Results 1  10
of
21
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
Abstract

Cited by 1112 (21 self)
 Add to MetaCart
In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader determination) for groups of discretetime agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing averageconsensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
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 ..."
Abstract

Cited by 436 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 192 (10 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 65 (5 self)
 Add to MetaCart
(Show Context)
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
A simple proof of the CuckerSmale flocking dynamics and meanfield limit
 Comm. Math. Sci
"... Abstract. We present a simple proof on the formation of flocking to the CuckerSmale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. For large par ..."
Abstract

Cited by 40 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We present a simple proof on the formation of flocking to the CuckerSmale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. For large particle systems, we give a rigorous justification for the meanfield limit from the many particle CuckerSmale system to the Vlasov equation with flocking dissipation as the number of particles goes to infinity. Key words. Flocking, swarming, emergence, selfdriven particles system, autonomous agents, Vlasov equation, Lyapunov functional, measure valued solution, KantorovichRubinstein distance. Subject classifications. Primary 92C17; secondary 82C22, 82C40.
SelfOrganized Flocking with Agent Failure: OffLine Optimization and Demonstration with Real Robots
, 2002
"... This paper presents an investigation of flocking, the formation and maintenance of coherent group movement, by teams of autonomous mobile robots using principles of Swarm Intelligence. First, we present a simple flocking task, and we describe a leaderless distributed flocking algorithm (LD) that is ..."
Abstract

Cited by 39 (0 self)
 Add to MetaCart
This paper presents an investigation of flocking, the formation and maintenance of coherent group movement, by teams of autonomous mobile robots using principles of Swarm Intelligence. First, we present a simple flocking task, and we describe a leaderless distributed flocking algorithm (LD) that is more conducive to implementation on embodied agents than the established algorithms used in computer animation. Next, we use an embodied simulator and reinforcement learning techniques to optimize LD performance under different conditions, showing that this method can be used not only to improve performance but also to gain insight into which algorithm components contribute most to system behavior. Finally, we demonstrate that a group of real robots executing LD with emulated sensors can successfully flock (even in the presence of individual agent failure) and that systematic characterization (and therefore optimization) of real robot flocking parameters is achievable.
Heterophilious dynamics enhances consensus
, 2013
"... We review a general class of models for selforganized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or “agents”, with the tendency to adjust to their ‘environmental averages’. This, in turn, leads to the formation of clusters, e.g., ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
(Show Context)
We review a general class of models for selforganized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or “agents”, with the tendency to adjust to their ‘environmental averages’. This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, etc. A natural question which arises in this context is to understand when and how clusters emerge through the selfalignment of agents, and what type of “rules of engagement ” influence the formation of such clusters. Of particular interest to us are cases in which the selforganized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking or concentration of other positions intrinsic to the dynamics. Many standard models for selforganized dynamics in social, biological and physical science assume that the intensity of alignment increases as agents get closer, reflecting a common tendency to align with those who think or act alike. Moreover, “Similarity breeds connection,” reflects our intuition that increasing the intensity of alignment as the difference of positions decreases, is more likely to lead to a consensus. We argue here that the converse is true: when the dynamics is driven by local interactions, it is more likely to approach a consensus when the interactions among agents increase as a function of their difference in position. Heterophily — the tendency to bond more with those who are different rather than with those who are similar, plays a decisive rôle in the process of clustering. We point out that the number of clusters in heterophilious dynamics decreases as the heterophily dependence among agents increases. In particular, sufficiently strong heterophilious interactions enhance consensus.
Analysis and simulations of a refined flocking and swarming model of CuckerSmale type. Kinetic and Related Models
"... (Communicated by the associate editor name) Abstract. The CuckerSmale model for flocking or swarming of birds or insects is generalized to scenarios where a typical bird will be subject to a) a friction force term driving it to fly at optimal speed, b) a repulsive short range force to avoid collis ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
(Show Context)
(Communicated by the associate editor name) Abstract. The CuckerSmale model for flocking or swarming of birds or insects is generalized to scenarios where a typical bird will be subject to a) a friction force term driving it to fly at optimal speed, b) a repulsive short range force to avoid collisions, c) an attractive “flocking ” force computed from the birds seen by each bird inside its vision cone, and d) a “boundary ” force which will entice birds to search for and return to the flock if they find themselves at some distance from the flock. We introduce these forces in detail, discuss the required cutoffs and their implications and show that there are natural bounds in velocity space. Wellposedness of the initial value problem is discussed in spaces of measurevalued functions. We conclude with a series of numerical simulations. 1. Introduction. Flocking