A Variational Integrator for the distance-based formation control of multi-agent systems

Leonardo J. Colombo, Hector Garcia de Marina

Publikation: Bidrag til tidsskriftKonferenceartikelForskningpeer review

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Resumé

Distance-based formation control of second order agents can be seen as a physical system of particles linked by springs, whose evolution can be described by a Lagrangian function. An interesting family of geometric integrators, called variational integrators, is defined by using discretizations of the Hamilton's principle of critical action. The variational integrators preserve some geometric features such as the symplectic structure, they preserve the momentum map, and the evolution of the system's energy presents a good (bounded) behavior. We derive variational integrators that can be employed in the context of distance-based formation control algorithms. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. Consequently, we can provide a faster identification of regions of attraction for desired distance-based shapes, and more computationally efficient estimation algorithms like Kalman filters that employ distance-based controllers as prediction models. We use a formation consisting of four autonomous planar agents as an example and benchmark to test and compare the performances of the proposed variational integrator.

OriginalsprogEngelsk
BogserieIFAC-PapersOnLine
Vol/bind51
Udgave nummer23
Sider (fra-til)76-81
ISSN2405-8963
DOI
StatusUdgivet - 2018
Begivenhed7th IFAC Workshop on Distributed Estimation and Control in Networked Systems - Groningen, Holland
Varighed: 27. aug. 201828. aug. 2018

Konference

Konference7th IFAC Workshop on Distributed Estimation and Control in Networked Systems
LandHolland
ByGroningen
Periode27/08/201828/08/2018

Fingeraftryk

Multi agent systems
Kalman filters
Momentum
Controllers
Costs

Citer dette

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title = "A Variational Integrator for the distance-based formation control of multi-agent systems",
abstract = "Distance-based formation control of second order agents can be seen as a physical system of particles linked by springs, whose evolution can be described by a Lagrangian function. An interesting family of geometric integrators, called variational integrators, is defined by using discretizations of the Hamilton's principle of critical action. The variational integrators preserve some geometric features such as the symplectic structure, they preserve the momentum map, and the evolution of the system's energy presents a good (bounded) behavior. We derive variational integrators that can be employed in the context of distance-based formation control algorithms. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. Consequently, we can provide a faster identification of regions of attraction for desired distance-based shapes, and more computationally efficient estimation algorithms like Kalman filters that employ distance-based controllers as prediction models. We use a formation consisting of four autonomous planar agents as an example and benchmark to test and compare the performances of the proposed variational integrator.",
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A Variational Integrator for the distance-based formation control of multi-agent systems. / Colombo, Leonardo J.; de Marina, Hector Garcia.

I: IFAC-PapersOnLine, Bind 51, Nr. 23, 2018, s. 76-81.

Publikation: Bidrag til tidsskriftKonferenceartikelForskningpeer review

TY - GEN

T1 - A Variational Integrator for the distance-based formation control of multi-agent systems

AU - Colombo, Leonardo J.

AU - de Marina, Hector Garcia

PY - 2018

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N2 - Distance-based formation control of second order agents can be seen as a physical system of particles linked by springs, whose evolution can be described by a Lagrangian function. An interesting family of geometric integrators, called variational integrators, is defined by using discretizations of the Hamilton's principle of critical action. The variational integrators preserve some geometric features such as the symplectic structure, they preserve the momentum map, and the evolution of the system's energy presents a good (bounded) behavior. We derive variational integrators that can be employed in the context of distance-based formation control algorithms. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. Consequently, we can provide a faster identification of regions of attraction for desired distance-based shapes, and more computationally efficient estimation algorithms like Kalman filters that employ distance-based controllers as prediction models. We use a formation consisting of four autonomous planar agents as an example and benchmark to test and compare the performances of the proposed variational integrator.

AB - Distance-based formation control of second order agents can be seen as a physical system of particles linked by springs, whose evolution can be described by a Lagrangian function. An interesting family of geometric integrators, called variational integrators, is defined by using discretizations of the Hamilton's principle of critical action. The variational integrators preserve some geometric features such as the symplectic structure, they preserve the momentum map, and the evolution of the system's energy presents a good (bounded) behavior. We derive variational integrators that can be employed in the context of distance-based formation control algorithms. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. Consequently, we can provide a faster identification of regions of attraction for desired distance-based shapes, and more computationally efficient estimation algorithms like Kalman filters that employ distance-based controllers as prediction models. We use a formation consisting of four autonomous planar agents as an example and benchmark to test and compare the performances of the proposed variational integrator.

KW - Distribute control

KW - Formation control

KW - Geometric integration

KW - Multi-agent systems

KW - Variational integrators

KW - Variational principles

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DO - 10.1016/j.ifacol.2018.12.014

M3 - Conference article

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EP - 81

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

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