Abstract

In this paper, we generalize our diffusion-based approach [8] to achieve coverage of a bounded domain by a robotic swarm according to a target probability density that is a function of a locally measurable scalar field. We generalize this approach in two different ways. First, we show that our method can be extended in a natural way to scenarios where the robots' state space is a compact Riemannian manifold, which is the case if the robots are confined to a surface or if their configuration space is non-Euclidean due to dynamical constraints such as those present in most mechanical systems. Then, we establish the stability properties of a weighted variation of the porous media equation, a nonlinear partial differential equation (PDE). Coverage strategies based on these nonlinear PDEs have the advantage that the robots stop moving once the equilibrium probability density is reached, in contrast to our original approach [8]. We establish long-time stability properties of the target probability densities using semigroup theoretic arguments. We validate our theoretical results through stochastic simulations of a linear diffusion-based coverage strategy on a 2-dimensional sphere and numerical solutions of the weighted porous media equation on the 2-dimensional torus.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1341-1346
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Swarm Robotics
Probability Density
Robotics
Porous Medium Equation
Coverage
Robot
Robots
Porous materials
Linear Diffusion
Generalise
Nonlinear PDE
Target
Stochastic Simulation
Configuration Space
Nonlinear Partial Differential Equations
Compact Manifold
Mechanical Systems
Scalar Field
Partial differential equations
Riemannian Manifold

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Elamvazhuthi, K., & Berman, S. (2019). Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 1341-1346). [8618889] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8618889

Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms. / Elamvazhuthi, Karthik; Berman, Spring.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1341-1346 8618889 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Elamvazhuthi, K & Berman, S 2019, Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8618889, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 1341-1346, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8618889
Elamvazhuthi K, Berman S. Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1341-1346. 8618889. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8618889
Elamvazhuthi, Karthik ; Berman, Spring. / Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 1341-1346 (Proceedings of the IEEE Conference on Decision and Control).
@inproceedings{77fe0a90dcf64542b699b3b4dc756d95,
title = "Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms",
abstract = "In this paper, we generalize our diffusion-based approach [8] to achieve coverage of a bounded domain by a robotic swarm according to a target probability density that is a function of a locally measurable scalar field. We generalize this approach in two different ways. First, we show that our method can be extended in a natural way to scenarios where the robots' state space is a compact Riemannian manifold, which is the case if the robots are confined to a surface or if their configuration space is non-Euclidean due to dynamical constraints such as those present in most mechanical systems. Then, we establish the stability properties of a weighted variation of the porous media equation, a nonlinear partial differential equation (PDE). Coverage strategies based on these nonlinear PDEs have the advantage that the robots stop moving once the equilibrium probability density is reached, in contrast to our original approach [8]. We establish long-time stability properties of the target probability densities using semigroup theoretic arguments. We validate our theoretical results through stochastic simulations of a linear diffusion-based coverage strategy on a 2-dimensional sphere and numerical solutions of the weighted porous media equation on the 2-dimensional torus.",
author = "Karthik Elamvazhuthi and Spring Berman",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8618889",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1341--1346",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",

}

TY - GEN

T1 - Nonlinear Generalizations of Diffusion-Based Coverage by Robotic Swarms

AU - Elamvazhuthi, Karthik

AU - Berman, Spring

PY - 2019/1/18

Y1 - 2019/1/18

N2 - In this paper, we generalize our diffusion-based approach [8] to achieve coverage of a bounded domain by a robotic swarm according to a target probability density that is a function of a locally measurable scalar field. We generalize this approach in two different ways. First, we show that our method can be extended in a natural way to scenarios where the robots' state space is a compact Riemannian manifold, which is the case if the robots are confined to a surface or if their configuration space is non-Euclidean due to dynamical constraints such as those present in most mechanical systems. Then, we establish the stability properties of a weighted variation of the porous media equation, a nonlinear partial differential equation (PDE). Coverage strategies based on these nonlinear PDEs have the advantage that the robots stop moving once the equilibrium probability density is reached, in contrast to our original approach [8]. We establish long-time stability properties of the target probability densities using semigroup theoretic arguments. We validate our theoretical results through stochastic simulations of a linear diffusion-based coverage strategy on a 2-dimensional sphere and numerical solutions of the weighted porous media equation on the 2-dimensional torus.

AB - In this paper, we generalize our diffusion-based approach [8] to achieve coverage of a bounded domain by a robotic swarm according to a target probability density that is a function of a locally measurable scalar field. We generalize this approach in two different ways. First, we show that our method can be extended in a natural way to scenarios where the robots' state space is a compact Riemannian manifold, which is the case if the robots are confined to a surface or if their configuration space is non-Euclidean due to dynamical constraints such as those present in most mechanical systems. Then, we establish the stability properties of a weighted variation of the porous media equation, a nonlinear partial differential equation (PDE). Coverage strategies based on these nonlinear PDEs have the advantage that the robots stop moving once the equilibrium probability density is reached, in contrast to our original approach [8]. We establish long-time stability properties of the target probability densities using semigroup theoretic arguments. We validate our theoretical results through stochastic simulations of a linear diffusion-based coverage strategy on a 2-dimensional sphere and numerical solutions of the weighted porous media equation on the 2-dimensional torus.

UR - http://www.scopus.com/inward/record.url?scp=85062169666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062169666&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8618889

DO - 10.1109/CDC.2018.8618889

M3 - Conference contribution

AN - SCOPUS:85062169666

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1341

EP - 1346

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -