Byzantine convergence in robot networks: The price of asynchrony

Abstract

We study the convergence problem in fully asynchronous, uni-dimensional robot networks that are prone to Byzantine (i.e. malicious) failures. In these settings, oblivious anonymous robots with arbitrary initial positions are required to eventually converge to an a priori unknown position despite a subset of them exhibiting Byzantine behavior. Our contribution is twofold. We propose a deterministic algorithm that solves the problem in the most generic settings: fully asynchronous robots that operate in the non-atomic CORDA model. Our algorithm provides convergence in 5f + 1-sized networks where f is the upper bound on the number of Byzantine robots. Additionally, we prove that 5f + 1 is a lower bound whenever robot scheduling is fully asynchronous. This constrasts with previous results in partially synchronous robot networks, where 3f + 1 robots are necessary and sufficient. © 2009 Springer-Verlag.