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35
Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
, 2002
"... In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the a ..."
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Cited by 613 (42 self)
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In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its \neighbors." In their paper, Vicsek et. al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models.
Flocking in Fixed and Switching Networks
, 2003
"... The work of this paper is inspired by the flocking phenomenon observed in Reynolds (1987). We introduce a class of local control laws for a group of mobile agents that result in: (i) global alignment of their velocity vectors, (ii) convergence of their speeds to a common one, (iii) collision avoidan ..."
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Cited by 75 (7 self)
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The work of this paper is inspired by the flocking phenomenon observed in Reynolds (1987). We introduce a class of local control laws for a group of mobile agents that result in: (i) global alignment of their velocity vectors, (ii) convergence of their speeds to a common one, (iii) collision avoidance, and (iv) minimization of the agents artificial potential energy. These are made possible through local control action by exploiting the algebraic graph theoretic properties of the underlying interconnection graph. Algebraic connectivity a#ects the performance and robustness properties of the overall closed loop system. We show how the stability of the flocking motion of the group is directly associated with the connectivity properties of the interconnection network and is robust to arbitrary switching of the network topology.
Emergent behavior in flocks
 IEEE Transactions on Automatic Control
, 2007
"... PRELIMINARY VERSION. As a motivating example we consider a population, say of birds or fish, whose members are moving in IR 3. It has been observed that under some initial conditions, for example on their positions and velocities, the state of the flock converges to one ..."
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Cited by 69 (2 self)
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PRELIMINARY VERSION. As a motivating example we consider a population, say of birds or fish, whose members are moving in IR 3. It has been observed that under some initial conditions, for example on their positions and velocities, the state of the flock converges to one
Agentbased computational models and generative social science
 Complexity
, 1999
"... This article argues that the agentbased computational model permits a distinctive approach to social science for which the term “generative ” is suitable. In defending this terminology, features distinguishing the approach from both “inductive ” and “deductive ” science are given. Then, the followi ..."
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Cited by 64 (0 self)
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This article argues that the agentbased computational model permits a distinctive approach to social science for which the term “generative ” is suitable. In defending this terminology, features distinguishing the approach from both “inductive ” and “deductive ” science are given. Then, the following specific contributions to social science are discussed: The agentbased computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agentbased modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agentbased (“bottom up”) models. The agentbased approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agentbased modeling offers powerful new forms of hybrid theoreticalcomputational work; these are particularly relevant to the study of nonequilibrium systems. The agentbased approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agentbased modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. � 1999 John Wiley &
Swarming patterns in a twodimensional kinematic model for biological groups
 SIAM J. Appl. Math
, 2004
"... Abstract. We construct a continuum model for the motion of biological organisms experiencing social interactions and study its patternforming behavior. The model takes the form of a conservation law in two spatial dimensions. The social interactions are modeled in the velocity term, which is nonloc ..."
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Cited by 64 (18 self)
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Abstract. We construct a continuum model for the motion of biological organisms experiencing social interactions and study its patternforming behavior. The model takes the form of a conservation law in two spatial dimensions. The social interactions are modeled in the velocity term, which is nonlocal in the population density and includes a parameter that controls the interaction length scale. The dynamics of the resulting partial integrodifferential equation may be uniquely decomposed into incompressible motion and potential motion. For the purely incompressible case, the model resembles one for fluid dynamical vortex patches. There exist solutions which have constant population density and compact support for all time. Numerical simulations produce rotating structures which have circular cores and spiral arms and are reminiscent of naturally observed phenomena such as ant mills. The sign of the social interaction term determines the direction of the rotation, and the interaction length scale affects the degree of spiral formation. For the purely potential case, the model resembles a nonlocal (forwards or backwards) porous media equation. The sign of the social interaction term controls whether the population aggregates or disperses, and the interaction length scale controls the balance between transport and smoothing of the density profile. For the aggregative case, the population clumps into regions of high and low density. The characteristic length scale of the density pattern is predicted and confirmed by numerical simulations.
