solved by direct/indirect hybrid method with continuation[J]. Acta Aeronautica et Astronautica Sinica,2017,38(1):259-280.
    [62] Zhu Z,Gao Y,Yang X,et al. Solving fuel-optimal low-thrust orbital transfers with bang-bang control using a novel continuation technique[J]. Acta Astronautica,accepted.
    [63] Shen H X,Casalino L,Luo Y Z. Global Searc������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
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出版历程
  • 收稿日期:  2017-01-10
  • 修回日期:  2017-03-29
  • 刊出日期:  2017-04-01

空间小推力轨道最优Bang-Bang控制的两类延拓解法综述

doi: 10.15982/j.issn.2095-7777.2017.02.001
    基金项目:  国家自然科学基金项目(11372311);中国科学院空间科学研究院培育项目;中国科学院国防科技创新基金项目(CXJJ-15M016)

摘要: 介绍了空间小推力轨道优化问题中的最优Bang-Bang控制问题,对两类延拓解法给出了描述:第一类解法首先求解能量最优解,然后采用能量-燃耗同伦得到最优Bang-Bang控制;第二类解法引入推力开关切换准则,以双脉冲解作为初解,通过参数延拓得到最优Bang-Bang控制。对两类延拓解法进行了比较,指出了各自的优势与特点。对延拓方法应用于求解更加复杂的小推力轨道设计问题进行了展望,提出了包含初解、延拓与拼接三要素的人工智能轨道优化概念。

English Abstract

朱政帆, 高扬. 空间小推力轨道最优Bang-Bang控制的两类延拓解法综述[J]. 深空探测学报(中英文), 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
引用本文: 朱政帆, 高扬. 空间小推力轨道最优Bang-Bang控制的两类延拓解法综述[J]. 深空探测学报(中英文), 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
ZHU Zhengfan, GAO Yang. Survey of Two Classes of Continuation Methods for Solving Optimal Bang-Bang Control of Low-Thrust Space Trajectories[J]. Journal of Deep Space Exploration, 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
Citation: ZHU Zhengfan, GAO Yang. Survey of Two Classes of Continuation Methods for Solving Optimal Bang-Bang Control of Low-Thrust Space Trajectories[J]. Journal of Deep Space Exploration, 2017, 4(2): 101-110. doi: 10.15982/j.issn.2095-7777.2017.02.001
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