空间科学与试验学报

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2022 , Vol. 22 >Issue 3: 26 - 36

DOI: https://doi.org/10.19963/j.cnki.2096-4099.2022.03.004

近地小行星防御问题中的几何力学与控制研究进展*

  • 刘世兴 ,
  • 史东华 ,
  • 陈菊 ,
  • 易中贵 ,
  • 王本亮 ,
  • 龚自正 ,
  • 郭永新
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  • 1.辽宁大学物理学院,沈阳 110036;
    2.辽宁大学空间科学与技术研究院,沈阳 110036;
    3.北京理工大学数学与统计学院,北京 100081;
    4.北京理工大学宇航学院,北京 100081;
    5.北京卫星环境工程研究所,北京 100094
刘世兴(1977—),男,主要研究方向:约束力学系统的几何动力学、几何数值积分方法与控制及相关研究。电子邮箱:liushixing@lnu.edu.cn
郭永新(1963—),男,主要研究方向:约束力学系统的几何动力学、对称性约化与几何控制及相关研究。 电子邮箱:yxguo@lnu.edu.cn

网络出版日期: 2023-12-11

基金资助

国家自然科学基金资助项目(11872030,12232009, 11972177,12202043,12272037,11872107);国防科工局民用航天技术预研项目(D020304);国防科工局空间碎片与近地小行星防御科研项目(KJSP2020020101)

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Advances on Geometric Mechanics and Control for Near-Earth Asteroid Defense

  • LIU Shi-xing ,
  • SHI Dong-hua ,
  • CHEN Ju ,
  • YI Zhong-gui ,
  • WANG Ben-liang ,
  • GONG Zi-zheng ,
  • GUO Yong-xin
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  • 1. College of Physics, Liaoning University, Shenyang 110036, China;
    2. Institute of Space Science and Technology, Liaoning University, Shenyang 110036, China;
    3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China;
    4. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
    5. Beijing Institute of Spacecraft Environment Engineering, Beijing 100094, China

Online published: 2023-12-11

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摘要

应对近地小行星撞击风险,开展小行星防御问题研究是未来国际天文界、航天界等多个领域所面临的重大科学和技术挑战。本文以面向近地小行星防御问题为背景,系统介绍了几何力学与控制研究及其在该领域的应用现状和前景,并根据小行星防御的实际问题,提出了“一来,二去,三绕,四控”的近地小行星防御策略和相关的亟待解决的科学问题,阐明了几何力学与控制在该防御策略下的重要作用,为近地小行星的防御理论提供了一种新的理论基础,为我国建设近地小行星防御系统提供理论参考。

关键词： 近地小行星; 几何力学与控制; Hamel场变分积分子; 轨道动力学; 探测/在轨处置航天器

本文引用格式

刘世兴 , 史东华 , 陈菊 , 易中贵 , 王本亮 , 龚自正 , 郭永新 . 近地小行星防御问题中的几何力学与控制研究进展*[J]. 空间科学与试验学报, 2022 , 22(3) : 26 -36 . DOI: 10.19963/j.cnki.2096-4099.2022.03.004

Abstract

Dealing with the risk of near-Earth asteroid (NEA) impact and conducting research on asteroid defense is a major scientific and technological challenge for the international astronomy, aerospace and other fields in the future.This paper systematically introduces the research on geometric dynamics and control and its application status and prospects in the field against the background of NEA defense.Based on the actual problems of asteroid defense, this paper proposes a NEA defense strategy of “Coming first, Going second, Circling third, Control fourth” and related scientific problems that need to be solved urgently, and clarifies the important role of geometric mechanics and control in this defense strategy, It provides a new theoretical basis for the near Earth asteroids defense, and a theoretical reference for the construction of defense system of NEA in China.

