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69
Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment
 IEEE Transactions on Automatic Control
, 2004
"... Abstract—We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy d ..."
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Cited by 239 (19 self)
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Abstract—We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy decouples, in part, the cooperative management of the network formation from the network maneuvers. The underlying coordination framework uses virtual bodies and artificial potentials. We focus on gradient climbing missions in which the mobile sensor network seeks out local maxima or minima in the environmental field. The network can adapt its configuration in response to the sensed environment in order to optimize its gradient climb. Index Terms—Adaptive systems, cooperative control, gradient methods, mobile robots, multiagent systems, sensor networks. I.
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 93 (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.
Macroscopic limit of selfdriven particles with orientation interaction, note
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Multivehicle flocking: Scalability of cooperative control algorithms using pairwise potentials
, 2006
"... Abstract — In this paper, we study cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles. An important issue is the role the potential plays in the stability and possible collapse of the group as agent number increases. We model a set ..."
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Cited by 39 (11 self)
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Abstract — In this paper, we study cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles. An important issue is the role the potential plays in the stability and possible collapse of the group as agent number increases. We model a set of interacting Dubins vehicles with fixed turning angle and speed. We perform simulations for a large number of agents and we show experimental realizations of the model on a testbed with a small number of vehicles. In both cases, critical thresholds exist between coherent, stable, and scalable flocking and dispersed or collapsing motion of the group.
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 32 (6 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.
Asymptotic dynamics of attractiverepulsive swarms
, 2008
"... We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractiverepulsive social in ..."
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Cited by 18 (0 self)
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We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractiverepulsive social interactions. The kernel’s first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steadystate. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactlysupported population has edges that behave like traveling waves whose speed, density and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers’ equation. We derive an analytical upper bound for the finite blowup time after which the solution forms one or more δfunctions.
Mathematical models of swarming and social aggregation, invited lecture
 The 2001 International Symposium on Nonlinear Theory and its Applications, (NOLTA 2001
"... Abstract  I survey some of the problems (both mathematical and biological) connected with aggregation of social organisms and indicate some mathematical and modelling challenges. I describe recent work with collegues on swarming behaviour. Examples discussed include (1) a model for locust migra ..."
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Cited by 18 (0 self)
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Abstract  I survey some of the problems (both mathematical and biological) connected with aggregation of social organisms and indicate some mathematical and modelling challenges. I describe recent work with collegues on swarming behaviour. Examples discussed include (1) a model for locust migration swarms, (2) the eect of nonlocal interactions on swarm shape and dynamics, and (3) an individualbased model for the spacing of neighbors in a group. I. Background and previous work Many chemical and physical systems are characterized by formation of patterns, clusters and aggregates, or phenomena such as wave and pulse propagation. In biology, swarming and social aggregation form a rich and diverse collection of such phenomena. The size scale of groups ranges from microscopic cellular populations to herds, flocks, schools, and swarms of macroscopic, and sometimes enormous size. In some cases, notably swarms of locusts, these aggregates have serious impact on ecology and human activity. These examples, and many others, have motivated studies in which both biological aspects as well as theoretical modeling and mathematical aspects of the phenomena have been investigated. Early works in the 1950’s were largely descriptive biological investigations of sh schools [3] or bird flocks [4]. Some theoretical concepts for the formation of herds and groups were discussed in a classic paper by Hamilton [9]. See also [22] for simulations and a model for animal group structure. The classic book by Okubo(1980) [16] (recently modernized [18]) presented some aspects of the initial mathematical concepts applied to studying swarms. Since that time, the literature has grown substantially, with many signicant contributions addressing such problems from the perspective of biology, mathematical modeling, or physics. Notable among
Particle, Kinetic, and Hydrodynamic Models of Swarming
"... Summary. We review the stateoftheart in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individualbased models based on “particle”like assumptions, we connect to hydrodynamic/macroscopic descr ..."
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Cited by 18 (7 self)
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Summary. We review the stateoftheart in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individualbased models based on “particle”like assumptions, we connect to hydrodynamic/macroscopic descriptions of collective motion via kinetic theory. We emphasize the role of the kinetic viewpoint in the modelling, in the derivation of continuum models and in the understanding of the complex behavior of the system. Key words: swarming, kinetic theory, particle models, hydrodynamic descriptions, mean fields, pattern formation 1
Large scale dynamics of the Persistent Turning Walker Model of fish behavior
 Journal of Statistical Physics
"... This paper considers a new model of individual displacement, based on fish motion, the socalled Persistent Turning Walker (PTW) model, which involves an OrnsteinUhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of dif ..."
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Cited by 18 (11 self)
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This paper considers a new model of individual displacement, based on fish motion, the socalled Persistent Turning Walker (PTW) model, which involves an OrnsteinUhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a FokkerPlanck type equation posed in an extended phasespace involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results. Acknowledgements: The authors wish to thank Guy Théraulaz and Jacques Gautrais of the ’Centre de Recherches sur la Cognition Animale ’ in Toulouse, for introducing them to the model and for stimulating discussions.