电子电气工程与控制

再入滑翔机动突防轨迹规划与制导方法综述

  • 闫循良 ,
  • 王培臣 ,
  • 郭杨
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  • 1.西北工业大学 航天学院,西安 710072
    2.陕西省空天飞行器设计重点实验室,西安 710072
    3.火箭军工程大学 智控重点实验室,西安 710072

收稿日期: 2025-01-15

  修回日期: 2025-02-18

  录用日期: 2025-03-31

  网络出版日期: 2025-04-07

基金资助

国家自然科学基金(11602296);智控实验室开放基金资助(ICL-2023-0402)

Review of trajectory planning and guidance methods for entry glide maneuvering penetration

  • Xunliang YAN ,
  • Peichen WANG ,
  • Yang GUO
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  • 1.School of Astronautics,Northwestern Polytechnical University,Xi’an 710072,China
    2.Shaanxi Aerospace Flight Vehicle Design Key Laboratory,Xi’an 710072,China
    3.Laboratory of Intelligent Control,Rocket Force University of Engineering,Xi’an 710072,China

Received date: 2025-01-15

  Revised date: 2025-02-18

  Accepted date: 2025-03-31

  Online published: 2025-04-07

Supported by

National Natural Science Foundation of China(11602296);Open Fund of Intelligent Control Laboratory(ICL-2023-0402)

摘要

随着新型防空反导技术的不断发展,再入滑翔飞行器面临多层次、多平台、多批次的防御体系威胁,其生存和任务完成能力显著下降。在此背景下,再入滑翔飞行器的机动突防轨迹规划与制导成为当前研究的热点问题之一。首先,分析了再入滑翔突防的性能优势与难点问题;其次,梳理了再入滑翔飞行过程中面临的典型禁飞区建模方法,并从禁飞区被动规避、强防御区主动绕飞、近距博弈对抗及多飞行器协同机动突防4类典型突防样式切入,对相应的机动突防轨迹规划与制导方法的研究现状进行了多角度、多层次总结归纳,同时分析了现有研究成果的特点和局限性;在此基础上,梳理给出了该类技术发展面临的挑战与难点。最后,结合当前研究进展、面临挑战及未来需求,分析了再入滑翔飞行器机动突防轨迹规划与制导技术的发展趋势,初步提出了该研究领域未来的5个发展方向,以期为相关技术的发展和研究提供新的思路和技术参考。

本文引用格式

闫循良 , 王培臣 , 郭杨 . 再入滑翔机动突防轨迹规划与制导方法综述[J]. 航空学报, 2025 , 46(17) : 331810 -331810 . DOI: 10.7527/S1000-6893.2025.31810

Abstract

With the continuous development of new air defense and anti-missile technologies, the entry vehicles face the threats from multi-level, multi-platform, and multi-batch defense systems, leading to a significantly decline in their survival and mission-completion capabilities. Against this backdrop, the maneuvering penetration trajectory planning and guidance of entry vehicles have become one of the major research topics. This paper firstly analyzes the performance advantages and difficult problems of entry penetration. Secondly, it reviews the typical no-fly zone modeling methods encountered during the entry flight process. Starting from four typical penetration patterns, namely passive evasion of no-fly zones, active detouring of defense zones, game confrontation, and coordinated maneuvering penetration of multiple vehicles, this paper summarizes and generalizes the research status of the corresponding maneuvering penetration trajectory planning and guidance methods from multiple perspectives and at multiple levels. The characteristics and limitations of the existing research results are also discussed. Based on this, this paper outlines the challenges and difficulties faced by the development of this type of technology. Finally, combined with the current research progress, challenges faced, and future requirements, this paper analyzes the development trends of the maneuvering penetration trajectory planning and guidance technology for entry vehicles, and preliminarily proposes five future development directions in this research field, aiming to provide new ideas and technical references for the development and research of related technologies.

