This report studies the emergent behavior of systems of agents performing cyclic pursuit controlled by an external broadcast signal detected by a random set of the agents. Two types of cyclic pursuit are analyzed: 1)linear cyclic pursuit, where each agent senses the relative position of its target or leading agent 2)non-linear cyclic pursuit, where the agents can sense only bearing to their leading agent and colliding agents merge and continue on the path of the pursued agent (a so-called "bugs" model). Cyclic pursuit is, in both cases, a gathering algorithm, which has been previously analyzed. The novelty of our work is the derivation of emergent behaviours, in both linear and non-linear cyclic pursuit, in the presence of an exogenous broadcast control detected by a random subset of agents. We show that the emergent behavior of the swarm depends on the type of cyclic pursuit. In the linear case, the agents asymptotically align in the desired direction and move with a common speed which is a proportional to the ratio of the number of agents detecting the broadcast control to the total number of agents in the swarm, for any magnitude of input (velocity) signal. In the non-linear case, the agents gather and move with a shared velocity, which equals the input velocity signal, independently of the number of agents detecting the broadcast signal.

中文翻译：

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代理在循环追踪中的指导

本报告研究了由一组随机代理检测到的外部广播信号控制的执行循环跟踪的代理系统的紧急行为。分析了两种类型的循环追踪：1) 线性循环追踪，其中每个智能体感知其目标或领先智能体的相对位置 2) 非线性循环追踪，其中智能体只能感知与其领先智能体和碰撞智能体合并的方向并继续沿着被追踪代理的路径前进（所谓的“错误”模型）。在这两种情况下，循环追踪都是一种收集算法，之前已经分析过。我们工作的新颖之处在于，在存在由随机代理子集检测到的外源广播控制的情况下，线性和非线性循环追踪中的紧急行为的推导。我们表明，群体的紧急行为取决于循环追踪的类型。在线性情况下，代理在所需方向上渐近对齐并以共同速度移动，该速度与检测广播控制的代理数量与群中代理总数的比率成正比，对于任何大小的输入（速度）信号。在非线性情况下，代理以共享速度聚集和移动，该速度等于输入速度信号，与检测广播信号的代理数量无关。对于任何幅度的输入（速度）信号。在非线性情况下，代理以共享速度聚集和移动，该速度等于输入速度信号，与检测广播信号的代理数量无关。对于任何幅度的输入（速度）信号。在非线性情况下，代理以共享速度聚集和移动，该速度等于输入速度信号，与检测广播信号的代理数量无关。