### Citations

7717 |
Topics in Matrix Analysis
- Horn, Johnson
- 1994
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Citation Context ...ij ] ∈ Rp×p, the directed graph of S, denoted by Γ(S), is the directed graph on p nodes i, i ∈ {1, 2, . . . , p}, such that there is an edge in Γ(S) from node j to node i if and only if sij = 0 (cf. =-=[20]-=-). Again, we assume that there is no self edge (i, i). B. Existing Consensus Algorithms for Double-integrator Dynamics Consider vehicles with double-integrator dynamics given by ṙi = vi, v̇i = ui, i ... |

1984 |
Distributed Algorithms
- Lynch
- 1997
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Citation Context ...r indirectly to all of the vehicles in the team. I. INTRODUCTION Consensus means that multiple vehicles reach an agreement on a common value. Consensus algorithms have a historical perspective in [1]–=-=[4]-=-, to name a few, and have recently been studied extensively in the context of cooperative control of multiple autonomous vehicles (see [5] and references therein). Some results in consensus algorithms... |

549 | Information flow and cooperative control of vehicle formations - Fax, Murray - 2004 |

436 | Flocking for multi-agent dynamic systems: Algorithms and theory
- Olfati-Saber
- 2006
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Citation Context ...–[17], to name a few. In particular, formation keeping strategies are addressed in [7], [9] for multi-vehicle formation maneuvers under the assumption of a bidirectional ring interaction graph. Refs. =-=[12]-=-, [13] study flocking algorithms that guarantee velocity matching, flock centering, and collision avoidance for a group of vehicles under undirected information exchange. In [11] the problem of decent... |

410 | Distributed asynchronous deterministic and stochastic gradient optimization algorithms,” - Tsitsiklis, Bertsekas, et al. - 1986 |

398 |
Reaching a consensus
- DeGroot
- 1974
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Citation Context ...ly or indirectly to all of the vehicles in the team. I. INTRODUCTION Consensus means that multiple vehicles reach an agreement on a common value. Consensus algorithms have a historical perspective in =-=[1]-=-–[4], to name a few, and have recently been studied extensively in the context of cooperative control of multiple autonomous vehicles (see [5] and references therein). Some results in consensus algori... |

240 | Information consensus in multivehicle cooperative control
- Ren, Beard, et al.
- 2007
(Show Context)
Citation Context ...ue. Consensus algorithms have a historical perspective in [1]–[4], to name a few, and have recently been studied extensively in the context of cooperative control of multiple autonomous vehicles (see =-=[5]-=- and references therein). Some results in consensus algorithms can be understood in the context of connective stability [6]. Consensus algorithms are primarily studied for vehicles with single-integra... |

191 | Flocking in fixed and switching networks
- Tanner, Jadbabaie, et al.
- 2007
(Show Context)
Citation Context ... to name a few. In particular, formation keeping strategies are addressed in [7], [9] for multi-vehicle formation maneuvers under the assumption of a bidirectional ring interaction graph. Refs. [12], =-=[13]-=- study flocking algorithms that guarantee velocity matching, flock centering, and collision avoidance for a group of vehicles under undirected information exchange. In [11] the problem of decentralize... |

177 |
Decentralized control of complex systems.
- Siljak
- 1991
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Citation Context ...y in the context of cooperative control of multiple autonomous vehicles (see [5] and references therein). Some results in consensus algorithms can be understood in the context of connective stability =-=[6]-=-. Consensus algorithms are primarily studied for vehicles with single-integrator kinematics in the literature. For vehicles with double-integrator dynamics, consensus related problems have been studie... |

146 |
Laplacian Matrices of Graphs: A Survey,” Linear Algebra Appl
- Merris
- 1994
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Citation Context ...1p is a p × 1 column vector of all ones. In the case of undirected graphs, 0 is a simple eigenvalue of L and all of the other eigenvalues are positive if and only if the undirected graph is connected =-=[18]-=-. In the case of directed graphs, 0 is a simple eigenvalue of L and all of the other eigenvalues have positive real parts if and only if the directed graph contains a directed spanning tree [19]. Give... |

133 | A decentralized approach to formation maneuvers
- Lawton, Beard, et al.
- 2003
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Citation Context ...sensus algorithms are primarily studied for vehicles with single-integrator kinematics in the literature. For vehicles with double-integrator dynamics, consensus related problems have been studied in =-=[7]-=-–[17], to name a few. In particular, formation keeping strategies are addressed in [7], [9] for multi-vehicle formation maneuvers under the assumption of a bidirectional ring interaction graph. Refs. ... |