参考文献

[1] 张远龙, 谢愈. 滑翔飞行器弹道规划与制导方法综述[J]. 航空学报202041(1): 023377.
  ZHANG Y L, XIE Y. Review of trajectory planning and guidance methods for gliding vehicles[J]. Acta Aeronautica et Astronautica Sinica202041(1): 023377 (in Chinese).
[2] 熊瑛, 夏薇, 王林. 2023年国外导弹防御发展综述[J]. 战术导弹技术2024(1): 1-6, 19.
  XIONG Y, XIA W, WANG L. Overview of foreign missile defense development in 2023[J]. Tactical Missile Technology2024(1): 1-6, 19 (in Chinese).
[3] 骆帅, 查旭, 陆红. 高速打击武器突防技术综述[J]. 战术导弹技术2023(5): 1-9.
  LUO S, ZHA X, LU H. Overview on penetration technology of high-speed strike weapon[J]. Tactical Missile Technology2023(5): 1-9 (in Chinese).
[4] 刘双喜, 刘世俊, 李勇, 等. 国外高超声速飞行器及防御体系发展现状[J]. 空天防御20236(3): 39-51.
  LIU S X, LIU S J, LI Y, et al. Current developments in foreign hypersonic vehicles and defense systems[J]. Air & Space Defense20236(3): 39-51 (in Chinese).
[5] 王铮, 邢晓露, 闫天, 等. 高超声速飞行器突防制导的发展现状与未来发展方向[J]. 飞航导弹2021(7): 18-24, 67.
  WANG Z, XING X L, YAN T, et al. The current status and future development direction of hypersonic aircraft penetration guidance[J]. Aerodynamic Missile Journal2021(7): 18-24, 67 (in Chinese).
[6] 汪民乐. 弹道导弹突防对策综述[J]. 飞航导弹2012(10): 45-51.
  WANG M L. Overview of ballistic missile penetration countermeasures[J]. Aerodynamic Missile Journal2012(10): 45-51 (in Chinese).
[7] 武天才, 王宏伦, 任斌, 等. 考虑规避与突防的高超声速飞行器智能容错制导控制一体化设计[J]. 航空学报202445(15): 329607.
  WU T C, WANG H L, REN B, et al. Learning-based integrated fault-tolerant guidance and control for hypersonic vehicles considering avoidance and penetration[J]. Acta Aeronautica et Astronautica Sinica202445(15): 329607 (in Chinese).
[8] XIA W J, WANG P C, YAN X L, et al. Rapid and near-analytical planning method for entry trajectory under time and full-state constraints[J]. Aerospace202411(7): 580.
[9] LIANG Z X, LONG J T, ZHU S Y, et al. Entry guidance with terminal approach angle constraint[J]. Aerospace Science and Technology2020102: 105876.
[10] 谢愈, 刘鲁华, 汤国建, 等. 高超声速滑翔飞行器摆动式机动突防弹道设计[J]. 航空学报201132(12): 2174-2181.
  XIE Y, LIU L H, TANG G J, et al. Weaving maneuver trajectory design for hypersonic glide vehicles[J]. Acta Aeronautica et Astronautica Sinica201132(12): 2174-2181 (in Chinese).
[11] 陈迎春, 齐欢. 基于协同进化的平面追逃对策研究[J]. 控制与决策200924(3): 383-387.
  CHEN Y C, QI H. Co-evolutionary pursuit-evasion game on a plane[J]. Control and Decision200924(3): 383-387 (in Chinese).
[12] 刘思源, 梁子璇, 任章, 等. 高超声速滑翔飞行器再入段制导方法综述[J]. 中国空间科学技术201636(6): 1-13.
  LIU S Y, LIANG Z X, REN Z, et al. Review of reentry guidance methods for hypersonic gliding vehicles[J]. Chinese Space Science and Technology201636(6): 1-13 (in Chinese).
[13] 潘亮, 谢愈, 彭双春, 等. 高超声速飞行器滑翔制导方法综述[J]. 国防科技大学学报201739(3): 15-22.
  PAN L, XIE Y, PENG S C, et al. A survey of gliding guidance methods for hypersonic vehicles[J]. Journal of National University of Defense Technology201739(3): 15-22 (in Chinese).
[14] 郭杰, 郑金库, 王浩凝, 等. 高超声速滑翔飞行器再入制导方法及热点问题研究综述[J]. 空天技术2022(1): 54-63.
  GUO J, ZHENG J K, WANG H N, et al. Review of research on reentry guidance methods and hot issues of hypersonic gliding vehicle[J]. Aerospace Technology2022(1): 54-63 (in Chinese).
[15] DING Y B, YUE X K, CHEN G S, et al. Review of control and guidance technology on hypersonic vehicle[J]. Chinese Journal of Aeronautics202235(7): 1-18.
[16] 陈万春, 陈中原, 龚晓鹏. 智能机动突防策略研究进展[J]. 飞行力学202442(5): 1-9.
  CHEN W C, CHEN Z Y, GONG X P. Advances in the study of intelligent maneuver penetration strategy[J]. Flight Dynamics202442(5): 1-9 (in Chinese).
[17] 江锐, 张欣, 王晓芳. 基于最优控制的高速飞行器突防技术研究[J]. 飞行力学202442(1): 32-38.
  JIANG R, ZHANG X, WANG X F. Research on penetration technology of high-speed aircraft based on optimal control[J]. Flight Dynamics202442(1): 32-38 (in Chinese).
[18] 安凯, 郭振云, 黄伟, 等. 低/高速飞行器系统编队协同控制方法研究进展[J]. 航空兵器202229(5): 53-65.
  AN K, GUO Z Y, HUANG W, et al. Research progress of formation-cooperative control methods for low-speed and high-speed vehicle systems[J]. Aero Weaponry202229(5): 53-65 (in Chinese).
[19] 向锦武, 董希旺, 丁文锐, 等. 复杂环境下无人集群系统自主协同关键技术[J]. 航空学报202243(10): 527570.
  XIANG J W, DONG X W, DING W R, et al. Key technologies for autonomous cooperation of unmanned swarm systems in complex environments[J]. Acta Aeronautica et Astronautica Sinica202243(10): 527570 (in Chinese).
