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## A Survey of Consensus Problems in Multi-agent Coordination (2005)

Citations: | 148 - 3 self |

### Citations

7559 |
Matrix analysis,
- Horn, Johnson
- 1985
(Show Context)
Citation Context ...ij = −aij where i = j. For an undirected graph, the Laplacian matrix is symmetric positive semi-definite. B. Matrix Theory Below we summarize some notation from nonnegative matrix theory (c.f. [6], =-=[7]-=-) which are important for studying consensus problems. Let Mn(IR) represent the set of all n× n real matrices. Given a matrix A = [aij ] ∈ Mn(IR), the digraph of A, denoted by Γ(A), is the digraph on ... |

1953 |
Distributed Algorithms,
- Lynch
- 1996
(Show Context)
Citation Context ...pproach a sufficiently common value. Convergence to a common value is called the consensus or agreement problem in the literature. Although consensus problems have a history in computer science (e.g. =-=[4]-=-), we will focus on their applications in cooperative control of multi-agent systems in this paper. The main purpose of this paper is to summarize the recent progress of consensus W. Ren and E. M. Atk... |

1497 |
Spectral Graph Theory.
- Chung
- 1997
(Show Context)
Citation Context ...s known that x converges to the kernel of L, that is, span{1}, which in turn implies that ‖xi − xj‖ → 0. It is well-known that zero is a simple eigenvalue of L if the graph of L is strongly connected =-=[16]-=-. However, this is only a sufficient condition rather than a necessary one. We have the formal statement that zero is a simple eigenvalue of the Laplacian matrix if and only if its digraph has a spann... |

1237 | Coordination of groups of mobile autonomous agents using nearest neighbor rules,”
- Jadbabaie, Lin, et al.
- 2003
(Show Context)
Citation Context ...ion state represents information that needs be coordinated between agents. The information state may be agent position, velocity, oscillation phase, decision variable, and so on. As described in [2], =-=[10]-=-, [11], [12], [13], [14], a continuous-time consensus protocol can be summarized as ẋi(t) = − ∑ j∈Ji(t) αij(t)(xi(t)− xj(t)), (1) where Ji(t) represents the set of agents whose information is availab... |

1053 | Consensus problems in networks of agents with switching topology and time-delays,”
- Olfati-Saber, Murray
- 2004
(Show Context)
Citation Context ...ate represents information that needs be coordinated between agents. The information state may be agent position, velocity, oscillation phase, decision variable, and so on. As described in [2], [10], =-=[11]-=-, [12], [13], [14], a continuous-time consensus protocol can be summarized as ẋi(t) = − ∑ j∈Ji(t) αij(t)(xi(t)− xj(t)), (1) where Ji(t) represents the set of agents whose information is available to ... |

867 | Algebraic Graph Theory.
- Godsil, Royle
- 2001
(Show Context)
Citation Context ...litate research in this area. II. BACKGROUND AND PROBLEM STATEMENT A. Graph Theory It is natural to model information exchange between agents in a cooperative team by directed/undirected graphs (e.g. =-=[5]-=-). A digraph (directed graph) consists of a pair (N , E), where N is a finite nonempty set of nodes and E ∈ N 2 is a set of ordered pairs of nodes, called edges. As a comparison, the pairs of nodes in... |

577 |
Novel type of phase transitions in a system of self-driven particles.
- Vicsek, Czirok, et al.
- 1995
(Show Context)
Citation Context ...hbors of an agent will likely change over time. Many research efforts on the coordination of multiple autonomous agents under switching information exchange topologies are motivated by Viscek’s model =-=[19]-=-. Viscek’s model can be thought of as a special case of a distributed behavioral model proposed in [20], where computer animations are used to generate the aggregate motions of a group of animals. One... |

558 |
Schools: A Distributed Behavioral Model
- Flocks, Herds
- 1987
(Show Context)
Citation Context ...utonomous agents under switching information exchange topologies are motivated by Viscek’s model [19]. Viscek’s model can be thought of as a special case of a distributed behavioral model proposed in =-=[20]-=-, where computer animations are used to generate the aggregate motions of a group of animals. One approach to tackling switching topologies is the algebraic graph, which typically associates graph top... |

516 |
Information flow and cooperative control of vehicle formations,”
- Fax, Murray
- 2004
(Show Context)
Citation Context ...iety of ways. For example, relative position sensors may enable vehicles to construct state information for other vehicles [1], knowledge may be communicated between vehicles using a wireless network =-=[2]-=-, or joint knowledge might be pre-programmed into the vehicles before a mission begins [3]. For cooperative control strategies to be effective, a team of agents must be able to respond to unanticipate... |

