三维空间“追-逃-防”三方微分对策方法
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摘要
针对三维空间中的多智能体参与的追逃博弈问题展开研究,提出了一种基于追踪器、逃逸器以及防御器3个智能体参与的追逃博弈模型。在该模型下,通过引入零控脱靶量的方法降低了系统的维数和计算复杂度;采用模糊综合评估的方法对追踪器的目标函数进行设计,结合微分对策理论,得出追踪器的最优控制策略。仿真对比结果表明:在追踪器控制量占优势的情况下,提出的最优控制策略可以使追踪器绕开防御器并且捕获逃逸器;在追踪器控制量不占优势的情况下,提出的最优控制策略可以延长追踪器被防御器拦截的时间。
The pursuit-evasion game of multiple-agent in three-dimensional space is studied.A pursuit-evasion game model based on three agents including the pursuer,the evader and the defender is proposed.In this model,the dimension and the calculation complexity of the system is reduced by employing zero effort miss method.The objective function of the pursuer is designed by using fuzzy comprehensive evaluation.Combined with differential game theory,the optimal control strategy of pursuer is obtained.The comparative simulation results show that the proposed optimal control strategies can let the pursuer avoid the defender and intercept the evader when the controlled quantity of pursuer is more predominant.When the controlled quantity of pursuer is less predominant,the proposed optimal control strategies can increase the interception time of the pursuer.
The pursuit-evasion game of multiple-agent in three-dimensional space is studied.A pursuit-evasion game model based on three agents including the pursuer,the evader and the defender is proposed.In this model,the dimension and the calculation complexity of the system is reduced by employing zero effort miss method.The objective function of the pursuer is designed by using fuzzy comprehensive evaluation.Combined with differential game theory,the optimal control strategy of pursuer is obtained.The comparative simulation results show that the proposed optimal control strategies can let the pursuer avoid the defender and intercept the evader when the controlled quantity of pursuer is more predominant.When the controlled quantity of pursuer is less predominant,the proposed optimal control strategies can increase the interception time of the pursuer.
引文
[1]李伟,黄瑞松,王芳,等.基于SDRE具有终端碰撞角约束的非线性微分对策制导律[J].系统工程与电子技术,2016,38(7):1606-1613.LI W,HUANG R S,WANG F,et al.Nonlinear differential games guidance law based on SDRE with terminal impact angular[J].Systems Engineering and Electronics,2016,38(7):1606-1613.
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[18]MERZ A W.Noisy satellite pursuit-evasion guidance[J].Journal of Guidance Control and Dynamics,1989,12(6):901-905.
[19]张秋华,孙松涛,谌颖,等.时间固定的两航天器追逃策略及数值求解[J].宇航学报,2014,35(5):537-544.ZHANG Q H,SUN S T,CHEN Y,et al.Strategy and numerical solution of pursuit-evasion with fixed duration for two spacecraft[J].Journal of Astronautics,2014,35(5):537-544.
[20]王强,叶东,范宁军,等.基于零控脱靶量的卫星末端追逃控制方法[J].北京理工大学学报,2016,36(11):1171-1176.WANG Q,YE D,FAN N J,et al.Terminal orbital control of satellite pursuit evasion game based on zero effort miss[J].Transactions of Beijing Institute of Technology,2016,36(11):1171-1176.
[21]RUBINSKY S,GUTMAN S.Vector guidance approach to three-player conflict in exoatmospheric interception[J].Journal of Guidance Control and Dynamics,2015,38(12):2270-2286.
[22]刘暾,赵钧.空间飞行器动力学[M].哈尔滨:哈尔滨工业大学出版社,2003:83-85.LIU D,ZHAO Y.The dynamics of space vehicle[M].Harbin:Harbin Institute of Technology Press,2003:83-85.
[23]袁建平,李俊峰,和兴锁,等.航天器相对运动轨道动力学[M].北京:中国宇航出版社,2013:18-19.YUAN J P,LI J F,HE X S,et al.Relative orbit dynamics of spacecraft[M].Beijing:Press of Chinese Astronautic,2013:18-19.
[2]李龙跃,刘付显,史向峰,等.导弹攻防对抗中追逃对策模型与配点求解法[J].系统工程与电子技术,2016,38(5):1067-1073.LI L Y,LIU F X,SHI X F,et al.Differential modeling and collocation solving method of missiles pursuit-evasion game[J].Systems Engineering and Electronics,2016,38(5):1067-1073.
[3]花文华,陈兴林.双重控制导弹微分对策制导方法[J].系统工程与电子技术,2011,33(3):627-632.HUA W H,CHEN X L.Differential game guidance law for dual control missiles[J].Systems Engineering and Electronics,2011,33(3):627-632.