101 | Decentralized scheme for spacecraft formation flying via the virtual structure approach,”
- Ren, Beard
- 2003
(Show Context)
Citation Context ...he literature. For vehicles with double-integrator dynamics, consensus related problems have been studied in [7]–[17], to name a few. In particular, formation keeping strategies are addressed in [7], =-=[9]-=- for multi-vehicle formation maneuvers under the assumption of a bidirectional ring interaction graph. Refs. [12], [13] study flocking algorithms that guarantee velocity matching, flock centering, and... |

79 | Coordination Variables and Consensus Building in Multiple Vehicle Systems.
- Ren, Beard, et al.
- 2003
(Show Context)
Citation Context ...ected [18]. In the case of directed graphs, 0 is a simple eigenvalue of L and all of the other eigenvalues have positive real parts if and only if the directed graph contains a directed spanning tree =-=[19]-=-. Given a matrix S = [sij ] ∈ Rp×p, the directed graph of S, denoted by Γ(S), is the directed graph on p nodes i, i ∈ {1, 2, . . . , p}, such that there is an edge in Γ(S) from node j to node i if and... |

72 |
Distributed multi-vehicle coordinated control via local information exchange,”
- Ren, Atkins
- 2007
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Citation Context ...on avoidance for a group of vehicles under undirected information exchange. In [11] the problem of decentralized stabilization of vehicle formations is studied under directed information exchange. In =-=[14]-=-, second-order consensus algorithms are proposed and analyzed under directed information exchange, where it is shown that both the interaction graph and the coupling strength of relative velocities be... |

71 | Asymptotic agreement in distributed estimation,” - Borkar, Varaiya - 1982 |

68 | Decentralized control of vehicle formations,”
- Lafferriere, Williams, et al.
- 2005
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Citation Context ...eraction graph. Refs. [12], [13] study flocking algorithms that guarantee velocity matching, flock centering, and collision avoidance for a group of vehicles under undirected information exchange. In =-=[11]-=- the problem of decentralized stabilization of vehicle formations is studied under directed information exchange. In [14], second-order consensus algorithms are proposed and analyzed under directed in... |

49 | Attitude Control Without Angular Velocity Measurement: A Passivity Approach,”
- Lizarralde, Wen
- 1996
(Show Context)
Citation Context ...y undirected connected interaction graph. IV. CONSENSUS WITHOUT RELATIVE VELOCITY MEASUREMENT Note that (4) requires measurement of relative velocities between neighboring vehicles. Motivated by [7], =-=[21]-=-, we propose a consensus algorithm without relative velocity measurement based on a passivity approach as ˙̂xi = Γx̂i + n∑ j=1 aij(ri − rj) yi = PΓx̂i + P n∑ j=1 aij(ri − rj) ui = − n∑ j=1 aij(ri − rj... |

46 |
Consensus control for a class of networks of dynamic agents,”
- Xie, Wang
- 2007
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Citation Context ...e result in the general case of directed information exchange. Refs. [16], [17] further extend [14] to incorporate a group reference velocity. A second-order consensus algorithm is also considered in =-=[15]-=- under undirected information exchange. The main purpose of the current paper is to extend some existing results in consensus algorithms for double-integrator dynamics in four aspects. First, we propo... |

38 |
Consensus strategies for cooperative control of vehicle formation.
- Ren
- 2007
(Show Context)
Citation Context ...that both the interaction graph and the coupling strength of relative velocities between neighboring vehicles affect the convergence result in the general case of directed information exchange. Refs. =-=[16]-=-, [17] further extend [14] to incorporate a group reference velocity. A second-order consensus algorithm is also considered in [15] under undirected information exchange. The main purpose of the curre... |

23 |
Formation and alignment of distributed sensing agents with double integrator dynamics,"
- Roy, Saberi, et al.
- 2004
(Show Context)
Citation Context ...any α > 0. It is left to show that the inequality (21) guarantees that all of the eigenvalues of Γ corresponding to µi that satisfies Re(µi) < 0 and Im(µi) = 0 have negative real parts. Motivated by =-=[10]-=-, [14], we use Fig. 1 to show the notations used in the proof. We only need to consider µi that satisfies Re(µi) < 0 and Im(µi) > 0 since any µi that satisfies Re(µi) < 0 and Im(µi) < 0 is a complex c... |