498 |
Non–negative matrices and Markov chains”,
- Seneta
- 1981
(Show Context)
Citation Context ... The classical result in Markov chains states that if a stochastic matrix A satisfies Am > 0 for some positive integer m, then limk→∞Ak → 1νT , where ν is a positive column vector satisfying 1T ν = 1 =-=[9]-=-. In fact, the condition Am > 0 for some positive integer m is equivalent to the condition that A is irreducible and ρ(A) is a unique eigenvalue of maximum modulus. C. Consensus Protocols Let xi be th... |

460 |
Stability of multi-agent systems with time-dependent communication links,”
- Moreau
- 2005
(Show Context)
Citation Context ...r consensus protocol (1) can be written in matrix form as ẋ = −Lx, where L is the graph Laplacian and x = [x1, · · · , xn]T . Correspondingly, a discrete-time consensus protocol as proposed in [10], =-=[15]-=-, [13] can be summarized as xi[k + 1] = ∑ j∈Ji[k] {i} βij [k]xj [k], (2) where ∑ j∈Ji[k] {i} βij [k] = 1, and βij [k] > 0 for j ∈Ji[k] ⋃{i}. In other words, the next state of each agent is updated as ... |

422 | Fast linear iterations for distributed averaging,”
- Xiao, Boyd
- 2004
(Show Context)
Citation Context ...or optimize some performance criteria. For example, in a network with a large number of agents, it may be desirable to solve the fastest distributed linear averaging (FDLA) problem defined as follows =-=[25]-=-. Let W = [Wij ] ∈ Mn(IR) such that Wij = 0 if there is no information exchange between agent i and agent j. Given x[k+1] = Wx[k], the FDLA problem is to find the weight matrix W that guarantees the f... |

418 | Flocking for multi-agent dynamic systems: Algorithms and theory,”
- Olfati-Saber
- 2006
(Show Context)
Citation Context ...ugh a network. The authors apply belief propagation as a message passing strategy to solve a distributed hypothesis testing problem for a prespecified network connectivity. E. Flocking In [42], [43], =-=[44]-=-, the authors study the flocking phenomenon observed in [20] by constructing local control laws that allow a group of mobile agents to align their velocities, move with a common speed and achieve desi... |

416 | Consensus seeking in multiagent systems under dynamically changing interaction topologies,”
- Ren, Beard
- 2005
(Show Context)
Citation Context ...ts information that needs be coordinated between agents. The information state may be agent position, velocity, oscillation phase, decision variable, and so on. As described in [2], [10], [11], [12], =-=[13]-=-, [14], a continuous-time consensus protocol can be summarized as ẋi(t) = − ∑ j∈Ji(t) αij(t)(xi(t)− xj(t)), (1) where Ji(t) represents the set of agents whose information is available to agent i at t... |

285 |
Virtual leaders, artificial potentials and coordinated control of groups. In:
- Leonard, Friorelli
- 2001
(Show Context)
Citation Context ...n speed and achieve desired inter-agent distances while avoiding collisions with each other under a fixed topology and switching topologies respectively. These results extend some results reported in =-=[45]-=-. F. Coupled Oscillators Ref. [46] studies connections between phase models of coupled oscillators and kinematic models of groups of self-propelled particles. The authors develop analysis and design t... |

193 | Local control strategies for groups of mobile autonomous
- Lin, Brouke, et al.
- 2004
(Show Context)
Citation Context ...presents information that needs be coordinated between agents. The information state may be agent position, velocity, oscillation phase, decision variable, and so on. As described in [2], [10], [11], =-=[12]-=-, [13], [14], a continuous-time consensus protocol can be summarized as ẋi(t) = − ∑ j∈Ji(t) αij(t)(xi(t)− xj(t)), (1) where Ji(t) represents the set of agents whose information is available to agent ... |

160 | Agreement over random networks,”
- Hatano, Mesbahi
- 2005
(Show Context)
Citation Context ...her Issues Under certain circumstances, it is desirable to construct nonlinear consensus protocols as shown in [11], [27], [24]. Agreement problems are also studied from a stochastic point of view in =-=[28]-=-, which relies on graph theoretic results developed in [29]. Furthermore, dynamic consensus problems are studied in [30], which focuses on how to achieve and analyze tracking of linear consensus on ti... |