[20] 陈洁卿, 孙瑞胜, 陈伟. 超声速导弹群协同博弈突防制导研究[J]. 无人系统技术20214(6): 65-74.
  CHEN J Q, SUN R S, CHEN W. Research on cooperative penetration game guidance of supersonic missile group[J]. Unmanned Systems Technology20214(6): 65-74 (in Chinese).
[21] 王宁宇, 白瑜亮, 魏金鹏, 等. 多弹最优协同诱导突防制导律[J]. 宇航学报202243(4): 434-444.
  WANG N Y, BAI Y L, WEI J P, et al. Guidance law for multi-missile optimal cooperative lured penetration[J]. Journal of Astronautics202243(4): 434-444 (in Chinese).
[22] ZHANG R H, CUI N G. Entry trajectory optimization with general polygonal no-fly zone constraints[J]. IEEE Transactions on Aerospace and Electronic Systems202359(6): 9205-9218.
[23] 张梦樱, 唐乾刚, 韩小军, 等. 复杂约束条件下的再入轨迹迭代求解方法[J]. 兵工学报201536(6): 1015-1023.
  ZHANG M Y, TANG Q G, HAN X J, et al. Iterative method to solving re-entry trajectory optimization with complex constraints[J]. Acta Armamentarii201536(6): 1015-1023 (in Chinese).
[24] 季荣涛. 基于威胁分析的战场空间划分及其在航迹规划中的应用[D]. 南京: 南京大学, 2016.
  JI R T. Battlefield space division based on threat analysis and its application in route planning[D]. Nanjing: Nanjing University, 2016 (in Chinese).
[25] ZHANG R H, XIE Z H, WEI C Z, et al. An enlarged polygon method without binary variables for obstacle avoidance trajectory optimization[J]. Chinese Journal of Aeronautics202336(8): 284-297.
[26] TIAN M Y, SHEN Z J. Air-breathing hypersonic vehicle trajectory optimization with uncertain no-fly zones[J]. Advances in Mechanical Engineering202214(7): 1-18.
[27] 郭行, 符文星, 付斌, 等. 复杂动态环境下无人飞行器动态避障近似最优轨迹规划[J]. 宇航学报201940(2): 182-190.
  GUO H, FU W X, FU B, et al. Near optimal dynamic obstacle avoidance trajectory programming for unmanned aerial vehicles[J]. Journal of Astronautics201940(2): 182-190 (in Chinese).
[28] COTTRILL G, HARMON F. Hybrid Gauss pseudospectral and generalized polynomial chaos algorithm to solve stochastic trajectory optimization problems[C]∥AIAA Guidance, Navigation, and Control Conference. Reston: AIAA, 2011.
[29] 陆遥, 李东生. 基于威胁概率图的无人机作战场景模型设计[J]. 电子信息对抗技术201833(5): 60-66, 79.
  LU Y, LI D S. Design of UAV combat scenario model based on threat probability graph[J]. Electronic Information Warfare Technology201833(5): 60-66, 79 (in Chinese).
[30] 蔡超, 葛超, 武振波, 等. 基于动态RCS的无人飞行器隐身突防航迹规划[J]. 华中科技大学学报(自然科学版)202250(11): 72-78.
  CAI C, GE C, WU Z B, et al. Stealth penetration path planning of unmanned aerial vehicle based on dynamic RCS[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition)202250(11): 72-78 (in Chinese).
[31] XIE Y, LIU L H, TANG G J, et al. Highly constrained entry trajectory generation[J]. Acta Astronautica201388: 44-60.
[32] GUO J, WU X Z, TANG S J. Autonomous gliding entry guidance with geographic constraints[J]. Chinese Journal of Aeronautics201528(5): 1343-1354.
[33] LIANG Z X, LIU S Y, LI Q D, et al. Lateral entry guidance with no-fly zone constraint[J]. Aerospace Science and Technology201760: 39-47.
[34] GAO B L, YAO Y D, CHENG H, et al. An online trajectory planning method for hypersonic aircraft considering maneuverability[C]∥2024 4th International Conference on Computer, Control and Robotics (ICCCR). Piscataway: IEEE Press, 2024: 323-327.
[35] SUN Z K, SUN L Y, QI J T, et al. Distributed path planning for UAVs based on A* algorithm of dubins path[C]∥2023 42nd Chinese Control Conference (CCC). Piscataway: IEEE Press, 2023: 5939-5944.
[36] HE R Z, LIU L H, TANG G J, et al. Rapid generation of entry trajectory with multiple no-fly zone constraints[J]. Advances in Space Research201760(7): 1430-1442.
[37] HE R Z, LIU L H, TANG G J, et al. Entry trajectory generation without reversal of bank angle[J]. Aerospace Science and Technology201771: 627-635.
[38] 张源, 张冉, 李惠峰. 复杂禁飞区高超声速飞行器路径—轨迹双层规划[J]. 宇航学报202243(5): 615-627.
  ZHANG Y, ZHANG R, LI H F. Dual-level path-trajectory generation with complex no-fly zone constraints for hypersonic vehicle[J]. Journal of Astronautics202243(5): 615-627 (in Chinese).
[39] ZHANG Y, ZHANG R, LI H F. Online path decision of no-fly zones avoidance for hypersonic vehicles based on a graph attention network[J]. IEEE Transactions on Aerospace and Electronic Systems202359(5): 5554-5567.
