Mutual Visibility with ASYNC Luminous Robots Having Inaccurate Movements

Abstract

In this paper, we initiate the study of the Mutual Visibility problem using oblivious luminous point robots that have inaccurate movements. Robots are opaque i.e., two robots see each other only if the line segment connecting them contains no robots. Each robot operates in Look-Compute-Move cycles. A robot has a light attached to it. We define the inaccuracy in the movement of a robot r as a deviation from its target point T to a point $T'$ such that $\angle TrT' <90^\circ$. From any initial configuration of the robots on the Euclidean plane, the aim of the problem is 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 a collision-free algorithm that uses 3 colors and runs in $\mathcal {O}(N)$ epoch under asynchronous setting, where N is the number of robots. An epoch is the smallest time interval in which all robots get activated and execute LCM cycle at least once. We also study the problem in presence of faulty robots, where by fault, we mean mobility failure in which the robots become immobile after fault. This fault does not affect the light of the robots. Any robot can encounter fault at any time. Moreover, a robot can be faulty along with exhibiting inaccuracy in its movement. We also present a fault-tolerant algorithm which aims to bring the robots in a configuration where no three non-faulty robots can collinear and no faulty robot lies between two non-faulty robot. We prove that the non-faulty robots achieve mutual visibility in $\mathcal {O}(N)$ epochs under asynchronous settings.

Supported by Prime Minister’s Research Fellowship (PMRF) scheme of the Govt. of India (PMRF-ID: 1902165).

Supported by CSIR, Govt. of India, Grant Number: 09/731(0178)/2020-EMR-I.