The Confinement-Escape Problem of a Defender Against an Evader Escaping from a Circular Region
研究了防御者与试图逃离圆形区域的逃逸者之间的围堵-逃逸问题，设计了两种生物启发控制策略，分析了逃逸时间、获胜集及系统相变。
In this paper, we first formulate the confinement-escape problem of a defender and an evader who attempts escaping from a circular region, which differs from the traditional pursuit-evasion problems. In our setting of the confinement-escape problem, the defender is restricted to move and patrol on the circle, trying to prevent possible escape of the evader who is initially located inside the circle. We describe and characterize some general properties of the problem, and then design two bio-inspired control strategies for the evader and the defender, respectively. In addition, we illustrate some possible motion patterns of the system, investigate the escaping time as a function of the relative-initial-positions of the agents, as well as the winning sets of the two players, respectively, under different system-parameters. To that end, we characterize the contour lines of the winning sets with their gradient properties. Finally, we indicate the abrupt phase transitions between successful confinement and escaping, revealing the strong sensitivity and nonlinearities of the system under critical conditions.