On the Synthesis of Mobile Robots Algorithms: the Case of Ring Gathering

TL;DR

This paper introduces a formal framework that automatically synthesizes distributed algorithms for mobile robot gathering in discrete spaces, demonstrated through a case study on ring topology with proven correctness.

Contribution

It presents a novel encoding of the gathering problem as a reachability game and automatically generates optimal algorithms for ring-shaped robot configurations.

Findings

Successfully generated an optimal gathering algorithm for three robots on a fixed ring.

Proved the algorithm's correctness for any ring size except when the number of robots divides the ring size.

Established the first formal framework for automatic algorithm synthesis in autonomous robot swarms.

Abstract

RecentadvancesinDistributedComputinghighlightmodelsandalgo- rithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs. This paper is the first to propose a formal framework to automatically design dis- tributed algorithms that are dedicated to autonomous mobile robots evolving in a discrete space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. Our contribution is threefold. First, we propose an encoding of the gathering problem as a reachability game. Then, we automatically generate an optimal distributed algorithm for three robots evolv- ing on a fixed size uniform ring. Finally, we prove by induction that the generated algorithm is also correct for any ring size except when an impossibility result holds (that is, when the number of robots divides the ring size).