Key words： near-Earth asteroid; geometric mechanics and control; Hamel's field variational integrators; orbital dynamics; detection/active planetary defense spacecraft

参考文献

[1] 欧阳自远.奔走天地间-欧阳自远科普文选[M]. 北京:科学出版社,2014.
[2] Alvarez LW, Alvarez W, Asaro F, et al. Extraterrestrial cause for the Cretaceous Tertiary extinctions [J]. Science, 1980, 208: 1095-1108.
[3] Chyba, Christopher F, Paul J Thomas,et al.The 1908 Tunguska Explosion: atmospheric disruption of a stony asteroid [J].Nature, 1993, 361(6407): 40-44.
[4] Brown PG.et al.A 500-Kiloton Airburst over chelyabinsk and an enhanced hazard from small impactors [J]. Nature, 2013, 503(7475): 238-41.
[5] Popova, Olga P.et al.Chelyabinsk Airburst, Damage Assessment, Meteorite Recovery, and Characterization [J]. Science, 2013, 342(6162): 1069-73.
[6] http://asteronomy.com/news/2019/07/a large asteroid just zipped between Earth and the Moon.
[7] 吴伟仁, 龚自正, 唐玉华,等.近地小行星撞击风险应对战略研究[J].中国工程科学, 2022, 22(2):140-151.
[8] 龚自正, 李明, 陈川, 等.小行星监测预警、安全防御和资源利用的前沿科学问题及关键技术[J].科学通报, 2020, 65(5): 346-372.
[9] National Near Earth Object Preparedness Strategy and Action Plan, Whitehouse[EB/OL].https://www. whitehouse.gov./wpcontent/uploads,2018-06-15.
[10] http://cneos.jpl.gov/stats/.
[11] 刘林, 季江徽.近地小行星轨道演化的研究[J].天文学报, 2001, 42(1): 75-80.
[12] 胡寿村, 季江徽, 赵玉晖, 等.嫦娥二号飞越小行星试验中图塔蒂斯轨道确定与精度分析[J].中国科学: 技术科学, 2013(5): 506-511.
[13] 陈媛媛, 马月华.近地小行星(10302)1989ML和(4660)Nereus的轨道特征及演化分析[J].天文学报, 2021, 62(5): 29-52.
[14] 刘林, 季江徽, 廖新浩.近地小行星轨道演化的数值研究与辛算法有效性的探讨[J].天文学报, 1998, 39(2): 141-152.
[15] 李明涛, 郑建华, 于锡峥, 等.IPS转移轨道设计技术[J].宇航学报, 2009, 30(1): 10.
[16] 龚胜平, 李俊峰, 宝音贺西, 等.基于不变流形的登月轨道设计[J].应用数学和力学, 2007, 28(2): 8.
[17] 俞辉, 宝音贺西, 李俊峰.双三体系统不变流形拼接成的低成本探月轨道[J].宇航学报, 2007, 3: 6.
[18] 李翔宇, 乔栋, 程潏.三体轨道动力学研究进展[J].力学学报, 2021, 53(5): 1223-1245.
[19] 祁瑞, 徐世杰.椭圆三体问题中的时间周期不变流形[J].空间控制技术与应用, 2013, 39(2): 6-9.
[20] 祁瑞, 徐世杰.限制性四体问题中的时间相关不变流形[J].宇航学报, 2013, 34(8): 1055-1062.
[21] 李俊峰, 宝音贺西.深空探测中的动力学与控制[J].力学与实践, 2007, 29(4): 8.
[22] 钱航, 郑建华, 李明涛, 等.星际探测太阳帆行星和太阳借力轨道全局优化[J].国防科技大学学报, 2016, 38(1): 6.
[23] 刘延杰, 朱圣英, 崔平远.序列凸优化的小天体附着轨迹优化[J].宇航学报, 2018, 29(2): 7.
[24] Li Y, Guan Y, Wei C, et al.Optimal control of ascent trajectory for launch vehicles: A convex approach[J]. IEEE Access, 2019, 7: 186491-186498.
[25] Thompson G.Integrable almost cotangent structures and Legendrian bundles[J].Math.Proc.Camb. Phil.Soc., 1987, 101: 61-78.
[26] Arnold V I, Kozlov V V, Neishtadt A I.Mathematical Aspects of Classical and Celestial Mechanics[M]. Third Edition.Berlin: Springer-Verlag, 2006.
[27] 郭永新, 刘世兴.关于分析力学的基础与展望[J].动力学与控制学报, 2019, 17(5): 391-408.
[28] 郭永新, 罗邵凯, 梅凤翔.非完整系统几何动力学研究进展:Lagrange理论及其它[J].力学进展, 2004, 34(4):477-492.
[29] Abraham R, Marsden J E.Foundations of Mechanics[M].Second Edition.New Jersey: Addison-Wesley Publishing Company Inc., 1978.
[30] Marsden J E, Ratiu T S.Introduction to Mechanics and Symmetry[M].Second Edition.New York: Springer, 1999.
[31] Marsden J E, West M.Discrete mechanics and variational integrators[J].Acta Numerica, 2001, 10: 357-514.
[32] Bloch A M, Baillieul J, Marsden J E, et al. Nonholonomic Mechanics and Control[M].New York: Springer-Verlag, 2003.
[33] 冯康, 秦孟兆.哈密尔顿系统的辛几何算法[M].杭州: 浙江科学技术出版社, 2003.
[34] 冯康.冯康文集(第二卷)[M].北京: 科学出版社, 1993.
[35] Hairer E, Lubich C, Wanner G.Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations[M].Switzerland: Springer, 2002.
[36] Shi D H, Zenkov D V, Bloch A M.Hamel's formalism for infinite-dimensional mechanical systems[J]. Journal of Nonlinear Science, 2017, 27: 241-283.