159 | Stable flocking of mobile agents, part I: Fixed topology,” in
- Tanner, Jadbabaie, et al.
- 2003
(Show Context)
Citation Context ...essages through a network. The authors apply belief propagation as a message passing strategy to solve a distributed hypothesis testing problem for a prespecified network connectivity. E. Flocking In =-=[42]-=-, [43], [44], the authors study the flocking phenomenon observed in [20] by constructing local control laws that allow a group of mobile agents to align their velocities, move with a common speed and ... |

132 | Stability of continuous-time distributed consensus algorithms.
- Moreau
- 2004
(Show Context)
Citation Context ...to all the other nodes across each interval of length T . For the continuous-time consensus protocol, a Lyapunov function candidate is proposed as V (x) = max{x1, · · · , xn} − min{x1, · · · , xn} in =-=[14]-=-. It is shown that V (x) decreases over a sufficient length of time intervals. In the case that L(t) is piecewise continuous and each nonzero entry ij , 1861 where i = j, is uniformly lower and uppe... |

126 | Necessary and sufficient graphical conditions for formation control of unicycles.
- Lin, Francis, et al.
- 2005
(Show Context)
Citation Context ...a simple eigenvalue of the Laplacian matrix if and only if its digraph has a spanning tree. This conclusion was shown in [17] by an induction approach while the same result is proven independently in =-=[18]-=- by a constructive approach. As a result, under a timeinvariant information exchange topology, the continuoustime protocol achieves consensus asymptotically if and only if the information exchange top... |

126 | A decentralized approach to formation maneuvers
- Lawton, Beard, et al.
- 2003
(Show Context)
Citation Context ...rs also derive a Nyquist-like stability criterion for formation stabilization. It is argued that vehicle formations can be achieved through reaching consensus on the center point of the formation. In =-=[31]-=-, a decentralized control strategy is implemented to maintain multiple robot formations, where each robot only needs position information of its two neighbors. Ref. [18] studies the formation stabiliz... |

99 |
The multi-agent rendezvous problem,”
- Lin, Morse, et al.
- 2003
(Show Context)
Citation Context ...r decentralized consensus protocols, where input constraints are also taken into account. C. Rendezvous Problem The rendezvous problem requires that each agent arrive at a location simultaneously. In =-=[39]-=-, consensus seeking ideas are applied to a rendezvous problem for a group of mobile autonomous agents, where both the synchronous case and the asynchronous case are considered. In [17], the “meet for ... |

95 | A Decentralized Scheme for Spacecraft Formation Flying via the Virtual Strutrure Approach”,
- Ren, Beard
- 2003
(Show Context)
Citation Context ...aft, where the attitude of each spacecraft is synchronized with its two adjacent neighbors via a bi-directional communication topology. Similarly, the bi-directional communication topology is used in =-=[37]-=- to synchronize instantiations of group level information, the formation state, among multiple spacecraft. Ref. [38] considers the attitude alignment problem for a team of UAVs using nonlinear decentr... |

93 |
Products of indecomposable, aperiodic, stochastic matrices,
- Wolfowitz
- 1963
(Show Context)
Citation Context ...s said to be a (row) stochastic matrix [7]. A stochastic matrix P is called indecomposable and aperiodic (SIA) if limk→∞ P k = 1νT , where 1 is a column vector of all ones and ν is some column vector =-=[8]-=-. The well-known Perron-Frobenius Theorem states that if a nonnegative matrix A is irreducible, that is, the digraph of matrix A is strongly connected, then ρ(A) is a simple 2005 American Control Conf... |

80 | Coordination Variables and Consensus Building in Multiple Vehicle Systems
- Ren, Beard, et al.
(Show Context)
Citation Context ...ndition rather than a necessary one. We have the formal statement that zero is a simple eigenvalue of the Laplacian matrix if and only if its digraph has a spanning tree. This conclusion was shown in =-=[17]-=- by an induction approach while the same result is proven independently in [18] by a constructive approach. As a result, under a timeinvariant information exchange topology, the continuoustime protoco... |

58 |
Robot Teams: From Diversity to Polymorphism
- Balch, Parker
- 2002
(Show Context)
Citation Context ...e information for other vehicles [1], knowledge may be communicated between vehicles using a wireless network [2], or joint knowledge might be pre-programmed into the vehicles before a mission begins =-=[3]-=-. For cooperative control strategies to be effective, a team of agents must be able to respond to unanticipated situations or changes in the environment that are sensed as a cooperative task is carrie... |

