Graph theoretic methods in the stability of vehicle formations

Lafferriere, Gerardo; Caughman, J.; Williams, A.

doi:10.23919/acc.2004.1384492

Cited by 52 publications

(24 citation statements)

References 12 publications

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“…We start with the following result which characterizes convergence to formation in terms of a spectral property of L G . A version of this appeared in [10].…”

Section: Stabilizabilitymentioning

confidence: 99%

“…The following result was proved in [10] for the case a 1 21 = · · · = a n 21 and G a connected undirected graph. A similar argument applies for our more general case.…”

Section: Stabilizabilitymentioning

confidence: 99%

“…These include the coordinated control of minisatellites, drone planes, and underwater vehicles [4,5,7,[9][10][11][12][13]20,[22][23][24][25]29]. One of the main goals is to achieve a coordinated objective while using only relative information concerning positions and velocity.…”

Section: Introductionmentioning

confidence: 99%

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Decentralized control of vehicle formations

Lafferriere

Williams

Caughman

et al. 2005

Systems & Control Letters

Self Cite

563

275

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This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a pre-specified communication digraph, G. A feedback control is designed using relative information between a vehicle and its in-neighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including symmetric communication graphs and formations with leaders. Several numerical simulations are used to illustrate the results.

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“…We start with the following result which characterizes convergence to formation in terms of a spectral property of L G . A version of this appeared in [10].…”

Section: Stabilizabilitymentioning

confidence: 99%

“…The following result was proved in [10] for the case a 1 21 = · · · = a n 21 and G a connected undirected graph. A similar argument applies for our more general case.…”

Section: Stabilizabilitymentioning

confidence: 99%

See 1 more Smart Citation

Decentralized control of vehicle formations

Lafferriere

Williams

Caughman

et al. 2005

Systems & Control Letters

Self Cite

563

275

View full text Add to dashboard Cite

show abstract

“…they are capable of moving in any direction at any time), thus yielding simpler control laws and tractable convergence properties. Other methods used to achieve such a holonomic rendezvous include Laplacian feedback [8,10], cyclic pursuit [21], potential fields [12] or even curve shortening [24]. Solving the rendezvous with nonholonomic agents is more complex and proving the convergence property can be difficult.…”

Section: Introductionmentioning

confidence: 99%

Bayesian rendezvous for distributed robotic systems

Gowal

Martinoli

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-In this paper, we state, using thorough mathematical analysis, sufficient conditions to perform a rendezvous maneuver with a group of differential-wheeled robots endowed with an on-board, noisy, local positioning system. In particular, we extend the existing framework of noise-free, graph-based distributed control with a layer of Bayesian reasoning allowing to solve the rendezvous problem more efficiently in presence of uncertainties and in a probabilistically sound way. Finally we perform extensive experiments with a team of four real robots, and simulation with their corresponding simulated counterpart, to confirm the benefits of our Bayesian approach.

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“…Esta variação pode ser realizada ao longo do tempo para se criar uma trajetória variável do líder. Os zeros nas colunas um e três de A veh são necessários para garantir a convergência dos robôs móveis para a formação (veja (Laferriere et al, 2004) Proposição 3.1 e Proposição 4.2).…”

Section: Geração Das Trajetórias De Re-ferênciaunclassified

Controle robusto de robos móveis em formação sujeitos a falhas

Siqueira

Terra

Francisco

2010

Sba Controle & Automação

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Robust and Fault Tolerant Control of Wheeled Mobile Robots In FormationThis paper deals with robust and fault tolerant controls of wheeled mobile robots (WMRs) in formation. The robust approach is based on output feedback nonlinear H ∞ control. The fault tolerant approach is based on output feedback H ∞ control of Markovian jump linear systems to ensure stability of the formation when one of the robots is lost during the coordinated motion. The coordination is performed with the robots following a leader, and any robot of the formation can assume the leadership randomly. The mobile robots exchange informations according to a pre-specified communication directed graph (digraph). tolerante a falhasé baseado em controle H ∞ por realimentação da saída de sistemas lineares sujeitos a saltos Markovianos para garantir estabilidade da formação quando um dos robôsé perdido durante o movimento coordenado. A coordenaçãoé realizada em função de um lider e qualquer robô da formação pode assumir a liderança de maneira aleatória. Os robôs móveis trocam informações de acordo com um grafo de comunicação direcionado (dígrafo), definido a-priori.

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Graph theoretic methods in the stability of vehicle formations

Cited by 52 publications

References 12 publications

Decentralized control of vehicle formations

Decentralized control of vehicle formations

Bayesian rendezvous for distributed robotic systems

Controle robusto de robos móveis em formação sujeitos a falhas

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