[37] Shi D H, Zenkov D V, Bloch A M.Hamel's formalism for classical field theories[J].Journal of Nonlinear Science, 2020, 30(1): 1307-1353.
[38] Zenkov D, Leok M, Bloch A M.Hamel's Formalism and Variational Integrators on a Sphere. Proceedings of the 51st IEEE Conference on Decision and Control[C].USA, 2012:7504-7510
[39] 王亮.几何精确梁的Hamel场变分积分子[D].北京: 北京理工大学, 2016.
[40] Chen J, Huang Z H, Tian Q, A multisymplectic Lie algebra variational integrator for flexible multibody dynamics on the special Euclidean group SE (3)[J].Mechanism and Machine Theory, 2022, 174: 104918.
[41] 高山, 史东华, 郭永新.Hamel框架下几何精确梁的离散动量守恒律[J].力学学报, 2021, 53(6): 1712-1719.
[42] An Z P, Shi D H, Zenkov D V.A variational integrator for the Chaplygin-Timoshenko Sleigh[J].Journal of Nonlinear Science, 2020, 30: 1381-1419.
[43] 安志朋.Hamel场变分积分子及其应用[D].北京: 北京理工大学, 2020.
[44] Liu H, Shi D .Optimal control of a mobile robot on sphere.Theoretical and Applied Mechanics Letters, 2019,9(1):27-31
[45] Chirikjian G S.Degenerate diffusions and harmonic analysis on SE (3): a tutorial[C]. Workshop Classic and Stochastic Geometric Mechanics. Springer, Cham, 2015: 77-99.
[46] Scheeres D J.Orbital mechanics about small bodi-es[J]. Acta Astronautica, 2012, 72: 1-14.
[47] Rubincam D P.Radiative spin-up and spin-down of small asteroids[J].Icarus, 2000, 148(1): 2-11.
[48] Scheeres D J.Orbital Motion in Strongly Perturbed Environments: Applications to Asteroid, Comet and Planetary Satellite Orbiters[M].Berlin: Springer-Verlag, 2016.
[49] Werner R A, Scheeres D J.Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia[J].Celestial Mechanics and Dynamical Astronomy, 1996, 65(3): 313-344.
[50] Bolatti D A, de Ruiter A H.Inclusion of non-nonservative forces in geometric integrators with application to orbit-attitude coupling[J].Journal of Guidance, Control, and Dynamics, 2021, 44(7), 1266-1279.
[51] Hall J, Leok M.Spectral variational integrators[J].Numerische Mathematik, 2015, 130(4): 681-740.
[52] 于洋, 宝音贺西.小天体附近的轨道动力学研究综述[J].深空探测学报, 2014, 1(2): 12.
[53] 辛晓生.小行星探测器轨道动力学[D].南京: 南京大学, 2017.
[54] Lippe C E.Optimal Guidance and Control of Spacecraft Swarms in Planetary and Asteroid Orbits[M].Stanford University, 2021.
[55] Porter M A, Cvitanović P.Ground control to Niels Bohr: Exploring outer space with atomic physics[J].Notices of the American Mathematical Society, 2005, 52(9): 1020-1025.
[56] Koon W S, Lo M W, Marsden J E, et al.Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics[J].Chaos: An Interdisciplinary Journal of Nonlinear Science, 2000, 10(2): 427-469.
[57] Marsden J E, Ross S.New methods in celestial mechanics and mission design[J].Bulletin of the American Mathematical Society, 2006, 43(1): 43-73.
[58] Koon W S, Lo M W, Marsden J E, et al.Resonance and capture of Jupiter comets [J] , In: Pretka-Ziomek H, Wnuk E, Seidelmann P K, et al.(eds) Dynamics of Natural and Artificial Celestial Bodies.Springer, Dordrecht[EB/OL].https://doi.org/10.1007/978-94-017-1327-6_3,2001.
[59] Gómez G, Koon W S, Lo M W, et al.Connecting orbits and invariant manifolds in the spatial restricted three-body problem[J].Nonlinearity, 2004, 17(5): 1571-1606.
[60] Todorović N, Wu D, Rosengren A J.The arches of chaos in the solar system[J].Science advances, 2020, 6(48): eabd1313.
[61] Shadden S C, Lekien F, Marsden J E.Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows[J].Physica D: Nonlinear Phenomena, 2005, 212(3-4): 271-304.
