追逃模型边防博弈算法研究  

Research on border defense game algorithms for pursuit-evasion models

作　　者：徐清雯 刘久富[1] 解晖 刘向武 杨忠[1] 王志胜[1] XU Qingwen;LIU Jiufu;XIE Hui;LIU Xiangwu;YANG Zhong;WANG Zhisheng(College of Automation Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学自动化学院,江苏南京211106

出　　处：《应用科技》2024年第5期298-304,共7页Applied Science and Technology

基　　金：国家自然科学基金项目(61473144)。

摘　　要：针对一个或多个追击者和一个躲避者的追逃微分对策,尽管博弈双方都具有简单的运动形式,但直接求解HJI(Hamilton-Jacobi-Isaacs)方程得到纳什均衡解是很困难的。为了得到博弈解,利用阿波罗尼斯圆通过几何方法求解出最佳解决方案。将舰艇运动简化为二维的数学模型,对其进行追逃博弈算法仿真。通过研究可知,对于在边界内实现的捕获,博弈双方的回报是捕获点到边界的距离;在程度博弈中,追击者总是可以抓到躲避者。基于几何特性导出的博弈解,在由不封闭的连续线段组成的边界下,对多追击者–单躲避者的程度博弈进行验证。仿真结果表明,在多追击单躲避博弈中,尽管捕获区域由多个追击者确定,但通常只由1个或2个追击者实现捕获;博弈有多个最优解时,存在散射曲面,不同的选择会对博弈的性能产生影响。该算法在一定程度上简化了追逃博弈的求解过程,可为边界条件下进行目标追踪与捕获提供参考。For the pursuit-evasion differential game with one or more pursuers and one evader,although both sides of the game have simple motion forms,it is difficult to directly solve Hamilton-Jacobi-Isaacs equation to obtain Nash equilibrium solution.In order to obtain the game solution,Appollonius is used to solve the optimal solution through geometric methods.The ship motion is simplified to a two-dimensional mathematical model,and the pursuit game algorithm is simulated.It can be known from the result that,for the capture achieved within the boundary,the reward for both parties in the game is the distance from the capture point to the boundary.In degree games,pursuers can always catch evaders.The game solution derived based on geometric characteristics is validated for the degree game of multiple pursuers and single evader under a boundary composed of unclosed continuous line segments.The simulation results indicate that in a multi-pursuer single-evader game,although the capture region is defined by multiple pursuers,the final capture is typically achieved by only one or two of these pursuers.When there are multiple optimal solutions in a game,there exists a dispersal surface,and different choices can have an impact on the performance of the game.To a certain degree,this algorithm simplifies the solving process of pursuit-evasion games and provides reference for target tracking and capturing under boundary conditions.

关 键 词：追逃博弈 微分对策 程度博弈 阿波罗尼斯圆 边界防御 目标捕获 几何方法 最优控制 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]