# Asynchronous Scattering

## TL;DR

This paper demonstrates that asynchronous scattering of mobile robots is achievable under certain sensing capabilities, providing a constructive probabilistic approach and identifying key limitations when sensors are absent.

## Contribution

It introduces a constructive, probabilistic protocol for asynchronous scattering with vision and multiplicity detection, and establishes impossibility results without these features.

## Key findings

- Asynchronous scattering is solvable with vision and multiplicity detection.
- Scattering remains unsolvable without either vision or multiplicity detection in certain cases.
- A new proof technique for probabilistic robot protocols is presented.

## Abstract

In this paper, we consider the problem of scattering a swarm of mobile oblivious robots in a continuous space. We consider the fully asynchronous setting where robots may base their computation on past observations, or may be observed by other robots while moving. It turns out that asynchronous scattering is solvable in the most general case when both vision (the ability to see others robots positions) and weak local multiplicity detection are available. In the case of a bidimensional Euclidean space, ASYNC scattering is also solvable with blind robots if moves are rigid. Our approach is constructive and modular, as we present a proof technique for probabilistic robot protocols that is of independent interest and can be reused for other purposes. On the negative side, we show that when robots are both blind and have no multiplicity detection, the problem is unsolvable, and when only one of those is available, the problem remains unsolvable on the line.