A Distributed Algorithm for Gathering Many Fat Mobile Robots in the Plane

TL;DR

This paper presents a distributed algorithm enabling a group of autonomous, fat, non-transparent robots to gather in the plane using only vision, achieving a connected convex formation regardless of initial positions.

Contribution

It introduces a novel vision-based, distributed algorithm for gathering fat robots in asynchronous settings, ensuring convergence to a connected convex configuration.

Findings

Robots reach a convex hull with all on the boundary

The configuration becomes connected with robots touching neighbors

The algorithm guarantees termination from any initial setup

Abstract

In this work we consider the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., fat) in an asynchronous setting. Vision is the only mean of coordination. Using a state-machine representation we formulate the gathering problem and develop a distributed algorithm that solves the problem for any number of robots. The main idea behind our algorithm is for the robots to reach a configuration in which all the following hold: (a) The robots' centers form a convex hull in which all robots are on the convex, (b) Each robot can see all other robots, and (c) The configuration is connected, that is, every robot touches another robot and all robots together form a connected formation. We show that starting from any initial configuration, the robots, making only local decisions and coordinate by vision, eventually reach such a configuration and terminate, yielding a solution to the gathering problem.