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## Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory (2006)

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Citations: | 436 - 2 self |

### Citations

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Citation Context ...s are made in Section 10. 2 Preliminaries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory =-=[2, 7, 15]-=-, algebraic graph theory [12], spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set... |

2506 |
Robot Motion Planning
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Citation Context ...le. A successful example of such an approach is the use of gyroscopic forces for obstacle avoidance in [3, 4]. For a comprehensive treatment of obstacle avoidance in robotics, please refer to Latombe =-=[20]-=-. 8 Simulation Results In this section, we present several simulation results of 2-D and 3-D flocking. For every case, a computer animation is available upon request. The following parameters remain f... |

2002 | A Survey on Sensor Networks
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Citation Context ...k performed by dynamic agents over (visually invisible) self-organized networks in nature. The self-organizing feature of flocks/schools [34] can provide a deeper insight in design of sensor networks =-=[5, 28, 13, 8, 1]-=-. Particle-based flocking is also one of the elements of 3-D animation technology that has revolutionized the entertainment industry. This success is partly owe to the pioneering work of Reynolds [40]... |

1558 | Modern Graph Theory, - Bollobas - 1998 |

1558 | Modern Graph Theory, - Bollobas - 1998 |

1345 | Real-time obstacle avoidance for manipulators and mobile robots.
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Citation Context ...networks and suggests analytical exploration of complex networks with dynamic topologies; Olfati-Saber & Murray [32] used potential functions induced by rigid graphs for formation control; and Khatib =-=[18]-=- and Rimon & Koditschek [44] used artificial potentials for obstacle avoidance. A number of recent papers on flocking/swarming, [17, 50, 11], make a set of assumptions that lead to algorithms with som... |

1316 | Flocks, herds and schools: A distributed behavioral model
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Citation Context ... including animal behavior, physics & biophysics, social sciences, and computer science have been fascinated by the emergence of flocking/swarming/schooling in groups of agents via local interactions =-=[47, 38, 37, 36, 29, 40, 53, 51, 48, 26, 14, 52, 34]-=-. Examples of these agents include birds, fish, penguins, ants, bees, and crowds. The engineering applications of flocking include massive mobile sensing in an environment; parallel and simultaneous t... |

1200 | Graph theory, - Diestel - 2000 |

1116 | Next century challenges: scalable coordination in sensor networks
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Citation Context ...k performed by dynamic agents over (visually invisible) self-organized networks in nature. The self-organizing feature of flocks/schools [34] can provide a deeper insight in design of sensor networks =-=[5, 28, 13, 8, 1]-=-. Particle-based flocking is also one of the elements of 3-D animation technology that has revolutionized the entertainment industry. This success is partly owe to the pioneering work of Reynolds [40]... |

1112 | Consensus problems in networks of agents with switching topology and time-delays”,
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Citation Context ...rol scientists in analysis of alignment phenomenon and consensus problems. This includes the alignment results in networks with switching topologies by Jadbabaie et al. [16] and Olfati-Saber & Murray =-=[33]-=-. The results in [16] were further extended to networks with directed topologies by Moreau [27] and Ren & Beard [39]. The convergence analysis of a nonlinear consensus/alignment protocol was first pre... |

892 | Algebraic Graph Theory, - Godsil, Royle - 2001 |

892 | Algebraic Graph Theory, - Godsil, Royle - 2001 |

674 |
Exploring complex networks,”
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Citation Context ...maneuver; Leonard & Fiorelli [21] used artificial potentials for formation keeping; Ogren et al. [28] use potential functions for mission planning and coordination of mobile sensor networks; Strogatz =-=[49]-=- elucidates the features of complex networks in physical, biological, and social networks and suggests analytical exploration of complex networks with dynamic topologies; Olfati-Saber & Murray [32] us... |

671 | Adaptive protocols for information dissemination in wireless sensor networks
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Citation Context ...k performed by dynamic agents over (visually invisible) self-organized networks in nature. The self-organizing feature of flocks/schools [34] can provide a deeper insight in design of sensor networks =-=[5, 28, 13, 8, 1]-=-. Particle-based flocking is also one of the elements of 3-D animation technology that has revolutionized the entertainment industry. This success is partly owe to the pioneering work of Reynolds [40]... |

667 |
Algebraic connectivity of graphs,”
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Citation Context ...Proof. All three results are well-known in the field of algebraic graph theory and their proofs can be found in Godsil and Royle [12]. The quantity λ2(L) is known as algebraic connectivity of a graph =-=[10]-=-. In [33], it was shown that the speed of convergence of a linear consensus protocol (defined in (22)) is equal to λ2 > 0. This consensus protocol will appear as a velocity matching term in all flocki... |

599 |
Novel type of phase transition in a system of self-driven particles,”
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- 1995
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Citation Context ... including animal behavior, physics & biophysics, social sciences, and computer science have been fascinated by the emergence of flocking/swarming/schooling in groups of agents via local interactions =-=[47, 38, 37, 36, 29, 40, 53, 51, 48, 26, 14, 52, 34]-=-. Examples of these agents include birds, fish, penguins, ants, bees, and crowds. The engineering applications of flocking include massive mobile sensing in an environment; parallel and simultaneous t... |

582 | Coverage control for mobile sensing networks,”
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- 2004
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Citation Context ...[23, 24] emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be examples of statedependent graphs); Cortes & Bullo [5] and Cortes et al. =-=[6]-=- introduced distributed algorithms for placement of mobile sensors that appears to be closely related to flocking in a constrained space; Rabichini & Frazzoli [43] proposed an energy-efficient method ... |

558 | Schools: A Distributed Behavioral Model - Flocks, Herds - 1987 |

558 | Schools: A Distributed Behavioral Model - Flocks, Herds - 1987 |

551 | Information flow and cooperative control of vehicle formations,”
- Fax, Murray
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Citation Context ...g. These phenomena do not constitute flocking in the sense described in Section 9. Some past research with strong connections to this paper include the work by the following researchers: Fax & Murray =-=[9]-=- used graph Laplacians for multi-vehicle formation stabilization; Mesbahi [23, 24] emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be... |

480 |
Exact robot navigation using artificial potential fields
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Citation Context ...ical exploration of complex networks with dynamic topologies; Olfati-Saber & Murray [32] used potential functions induced by rigid graphs for formation control; and Khatib [18] and Rimon & Koditschek =-=[44]-=- used artificial potentials for obstacle avoidance. A number of recent papers on flocking/swarming, [17, 50, 11], make a set of assumptions that lead to algorithms with some (or all) of the following ... |

478 | Stability of multiagent systems with time-dependent communication links, - Moreau - 2005 |

478 | Stability of multiagent systems with time-dependent communication links, - Moreau - 2005 |

449 | Consensus seeking in multiagent systems under dynamically changing interaction topologies,” - Ren, Beard - 2005 |

449 | Consensus seeking in multiagent systems under dynamically changing interaction topologies,” - Ren, Beard - 2005 |

299 |
Virtual leaders, artificial potentials and coordinated control of groups
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Citation Context ...y related to flocking in a constrained space; Rabichini & Frazzoli [43] proposed an energy-efficient method for determining the split time in a multi-vehicle rejoin/split maneuver; Leonard & Fiorelli =-=[21]-=- used artificial potentials for formation keeping; Ogren et al. [28] use potential functions for mission planning and coordination of mobile sensor networks; Strogatz [49] elucidates the features of c... |

275 | Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment,” Automatic Control,
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Citation Context |

269 |
Graph theory, volume 173 of Graduate Texts in Mathematics.
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Citation Context ...s are made in Section 10. 2 Preliminaries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory =-=[2, 7, 15]-=-, algebraic graph theory [12], spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set... |

254 | Simulating dynamical features of escape panic.
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Citation Context ... including animal behavior, physics & biophysics, social sciences, and computer science have been fascinated by the emergence of flocking/swarming/schooling in groups of agents via local interactions =-=[47, 38, 37, 36, 29, 40, 53, 51, 48, 26, 14, 52, 34]-=-. Examples of these agents include birds, fish, penguins, ants, bees, and crowds. The engineering applications of flocking include massive mobile sensing in an environment; parallel and simultaneous t... |

197 | Stability Analysis of Swarms,”
- Gazi, Passino
- 2003
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Citation Context ... fixed topology is studied. In [17], Justh & Krishnaprasad proposed an algorithm for swarming that requires all-to-all interconnections and is only analyzed for the case of two agents. Gazi & Passino =-=[11]-=- employed social potentials to study cohesion in swarms using a centralized mechanism. Tanner et al. in [50] proposed a centralized algorithm for a particle system that leads to irregular collapse for... |

192 | Flocking in fixed and switching networks.
- Tanner, Jadbabaie, et al.
- 2007
(Show Context)
Citation Context ...all-to-all interconnections and is only analyzed for the case of two agents. Gazi & Passino [11] employed social potentials to study cohesion in swarms using a centralized mechanism. Tanner et al. in =-=[50]-=- proposed a centralized algorithm for a particle system that leads to irregular collapse for generic initial states. They also proposed a distributed algorithm that leads to irregular fragmentation 1 ... |

