Complete Visibility for Mobile Robots with Lights Tolerating Faults

Abstract

We consider the distributed setting of N autonomous mobile robots that operate in LookCompute-Move (LCM) cycles and communicate with other robots using colored lights (the robots with lights model). We study the fundamental Complete Visibility problem of repositioning N robots on a plane so that each robot is visible to all others. 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 are interested in fault-tolerant algorithms; all existing algorithms for this problem are not fault-tolerant (except handling some special cases). 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, independently of the behavior of the faulty ones. We model mobility failures as crash faults in which each faulty robot is allowed to stop its movement at any time and, once the faulty robot stopped moving, that robot will remain stationary indefinitely. In this paper, we present and analyze an algorithm that solves Complete Visibility tolerating one crash-faulty robot in a system of N ≥ 3 robots, starting from any arbitrary initial configuration. We also provide an impossibility result on solving Complete Visibility if a single robot is Byzantine-faulty in a system of N = 3 robots; in the Byzantine fault model, a faulty robot might behave in an unpredictable, arbitrary, and unforeseeable ways. Furthermore, we discuss how to solve Complete Visibility for some initial configurations of robots (which we call feasible initial configurations) in the crash fault model, where two robots are (crash) faulty.

Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case

“…Di Luna et al [6] observed that their COMPLETE VISIBILITY algorithm for non-faulty robots can solve COMPLETE VISIBILITY tolerating a faulty robot if the faulty robot is in the perimeter of the convex hull formed by the initial configuration of the robots. Aljohani and Sharma [16] provided an algorithm that tolerates one faulty robot (irrespective of whether the faulty robot is in the interior or not) when robots have both-axis agreement in the semi-synchronous setting under rigid movements. The idea was to position all the robots on the corners of a convex hull except the faulty robot that may still be in the interior of the hull in the final configuration.…”

“…The idea was to position all the robots on the corners of a convex hull except the faulty robot that may still be in the interior of the hull in the final configuration. Aljohani and Sharma [16] also showed that COMPLETE VISIBILITY can be solved tolerating, at most, 2 faulty robots under certain assumptions on initial configurations. Recently, Poudel et al [17] assumed a weaker one-axis agreement and presented an algorithm for COMPLETE VISIBILITY in the asynchronous setting that can tolerate any number of faulty robots.…”

On the mutual visibility in Cartesian products and triangle-free graphs

“…Namely, satisfying that for any exchanged information there should be a channel which does not pass through other entities. For some of these applied researches see for instance [1,2,8,15,31].…”

Traversing a Graph in General Position

“…In fact this research was inspired by the delivery robots belonging to Starship Technologies [14] that deliver groceries to the inhabitants of cities including Milton Keynes, home of the Open University. For some related studies on robot mobility in computer science see [1, 2, 4]. We introduce a variant that describes the largest number of robots that can travel through a network such that each vertex of the network can be visited by a robot, while at every stage any pair of robots can see each other through any shortest path between their positions without being obstructed by another robot.…”