有向拓扑条件下有限时间收敛协同制导律设计  

Design of finite time convergent cooperative guidance law with directed communication topologies

作　　者：谢子涵 郎博 孙立伟 韦常柱[1] Xie Zihan;Lang Bo;Sun Liwei;Wei Changzhu(Harbin Institute of Technology,Harbin 150000,China;Norinco Group Aviation Ammunition Institute,Harbin 150030,China)

机构地区：[1]哈尔滨工业大学,哈尔滨150000 [2]中国兵器工业集团航空弹药研究院,哈尔滨150030

出　　处：《战术导弹技术》2022年第4期60-68,共9页Tactical Missile Technology

基　　金：国防基础科研项目(JCKY2019208C017);上海航天科技创新基金(SAST2019-005)。

摘　　要：针对多导弹打击地面固定目标问题,基于图论知识和滑模控制理论,提出了一种有向拓扑条件下有限时间收敛的三维协同制导律。制导律可使各导弹的打击时间趋于一致,同时满足导弹终端高低视线角和方位视线角约束。建立了弹目三维相对运动模型,并对时间协同制导问题和角度协同制导问题进行了描述。通过对协同制导问题的分析,将制导问题分为视线方向和视线法向两个通道分别进行考虑。在视线方向上,选取相邻导弹间的距离误差和接近速度误差为状态变量,设计时间协同制导律,并证明了制导律在具有有向生成树的有向拓扑条件下,可使各导弹打击时间在有限时间内趋于一致;在视线法向上,考虑高低视线角和方位视线角之间的耦合关系,设计三维角度约束制导律,通过理论证明了制导律的有限时间收敛性。设置了典型仿真条件进行了仿真,仿真结果显示制导律具有较高的制导精度,可在有限时间内满足时间协同和角度协同要求,验证了制导律的可行性。Based on graph theory and sliding mode control theory,a finite-time convergent threedimensional cooperative guidance law with directed communication topology is proposed to solve the problem of multi-missiles attacking a stationary target simultaneously.The guidance law can make the impact time of each missile tend to be consistent,and meet the constraints of impact angle at the same time.The threedimensional relative motion model of missile and target is established,and the time cooperative guidance problem and angle cooperative guidance problem are described.After analysis,the guidance problem is divided into two channels:line of sight direction and line of sight normal direction.In the line of sight direction,the distance error and approach speed error between adjacent missiles are selected as state variables,and the time cooperative guidance law is designed.It is proved that the guidance law can make the impact time of each missile tend to be consistent in a finite time in the condition of directed topology with directed spanning tree.In the line of sight normal direction,considering the coupling relationship between elevation line of sight angle and azimuth line of sight angle,a three-dimensional guidance law with impact angle constrained is designed.And the finite time convergence of the guidance law is proved.Then,a typical simulation conditions are set for simulation.The simulation results show that the guidance law has high guidance accuracy and can meet the requirements of time cooperation and angle cooperation in finite time,which verifies the feasibility of the guidance law.

关 键 词：协同制导 有向拓扑 有限时间 碰撞时间 碰撞角 三维制导律 时间协同 角度约束 

分 类 号：V412.1[航空宇航科学与技术—航空宇航推进理论与工程]