150 | A non-local model for a swarm
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145 | Distributed kalman filter with embedded consensus filters,” CDC-ECC ’05 - Olfati-Saber - 2005 |

145 | Distributed kalman filter with embedded consensus filters,” CDC-ECC ’05 - Olfati-Saber - 2005 |

141 |
Dynamical aspects of animal grouping: swarms, schools, flocks, and herds
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136 | Distributed cooperative control of multiple vehicle formations using structural potential fields,” IFAC World Congress, - Olfati-Saber, Murray - 2002 |

118 | Swarming patterns in two-dimensional kinematic model for biological groups, - Topaz, Bertozzi - 2004 |

118 | Swarming patterns in two-dimensional kinematic model for biological groups, - Topaz, Bertozzi - 2004 |

114 | Self-organized fish schools: An examination of emergent properties,” - Parrish, Viscido, et al. - 2002 |

114 | Consensus protocols for networks of dynamic agents,”
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Citation Context ...lts in [16] were further extended to networks with directed topologies by Moreau [27] and Ren & Beard [39]. The convergence analysis of a nonlinear consensus/alignment protocol was first presented in =-=[45]-=-. Helbing et al. [14] studied the escape panic phenomenon in which a crowd that is trapped in a large building (or arena) attempts to evacuate that location in case of an emergency. In Liu et al. [22]... |

101 |
Algebraic graph theory, volume 207 of Graduate Texts in Mathematics
- Godsil, Royle
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Citation Context ...naries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory [2, 7, 15], algebraic graph theory =-=[12]-=-, spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set of vertices V = {1, 2 . . . ... |

99 | Self-organization in systems of self-propelled particles - Levine, Rappel, et al. |

99 | Stable flocking of mobile agents, part ii: dynamic topology. - Tanner, Jadbabai, et al. - 2003 |

99 | Self-organization in systems of self-propelled particles - Levine, Rappel, et al. |

98 | Coordination and geometric optimization via distributed dynamical systems,”
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91 | Self-Propelled particles with Soft-Core interactions: Patterns, stability, and collapse - D’Orsogna, Chuang, et al. |

91 | Self-Propelled particles with Soft-Core interactions: Patterns, stability, and collapse - D’Orsogna, Chuang, et al. |

77 |
The Structure and Function of Fish Schools,"
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Citation Context |

76 |
Modern graph theory, volume 184 of Graduate Texts in Mathematics.
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Citation Context ...s are made in Section 10. 2 Preliminaries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory =-=[2, 7, 15]-=-, algebraic graph theory [12], spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set... |

68 | Ultra-fast consensus in small-world networks.. - Olfati-Saber - 2005 |

68 | Ultra-fast consensus in small-world networks.. - Olfati-Saber - 2005 |

63 |
Stability analysis of mdimensional asynchronous swarms with a fixed communication topology,”
- Liu, Passino, et al.
- 2003
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Citation Context ...[45]. Helbing et al. [14] studied the escape panic phenomenon in which a crowd that is trapped in a large building (or arena) attempts to evacuate that location in case of an emergency. In Liu et al. =-=[22]-=-, stability analysis of one-dimensional swarms with a fixed topology is studied. In [17], Justh & Krishnaprasad proposed an algorithm for swarming that requires all-to-all interconnections and is only... |

50 | Collision Avoidance for Multiple Agent Systems,”
- Chang, Shadden, et al.
- 2003
(Show Context)
Citation Context ... only two classes of scalable flocking algorithms that do not possess properties a) through e) and successfully lead to creation of flocking in presence of obstacles. Namely, the work by Chang et al. =-=[4]-=- that uses gyroscopic forces for collision avoidance and the work by Olfati-Saber [31] (summarized in [46]) which uses multi-species collective potential functions for both imposing inter-agent constr... |

46 |
Coordination of groups of mobile agents using nearest neighbor rules.
- Jadbabaie, Lin, et al.
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Citation Context ...een a great interest among control scientists in analysis of alignment phenomenon and consensus problems. This includes the alignment results in networks with switching topologies by Jadbabaie et al. =-=[16]-=- and Olfati-Saber & Murray [33]. The results in [16] were further extended to networks with directed topologies by Moreau [27] and Ren & Beard [39]. The convergence analysis of a nonlinear consensus/a... |