[40] 赵吉松, 尚腾, 张金明, 等. 带有控制变量变化率约束的伪谱轨迹优化方法[J]. 宇航学报202243(10): 1368-1377.
  ZHAO J S, SHANG T, ZHANG J M, et al. Pseudo-spectral trajectory optimization method with constraint on the change rate of control variables[J]. Journal of Astronautics202243(10): 1368-1377 (in Chinese).
[41] 梅映雪, 冯玥, 王容顺, 等. 高超声速飞行器多约束再入轨迹快速优化[J]. 宇航学报201940(7): 758-767.
  MEI Y X, FENG Y, WANG R S, et al. Fast optimization of reentry trajectory for hypersonic vehicles with multiple constraints[J]. Journal of Astronautics201940(7): 758-767 (in Chinese).
[42] SUN X, ZHANG B H, CHAI R Q, et al. UAV trajectory optimization using chance-constrained second-order cone programming[J]. Aerospace Science and Technology2022121: 107283.
[43] HUANG A, YU J L, LIU Y M, et al. Multitask-constrained reentry trajectory planning for hypersonic gliding vehicle[J]. Aerospace Science and Technology2024155: 109636.
[44] ZHANG Y, ZHANG R, LI H F. Graph-based path decision modeling for hypersonic vehicles with no-fly zone constraints[J]. Aerospace Science and Technology2021116: 106857.
[45] ZHANG D, LIU L, WANG Y J. On-line reentry guidance algorithm with both path and no-fly zone constraints[J]. Acta Astronautica2015117: 243-253.
[46] LI Z H, YANG X J, SUN X D, et al. Improved artificial potential field based lateral entry guidance for waypoints passage and no-fly zones avoidance[J]. Aerospace Science and Technology201986: 119-131.
[47] TONG X D, SONG J, LI W L, et al. Penetration game strategy of high dynamic vehicles with constraints of no-fly zones and interceptors[J]. Engineering Applications of Artificial Intelligence2024136: 109018.
[48] HU Y D, GAO C S, LI J L, et al. A novel adaptive lateral reentry guidance algorithm with complex distributed no-fly zones constraints[J]. Chinese Journal of Aeronautics202235(7): 128-143.
[49] LIANG Z X, REN Z. Tentacle-based guidance for entry flight with no-fly zone constraint[J]. Journal of Guidance, Control, and Dynamics201741(4): 996-1005.
[50] GAO Y, CAI G B, YANG X G, et al. Improved tentacle-based guidance for reentry gliding hypersonic vehicle with no-fly zone constraint[J]. IEEE Access20197: 119246-119258.
[51] 高杨, 蔡光斌, 徐慧, 等. 虚拟多触角探测的高超声速滑翔飞行器再入机动制导[J]. 航空学报202041(11): 623703.
  GAO Y, CAI G B, XU H, et al. Reentry maneuver guidance of hypersonic glide vehicle under virtual multi-tentacle detection[J]. Acta Aeronautica et Astronautica Sinica202041(11): 623703 (in Chinese).
[52] HU J M, YANG X X, WANG W C, et al. Obstacle avoidance for UAS in continuous action space using deep reinforcement learning[J]. IEEE Access202210: 90623-90634.
[53] HONG D, PARK S. Avoiding obstacles via missile real-time inference by reinforcement learning[J]. Applied Sciences202212(9): 4142.
[54] WU T C, WANG H L, LIU Y H, et al. Learning-based interfered fluid avoidance guidance for hypersonic reentry vehicles with multiple constraints[J]. ISA Transactions2023139: 291-307.
[55] WU J F, WANG H L, LIU Y H, et al. Learning-based fixed-wing UAV reactive maneuver control for obstacle avoidance[J]. Aerospace Science and Technology2022126: 107623.
[56] 惠俊鹏, 汪韧, 郭继峰. 基于强化学习的禁飞区绕飞智能制导技术[J]. 航空学报202344(11): 327416.
  HUI J P, WANG R, GUO J F. Intelligent guidance for no-fly zone avoidance based on reinforcement learning[J]. Acta Aeronautica et Astronautica Sinica202344(11): 327416 (in Chinese).
[57] LI X, WANG X G, ZHOU H Y. Entry guidance for spatial no-fly zones avoidance via model-based reinforcement learning[J]. Aerospace Science and Technology2024153: 109405.
[58] GAO Y, ZHOU R, CHEN J Y. Integrated entry guidance with no-fly zone constraint using reinforcement learning and predictor-corrector technique[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2024238(7): 728-741.
[59] YAO P, WANG H L, SU Z K. Real-time path planning of unmanned aerial vehicle for target tracking and obstacle avoidance in complex dynamic environment[J]. Aerospace Science and Technology201547: 269-279.
[60] 万兵, 梁勇, 邓力, 等. 基于滚动时域优化的反舰导弹航路规划[J]. 兵器装备工程学报202344(9): 49-57.
