Global Swarming While Preserving Connectivity via Lagrange–Poincarè Equations

Aykut Cihan Satici

doi:10.1016/j.automatica.2016.04.042

Global Swarming While Preserving Connectivity via Lagrange–Poincarè Equations

Aykut Cihan Satici

Mechanical and Biomedical Engineering Department

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

Abstract

<div class="line" id="line-5"> <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: medium;'> In this paper, we exploit symmetry properties of multi-agent robot systems to design control laws that preserve connectivity while swarming. We start by designing a connectivity control law for agents with configuration spaces  &reals; <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 14.4px;'> 3 <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: medium;'> and  <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 14.4px;'> SO (3) <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: medium;'>  that is invariant under the action of the special Euclidean group  <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 14.4px;'> SE (3) <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: medium;'>  and the special orthogonal group  <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: 14.4px;'> SO (3) <span style='color: rgb(80, 80, 80); font-family: Arial, Helvetica, "Lucida Sans Unicode", "Microsoft Sans Serif", "Segoe UI Symbol", STIXGeneral, "Cambria Math", "Arial Unicode MS", sans-serif; font-size: medium;'> , respectively. Therefore, the dynamics of such multi-agent systems is amenable to be reduced by these group actions. We then utilize the Lagrange–Poincaré equations that split the Euler–Lagrange equations for the multi-agent system into horizontal and vertical parts. The invariance of the connectivity controller implies that its control effort has zero vertical component. We then use the resulting vertical equations of motion to design a control law that asymptotically stabilizes the centroid and the orientation of the swarm at a desired pose. </div>

Original language	American English
Journal	Automatica
Volume	71
DOIs	https://doi.org/10.1016/j.automatica.2016.04.042
State	Published - Sep 2016

Keywords

Lagrange–Poincaré
horizontal-vertical
multi-agent systems
principle bundles
swarming
symmetry

EGS Disciplines

Mechanical Engineering

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@article{84d94d8268ed4067aa9da5edfccb9689,

title = "Global Swarming While Preserving Connectivity via Lagrange–Poincar{\`e} Equations",

abstract = " In this paper, we exploit symmetry properties of multi-agent robot systems to design control laws that preserve connectivity while swarming. We start by designing a connectivity control law for agents with configuration spaces  &reals; 3 and  SO (3)  that is invariant under the action of the special Euclidean group  SE (3)  and the special orthogonal group  SO (3) , respectively. Therefore, the dynamics of such multi-agent systems is amenable to be reduced by these group actions. We then utilize the Lagrange–Poincaré equations that split the Euler–Lagrange equations for the multi-agent system into horizontal and vertical parts. The invariance of the connectivity controller implies that its control effort has zero vertical component. We then use the resulting vertical equations of motion to design a control law that asymptotically stabilizes the centroid and the orientation of the swarm at a desired pose. ",

keywords = "Lagrange–Poincar{\'e}, horizontal-vertical, multi-agent systems, principle bundles, swarming, symmetry",

author = "Satici, {Aykut Cihan}",

year = "2016",

month = sep,

doi = "10.1016/j.automatica.2016.04.042",

language = "American English",

volume = "71",

}

TY - JOUR

T1 - Global Swarming While Preserving Connectivity via Lagrange–Poincarè Equations

AU - Satici, Aykut Cihan

PY - 2016/9

Y1 - 2016/9

N2 - In this paper, we exploit symmetry properties of multi-agent robot systems to design control laws that preserve connectivity while swarming. We start by designing a connectivity control law for agents with configuration spaces  &reals; 3 and  SO (3)  that is invariant under the action of the special Euclidean group  SE (3)  and the special orthogonal group  SO (3) , respectively. Therefore, the dynamics of such multi-agent systems is amenable to be reduced by these group actions. We then utilize the Lagrange–Poincaré equations that split the Euler–Lagrange equations for the multi-agent system into horizontal and vertical parts. The invariance of the connectivity controller implies that its control effort has zero vertical component. We then use the resulting vertical equations of motion to design a control law that asymptotically stabilizes the centroid and the orientation of the swarm at a desired pose.

AB - In this paper, we exploit symmetry properties of multi-agent robot systems to design control laws that preserve connectivity while swarming. We start by designing a connectivity control law for agents with configuration spaces  &reals; 3 and  SO (3)  that is invariant under the action of the special Euclidean group  SE (3)  and the special orthogonal group  SO (3) , respectively. Therefore, the dynamics of such multi-agent systems is amenable to be reduced by these group actions. We then utilize the Lagrange–Poincaré equations that split the Euler–Lagrange equations for the multi-agent system into horizontal and vertical parts. The invariance of the connectivity controller implies that its control effort has zero vertical component. We then use the resulting vertical equations of motion to design a control law that asymptotically stabilizes the centroid and the orientation of the swarm at a desired pose.

KW - Lagrange–Poincaré

KW - horizontal-vertical

KW - multi-agent systems

KW - principle bundles

KW - swarming

KW - symmetry

UR - https://doi.org/10.1016/j.automatica.2016.04.042

U2 - 10.1016/j.automatica.2016.04.042

DO - 10.1016/j.automatica.2016.04.042

M3 - Article

VL - 71

JO - Automatica

JF - Automatica

ER -

Global Swarming While Preserving Connectivity via Lagrange–Poincarè Equations

Abstract

Keywords

EGS Disciplines

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