Stabilization of planar collective motion: All-to-all communication

Rodolphe Sepulchre; Derek A. Paley; Naomi Ehrich Leonard

doi:10.1109/TAC.2007.898077

Stabilization of planar collective motion: All-to-all communication

Rodolphe Sepulchre, Derek A. Paley, Naomi Ehrich Leonard

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

455 Scopus citations

Abstract

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.

Original language	English (US)
Pages (from-to)	811-824
Number of pages	14
Journal	IEEE Transactions on Automatic Control
Volume	52
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2007.898077
State	Published - May 2007

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Keywords

Cooperative control
Geometric control
Multi-agent systems
Stabilization

Access to Document

10.1109/TAC.2007.898077

Cite this

@article{f3c39986a7fa47f8a7655996c1168137,

title = "Stabilization of planar collective motion: All-to-all communication",

abstract = "This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.",

keywords = "Cooperative control, Geometric control, Multi-agent systems, Stabilization",

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

note = "Funding Information: Manuscript received June 27, 2005; revised February 20, 2006 and July 24, 2006. Recommended by Associate Editor F. Bullo. The work of D. A. Paley was supported by the National Science Foundation Graduate Research Fellowship, the Princeton University Gordon Wu Graduate Fellowship, and the Pew Charitable Trust under Grant 2000-002558. The work of N. E. Leonard was supported in part by the Office of Naval Research under Grants N00014-02-1-0861 and N00014-04-1-0534. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its author(s).",

year = "2007",

month = may,

doi = "10.1109/TAC.2007.898077",

language = "English (US)",

volume = "52",

pages = "811--824",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "5",

}

TY - JOUR

T1 - Stabilization of planar collective motion

T2 - All-to-all communication

AU - Sepulchre, Rodolphe

AU - Paley, Derek A.

AU - Leonard, Naomi Ehrich

N1 - Funding Information: Manuscript received June 27, 2005; revised February 20, 2006 and July 24, 2006. Recommended by Associate Editor F. Bullo. The work of D. A. Paley was supported by the National Science Foundation Graduate Research Fellowship, the Princeton University Gordon Wu Graduate Fellowship, and the Pew Charitable Trust under Grant 2000-002558. The work of N. E. Leonard was supported in part by the Office of Naval Research under Grants N00014-02-1-0861 and N00014-04-1-0534. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its author(s).

PY - 2007/5

Y1 - 2007/5

N2 - This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.

AB - This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.

KW - Cooperative control

KW - Geometric control

KW - Multi-agent systems

KW - Stabilization

UR - http://www.scopus.com/inward/record.url?scp=34249023580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249023580&partnerID=8YFLogxK

U2 - 10.1109/TAC.2007.898077

DO - 10.1109/TAC.2007.898077

M3 - Article

AN - SCOPUS:34249023580

SN - 0018-9286

VL - 52

SP - 811

EP - 824

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 5

ER -

Stabilization of planar collective motion: All-to-all communication

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this