  WAN B, LIANG Y, DENG L, et al. A path planning method for an anti-ship missile based on receding horizon optimal procedure[J]. Journal of Ordnance Equipment Engineering202344(9): 49-57 (in Chinese).
[61] 刘畅, 谢文俊, 张鹏, 等. 多重威胁下的无人机自主避障航迹规划[J]. 哈尔滨工业大学学报202052(4): 119-126.
  LIU C, XIE W J, ZHANG P, et al. UAV autonomous obstacle avoidance path planning under multiple threats[J]. Journal of Harbin Institute of Technology202052(4): 119-126 (in Chinese).
[62] 高昂, 董志明, 叶红兵, 等. 基于深度强化学习的巡飞弹突防控制决策[J]. 兵工学报202142(5): 1101-1110.
  GAO A, DONG Z M, YE H B, et al. Loitering munition penetration control decision based on deep reinforcement learning[J]. Acta Armamentarii202142(5): 1101-1110 (in Chinese).
[63] JIANG Q J, WANG X G, LI Y. Intelligent reentry guidance with dynamic no-fly zones based on deep reinforcement learning[C]∥Computational and Experimental Simulations in Engineering. Cham: Springer International Publishing, 2024: 291-313.
[64] 王浩凝, 郭杰, 张宝超, 等. 多禁飞区在线遭遇的自主规避再入制导方法[J]. 宇航学报202445(9): 1429-1444.
  WANG H N, GUO J, ZHANG B C, et al. Autonomous entry guidance method for online encounters with multiple no-fly zones[J]. Journal of Astronautics202445(9): 1429-1444 (in Chinese).
[65] WANG H N, GUO J, ZHANG B C, et al. Learning-based guidance method of avoiding multiple online-detected no-fly zones for hypersonic cruise vehicles[J]. Journal of Aerospace Engineering202538(1): 04024107.
[66] 杨浩东, 王剑颖, 吴志刚, 等. 面向动态禁飞区的自适应触角探测机动制导方法[J]. 宇航学报202445(2): 192-202.
  YANG H D, WANG J Y, WU Z G, et al. Adaptive tentacle detection and maneuvering guidance method for dynamic no-fly zones[J]. Journal of Astronautics202445(2): 192-202 (in Chinese).
[67] BLACKMORE L, ONO M, WILLIAMS B C. Chance-constrained optimal path planning with obstacles[J]. IEEE Transactions on Robotics201127(6): 1080-1094.
[68] BUJARBARUAH M, ROSOLIA U, STüRZ Y R, et al. A simple robust MPC for linear systems with parametric and additive uncertainty[C]∥2021 American Control Conference (ACC). Piscataway: IEEE Press, 2021: 2108-2113.
[69] ZHANG Y Q, CHENG M, NAN B, et al. Stochastic trajectory optimization for 6-DOF spacecraft autonomous rendezvous and docking with nonlinear chance constraints[J]. Acta Astronautica2023208: 62-73.
[70] ONO M, WILLIAMS B C. Iterative Risk Allocation: A new approach to robust model predictive control with a joint chance constraint[C]∥2008 47th IEEE Conference on Decision and Control. Piscataway: IEEE Press, 2008: 3427-3432.
[71] DING Y F, MORSTYN T, MCCULLOCH M D. Distributionally robust joint chance-constrained optimization for networked microgrids considering contingencies and renewable uncertainty[J]. IEEE Transactions on Smart Grid202213(3): 2467-2478.
[72] PILIPOVSKY J, TSIOTRAS P. Covariance steering with optimal risk allocation[J]. IEEE Transactions on Aerospace and Electronic Systems202157(6): 3719-3733.
[73] 田牧垠, 沈作军. 一类不确定环境下的再入滑翔飞行器轨迹规划[J]. 北京航空航天大学学报202450(8): 2514-2523.
  TIAN M Y, SHEN Z J. Trajectory planning of re-entry gliding vehicle in a class of uncertain environment[J]. Journal of Beijing University of Aeronautics and Astronautics202450(8): 2514-2523 (in Chinese).
[74] 闫循良, 王培臣, 夏文杰, 等. 基于混沌多项式的再入滑翔鲁棒轨迹凸优化[J]. 西北工业大学学报202341(5): 850-859.
  YAN X L, WANG P C, XIA W J, et al. Robust convex optimization for reentry glide trajectory using polynomial chaos[J]. Journal of Northwestern Polytechnical University202341(5): 850-859 (in Chinese).
[75] 王培臣, 闫循良, 王宽, 等. 基于随机响应面与混沌多项式的鲁棒轨迹优化[J]. 系统工程与电子技术202345(10): 3226-3239.
  WANG P C, YAN X L, WANG K, et al. Robust trajectory optimization method based on stochastic response surface and polynomial chaos[J]. Systems Engineering and Electronics202345(10): 3226-3239 (in Chinese).
[76] 龚宇莲, 孟斌, 李毛毛. 基于单参数迭代的TAEM在线轨迹生成方法[J]. 航空学报202041(): 724289.
  GONG Y L, MENG B, LI M M. Online trajectory design method for terminal area energy management based on single parameter iteration [J]. Acta Aeronautica et Astronautica Sinica202041(Sup 2): 724289 (in Chinese).
[77] WANG X, GUO J, TANG S J, et al. Entry trajectory planning with terminal full states constraints and multiple geographic constraints[J]. Aerospace Science and Technology201984: 620-631.
