# Arbitrary Pattern Formation by Asynchronous Opaque Robots with Lights

## TL;DR

This paper addresses the arbitrary pattern formation problem for autonomous, opaque robots with lights in obstructed visibility, providing algorithms for different levels of coordinate system agreement and characterizing initial configurations for pattern formation.

## Contribution

It introduces algorithms for pattern formation with opaque robots under obstructed visibility, considering one and two axis agreement scenarios, and characterizes initial configurations for success.

## Key findings

- Algorithms for pattern formation in obstructed visibility
- Full characterization of initial configurations for success
- Works under asynchronous, rigid movement assumptions

## Abstract

The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input. The robots are assumed to be autonomous, anonymous and identical. They operate in Look-Compute-Move cycles under an asynchronous scheduler. The robots do not have access to any global coordinate system. The movement of the robots is assumed to be rigid, which means that each robot is able to reach its desired destination without interruption. The existing literature that investigates this problem, considers robots with unobstructed visibility. This work considers the problem in the more realistic obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. The robots are assumed to be punctiform and equipped with visible lights that can assume a constant number of predefined colors. We have studied the problem in two settings based on the level of consistency among the local coordinate systems of the robots: two axis agreement (they agree on the direction and orientation of both coordinate axes) and one axis agreement (they agree on the direction and orientation of only one coordinate axis). In both settings, we have provided a full characterization of initial configurations from where any arbitrary pattern can be formed.