Fault-tolerant complete visibility for asynchronous robots with lights under one-axis agreement

Abstract

We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles and communicate with other robots using colored lights following the robots with lights model. We assume obstructed visibility under which a robot cannot see another robot if a third robot is positioned between them on the straight line connecting them. We study the fundamental Complete Visibility problem of repositioning N robots, starting from N distinct points, on a plane so that each robot is visible to all others. We are interested in fault-tolerant algorithms. We study fault-tolerance with respect to failures on the mobility of robots. Therefore, any algorithm for Complete Visibility is required to provide visibility between all non-faulty robots (i.e., no three non-faulty robots are collinear and no faulty robot is between two non-faulty robots on the straight line connecting them), independently of the behavior of the faulty ones. We model mobility failures as crash faults in which each faulty robot may stop its movement at any time and, once it stopped moving, it will remain stationary indefinitely thereafter. There exists an algorithm for this problem that tolerates a single faulty robot in the semi-synchronous setting under both-axis agreement. In that algorithm, the light of the faulty robot does not need to work correctly after the robot experiences fault. In this article, we assume the model in which, even after a robot experiences fault, its light still operates correctly and provide the first algorithm for Complete Visibility that tolerates f≤N faulty robots in the asynchronous setting under one-axis agreement. The proposed algorithm has many interesting properties.