[78] SHI P, XU J J, CHENG L, et al. Real-time lateral predictor-corrector entry guidance with terminal heading angle constraint[J]. IEEE Transactions on Aerospace and Electronic Systems202561(2): 2106-2119.
[79] LIANG Z X, YU J L, REN Z, et al. Trajectory planning for cooperative flight of two hypersonic entry vehicles[C]∥21st AIAA International Space Planes and Hypersonics Technologies Conference. Reston: AIAA, 2017: 2251.
[80] 王肖, 郭杰, 唐胜景, 等. 基于解析剖面的时间协同再入制导[J]. 航空学报201940(3): 322565.
  WANG X, GUO J, TANG S J, et al. Time-cooperative entry guidance based on analytical profile[J]. Acta Aeronautica et Astronautica Sinica201940(3): 322565 (in Chinese).
[81] LI Z H, HE B, WANG M H, et al. Time-coordination entry guidance for multi-hypersonic vehicles[J]. Aerospace Science and Technology201989: 123-135.
[82] 刘旭, 李响, 王晓鹏. 高超声速滑翔飞行器解析协同再入制导[J]. 宇航学报202344(5): 731-742.
  LIU X, LI X, WANG X P. Analytical cooperative reentry guidance for hypersonic glide vehicles[J]. Journal of Astronautics202344(5): 731-742 (in Chinese).
[83] YU W B, CHEN W C, JIANG Z G, et al. Analytical entry guidance for coordinated flight with multiple no-fly-zone constraints[J]. Aerospace Science and Technology201984: 273-290.
[84] 王培臣, 闫循良, 李新国, 等. 考虑时间约束的解析再入滑翔制导[J]. 航空学报202445(23): 229-246.
  WANG P C, YAN X L, LI X G, et al. Reentry glide analytical guidance considering time constraints[J]. Acta Aeronautica et Astronautica Sinica202445(23): 229-246 (in Chinese).
[85] 方科, 张庆振, 倪昆, 等. 高超声速飞行器时间协同再入制导[J]. 航空学报201839(5): 321958.
  FANG K, ZHANG Q Z, NI K, et al. Time-coordinated reentry guidance law for hypersonic vehicle[J]. Acta Aeronautica et Astronautica Sinica201839(5): 321958 (in Chinese).
[86] 张晚晴, 余文斌, 李静琳, 等. 基于纵程解析解的飞行器智能横程机动再入协同制导[J]. 兵工学报202142(7): 1400-1411.
  ZHANG W Q, YU W B, LI J L, et al. Cooperative reentry guidance for intelligent lateral maneuver of hypersonic vehicle based on downrange analytical solution[J]. Acta Armamentarii202142(7): 1400-1411 (in Chinese).
[87] 方科, 张庆振, 倪昆, 等. 飞行时间约束下的再入制导律[J]. 哈尔滨工业大学学报201951(10): 90-97.
  FANG K, ZHANG Q Z, NI K, et al. Reentry guidance law with flight time constraint[J]. Journal of Harbin Institute of Technology201951(10): 90-97 (in Chinese).
[88] 刘哲, 陆浩然, 郑伟, 等. 多滑翔飞行器时间协同轨迹快速规划[J]. 航空学报202142(11): 524497.
  LIU Z, LU H R, ZHENG W, et al. Rapid time-coordination trajectory planning method for multi-glide vehicles[J]. Acta Aeronautica et Astronautica Sinica202142(11): 524497 (in Chinese).
[89] YU J L, DONG X W, LI Q D, et al. Cooperative guidance strategy for multiple hypersonic gliding vehicles system[J]. Chinese Journal of Aeronautics202033(3): 990-1005.
[90] YU W B, YAO Y Z, CHEN W C. Analytical cooperative entry guidance for rendezvous and formation flight[J]. Acta Astronautica2020171: 118-138.
[91] JARMARK B, MERZ AW, BREAKWELL J. The variable-speed tail-chase aerial combat problem[J]. Journal of Guidance, Control, and Dynamics19814(3): 323-328.
[92] ALMEIDA F. Improving maneuver performance in unmanned aerial vehicles through learning-based reference management[C]∥AIAA Guidance, Navigation, and Control (GNC) Conference. Reston: AIAA, 2013.
[93] REN L L, GUO W L, XIAN Y, et al. Deep reinforcement learning based integrated evasion and impact hierarchical intelligent policy of exo-atmospheric vehicles[J]. Chinese Journal of Aeronautics202538(1): 103193.
[94] 何磊, 闫晓东, 唐硕. 螺旋俯冲机动突防的制导律设计[J]. 航空学报201940(5): 322457.
  HE L, YAN X D, TANG S. Guidance law design for spiral-diving maneuver penetration[J]. Acta Aeronautica et Astronautica Sinica201940(5): 322457 (in Chinese).
[95] 段安娜, 闫循良. 多约束螺旋机动变结构制导律设计[J]. 固体火箭技术202043(3): 400-406.
  DUAN A N, YAN X L. Design of multi-constrained spiral maneuvering variable structure guidance law[J]. Journal of Solid Rocket Technology202043(3): 400-406 (in Chinese).
[96] ZHU J W, LIU L H, TANG G J, et al. Optimal diving maneuver strategy considering guidance accuracy for hypersonic vehicle[J]. Acta Astronautica2014104(1): 231-242.
[97] ZHU J W, HE R Z, TANG G J, et al. Pendulum maneuvering strategy for hypersonic glide vehicles[J]. Aerospace Science and Technology201878: 62-70.
[98] 周啟航, 刘延芳, 齐乃明, 等. 基于反预警的反拦截中段规避突防策略[J]. 航空学报201738(1): 319922.