54 | Multi-agent Kalman consensus with relative uncertainty
- Ren, Beard, et al.
- 2005
(Show Context)
Citation Context ...time consensus protocol if there exist infinitely many consecutive uniformly bounded time intervals such that the union of the information exchange graph across each such interval has a spanning tree =-=[23]-=-. In contrast to the algebraic graph approach, nonlinear tools are used by some other researchers to study consensus problems. For the discrete-time consensus protocol, a set-valued function V is defi... |

52 |
Dynamic consensus for mobile networks,”
- Spanos, Olfati-Saber, et al.
- 2005
(Show Context)
Citation Context ...], [24]. Agreement problems are also studied from a stochastic point of view in [28], which relies on graph theoretic results developed in [29]. Furthermore, dynamic consensus problems are studied in =-=[30]-=-, which focuses on how to achieve and analyze tracking of linear consensus on time-varying inputs. IV. MULTI-AGENT COORDINATION VIA CONSENSUS SCHEMES In this section, we investigate applications of th... |

47 |
Synchronized multiple spacecraft rotations,”
- Lawton, Beard
- 2002
(Show Context)
Citation Context ...ics are applied in [35] to study formation stabilization problems in the general framework of sensing/communication architectures, which is related to the consensus problems. B. Attitude Alignment In =-=[36]-=-, formation control laws are presented for maintaining attitude alignment among a group of spacecraft, where the attitude of each spacecraft is synchronized with its two adjacent neighbors via a bi-di... |

36 | Collective motion and oscillator synchronization.
- Sepulchre, Paley, et al.
- 2003
(Show Context)
Citation Context ...agent distances while avoiding collisions with each other under a fixed topology and switching topologies respectively. These results extend some results reported in [45]. F. Coupled Oscillators Ref. =-=[46]-=- studies connections between phase models of coupled oscillators and kinematic models of groups of self-propelled particles. The authors develop analysis and design tools for stabilization of collecti... |

30 |
Coordinated collective motion of groups of autonomous mobile robots: analysis of Vicsek’s model.
- Savkin
- 2004
(Show Context)
Citation Context ...hat consensus is achieved asymptotically if the union of the information exchange graphs for the team is connected most of the time as the system evolves. This result is further discussed in [21] and =-=[22]-=-. Taking into account the fact that sensors may have a limited field of view, the authors in [12] use digraphs to derive consensus seeking results under switching information exchange topologies. It i... |

29 |
A study of synchronization and group cooperation using partial contraction theory,” in Cooperative Control,
- Slotine, Wang
- 2004
(Show Context)
Citation Context ...s an index k ∈ {1, · · · , n} and an interval length T > 0 such that for all t the digraph of∫ t+T t (−L(s))ds has the property that node k has a directed path to all the other nodes. In addition, in =-=[24]-=-, nonlinear contraction theory is used to study synchronization and schooling applications, which are related to the consensus problem. In particular, the continuous-time consensus protocol is analyze... |

29 | Distributed bayesian hypothesis testing in sensor networks
- Alanyali, Venkatesh, et al.
- 2004
(Show Context)
Citation Context ...sus protocol is introduced to coordinate orders of a network of buyers. The authors prove that distributed protocols can achieve the same coordination as the centralized decision making process. Ref. =-=[41]-=- considers a scenario of multiple distributed noisy sensors observing a single event, where those sensors need to reach consensus about the event after exchanging messages through a network. The autho... |

22 |
Formation and alignment of distributed sensing agents with double-integrator dynamics and actuator saturation
- Roy, Saberi, et al.
- 2007
(Show Context)
Citation Context ...ion stabilization problems, where the effect of formation switching is addressed for both single integrator dynamics and general plant dynamics. In addition, double integrator dynamics are applied in =-=[35]-=- to study formation stabilization problems in the general framework of sensing/communication architectures, which is related to the consensus problems. B. Attitude Alignment In [36], formation control... |

18 |
Decentralized control of satellite formations
- Carpenter
(Show Context)
Citation Context ... or a world map. Information necessary for cooperation may be shared in a variety of ways. For example, relative position sensors may enable vehicles to construct state information for other vehicles =-=[1]-=-, knowledge may be communicated between vehicles using a wireless network [2], or joint knowledge might be pre-programmed into the vehicles before a mission begins [3]. For cooperative control strateg... |

17 |
Consensus algorithms are input-to-state stable
- Kingston, Wei, et al.
- 2005
(Show Context)
Citation Context ...is addressed in the context of consensus seeking. A similar idea is extended for multiple UAVs to converge on the boundary of a radar detection area simultaneously to maximize the element of surprise =-=[40]-=-. D. Coordinated Decision Making In multi-agent systems, distributed decision making has an advantage over centralized decision making in the sense that a decision maker is not required to access info... |

