Uniform Circle Formation by Transparent Fat Robots

TL;DR

This paper presents a novel collision-free algorithm enabling transparent fat robots to form a uniform circle without explicit communication, despite limited sensing and no shared coordinate system.

Contribution

It introduces the first known method for uniform circle formation by fat robots under semi-synchronous, no-communication, and limited orientation assumptions.

Findings

Robots successfully form a uniform circle in finite steps.

The proposed strategy ensures collision-free movement.

First solution for fat robots in this model.

Abstract

This paper addresses the problem of Uniform Circle Formation by n > 1 transparent disc robots (fat robots). The robots execute repetitive cycles of the states look-compute-move in semi-synchronous manner where a set of robots execute the cycle simultaneously. They do not communicate by any explicit message passing. However, they can sense or observes the positions of other robots around themselves through sensors or camera. The robots are unable to recover the past actions and observations. They have no unique identity. The robots do not have any global coordinate system. They agree upon only y-axis (South and North direction). However, they do not have chirality or common orientation of Y axis with respect to X axis. Being transparent the robots do not cause any visual obstructions for other robots. But, they act as physical obstacles for other robots. This paper proposes a collision free movement strategy for the robots to form a uniform circle (in other words convex regular polygon) executing finite number of cycles. To the best of our knowledge this is the first reported results on uniform circle formation for fat robots under the considered model.