Stabilization of symmetric formations to motion around convex loops

Derek A. Paley; Naomi Ehrich Leonard; Rodolphe Sepulchre

doi:10.1016/j.sysconle.2007.08.005

Stabilization of symmetric formations to motion around convex loops

Derek A. Paley
, Naomi Ehrich Leonard
, Rodolphe Sepulchre

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.

Original language	English (US)
Pages (from-to)	209-215
Number of pages	7
Journal	Systems and Control Letters
Volume	57
Issue number	3
DOIs	https://doi.org/10.1016/j.sysconle.2007.08.005
State	Published - Mar 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Keywords

Cooperative control
Curvature
Laplacian
Oscillators
Sensor networks

Access to Document

10.1016/j.sysconle.2007.08.005

Cite this

@article{c538b2f4b03543ccabd5fd83bbabdf0d,

title = "Stabilization of symmetric formations to motion around convex loops",

abstract = "We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.",

keywords = "Cooperative control, Curvature, Laplacian, Oscillators, Sensor networks",

author = "Paley, \{Derek A.\} and Leonard, \{Naomi Ehrich\} and Rodolphe Sepulchre",

note = "Funding Information: The authors would like to acknowledge discussions with Fumin Zhang regarding an earlier version of this paper [9] . This research was supported by the NSF Graduate Research Fellowship, the Princeton Gordon Wu Graduate Fellowship, the Pew Charitable Trust Grant 2000-002558, and ONR Grants N00014-02-1-0826, N00014-02-1-0861, and N00014-04-1-0534. This paper presents research results of the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its authors. ",

year = "2008",

month = mar,

doi = "10.1016/j.sysconle.2007.08.005",

language = "English (US)",

volume = "57",

pages = "209--215",

journal = "Systems and Control Letters",

issn = "0167-6911",

publisher = "Elsevier B.V.",

number = "3",

}

TY - JOUR

T1 - Stabilization of symmetric formations to motion around convex loops

AU - Paley, Derek A.

AU - Leonard, Naomi Ehrich

AU - Sepulchre, Rodolphe

N1 - Funding Information: The authors would like to acknowledge discussions with Fumin Zhang regarding an earlier version of this paper [9] . This research was supported by the NSF Graduate Research Fellowship, the Princeton Gordon Wu Graduate Fellowship, the Pew Charitable Trust Grant 2000-002558, and ONR Grants N00014-02-1-0826, N00014-02-1-0861, and N00014-04-1-0534. This paper presents research results of the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its authors.

PY - 2008/3

Y1 - 2008/3

N2 - We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.

AB - We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.

KW - Cooperative control

KW - Curvature

KW - Laplacian

KW - Oscillators

KW - Sensor networks

UR - https://www.scopus.com/pages/publications/43049140503

UR - https://www.scopus.com/pages/publications/43049140503#tab=citedBy

U2 - 10.1016/j.sysconle.2007.08.005

DO - 10.1016/j.sysconle.2007.08.005

M3 - Article

AN - SCOPUS:43049140503

SN - 0167-6911

VL - 57

SP - 209

EP - 215

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 3

ER -

Stabilization of symmetric formations to motion around convex loops

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this