Separation of Unconscious Robots with Obstructed Visibility

TL;DR

This paper introduces a collision-free algorithm for unconscious, opaque robots with obstructed visibility to separate into concentric semicircles, advancing understanding of autonomous robot coordination under limited visibility conditions.

Contribution

It presents the first algorithm for unconscious opaque robots with obstructed visibility to achieve separation into semicircles, under semi-synchronous scheduling.

Findings

Algorithm operates in O(n) epochs.

Robots coordinate with one axis without knowing total number.

Achieves collision-free separation from arbitrary configurations.

Abstract

We study a recently introduced \textit{unconscious} mobile robot model, where each robot is associated with a \textit{color}, which is visible to other robots but not to itself. The robots are autonomous, anonymous, oblivious and silent, operating in the Euclidean plane under the conventional \textit{Look-Compute-Move} cycle. A primary task in this model is the \textit{separation problem}, where unconscious robots sharing the same color must separate from others, forming recognizable geometric shapes such as circles, points, or lines. All prior works model the robots as \textit{transparent}, enabling each to know the positions and colors of all other robots. In contrast, we model the robots as \textit{opaque}, where a robot can obstruct the visibility of two other robots, if it lies on the line segment between them. Under this obstructed visibility, we consider a variant of the separation problem in which robots, starting from any arbitrary initial configuration, are required to separate into concentric semicircles. We present a collision-free algorithm that solves the separation problem under a semi-synchronous scheduler in $O(n)$ epochs, where $n$ is the number of robots. The robots agree on one coordinate axis but have no knowledge of $n$.