Stable Flocking of Mobile Agents, Part II: Dynamic Topology
 In IEEE Conference on Decision and Control
, 2003
"... This is the second of a twopart paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control interconnections between the agents in the group to vary with time. Specifically, the contro ..."
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Cited by 48 (4 self)
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This is the second of a twopart paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control interconnections between the agents in the group to vary with time. Specifically, the control law of an agent depends on the state of a set of agents that are within a certain neighborhood around it. As the agents move around, this set changes giving rise to a dynamic control interconnection topology and a switching control law. This control law consists of a a combination of attractive/repulsive and alignment forces. The former ensure collision avoidance and cohesion of the group and the latter result to all agents attaining a common heading angle, exhibiting flocking motion. Despite the use of only local information and the time varying nature of agent interaction which affects the local controllers, flocking motion can still be established, as long as connectivity in the neighboring graph is maintained.
On the mathematics of emergence
 Japan J. Math
, 2006
"... A common situation occurring in a number of disciplines is that in which a number of autonomous agents reach a consensus without a central direction. An example of this is the emergence of a common belief in a price system when activity takes place in a given market. Another example is the emergence ..."
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Cited by 31 (1 self)
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A common situation occurring in a number of disciplines is that in which a number of autonomous agents reach a consensus without a central direction. An example of this is the emergence of a common belief in a price system when activity takes place in a given market. Another example is the emergence of common languages in primitive societies, or the dawn of vowel systems. Yet a third example is the way in which populations of animals move together (referred as “schooling”, “flocking”, or “herding ” depending on the considered animals). As a motivating example in this introduction we consider a population, say of birds, whose members are moving in IE = IR 3. This situation has been recently studied in [6] and in what follows we freely draw from this paper. It has been observed that under some initial conditions, for example on the positions and velocities of the birds, the state of the flock converges to one in which all birds fly with the same velocity. A way to justify this observation is to postulate a model for the evolution of the flock and exhibit conditions on the initial state under which a convergence as above is established. In case these conditions are not satisfied, dispersion of the flock may occur. ∗ For the Japanese Journal of Mathematics. † Partially supported by an NSF grant.
Finitetime singularities of an aggregation equation in R n with fractional dissipation
"... Abstract. We consider an aggregation equation in R n, n ≥ 2, with fractional dissipation, namely, ut + ∇ · (u∇K ∗ u) = −ν(−∆) γ/2 u, where 0 ≤ γ ≤ 2 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e −x . We prove that for 0 ≤ γ < 1 the solutions ..."
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Cited by 17 (1 self)
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Abstract. We consider an aggregation equation in R n, n ≥ 2, with fractional dissipation, namely, ut + ∇ · (u∇K ∗ u) = −ν(−∆) γ/2 u, where 0 ≤ γ ≤ 2 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e −x . We prove that for 0 ≤ γ < 1 the solutions develop blowup in finite for a general class of initial data. In contrast we prove that for 1 < γ ≤ 2 the equation is globally wellposed. 1. Introduction and
Multiagent coordination using nearestneighbor rules: revisiting the Vicsek model”; http://arxiv.org/abs/cs.MA/0407021
"... Recently Jadbabaie, Lin and Morse (IEEE Transactions on Automatic Control, 48(6):9881001, 2003.) give a mathematical analysis for the discrete time model of groups of mobile autonomous agents raised by Vicsek et al. in 1995. In their paper, Jadbabaie et al. show that all agents shall move in the sa ..."
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Cited by 16 (0 self)
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Recently Jadbabaie, Lin and Morse (IEEE Transactions on Automatic Control, 48(6):9881001, 2003.) give a mathematical analysis for the discrete time model of groups of mobile autonomous agents raised by Vicsek et al. in 1995. In their paper, Jadbabaie et al. show that all agents shall move in the same heading provided that these agents are periodically linked together. This paper sharpens this result by showing that coordination will be reached under very mild condition. This also gives an affirmative answer to one question raised by Jadbabie et al. Index Terms—Decentralized control, multiagent coordination, switched systems. 1