Stand Up Indulgent Gathering

TL;DR

This paper introduces a novel algorithm for fully synchronous mobile robots to achieve crash-tolerant gathering in a plane, even from arbitrary initial configurations, with proven efficiency proportional to initial distances.

Contribution

It provides the first solution for crash-tolerant gathering in the fully synchronous setting under minimal assumptions, without additional hypotheses.

Findings

Robots gather at the same location if no crashes occur.

Remaining robots gather at crash points if crashes occur.

Gathering time is proportional to initial maximum distance.

Abstract

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.