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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.
Information Consensus in Multivehicle Cooperative Control
, 2007
"... The abundance of embedded computational resources in autonomous vehicles enables enhanced operational effectiveness through cooperative teamwork in civilian and military applications. Compared to autonomous vehicles that perform solo missions, greater efficiency and operational capability can be rea ..."
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Cited by 240 (24 self)
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The abundance of embedded computational resources in autonomous vehicles enables enhanced operational effectiveness through cooperative teamwork in civilian and military applications. Compared to autonomous vehicles that perform solo missions, greater efficiency and operational capability can be realized from teams of autonomous vehicles operating in a coordinated fashion. Potential applications for multivehicle systems include spacebased interferometers, combat, surveillance, and reconnaissance systems, hazardous material handling, and distributed reconfigurable sensor networks. To enable these applications, various cooperative control capabilities need to be developed, including formation control, rendezvous, attitude alignment, flocking, foraging, task and role assign
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.
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 172 (3 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
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 106 (13 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.
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 70 (2 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.
Decentralized control of vehicle formations
, 2005
"... This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a prespecified communication digraph, G. A feedback control is designed using relative information between a vehicle an ..."
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Cited by 68 (0 self)
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This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a prespecified communication digraph, G. A feedback control is designed using relative information between a vehicle and its inneighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including symmetric communication graphs and formations with leaders. Several numerical simulations are used to illustrate the results.
Multivehicle consensus with a timevarying reference state
, 2007
"... In this paper, we study the consensus problem in multivehicle systems, where the information states of all vehicles approach a timevarying reference state under the condition that only a portion of the vehicles (e.g., the unique team leader) have access to the reference state and the portion of th ..."
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Cited by 53 (13 self)
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In this paper, we study the consensus problem in multivehicle systems, where the information states of all vehicles approach a timevarying reference state under the condition that only a portion of the vehicles (e.g., the unique team leader) have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team. We first analyze a consensus algorithm with a constant reference state using graph theoretical tools. We then propose consensus algorithms with a timevarying reference state and show necessary and sufficient conditions under which consensus is reached on the timevarying reference state. The timevarying reference state can be an exogenous signal or evolve according to a nonlinear model. These consensus algorithms are also extended to achieve relative state deviations among the vehicles. An application example to multivehicle formation control is given as a proof of concept.
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 36 (7 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.