45 |
On state-dependent dynamic graphs and their controllability properties.
- Mesbahi
- 2005
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Citation Context ...on 9. Some past research with strong connections to this paper include the work by the following researchers: Fax & Murray [9] used graph Laplacians for multi-vehicle formation stabilization; Mesbahi =-=[23, 24]-=- emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be examples of statedependent graphs); Cortes & Bullo [5] and Cortes et al. [6] intr... |

45 |
Flocking With Obstacle Avoidance: Cooperation With Limited Communication in Mobile Networks,”
- Olfati-Saber, Murray
- 2022
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Citation Context ...sfully lead to creation of flocking in presence of obstacles. Namely, the work by Chang et al. [4] that uses gyroscopic forces for collision avoidance and the work by Olfati-Saber [31] (summarized in =-=[46]-=-) which uses multi-species collective potential functions for both imposing inter-agent constraints and obstacle avoidance. So far, there are no analytical results that relate the algorithm in [4] to ... |

44 | Interaction with a group of autonomous charachters.
- Reynolds
- 2000
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Citation Context ...lementation or analysis of the above rules is that they have broad interpretations. The issue of how to interpret Reynolds rules was resolved after publication of more recent papers by Reynolds [41], =-=[42]-=-. Among the first groups of physicists who studied flocking from a theoretical perspective were Viscek et al. [53], Toner & Tu [51], and Shimoyama et al. [48]. The work of Vicsek et al. was mainly foc... |

42 | Consensus of information under dynamically changing interaction topologies,”
- Ren, Beard
- 2004
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Citation Context ...tworks with switching topologies by Jadbabaie et al. [16] and Olfati-Saber & Murray [33]. The results in [16] were further extended to networks with directed topologies by Moreau [27] and Ren & Beard =-=[39]-=-. The convergence analysis of a nonlinear consensus/alignment protocol was first presented in [45]. Helbing et al. [14] studied the escape panic phenomenon in which a crowd that is trapped in a large ... |

42 |
Collective motion in a system of motile elements.
- Shimoyama, Sugawara, et al.
- 1996
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Citation Context |

41 |
Leaderless coordination via bidirectional and unidirectional time-dependent communication’,
- Moreau
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Citation Context ...ignment results in networks with switching topologies by Jadbabaie et al. [16] and Olfati-Saber & Murray [33]. The results in [16] were further extended to networks with directed topologies by Moreau =-=[27]-=- and Ren & Beard [39]. The convergence analysis of a nonlinear consensus/alignment protocol was first presented in [45]. Helbing et al. [14] studied the escape panic phenomenon in which a crowd that i... |

38 | A Simple Control Law for UAV Formation Flying,”
- Justh，E, Krishnaprasad
- 2002
(Show Context)
Citation Context ...rapped in a large building (or arena) attempts to evacuate that location in case of an emergency. In Liu et al. [22], stability analysis of one-dimensional swarms with a fixed topology is studied. In =-=[17]-=-, Justh & Krishnaprasad proposed an algorithm for swarming that requires all-to-all interconnections and is only analyzed for the case of two agents. Gazi & Passino [11] employed social potentials to ... |

37 | Spatio-angular order in populations of self-aligning objects: formation of oriented patches.
- Mogilner, Edelstein-Keshet
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Citation Context ...forms of swarming behaviors using a network with all-to-all interconnections (i.e. a centralized algorithm). Other continuum models of alignment/swarming were proposed by Mogilner and Eldstein-Keshet =-=[25, 26]-=- with consideration of the sensing issues. Recently, there has been a great interest among control scientists in analysis of alignment phenomenon and consensus problems. This includes the alignment re... |

35 | Graph theory, vol. 173 of Graduate Texts in Mathematics - Diestel - 2010 |

31 |
A question of scale,
- Vicsek
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Citation Context |

28 | Communication complexity of multi-robot systems.
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Citation Context ...|V| and |E| are, respectively, called order and size of the graph. In the context of networked dynamic systems, |E| is referred to as the communication complexity of a network with information flow G =-=[19]-=-. The adjacency matrix A = [aij] of a graph is a matrix with nonzero elements satisfying the property aij �= 0 ⇐⇒ (i, j) ∈ E. The graph is called weighted whenever the elements of its adjacency matrix... |

27 | Flocking with obstacle avoidance: cooperation with limited communication in mobile networks,” Decision and Control, - Saber, Murray - 2003 |

27 | Flocking with obstacle avoidance: cooperation with limited communication in mobile networks,” Decision and Control, - Saber, Murray - 2003 |

26 |
schools: A quantitative theory of flocking
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26 | Consensus and cooperation in multi-agent networked systems. - Olfati-Saber, Fax, et al. - 2006 |