16 |
Advection on graphs,” in
- Chapman, Mesbahi
- 2011
(Show Context)
Citation Context ...construct nonlinear consensus protocols as shown in [11], [27], [24]. Agreement problems are also studied from a stochastic point of view in [28], which relies on graph theoretic results developed in =-=[29]-=-. Furthermore, dynamic consensus problems are studied in [30], which focuses on how to achieve and analyze tracking of linear consensus on time-varying inputs. IV. MULTI-AGENT COORDINATION VIA CONSENS... |

16 |
A Pursuit Strategy for Wheeled-Vehicle Formations
- Marshall, Lin, et al.
- 2003
(Show Context)
Citation Context ...here results are given for formation stabilization of the unicycles to a point, a line, and a general formation pattern. In addition, the simplified pursuit strategy for wheeled-vehicle formations in =-=[32]-=- can be thought of as a special case of the continuous-time linear consensus protocol, where the information exchange topology is a uni-directional ring. In [33], a network of 1862 vehicles are requir... |

15 |
Convex synthesis of controllers for consensus
- Castro, Paganini
- 2004
(Show Context)
Citation Context ... dynamics given by ẋi = ∑n j=1 Aijxj + B (1) i wi + B (2) i ui, where xi ∈ IRn denotes the state, wi ∈ IRm denotes the disturbance, and ui ∈ IRr denotes the control input with i = 1, · · · , n. Ref. =-=[26]-=- focuses on synthesizing a state feedback controller that guarantees consensus for the closed loop system without disturbance as well as a state feedback controller that achieves not only consensus bu... |

12 | Vehicle networks: Achieving regular formation.
- Chaves, Day, et al.
- 2002
(Show Context)
Citation Context ...tegy for wheeled-vehicle formations in [32] can be thought of as a special case of the continuous-time linear consensus protocol, where the information exchange topology is a uni-directional ring. In =-=[33]-=-, a network of 1862 vehicles are required to achieve a polygonal formation by exchanging information among themselves, where stochastic disturbance is introduced to the communication graph and the eff... |

12 |
Stability analysis of stochastically varying formations of dynamic agents.
- Gupta, Hassibi, et al.
- 2003
(Show Context)
Citation Context ...changing information among themselves, where stochastic disturbance is introduced to the communication graph and the effect of stochastic loss of information is studied by Monte Carlo simulations. In =-=[34]-=-, a general framework is provided to analyze both consensus problems and formation stabilization problems, where the effect of formation switching is addressed for both single integrator dynamics and ... |

8 |
Distributed consensus protocols for coordinating buyers
- Bauso, Pesenti
- 2003
(Show Context)
Citation Context ... conditions are derived for the existence of such state feedback controllers. G. Other Issues Under certain circumstances, it is desirable to construct nonlinear consensus protocols as shown in [11], =-=[27]-=-, [24]. Agreement problems are also studied from a stochastic point of view in [28], which relies on graph theoretic results developed in [29]. Furthermore, dynamic consensus problems are studied in [... |

8 |
Attitude alignment of a team of UAVs under decentralized information structure
- Bauso, Giarr’e, et al.
- 2003
(Show Context)
Citation Context ...unication topology. Similarly, the bi-directional communication topology is used in [37] to synchronize instantiations of group level information, the formation state, among multiple spacecraft. Ref. =-=[38]-=- considers the attitude alignment problem for a team of UAVs using nonlinear decentralized consensus protocols, where input constraints are also taken into account. C. Rendezvous Problem The rendezvou... |

7 |
Stable Flocking of Mobile Agents, Part I: Dynamic Topology.
- Tanner, Jadbabaie, et al.
- 2003
(Show Context)
Citation Context ...s through a network. The authors apply belief propagation as a message passing strategy to solve a distributed hypothesis testing problem for a prespecified network connectivity. E. Flocking In [42], =-=[43]-=-, [44], the authors study the flocking phenomenon observed in [20] by constructing local control laws that allow a group of mobile agents to align their velocities, move with a common speed and achiev... |

2 |
On coordination strategies for mobile agents with changing nearest neighbor sets
- Jadbabaie
- 2003
(Show Context)
Citation Context ...s shown that consensus is achieved asymptotically if the union of the information exchange graphs for the team is connected most of the time as the system evolves. This result is further discussed in =-=[21]-=- and [22]. Taking into account the fact that sensors may have a limited field of view, the authors in [12] use digraphs to derive consensus seeking results under switching information exchange topolog... |