The goal of this research is to devise guaranteed defense policies that allow to protect a given region from the entrance of smart mobile invaders by detecting them using a team of defending agents equipped with identical line sensors. By designing cooperative defense strategies that ensure all invaders are detected, conditions on the defenders' speed are derived. Successful accomplishment of the defense task implies invaders with a known limit on their speed cannot slip past the defenders and enter the guarded region undetected. The desired outcome of the defense protocols is to defend the area and additionally to expand it as much as possible. Expansion becomes possible if the defenders' speed exceeds a critical speed that is necessary to only defend the initial region. We present results on the total search time, critical speeds and maximal expansion possible for two types of novel pincer-movement defense processes, circular and spiral, for any even number of defenders. The proposed spiral process allows to detect invaders at nearly the lowest theoretically optimal speed, and if this speed is exceeded, it also allows to expand the protected region almost to the maximal area.

翻译：本研究旨在设计可保障的防御策略，通过配备相同线性传感器的防御代理集群，实现对给定区域的保护，防止智能移动入侵者进入。通过设计确保所有入侵者被探测的协同防御策略，推导出防御者速度的约束条件。成功完成防御任务意味着速度已知上限的入侵者无法在未被探测的情况下穿过防御者进入受保护区域。防御协议的目标是保卫该区域，并尽可能扩大其范围。当防御者速度超过仅需保卫初始区域的关键速度时，区域扩张成为可能。我们针对两种新型钳形运动防御过程（环形与螺旋形），给出了任意偶数个防御者下的总搜索时间、关键速度及最大扩张范围的结果。所提出的螺旋过程能以接近理论最优下限的速度探测入侵者，若速度超过该阈值，还可将受保护区域扩展至接近最大面积。