Coverage and field estimation on bounded domains by diffusive swarms

Karthik Elamvazhuthi, Chase Adams, Spring Berman

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

6 Citations (Scopus)

Abstract

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2867-2874
Number of pages8
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

Fingerprint

Swarm
Bounded Domain
Coverage
Scalar Field
Robots
Robot
Observability
Operator Semigroups
Advection
Scenarios
Advection-diffusion
Exponential Convergence
Reaction-diffusion
Heat Equation
Diffusion Process
Diffusion Coefficient
Control Strategy
Boundedness
Semigroup
Directly proportional

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

Cite this

Elamvazhuthi, K., Adams, C., & Berman, S. (2016). Coverage and field estimation on bounded domains by diffusive swarms. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 2867-2874). [7798696] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798696

Coverage and field estimation on bounded domains by diffusive swarms. / Elamvazhuthi, Karthik; Adams, Chase; Berman, Spring.

2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2867-2874 7798696.

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

Elamvazhuthi, K, Adams, C & Berman, S 2016, Coverage and field estimation on bounded domains by diffusive swarms. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798696, Institute of Electrical and Electronics Engineers Inc., pp. 2867-2874, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798696
Elamvazhuthi K, Adams C, Berman S. Coverage and field estimation on bounded domains by diffusive swarms. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2867-2874. 7798696 https://doi.org/10.1109/CDC.2016.7798696
Elamvazhuthi, Karthik ; Adams, Chase ; Berman, Spring. / Coverage and field estimation on bounded domains by diffusive swarms. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 2867-2874
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