  ZHOU Q H, LIU Y F, QI N M, et al. Anti-warning-based anti-interception avoiding penetration strategy in midcourse[J]. Acta Aeronautica et Astronautica Sinica201738(1): 319922 (in Chinese).
[99] HE L, YAN X D, TANG S. Spiral-diving trajectory optimization for hypersonic vehicles by second-order cone programming[J]. Aerospace Science and Technology201995: 105427.
[100] YAN B B, LIU R F, DAI P, et al. A rapid penetration trajectory optimization method for hypersonic vehicles[J]. International Journal of Aerospace Engineering20192019(1): 1490342.
[101] SHEN Z P, YU J L, DONG X W, et al. Penetration trajectory optimization for the hypersonic gliding vehicle encountering two interceptors[J]. Aerospace Science and Technology2022121: 107363.
[102] SHINAR J, STEINBERG D. Analysis of optimal evasive maneuvers based on a linearized two-dimensional kinematic model[J]. Journal of Aircraft197714(8): 795-802.
[103] ONG S Y, PIERSON B L. Optimal planar evasive aircraft maneuvers against proportional navigation missiles[J]. Journal of Guidance, Control, and Dynamics199619(6): 1210-1215.
[104] KANG S, KIM H J, TAHK M J. Aerial pursuit-evasion game using nonlinear model predictive guidance[C]∥AIAA Guidance, Navigation, and Control Conference. Reston: AIAA, 2010: 7880.
[105] 王雨琪, 宁国栋, 王晓峰, 等. 基于微分对策的临近空间飞行器机动突防策略[J]. 航空学报202041(): 724276.
  WANG Y Q, NING G D, WANG X F, et al. Maneuver penetration strategy of near space vehicle based on differential game[J]. Acta Aeronautica et Astronautica Sinica202041(Sup 2): 724276 (in Chinese).
[106] LIANG H Z, WANG J Y, WANG Y H, et al. Optimal guidance against active defense ballistic missiles via differential game strategies[J]. Chinese Journal of Aeronautics202033(3): 978-989.
[107] BEN-ASHER J, CLIFF E M, KELLEY H J. Optimal evasion with a path-angle constraint and against two pursuers[J]. Journal of Guidance, Control, and Dynamics198811(4): 300-304.
[108] SUN A, LIU H. Multi-pursuer evasion[C]∥AIAA Guidance, Navigation and Control Conference and Exhibit. Reston: AIAA, 2008.
[109] ZHANG P, FANG Y W, ZHANG F M, et al. An adaptive weighted differential game guidance law[J]. Chinese Journal of Aeronautics201225(5): 739-746.
[110] BARDHAN R, GHOSE D. An SDRE based differential game approach for maneuvering target interception[C]∥AIAA Guidance, Navigation, and Control Conference. Reston: AIAA, 2015.
[111] SHAFERMAN V, SHIMA T Y. A cooperative differential game for imposing a relative intercept angle[C]∥AIAA Guidance, Navigation, and Control Conference. Reston: AIAA, 2017.
[112] YAN T, CAI Y L, XU B. Evasion guidance algorithms for air-breathing hypersonic vehicles in three-player pursuit-evasion games[J]. Chinese Journal of Aeronautics202033(12): 3423-3436.
[113] PERELMAN A, SHIMA T, RUSNAK I. Cooperative differential games strategies for active aircraft protection from a homing missile[J]. Journal of Guidance, Control, and Dynamics201134(3): 761-773.
[114] RUBINSKY S, GUTMAN S. Three-player pursuit and evasion conflict[J]. Journal of Guidance, Control, and Dynamics201337(1): 98-110.
[115] WEISS M, SHIMA T, CASTANEDA D, et al. Combined and cooperative minimum-effort guidance algorithms in an active aircraft defense scenario[J]. Journal of Guidance, Control, and Dynamics201740(5): 1241-1254.
[116] 王子瑶, 唐胜景, 郭杰, 等. 高超声速攻防博弈自适应微分对策三维制导[J]. 兵工学报202344(8): 2342-2353.
  WANG Z Y, TANG S J, GUO J, et al. Adaptive 3-dimensional differential game guidance for hypersonic attack and defense[J]. Acta Armamentarii202344(8): 2342-2353 (in Chinese).
[117] SHEN Z P, YU J L, DONG X W, et al. Deep neural network-based penetration trajectory generation for hypersonic gliding vehicles encountering two interceptors[C]∥2022 41st Chinese Control Conference (CCC). Piscataway: IEEE Press, 2022: 3392-3397.
[118] 左家亮, 杨任农, 张滢, 等. 基于启发式强化学习的空战机动智能决策[J]. 航空学报201738(10): 321168.
  ZUO J L, YANG R N, ZHANG Y, et al. Intelligent decision-making in air combat maneuvering based on heuristic reinforcement learning[J]. Acta Aeronautica et Astronautica Sinica201738(10): 321168 (in Chinese).
[119] JIANG L, NAN Y, ZHANG Y, et al. Anti-interception guidance for hypersonic glide vehicle: A deep reinforcement learning approach[J]. Aerospace20229(8): 424.