26 | Consensus and cooperation in multi-agent networked systems. - Olfati-Saber, Fax, et al. - 2006 |

23 | schools: a quantitative theory of flocking. Phys - Toner, Tu, et al. - 1998 |

21 | schools: a quantitative theory of flocking - Toner, Tu, et al. - 1998 |

20 |
Blind Fish Can School,"
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20 |
Fish in Schools,"
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Citation Context |

16 |
Advection on graphs,” in
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Citation Context ...on 9. Some past research with strong connections to this paper include the work by the following researchers: Fax & Murray [9] used graph Laplacians for multi-vehicle formation stabilization; Mesbahi =-=[23, 24]-=- emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be examples of statedependent graphs); Cortes & Bullo [5] and Cortes et al. [6] intr... |

7 |
Efficient coordination of multipleaircraft systems,”
- Ribichini, Frazzoli
- 2003
(Show Context)
Citation Context ... Cortes & Bullo [5] and Cortes et al. [6] introduced distributed algorithms for placement of mobile sensors that appears to be closely related to flocking in a constrained space; Rabichini & Frazzoli =-=[43]-=- proposed an energy-efficient method for determining the split time in a multi-vehicle rejoin/split maneuver; Leonard & Fiorelli [21] used artificial potentials for formation keeping; Ogren et al. [28... |

7 | Stability Analysis of M Dimensional Asynchronous Swarms with a Fixed Communication Topology - Liu, Passino, et al. - 2003 |

6 |
Gyroscopic forces and collision avoidance
- Chang, Marsden
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(Show Context)
Citation Context ...e of a more sophisticated obstacle avoidance approach eliminates getting trapped behind an obstacle. A successful example of such an approach is the use of gyroscopic forces for obstacle avoidance in =-=[3, 4]-=-. For a comprehensive treatment of obstacle avoidance in robotics, please refer to Latombe [20]. 8 Simulation Results In this section, we present several simulation results of 2-D and 3-D flocking. Fo... |

6 | Communication complexity of multi-robot systems,” in Algorithmic Foundations of Robotics V - Klavins - 2003 |

5 |
The Chorus-Line Hypothesis of Maneuver in Avian Flocks.
- Partridge
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Citation Context |

4 | Stability analysis of w-dimensional asynchronous swarms with a fixed communication topology - Liu, Passino, et al. |

3 |
Flocking with obstacle avoidance
- Olfati-Saber
- 2003
(Show Context)
Citation Context ...hrough e) and successfully lead to creation of flocking in presence of obstacles. Namely, the work by Chang et al. [4] that uses gyroscopic forces for collision avoidance and the work by Olfati-Saber =-=[31]-=- (summarized in [46]) which uses multi-species collective potential functions for both imposing inter-agent constraints and obstacle avoidance. So far, there are no analytical results that relate the ... |

2 | state-dependent dynamic graphs and their controllability properties - “On - 2005 |

2 | Flocking with obstacle avoidance,” California Inst - Olfati-Saber - 2003 |

1 |
A unified analytical look at Renoldys flocking rules
- Olfati-Saber
- 2003
(Show Context)
Citation Context ...ts that use Algorithm 1 is drastically different than a group of agents applying Algorithm 2. Remark 4. We will demonstrate that protocol (24) unifies all three rules of Reynolds in a single equation =-=[30]-=-. This is not the result of applying a gradient-based algorithm. It is due to the fact that the gradient-based term of the protocol can be expressed in terms of position-dependent stress elements of a... |

1 |
Rigid definitions of schooling behavior are inadequate
- Partridge
- 1982
(Show Context)
Citation Context ...oup does not stop near qd and moves along the specified desired group velocity pd. After passing both obstacles, the agents form a giant flock as shown in Fig. 17 (f). 9 What Constitutes Flocking? In =-=[35]-=-, Partridge provides a brief survey of various definitions of “schooling in fish” by animal behavior scientists that spans half a century from 1927 to 1981. The length of this period is a clear indica... |

1 |
Steering behaviors for autonomous charachters
- Reynolds
- 1999
(Show Context)
Citation Context ...th implementation or analysis of the above rules is that they have broad interpretations. The issue of how to interpret Reynolds rules was resolved after publication of more recent papers by Reynolds =-=[41]-=-, [42]. Among the first groups of physicists who studied flocking from a theoretical perspective were Viscek et al. [53], Toner & Tu [51], and Shimoyama et al. [48]. The work of Vicsek et al. was main... |

1 | structure and function of fish schools - “The - 1982 |

1 | Flocking in fixed and switching networks,” Submitted - Tanner, Jadbabaie, et al. - 2005 |