Gathering Despite Defected View

TL;DR

This paper introduces a new defected view model for robot observation, proposing algorithms for the gathering problem under specific defected conditions and proving impossibility results for others.

Contribution

It presents novel algorithms for robot gathering in defected view models and establishes fundamental impossibility results for certain defected observation scenarios.

Findings

Algorithms successfully solve gathering in (N,N-2)-defected and (4,2)-defected models.

Impossibility results show no deterministic gathering in (3,1)-defected models.

Certain defected models prevent deterministic gathering, highlighting limitations of robot observation.

Abstract

An autonomous mobile robot system consisting of many mobile computational entities (called robots) attracts much attention of researchers, and to clarify the relation between the capabilities of robots and solvability of the problems is an emerging issue for a recent couple of decades. Generally, each robot can observe all other robots as long as there are no restrictions for visibility range or obstructions, regardless of the number of robots. In this paper, we provide a new perspective on the observation by robots; a robot cannot necessarily observe all other robots regardless of distances to them. We call this new computational model defected view model. Under this model, in this paper, we consider the gathering problem that requires all the robots to gather at the same point and propose two algorithms to solve the gathering problem in the adversarial ($N$,$N-2$)-defected model for $N \geq 5$ (where each robot observes at most $N-2$ robots chosen adversarially) and the distance-based (4,2)-defected model (where each robot observes at most 2 closest robots to itself) respectively, where $N$ is the number of robots. Moreover, we present an impossibility result showing that there is no (deterministic) gathering algorithm in the adversarial or distance-based (3,1)-defected model. Moreover, we show an impossibility result for the gathering in a relaxed ($N$, $N-2$)-defected model.