[120] 张鸿林, 罗建军, 马卫华. 基于机器学习的航天器规避目标威胁博弈决策[J]. 航空学报202445(8): 329136.
  ZHANG H L, LUO J J, MA W H. Spacecraft game decision making for threat avoidance of space targets based on machine learning[J]. Acta Aeronautica et Astronautica Sinica202445(8): 329136 (in Chinese).
[121] HU X, WANG T S, GONG M, et al. Guidance design for escape flight vehicle using evolution strategy enhanced deep reinforcement learning[J]. IEEE Access202412: 48210-48222.
[122] HU X, WANG H B, GONG M, et al. Guidance design for escape flight vehicle against multiple pursuit flight vehicles using the RNN-based proximal policy optimization algorithm[J]. Aerospace202411(5): 361.
[123] GUO Y H, JIANG Z J, HUANG H Q, et al. Intelligent maneuver strategy for a hypersonic pursuit-evasion game based on deep reinforcement learning[J]. Aerospace202310(9): 783.
[124] LI X, WANG X G, ZHOU H Y, et al. A novel evasion guidance for hypersonic morphing vehicle via intelligent maneuver strategy[J]. Chinese Journal of Aeronautics202437(5): 441-461.
[125] JEON I S, LEE J I, TAHK M J. Impact-time-control guidance law for anti-ship missiles[J]. IEEE Transactions on Control Systems Technology200614(2): 260-266.
[126] 崔乃刚, 韦常柱, 郭继峰. 导弹协同作战飞行时间裕度[J]. 航空学报201031(7): 1351-1359.
  CUI N G, WEI C Z, GUO J F. Flight time margin of missile cooperative engagement[J]. Acta Aeronautica et Astronautica Sinica201031(7): 1351-1359 (in Chinese).
[127] 乔浩, 白风科, 毛瑞. 高超声速滑翔导弹协同再入影响因素分析[J]. 飞行力学202038(6): 63-69.
  QIAO H, BAI F K, MAO R. Analysis of influence factors for cooperative reentry of hypersonic glide missile[J]. Flight Dynamics202038(6): 63-69 (in Chinese).
[128] LIANG Z X, LV C, ZHU S Y. Lateral entry guidance with terminal time constraint[J]. IEEE Transactions on Aerospace and Electronic Systems202359(3): 2544-2553.
[129] PARK B G, KWON H H, KIM Y H, et al. Composite guidance scheme for impact angle control against a nonmaneuvering moving target[J]. Journal of Guidance, Control, and Dynamics201639(5): 1132-1139.
[130] LEE S, KIM Y. Capturability of impact-angle control composite guidance law considering field-of-view limit[J]. IEEE Transactions on Aerospace and Electronic Systems202056(2): 1077-1093.
[131] 赵启伦, 陈建, 李清东, 等. 高超武器与常规导弹协同攻击策略可行域研究[J]. 航空学报201536(7): 2291-2300.
  ZHAO Q L, CHEN J, LI Q D, et al. Feasible region of hypersonic and ballistic missiles’cooperative attack strategy[J]. Acta Aeronautica et Astronautica Sinica201536(7): 2291-2300 (in Chinese).
[132] ZHANG M H, WANG H L, LI Z Y, et al. Fluid-based moderate collision avoidance for UAV formation in 3-D low-altitude environments[J]. Chinese Journal of Aeronautics202538(6): 103222.
[133] 徐星光, 于江龙, 郭鸿飞, 等. 有翼飞行器编队协同突防构型和通信拓扑优化方法[J/OL]. 北京航空航天大学学报, (2024-05-16)[2025-07-16]. .
  XU X G, YU J L, GUO H F, et al. Optimization method of cooperative penetration configuration and communication topology of winged aircraft formation[J/OL]. Journal of Beijing University of Aeronautics and Astronautics, (2024-05-16)[2025-07-16]. (in Chinese).
[134] Shui X, Wang X, Lin P, et al. A formation control method of multiple hypersonic missiles[J]. Tactical Missile Technology20205:139-148.
[135] 陆浩然, 邱薇, 孙海亮, 等. 高速飞行器编队队形快速成形设计方法[J]. 航天控制202139(2): 33-38, 44.
  LU H R, QIU W, SUN H L, et al. Design method of rapid forming for high-speed aircraft formation[J]. Aerospace Control202139(2): 33-38, 44 (in Chinese).
[136] ZHANG Z, LUO Y F, QU Y H. Distributed formation control with obstacle and collision avoidance for hypersonic gliding vehicles subject to multiple constraints[J]. International Journal of Aerospace Engineering20232023(1): 9973653.
[137] ZHANG Y, WANG X, TANG S J. A globally fixed-time solution of distributed formation control for multiple hypersonic gliding vehicles[J]. Aerospace Science and Technology202098: 105643.
[138] 胡砚洋, 何凡, 白成超. 高超声速飞行器末制导段协同避障决策方法[J]. 兵工学报202445(9): 3147-3160.
  HU Y Y, HE F, BAI C C. Cooperative obstacle avoidance decision method for the terminal guidance phase of hypersonic vehicles[J]. Acta Armamentarii202445(9): 3147-3160 (in Chinese).
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