# Fast Uniform Dispersion of a Crash-prone Swarm

## TL;DR

This paper presents a model for a swarm of autonomous robots that can quickly and reliably cover an unknown environment despite frequent crashes and limited space, using simple local rules and a process inspired by statistical mechanics.

## Contribution

It introduces a new model for robot swarm coverage that accounts for crashes and asynchronicity, demonstrating linear-time completion under these challenging conditions.

## Key findings

- Robots complete coverage in linear time asymptotically almost surely.
- Coverage time degrades gracefully with crash frequency.
- The model is based on the totally asymmetric simple exclusion process.

## Abstract

We consider the problem of completely covering an unknown discrete environment with a swarm of asynchronous, frequently-crashing autonomous mobile robots. We represent the environment by a discrete graph, and task the robots with occupying every vertex and with constructing an implicit distributed spanning tree of the graph. The robotic agents activate independently at random exponential waiting times of mean $1$ and enter the graph environment over time from a source location. They grow the environment's coverage by 'settling' at empty locations and aiding other robots' navigation from these locations. The robots are identical and make decisions driven by the same simple and local rule of behaviour. The local rule is based only on the presence of neighbouring robots, and on whether a settled robot points to the current location. Whenever a robot moves, it may crash and disappear from the environment. Each vertex in the environment has limited physical space, so robots frequently obstruct each other. Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile robots complete their mission in linear time asymptotically almost surely, and time to completion degrades gracefully with the frequency of the crashes. Our model and analysis are based on the well-studied "totally asymmetric simple exclusion process" in statistical mechanics.