[62] Moor A, Ober-Blöbaum S, Marsden J E, Trajectory design combining invariant manifolds with discrete mechanics and optimal control[J].Journal of Guidance, Control, and Dynamics, 2012, 35(5):1707-1525.
[63] Garcia I, How J P.Trajectory optimization for satellite reconfiguration maneuvers with position and attitude constraints[C].Proceedings of the 2005, American Control Conference, 2005.IEEE, 2005: 889-894.
[64] Kim D Y, Woo B, Park S Y, et al.Hybrid optimization for multiple-impulse reconfiguration trajectories of satellite formation flying[J].Advances in Space Research, 2009, 44(11): 1257-1269.
[65] Junge O, Ober-Blobaum S.Optimal reconfiguration of formation flying satellites[C]. Proceedings of the 44th IEEE Conference on Decision and Control.IEEE, 2005: 66-71.
[66] Milam M B, Petit N, Murray R M.Constrained trajectory generation for micro-satellite formation flying[C].AIAA Guidance, Navigation and Control Conference.2001: 328-333.
[67] Park H E, Park S Y, Choi K H.Satellite formation reconfiguration and station-keeping using state-dependent riccati equation technique[J].Aerospace Science and Technology, 2011, 15(6): 440-452.
[68] Sun C, Duan H, Shi Y.Optimal satellite formation reconfiguration based on closed-loop brain storm optimization[J].IEEE Computational Intelligence Magazine, 2013, 8(4): 39-51.
[69] Mahajan B, Vadali S R, Alfriend K T.Analytic solution for satellite relative motion with zonal gravity perturbations[C].Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Univelt, Inc., San Diego, CA, Advances in the Astronautical Sciences.2016, 156: 3583-3598.
[70] Guffanti T, Amico S D.Linear models for spacecraft relative motion perturbed by solar radiation pressure[J].Journal of Guidance, Control, and Dynamics, 2019, 42(9): 1962-1981.
[71] Gaias G, Lara M, Colombo C.Accurate osculating/mean orbital elements conversions for spaceborne formation flying[C].AIAC18: 18th Australian International Aerospace Congress (2019): HUMS-11th Defence Science and Technology (DST) International Conference on Health and Usage Monitoring (HUMS 2019): ISSFD-27th International Symposium on Space Flight Dynamics (ISSFD). Engineers Australia, Royal Aeronautical Society., 2019: 1171.
[72] Ely T A.Transforming mean and osculating elements using numerical methods[J].The Journal of the Astronautical Sciences, 2015, 62(1): 21-43.
[73] Zhong W, Gurfil P.Mean orbital elements estimation for autonomous satellite guidance and orbit control[J].Journal of Guidance, Control, and Dynamics, 2013, 36(6): 1624-1641.
[74] Efroimsky M.Gauge freedom in orbital mechanics[J].Annals of the New York Academy of Sciences, 2005, 1065(1): 346-374.
[75] Tillerson M, How J P.Advanced guidance algorithms for spacecraft formation-keeping[C].Proceedings of the 2002 American Control Conference (IEEE Cat.No.CH37301). IEEE, 2002, 4: 2830-2835.
[76] Wu B, Poh E K, Wang D, et al.Satellite formation keeping via real-time optimal control and iterative learning control[C].2009 IEEE Aerospace conference.IEEE, 2009: 1-8.
[77] Sparks A.Satellite formation keeping control in the presence of gravity perturbations[C].Proceedings of the 2000 American Control Conference.ACC(IEEE Cat.No.00CH36334). IEEE, 2000, 2: 844-848.
[78] Stansbery D, Cloutier J.Nonlinear control of satellite formation flight[C].AIAA Guidance, Navigation, and Control Conference and Exhibit.2000: 4436.
