Pattern Formation for Asynchronous Robots without Agreement in Chirality

TL;DR

This paper introduces a deterministic algorithm enabling autonomous, homogeneous robots without agreement on chirality to form any specified asymmetric pattern in finite time, solely through observation.

Contribution

It presents the first finite-time pattern formation algorithm for asymmetric patterns without requiring agreement on chirality among robots.

Findings

Robots can form any asymmetric pattern in finite time.

The algorithm works under the CORDA model with no explicit communication.

Pattern formation is achieved solely through local observations.

Abstract

This paper presents a deterministic algorithm for forming a given asymmetric pattern in finite time by a set of autonomous, homogeneous, oblivious mobile robots under the CORDA model. The robots are represented as points on the 2D plane. There is no explicit communication between the robots. The robots coordinate among themselves by observing the positions of the other robots on the plane. Initially all the robots are assumed to be stationary. The robots have local coordinate systems defined by Sense of Direction (SoD), orientation or chirality and scale. Initially the robots are in asymmetric configuration. We show that these robots can form any given asymmetric pattern in finite time.