We consider a swarm of mobile robots evolving in a bidimensional Euclidean space. We study a variant of the crash-tolerant gathering problem: if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in finite time; if one or several robots crash at the same location, the remaining correct robots gather at the crash location to rescue them. Motivated by impossibility results in the semi-synchronous setting, we present the first solution to the problem for the fully synchronous setting that operates in the vanilla Look-Compute-Move model with no additional hypotheses: robots are oblivious, disoriented, have no multiplicity detection capacity, and may start from arbitrary positions (including those with multiplicity points). We furthermore show that robots gather in a time that is proportional to the initial maximum distance between robots.

翻译：考虑在二维欧几里得空间中演化的一群移动机器人。我们研究容错聚集问题的一个变种：若无机器人崩溃，所有机器人需在有限时间内会合于同一任意未知位置；若一个或多个机器人崩溃于同一位置，其余正常机器人则聚集至崩溃位置以实施救援。鉴于半同步设置下存在的不可能性结论，我们针对全同步设置首次提出了解决方案，该方案基于经典"观-算-动"（Look-Compute-Move）模型，且无需额外假设：机器人具有无记忆性、方向迷失、无多重性检测能力，并可起始于任意位置（包括存在多重点的位置）。此外，我们证明机器人聚集所需时间与初始机器人间最大距离成正比。