SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 620-640, January 2021.
Gathering is a fundamental task for multiagent systems. The problem has been studied under various assumptions on the sensing capabilities of mobile agents. This paper addresses the problem for a group of agents that are identical and indistinguishable, oblivious, and lack the capacity of direct communication. At the beginning of unit time-intervals, the agents select random headings in the plane and then detect the presence of other agents behind them. Then they move forward only if no agents are detected in their sensing “back half-plane.” Two types of motion are considered: when no peers are detected behind them, either the agents perform unit jumps forward, or they start to move with unit speed while continuously sensing their back half-plane, and stop whenever another agent appears there. For the first type of motion extensive empirical evidence suggests that with high probability clustering occurs in finite expected time to a small region with diameter of about the size of the unit jump, while for continuous sensing and motion we can prove gathering in finite expected time if a “blind-zone” is assumed in their sensing half-plane. Relationships between the number of agents or the size of the blind-zone and convergence time are empirically studied and compared to a theoretical upper-bound dependent on these factors.

中文翻译：

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具有简单传感器的代理的概率收集

SIAM应用数学杂志，第81卷，第2期，第620-640页，2021年1月。
收集是多代理系统的一项基本任务。已经在关于移动代理的感测能力的各种假设下研究了该问题。本文针对一组相同且不可区分，遗忘且缺乏直接沟通能力的特工解决此问题。在单位时间间隔开始时，代理会选择平面中的随机航向，然后检测其后是否存在其他代理。然后，只有在其感测到的“后半平面”中未检测到任何代理时，它们才会向前移动。考虑两种类型的运动：当在他们后面未检测到任何同伴时，这些特工要么执行单位向前跳跃，要么在连续感测其后半平面的同时开始以单位速度运动，并在其他特工出现时停止。对于第一种运动，广泛的经验证据表明，在有限的预期时间内，高概率聚类会发生在直径约为单位跳跃大小的小区域，而对于连续感测和运动，如果存在，则可以证明在有限的预期时间内聚集在它们的感测半平面中假定为“盲区”。凭经验研究了代理数量或盲区大小与收敛时间之间的关系，并将其与取决于这些因素的理论上限进行了比较。