# Gathering at Fixed Nodes by Oblivious Mobile Robots

## Date of Submission

June 2023

## Date of Award

6-1-2024

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Doctoral Thesis

## Degree Name

Doctor of Philosophy

## Subject Name

Computer Science

## Department

Advance Computing and Microelectronics Unit (ACMU-Kolkata)

## Supervisor

Mukhopadhyay, Krishnendu (ACMU-Kolkata; ISI)

## Abstract (Summary of the Work)

A swarm of robots is a distributed system of small, autonomous, inexpensive mobile robots that work collaboratively to achieve some specific goal. This thesis aims to study the gathering problem, which is a fundamental coordination problem. In the initial configuration, the robots are located at distinct nodes of an input graph. The main objective of the problem is that all the robots must meet at a point. In this thesis, the deployment space of the robots is assumed to be an infinite grid graph. This thesis considers the gathering over meeting nodes problem in an infinite grid do- main. The input grid graph consists of some nodes which are marked as meeting nodes. The problem requires the mobile robots to gather at one of the pre-fixed meeting nodes. Several variations of the problem have been considered. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deter- ministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The problem has also been studied under the objective function that minimizes the total number of moves made by all the robots to finalize the gathering task. A deterministic distributed algorithm has been proposed to solve the problem for all those solvable configurations, and the initial configurations for which the problem is unsolvable have been characterized. The proposed gathering algorithm is optimal with respect to the total number of moves performed by all the robots in order to finalize the gathering. Another variation of the problem considers two disjoint and finite groups of anonymous robots. The initial configurations also consist of two finite and disjoint sets of heteroge- neous meeting nodes. The objective is to design a distributed algorithm that gathers all the robots belonging to the first team at one of the meeting nodes belonging to the first type. Similarly, all the robots in the second team must gather at one of the meeting nodes belonging to the second type. The initial configurations for which the gathering problem is unsolvable have been characterized. For the remaining initial configurations, a distributed gathering algorithm has been proposed. The parking problem can also be considered as a variation of the problem. As a solution to the parking problem, the robots need to partition themselves into groups so that each parking node contains a number of robots equal to the capacity of the node. It is assumed that the number of robots in the initial configuration represents the sum of the capacities of the parking nodes. Under this setup, we have characterized all the initial configurations and the values of ki for which the problem is unsolvable. For the remaining configurations, a deterministic distributed algorithm was proposed.

## Control Number

ISILib-TH

## Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

## DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

## Recommended Citation

Chakraborty, Abhinav Dr., "Gathering at Fixed Nodes by Oblivious Mobile Robots" (2024). *Doctoral Theses*. 504.

https://digitalcommons.isical.ac.in/doctoral-theses/504

## Comments

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