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24
Flocking for multiagent dynamic systems: Algorithms and theory
 IEEE Transactions on Automatic Control
, 2006
"... Submitted to the IEEE Transactions on Automatic Control Technical Report CITCDS 2004005 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 th ..."
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Cited by 147 (1 self)
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Submitted to the IEEE Transactions on Automatic Control Technical Report CITCDS 2004005 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 the tracking/migration problem for flocks can be solved using an algorithm with a peertopeer architecture. Each node (or macroagent) of this peertopeer network is the aggregation of all three species of agents. The implication of this fact is that “flocks
Formations of vehicles in cyclic pursuit
 IEEE Transactions on Automatic Control
, 2004
"... Abstract—Inspired by the socalled “bugs ” problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system ..."
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Cited by 77 (1 self)
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Abstract—Inspired by the socalled “bugs ” problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system of wheeled vehicles, each subject to a single nonholonomic constraint (i.e., unicycles), which is the principal focus of this paper. The pursuit framework is particularly simple in that the identical vehicles are ordered such that vehicle pursues vehicle CImodulo. In this paper, we assume each vehicle has the same constant forward speed. We show that the system’s equilibrium formations are generalized regular polygons and it is exposed how the multivehicle system’s global behavior can be shaped through appropriate controller gain assignments. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not. Index Terms—Circulant matrices, cooperative control, multiagent systems, pursuit problems. 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 73 (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.
On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
 In Proceedings of the American Control Conference
, 2004
"... We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral gra ..."
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Cited by 58 (8 self)
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We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase di#erences 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.
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 45 (19 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.
Stabilization of planar collective motion with limited communication
 IEEE Trans. Automat. Contr
"... Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particle ..."
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Cited by 41 (21 self)
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Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and timeinvariant or timevarying. The emphasis of this paper is to show how previous results assuming alltoall communication can be extended to a general communication framework. Index Terms—Cooperative control, geometric control, multiagent systems, stabilization. I.
Collective motion and oscillator synchronization
 Proc. Block Island Workshop on Cooperative Control
, 2003
"... Summary. This paper studies connections between phase models of coupled oscillators and kinematic models of groups of selfpropelled particles. These connections are exploited in the analysis and design of feedback control laws for the individuals that stabilize collective motions for the group. 1 ..."
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Cited by 23 (7 self)
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Summary. This paper studies connections between phase models of coupled oscillators and kinematic models of groups of selfpropelled particles. These connections are exploited in the analysis and design of feedback control laws for the individuals that stabilize collective motions for the group. 1
CONSENSUS OPTIMIZATION ON MANIFOLDS
 VOL. 48, NO. 1, PP. 56–76 C ○ 2009 SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
, 2009
"... The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of th ..."
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Cited by 23 (8 self)
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The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and timevarying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) andthe Grassmann manifold Grass(p, n) are treated as original examples. A link is also drawn with the many existing results on the circle.
Oscillator models and collective motion: Splay state stabilization of selfpropelled particles
 in Proc. 44th IEEE Conference on Decision and Control
, 2005
"... Abstract — This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spac ..."
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Cited by 15 (9 self)
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Abstract — This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles in the splay state formation around the center of mass of the group. I.
Collective Motion: Bistability and Trajectory Tracking
 in Proc. 43rd IEEE Conf. Decision and Control
, 2004
"... Abstract — This paper presents analysis and application of steering control laws for a network of selfpropelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered ..."
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Cited by 13 (9 self)
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Abstract — This paper presents analysis and application of steering control laws for a network of selfpropelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to bistability and hysteresis. We also present behavior primitives that enable piecewiselinear network trajectory tracking. I.