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98
Flocking for MultiAgent Dynamic Systems: Algorithms and Theory
, 2006
"... In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A compre ..."
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Cited by 436 (2 self)
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In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of latticeshape objects called αlattices. We use a multispecies framework for construction of collective potentials that consist of flockmembers, or αagents, and virtual agents associated with αagents called β and γagents. We show that migration of flocks can be performed using a peertopeer network of agents, i.e. “flocks need no leaders.” A “universal” definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2D and 3D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
Stability analysis of swarms
 IEEE Transactions on Automatic Control
, 2003
"... Abstract — In this brief article we specify an “individualbased ” continuous time model for swarm aggregation in ndimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we ..."
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Cited by 197 (9 self)
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Abstract — In this brief article we specify an “individualbased ” continuous time model for swarm aggregation in ndimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model. I.
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 192 (10 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.
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 118 (15 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.
Stability analysis of social foraging swarms
 IEEE TRANS. ON SYSTEMS, MAN AND CYBERNETICS
, 2004
"... In this article we specify anmember “individualbased” continuous time swarm model with individuals that move in andimensional space according to an attractant/repellent or a nutrient profile. The motion of each individual is determined by three factors: i) attraction to the other individuals on ..."
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Cited by 100 (4 self)
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In this article we specify anmember “individualbased” continuous time swarm model with individuals that move in andimensional space according to an attractant/repellent or a nutrient profile. The motion of each individual is determined by three factors: i) attraction to the other individuals on long distances; ii) repulsion from the other individuals on short distances; and iii) attraction to the more favorable regions (or repulsion from the unfavorable regions) of the attractant/repellent profile. The emergent behavior of the swarm motion is the result of a balance between interindividual interactions and the simultaneous interactions of the swarm members with their environment. We study the stability properties of the collective behavior of the swarm for different profiles and provide conditions for collective convergence to more favorable regions of the profile.
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 99 (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.
Stabilization of planar collective motion: alltoall communication
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2007
"... This paper proposes a design methodology to stabilize isolated relative equilibria in a model of alltoall coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or circular motio ..."
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Cited by 91 (32 self)
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This paper proposes a design methodology to stabilize isolated relative equilibria in a model of alltoall coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a loworder parametric family of stabilizable collectives that offer a set of primitives for the design of higherlevel tasks at the group level.
From particle to kinetic and hydrodynamic descriptions of flocking
 Kinetic and Related Methods
"... Abstract. We discuss the CuckerSmale’s (CS) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasovtype kinetic model for the CS particle model and prove it exhibits timeasymptotic floc ..."
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Cited by 65 (5 self)
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Abstract. We discuss the CuckerSmale’s (CS) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasovtype kinetic model for the CS particle model and prove it exhibits timeasymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynamic description of flocking based on the CS Vlasovtype kinetic model and prove flocking behavior without closure of higher moments. 1. Introduction. Collective
DOUBLE MILLING IN SELFPROPELLED SWARMS FROM KINETIC THEORY
"... (Communicated by Tong Yang) Abstract. We present a kinetic theory for swarming systems of interacting, selfpropelled discrete particles. Starting from the Liouville equation for the manybody problem we derive a kinetic equation for the single particle probability distribution function and the rela ..."
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Cited by 47 (13 self)
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(Communicated by Tong Yang) Abstract. We present a kinetic theory for swarming systems of interacting, selfpropelled discrete particles. Starting from the Liouville equation for the manybody problem we derive a kinetic equation for the single particle probability distribution function and the related macroscopic hydrodynamic equations. General solutions include flocks of constant density and fixed velocity and other nontrivial morphologies such as compactly supported rotating mills. The kinetic theory approach leads us to the identification of macroscopic structures otherwise not recognized as solutions of the hydrodynamic equations, such as double mills of two superimposed flows. We find the conditions allowing for the existence of such solutions and compare to the case of single mills.