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arXiv · 2610.06939

When Robots Crash: Optimal Asynchronous Gathering at Weber Meeting Nodes

Animesh Maiti·Prakhar Shukla·Abhinav Chakraborty·Subhash Bhagat
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Abstract

We study the \textit{optimal gathering} problem over a finite set of designated \textit{meeting nodes} for \textit{asynchronous, anonymous,} and \textit{oblivious} mobile robots on an infinite grid under crash faults. The robots have global visibility and strong multiplicity detection, but share neither a coordinate system nor chirality. The objective is to gather all non-faulty robots at a \textsc{Weber Meeting Node}, minimizing the total Manhattan distance from their initial positions. Up to $n-2$ robots may crash permanently, and such crashes are indistinguishable from arbitrary delays. Existing approaches often rely on a designated robot to break symmetry, whose crash may block the remaining robots indefinitely. Instead, our approach enables every robot to independently select the same target from its snapshot, while target-dependent restricted shortest paths preserve the target as a \textsc{Weber Meeting Node}. We prove that, under strong multiplicity detection, optimal gathering is impossible from certain fully symmetric configurations. For all remaining configurations, our algorithm \textsc{CrashTolerantWeberGathering()} selects a unique common target, preserves its optimality throughout the execution, and allows non-faulty robots to progress without waiting for crashed robots, thereby guaranteeing gathering in finite time.

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Animesh Maiti, Prakhar Shukla, Abhinav Chakraborty, Subhash Bhagat. 2026-10-03. When Robots Crash: Optimal Asynchronous Gathering at Weber Meeting Nodes. https://arxiv.org/abs/2610.06939

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