Mutual visibility of luminous robots despite angular inaccuracy

Abstract

We initiate the study of the Mutual Visibility problem using N opaque luminous point robots that have inaccurate movements. Each robot operates in Look-Compute-Move cycles and has a persistent light attached to it to have a weak form of communication between robots using a constant number of colors. The inaccuracy for a robot r is an angular deviation from its target point T to a point T′ such that the angle ∠TrT′<90∘. The problem becomes unsolvable if this angle is ≥90∘. From any initial configuration of the robots on the Euclidean plane, the problem aims to arrange the robots in a configuration such that any two robots are visible to each other. We assume that the robots agree on one coordinate axis. We present two collision-free algorithms, a 2 color algorithm (which is optimal in the number of colors used) for semi-synchronous setting and a 3 color algorithm for asynchronous setting, both of which run in O(N) epochs. We also study the problem in the presence of mobile faulty robots. A robot can exhibit both mobility failure and angular inaccuracies in its movement. We present a fault-tolerant algorithm that aims to bring the robots in a configuration where no three non-faulty robots are collinear, and no faulty robot lies between two non-faulty robots. This algorithm uses 10 colors and takes O(N) epochs under asynchronous settings.