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24
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 333 (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.
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 158 (9 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.
On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
, 2005
"... We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using ..."
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Cited by 95 (12 self)
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We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.
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 85 (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.
Stable flocking of multiple inertial agents on balanced graphs
 Computer Science, The University of Newcastle
, 2006
"... and the optimum value of max[P (0)] was max[P (0)] = 00:40844 < 0 which indicates that this system has no robustly unobservable states. For the optimal value of given above, a plot of max[P (t)] as a function of t is shown in Fig. 6. ..."
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Cited by 31 (5 self)
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and the optimum value of max[P (0)] was max[P (0)] = 00:40844 < 0 which indicates that this system has no robustly unobservable states. For the optimal value of given above, a plot of max[P (t)] as a function of t is shown in Fig. 6.
Synchronization in Oscillator Networks: Switching Topologies and Nonhomogeneous Delays
, 2005
"... In this paper we investigate the problem of synchronization in oscillator networks when the delay inherent in such systems is taken into account. We first investigate a general Kuramototype model with heterogeneous time delays, both with a nearest neighbor as well as a more general network interac ..."
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Cited by 21 (3 self)
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In this paper we investigate the problem of synchronization in oscillator networks when the delay inherent in such systems is taken into account. We first investigate a general Kuramototype model with heterogeneous time delays, both with a nearest neighbor as well as a more general network interaction, for which we propose conditions for synchronization around a rotating frequency. Then, we turn our attention to the problem of synchronization when the topologies are allowed to change. We show that synchronization is possible in the presence of delay, using a common Lyapunov functional argument.
Agreement with NonUniform Information Delays
, 2006
"... We propose a novel agreement framework for multiple (possibly heterogeneous) agents evolving on a directed information graph with nonuniform delays. Our proposed framework can ensure agreement of a certain scalar quantity among the agents, as long as 1) for each agent, we can design a local contr ..."
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Cited by 19 (1 self)
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We propose a novel agreement framework for multiple (possibly heterogeneous) agents evolving on a directed information graph with nonuniform delays. Our proposed framework can ensure agreement of a certain scalar quantity among the agents, as long as 1) for each agent, we can design a local control s.t. its closedloop transfer function has unit gain at dc and gain strictly less than unity elsewhere; 2) the information graph has a globally reachable node (i.e. there exists a path from it to every other nodes); and 3) the information delays are finite constants. Rendezvous simulation is performed to verify the theory.
Scaling universality in the microstructure of urban space, Physica A 332
, 2004
"... We present a broad, phenomenological picture of the distribution of the length of urban linear segments, l, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of l, we obtain two master curves for a sample of cities, which are not a function of city size. We show that ..."
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Cited by 11 (2 self)
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We present a broad, phenomenological picture of the distribution of the length of urban linear segments, l, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of l, we obtain two master curves for a sample of cities, which are not a function of city size. We show that a third class of cities is not easily classifiable into these two universality classes. The cumulative distribution of l displays powerlaw tails with two distinct exponents, and. We suggest a link between our observations and the possibility of observing and modelling urban growth using Levy processes. 1.
Stability of Flocking Motion
, 2003
"... This paper in vestigates the aggregated stability properties of of a system of multiple mobileagen ts described by simpledynleS55 systems. Theagen ts are steered through local coordin2Sfi5 con trol laws that arise as a combin7 tion of attractive/repulsivean align2F t forces. These forces ences colli ..."
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Cited by 11 (0 self)
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This paper in vestigates the aggregated stability properties of of a system of multiple mobileagen ts described by simpledynleS55 systems. Theagen ts are steered through local coordin2Sfi5 con trol laws that arise as a combin7 tion of attractive/repulsivean align2F t forces. These forces ences collision avoidan e a n cohesion of the groupan result to all agen ts attain[S a common headin anin exhibitin flockin motion Two cases are con197 ered: in the first, position in[]5 ation from all group members is available to each agen t; in the seconc each agen t has access to position i n ormation of on( the agen ts layin in ide its n ighborhood. It is then shown that regardless ofan y arbitrary chan[1 in thenS[9 bor set, the flockinmotion remain stable aslon as the graph that describes the n ighborin relation amon the agen ts in the group is always con9 cted. 1
Synchonization in Oscillator Networks with Heterogeneous Delays, Switching Topologies and Nonlinear Dynamics
, 2006
"... This paper investigates the attractivity properties of the lockedinphase equilibria set in oscillator networks, in the presence of multiple, noncommensurate communication delays. The dynamics that the oscillators are endowed with are in the form of nonlinear delay differential equations, with Ku ..."
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Cited by 7 (0 self)
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This paper investigates the attractivity properties of the lockedinphase equilibria set in oscillator networks, in the presence of multiple, noncommensurate communication delays. The dynamics that the oscillators are endowed with are in the form of nonlinear delay differential equations, with Kuramototype interactions. Using an appropriate LaSalle invariance principle we assess the attractivity properties of this set for arbitrary topology interconnections. We then show that this set is also asymptotically attracting even if the network topology is allowed to change.