Results 1  10
of
19
Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
, 2002
"... In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on ..."
Abstract

Cited by 713 (47 self)
 Add to MetaCart
In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its \neighbors." In their paper, Vicsek et. al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models.
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 516 (15 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 182 (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 90 (8 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.
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 ..."
Abstract

Cited by 76 (18 self)
 Add to MetaCart
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.
A simple control law for UAV formation flying
"... ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, ..."
Abstract

Cited by 29 (0 self)
 Add to MetaCart
ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical,
Steering laws and continuum models for planar formations
 in IEEE Conf. on Decision and Control, (Maui, Hawaii
, 2003
"... Abstract — We consider a Lie group formulation for the problem of control of formations. Vehicle trajectories are described using the planar FrenetSerret equations of motion, which capture the evolution of both vehicle position and orientation for unitspeed motion subject to curvature (steering) c ..."
Abstract

Cited by 26 (5 self)
 Add to MetaCart
Abstract — We consider a Lie group formulation for the problem of control of formations. Vehicle trajectories are described using the planar FrenetSerret equations of motion, which capture the evolution of both vehicle position and orientation for unitspeed motion subject to curvature (steering) control. The Lie group structure can be exploited to determine the set of all possible (relative) equilibria for arbitrary Ginvariant curvature controls, where G = SE(2) is a symmetry group for the control law. The main result is a convergence result for n vehicles (for finite n), using a Lyapunov function which for n = 2, has been previously shown to yield global convergence. A continuum formulation of the basic equations is also presented. I.
Finitetime singularities of an aggregation equation in R n with fractional dissipation
"... Abstract. We consider an aggregation equation in R n, n ≥ 2, with fractional dissipation, namely, ut + ∇ · (u∇K ∗ u) = −ν(−∆) γ/2 u, where 0 ≤ γ ≤ 2 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e −x . We prove that for 0 ≤ γ < 1 the soluti ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
Abstract. We consider an aggregation equation in R n, n ≥ 2, with fractional dissipation, namely, ut + ∇ · (u∇K ∗ u) = −ν(−∆) γ/2 u, where 0 ≤ γ ≤ 2 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e −x . We prove that for 0 ≤ γ < 1 the solutions develop blowup in finite for a general class of initial data. In contrast we prove that for 1 < γ ≤ 2 the equation is globally wellposed. 1. Introduction and
On a nonlocal aggregation model with nonlinear diffusion
, 2008
"... Abstract. We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the wellposedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Abstract. We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the wellposedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative smooth initial data we prove that the gradient of the solution develops L ∞ xnorm blowup in finite time. 1. Introduction and
Flocking of multiagents with a virtual leader
 IEEE Transactions on Automatic Control
, 2009
"... Abstract—All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multiagent systems. Under these assumptions, OlfatiSaber in a recent IEEE TRANSACTIONS ON AUTOMATIC CONTROL paper proposed a flo ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Abstract—All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multiagent systems. Under these assumptions, OlfatiSaber in a recent IEEE TRANSACTIONS ON AUTOMATIC CONTROL paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multiagent flocking in the absence of the above two assumptions. We first show that, even when only a fraction of agents are informed, the OlfatiSaber flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be influenced by the informed agents from time to time during the evolution. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity. In the situation where the virtual leader travels with a varying velocity, we propose modification to the OlfatiSaber algorithm and show that the resulting algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given. Index Terms—Distributed control, flocking, informed agents, nonlinear systems, virtual leader. I.