Flocking Control of Groups of Mobile Autonomous Agents Via Local Feedback
27 Jun 2005-pp 441-446
TL;DR: A set of coordination control laws are introduced that enable the group of mobile autonomous agents moving in Euclidean space with point mass dynamics to generate the desired stable flocking motion.
Abstract: This paper considers a group of mobile autonomous agents moving in Euclidean space with point mass dynamics. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces. By using the control laws, all agent velocities asymptotically approach the desired velocity, collisions can be avoided between agents, and the final tight formation minimizes all agent potentials. Moreover, we prove that the velocity of the center of mass (CoM) either is equal to the desired velocity or exponentially converges to it. Finally, for the case that not all agents know the desired final velocity, we show that the desired flocking motion can still be guaranteed
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TL;DR: This paper introduces a set of coordination control laws that enable the group of mobile autonomous agents moving in Euclidean space with a virtual leader to generate the desired stable flocking motion, and considers the effect of white noise on the collective dynamics of the group.
176 citations
12 Dec 2005
TL;DR: In this article, a set of coordination control laws that enable the group to generate the desired stable flocking motion is introduced. But the control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the state information of its flockmates and the external reference signal.
Abstract: This paper considers multiple mobile agents moving in the space with point mass dynamics. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the state information of its flockmates and the external reference signal. By using the control laws, all agent velocities asymptotically approach the desired velocity, collisions are avoided between the agents, and the final tight formation minimizes all agent global potentials. Moreover, we show that the velocity of the center of mass either is equal to the desired velocity or exponentially converges to it. Furthermore, when the velocity damping is taken into account, we can properly modify the control laws to generate the same stable flocking motion. Finally, for the case that not all agents know the desired common velocity, we show that the desired flocking motion can still be guaranteed. Numerical simulations are worked out to illustrate our theoretical results.
122 citations
Cites background from "Flocking Control of Groups of Mobil..."
...There has been considerable effort in modelling and exploring the collective dynamics, and trying to understand how a group of autonomous creatures or man-made mobile autonomous agents/robots can cluster in formations without centralized coordination and control [9–29]....
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TL;DR: In this article, a new flocking algorithm is proposed to guarantee the states of the velocity variables of all the dynamical agents to converge to consensus while ensuring collision avoidance of the whole group, where each agent is assumed to obtain some nonlinear measurements of the relative velocity between itself and its neighbors only on a sequence of non-overlapping time intervals.
Abstract: SUMMARY
In this paper, the problem of flocking control in networks of multiple dynamical agents with intermittent nonlinear velocity measurements is studied. A new flocking algorithm is proposed to guarantee the states of the velocity variables of all the dynamical agents to converge to consensus while ensuring collision avoidance of the whole group, where each agent is assumed to obtain some nonlinear measurements of the relative velocity between itself and its neighbors only on a sequence of non-overlapping time intervals. The results are then extended to the scenario of flocking with a nonlinearly dynamical virtual leader, where only a small fraction of agents are informed and each informed agent can obtain intermittent nonlinear measurements of the relative velocity between itself and the virtual leader. Theoretical analysis shows that the achieved flocking in systems with or without a virtual leader is robust against the time spans of the agent speed-sensors. Finally, some numerical simulations are provided to illustrate the effectiveness of the new design. Copyright © 2011 John Wiley & Sons, Ltd.
85 citations
Cites background or result from "Flocking Control of Groups of Mobil..."
...Recently, the problem of flocking control in multi-agent systems has attracted increasing attention, which can be generally described as how to design distributed feedback algorithms based only on local information to guarantee the whole group to organize into a global flocking behavior [5–30]....
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...Motivated by the results of [19, 21–27, 38–40], two problems of flocking control in multiagent systems with intermittent nonlinear velocity measurements are precisely formulated and investigated in the next section....
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...Today, a great deal of research on flocking control is still ongoing, for example, flocking with a single or multiple virtual leaders [21–28], flocking in noisy environments [29], flocking with input saturation [30], and leader–followerflocking [31–36]....
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TL;DR: Two suitable Lyapunov-Krasovskii functionals will be given to obtaining sufficient consensus conditions and multiple randomly varying leader-follower consensus stability criteria for the Markovian switching swarm system, and it will be proved that the swarm system is stochastically stable.
Abstract: The limited communication consensus control problem is studied for leader-following multi-UUVs (multiple unmanned underwater vehicles) in a swarm system that contains multiple second-order UUVs with the time-varying delay. The multi-UUV swarm will be divided into many sub-groups that each includes one leader and many follower UUVs, and a leaders-group will be composed of all leaders of the sub-groups. In the leaders-group, one leader is called the commander, and the swarm will follow the commander. Under the swarm system mechanism, multi-independent switching topologies are proposed for the swarm hybrid structure under limited communication. Two suitable Lyapunov-Krasovskii functionals will be given to obtaining sufficient consensus conditions and multiple randomly varying leader-follower consensus stability criteria for the Markovian switching swarm system. Then, it will be proved that the swarm system is stochastically stable. Furthermore, a state feedback controller is designed such that the resulting closed-loop system is stochastically stable. Finally, numerical examples are shown to demonstrate the effectiveness of the discussed methods.
16 citations
Cites background from "Flocking Control of Groups of Mobil..."
...A set of control laws that are a combination of attractive/repulsive forces are introduced in [8], which enables the group to generate the desired stable flocking motion....
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TL;DR: Results show that an optimal path can be dynamically planned with fewer path nodes and smaller fitness, even with a concave obstacle, and it has been also proven that different formation-keeping strategies can be adaptively selected and the formation can change its structure in a narrow area and restore back after passing the obstacle.
Abstract: Path planning and formation structure forming are two of the most important problems for autonomous underwater vehicles (AUVs) to collaborate with each other. In this work, a dynamic formation model was proposed, in which several algorithms were developed for the complex underwater environment. Dimension changeable particle swarm algorithm was used to find an optimized path by dynamically adjusting the number and the distribution of the path nodes. Position relationship based obstacle avoidance algorithm was designed to detour along the edges of obstacles. Virtual potential point based formation-keeping algorithm was employed by incorporating dynamic strategies which were decided by the current states of the formation. The virtual potential point was used to keep the formation structure when the AUV or the formation was deviated. Simulation results show that an optimal path can be dynamically planned with fewer path nodes and smaller fitness, even with a concave obstacle. It has been also proven that different formation-keeping strategies can be adaptively selected and the formation can change its structure in a narrow area and restore back after passing the obstacle.
8 citations
References
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Book•
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TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
23,986 citations
TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. 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.
11,658 citations
"Flocking Control of Groups of Mobil..." refers background in this paper
... vehicles (UAVs), scheduling of automated highway systems, coordination/formation of underwater vehicles, attitude alignment of satellite clusters and congestion control of communication networks [5]–[8]. There has been considerable effort in modelling and exploring the collective dynamics, and trying to understand how a group of autonomous creatures or man-made mobile autonomous agents/robots can clu...
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Book•
01 Jan 2009
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Abstract: Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.
8,307 citations
"Flocking Control of Groups of Mobil..." refers background in this paper
...Some basic concepts and results can be found in [9]–[10]....
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TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Abstract: In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different 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. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
8,233 citations
"Flocking Control of Groups of Mobil..." refers background in this paper
...[5] and [8] considered the cohesion/coordination of a group of mobile autonomous agents following an actual leader by the so-called nearest neighbor rules....
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