引用本文: 方宝富, 潘启树, 洪炳镕, 丁磊, 蔡则苏. 多追捕者-单一逃跑者追逃问题实现成功捕获的约束条件[J]. 机器人, 2012, 34(3): 282-291.
FANG Baofu, PAN Qishu, HONG Bingrong, DING Lei, CAI Zesu. Constraint Conditions of Successful Capture in Multi-Pursuers vs One-Evader Games[J]. ROBOT, 2012, 34(3): 282-291.
 Citation: FANG Baofu, PAN Qishu, HONG Bingrong, DING Lei, CAI Zesu. Constraint Conditions of Successful Capture in Multi-Pursuers vs One-Evader Games[J]. ROBOT, 2012, 34(3): 282-291.

## Constraint Conditions of Successful Capture in Multi-Pursuers vs One-Evader Games

• 摘要: 针对包含有n个追捕者及1个逃跑者的2维平面多机器人追逃问题， 对实现成功捕获的约束条件进行了研究． 经过理论分析得出： 在机器人拥有全局视野的情况下，即使单一逃跑者性能优于每个追捕者， 只要满足追捕者与逃跑者的速率比大于sin（π/n）， 逃跑机器人落在追捕机器人所构成的凸多边形内部且逃跑者和追捕者构成的相邻追-逃阿波罗尼奥斯圆满足两两相交（相切）这2个约束条件， 则追捕者通过选择合适的追捕策略就一定可以实现成功抓捕． 此外，还给出了在此约束条件下的追捕者和逃跑者的追逃策略． 多组仿真实验同样证明了本文提出的约束条件是正确的．

Abstract: The constraint conditions of successful capture in multi-robot 2D pursuit-evasion game with n pursuers and one evader are researched. Based on the theoretical analyses, under the condition that all robots have global visual field, the pursuers using appropriate strategy can always capture the evader, even if the top speed of the pursuers is lower than that of the evader when the following two conditions are both satisfied. One is that the speed ratio of each pursuer to the evader is higher than sin (π/n), and the other is that the evader should be located in the convex polygon which takes the multiple pursuers as vertexes, and that the adjacent Apollonius circles formed by the evader and each pursuer should be intersected or tangent. In addition, the pursuit-evasion strategies for pursuer and evader are designed under the proposed constraint conditions. Results of many simulation experiments can also prove that the constraint conditions are correct.

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