[79] Xing J, Tang G, Xi X, et al.Satellite formation design and optimal station keeping considering nonlinearity and eccentricity[J].Journal of Guidance, Control, and Dynamics, 2007, 30(5): 1523-1528.K
[80] He D L, Cao X B.Predictive control for satellite formation keeping[J].Journal of Systems Engineering and Electronics, 2008, 19(1): 161-166.
[81] Kang W, Sparks A, Banda S.Multi-satellite formation and reconfiguration[C].Proceedings of the 2000 American Control Conference.ACC (IEEE Cat.No. 00CH36334). IEEE, 2000, 1(6): 379-383.
[82] Koenig A W, D’Amico S.Robust and safe n-spacecraft swarming in perturbed near-circular orbits[J].Journal of Guidance, Control, and Dynamics, 2018, 41(8): 1643-1662.
[83] Yan H, Vadali S, Alfriend K.Formation maintenance and fuel balancing for satellites with implusive control[C].AIAA/AAS Astrodynamics Specialist Conference and Exhibit.2008: 7359.
[84] Zeng G, Hu M, Yao H.Relative orbit estimation and formation keeping control of satellite formations in low earth orbits[J].Acta Astronautica, 2012, 76: 164-175.
[85] Chen H, Sun J, Li K, et al.Autonomous spacecraft swarm formation planning using artificial field based on nonlinear bifurcation dynamics[C].AIAA Guidance, Navigation, and Control Conference. 2017: 1269.
[86] Saaj C M, Lappas V, Gazi V.Spacecraft swarm navigation and control using artificial potential field and sliding mode control[C]. 2006 IEEE international conference on industrial technology, 2006: 2646-2651.
[87] Huang H, Ma G, Lv Y, et al.Optimal spacecraft formation reconfiguration with collision avoidance using particle swarm optimization[J].Information Technology and Control, 2012, 41(2): 143-150.
[88] Zhang S, Duan H.Gaussian pigeon-inspired optimization approach to orbital spacecraft formation reconfiguration[J].Chinese Journal of Aeronautics, 2015, 28(1): 200-205.
[89] Wang J, Zhang J, Wang F, et al.Optimal satellite formation reconfiguration strategy based on relative orbital elements[J].Acta Astronautica, 2012, 76: 99-114.
[90] Chernick M, D’Amico S.New closed-form solutions for optimal impulsive control of spacecraft relative motion[J].Journal of Guidance, Control, and Dynamics, 2018, 41(2): 301-319.
[91] Steindorf L M, D' Amico S, Scharnagl J, et al. Constrained low-thrust satellite formation-flying using relative orbit elements[C].27th AAS/AIAA Space Flight Mechanics Meeting.2017, 160: 3563-3583.
[92] Morgan D, Chung S J, Blackmore L, et al.Swarm-keeping strategies for spacecraft under J2 and atmospheric drag perturbations[J].Journal of Guidance, Control, and Dynamics, 2012, 35(5): 1492-1506.
[93] Burnett E R, Schaub H.Spacecraft formation and orbit control using attitude-dependent solar radiation pressure[C].Proc.11th Int.Workshop Satell.Constellations Formation Flying (IWSCFF). 2019.
[94] Larbi M, Jusko T, Stoll E.Spacecraft formation feedforward control via differential drag using relative orbital elements[C].Proc.11th Int.Workshop Satellite Constellations Formation Flying (IWSCFF). 2019.
[95] Farrag A, Othman S, Mahmoud T, et al.Satellite swarm survey and new conceptual design for Earth observation applications[J].The Egyptian Journal of Remote Sensing and Space Science, 2021, 24(1): 47-54.
[96] Behrendt K, Fodero K.The perfect time: An examination of time-synchronization techniques [J].Publication, Schweitzer Engineering Laboratories, Inc, 2006: 1-18.
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