[4]SUN S,ZHANG Q,LOXTON R,et al.Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit[J].Journal of Industrial and Management Optimization,2015,11(4):1127-1147.
[5]JAGAT A,SINCLAIR A J.Nonlinear control for spacecraft pursuit-evasion game using the state-dependent Riccati equation method[J].IEEE Trans.on Aerospace and Electronic Systems,2017,53(6):3032-3042.
[6]RUIZ U,MURRIETACID R.A differential pursuit/evasion game of capture between an omnidirectional agent and a differential drive robot,and their winning roles[J].International Journal of Control,2016,89(11):2169-2184.
[7]NOORI N,BEVERIDGE A,ISLER V.Pursuit-evasion:a tool kit to make applications more accessible[J].IEEE Robotics&Automation Magazine,2016,23(4):138-149.
[8]HAYOUN S Y,WEISS M,SHIMA T.A mixed L2/Lαdifferential game approach to pursuit-evasion guidance[J].IEEE Trans.on Aerospace and Electronic Systems,2016,52(6):2775-2788.
[9]HUANG H,ZHANG W,DING J,et al.Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers[C]∥Proc.of the 50th IEEE Conference on Decision and Control and European Control Conference,2011:4835-4840.
[10]KOTHARI M,MANATHARA J G,POSTLETHWAITE I.A cooperative pursuit-evasion game for non-holonomic systems[C]∥Proc.of the 19th World Congress on International Federation of Automatic Control,2014:1977-1984.
[11]RAMANA M V,KOTHARI M.Pursuit strategy to capture high-speed evaders using multiple pursuers[J].Journal of Guidance,Control,and Dynamics,2017,40(1):139-149.
[12]FUCHS Z E,KHARGONEKAR P P,EVERS J.Cooperative defense within a single-pursuer,two-evader pursuit evasion differential game[C]∥Proc.of the 49th IEEE Conference on Decision and Control,2010:3091-3097.
[13]SCOTT W,LEONARD N E.Pursuit,herding and evasion:A three-agent model of caribou predation[C]∥Proc.of the American Control Conference,2013:2978-2983.
[14]GIVIGI S N,SCHWARTZ H M.Decentralized strategy selection with learning automata for multiple pursuer-evader games[J].Adaptive Behavior,2014,22(4):221-234.
[15]WEI M,CHEN G,CRUZ J B,et al.Multi-pursuer multievader pursuit-evasion games with jamming confrontation[J].Journal of Aerospace Computing Information and Communication,2007,4(3):693-706.
[16]RUBINSKY S,GUTMAN S.Three-player pursuit and evasion conflict[J].Journal of Guidance Control and Dynamics,2014,37(1):98-110.
[17]YU D,WANG H,LI K,et al.The capture region of TPN guidance law for orbital pursuit-evasion with limited maneuverability[C]∥Proc.of IEEE Chinese Guidance,Navigation and Control Conference,2016:937-942.
[18]MERZ A W.Noisy satellite pursuit-evasion guidance[J].Journal of Guidance Control and Dynamics,1989,12(6):901-905.
[19]张秋华,孙松涛,谌颖,等.时间固定的两航天器追逃策略及数值求解[J].宇航学报,2014,35(5):537-544.ZHANG Q H,SUN S T,CHEN Y,et al.Strategy and numerical solution of pursuit-evasion with fixed duration for two spacecraft[J].Journal of Astronautics,2014,35(5):537-544.
[20]王强,叶东,范宁军,等.基于零控脱靶量的卫星末端追逃控制方法[J].北京理工大学学报,2016,36(11):1171-1176.WANG Q,YE D,FAN N J,et al.Terminal orbital control of satellite pursuit evasion game based on zero effort miss[J].Transactions of Beijing Institute of Technology,2016,36(11):1171-1176.
[21]RUBINSKY S,GUTMAN S.Vector guidance approach to three-player conflict in exoatmospheric interception[J].Journal of Guidance Control and Dynamics,2015,38(12):2270-2286.
[22]刘暾,赵钧.空间飞行器动力学[M].哈尔滨:哈尔滨工业大学出版社,2003:83-85.LIU D,ZHAO Y.The dynamics of space vehicle[M].Harbin:Harbin Institute of Technology Press,2003:83-85.
[23]袁建平,李俊峰,和兴锁,等.航天器相对运动轨道动力学[M].北京:中国宇航出版社,2013:18-19.YUAN J P,LI J F,HE X S,et al.Relative orbit dynamics of spacecraft[M].Beijing:Press of Chinese Astronautic,2013:18-19.