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Proceedings ArticleDOI

Achieving a desired collective centroid by a formation of agents moving in a controllable force field

TL;DR: In this article, an all-to-all coupled planar motion model is proposed to solve the problem of a formation of agents trying to achieve a desired stationary or moving collective centroid.
Abstract: In this paper, we study the problem of a formation of agents trying to achieve a desired stationary or moving collective centroid. The agents are assumed to be moving in a force field which is controlled externally. The stabilization of the collective centroid to a fixed desired location results in a balanced formation of the agents about that point. Similarly, the centroid of the system of agents may be required to move along a certain given trajectory. For this, the centroid of the formation must converge to the desired trajectory. To solve this problem, we propose an all-to-all coupled planar motion model that explicitly incorporates an additional control pertaining to the external force field. Simulation results are presented to support the theoretical findings.
Citations
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TL;DR: This paper considers circular motion of multi-agent systems in which all the agents are required to traverse different circles or a common circle at a desired angular frequency by using Lyapunov theory and LaSalles invariance principle.
Abstract: This paper considers circular motion of multi-agent systems in which all the agents are required to traverse different circles or a common circle at a desired angular frequency. It is required to achieve these collective motions with the heading angles of the agents synchronized or balanced. In synchronization, the agents and their centroid have a common velocity direction, while in balancing, the movement of agents causes the location of the centroid to become stationary. It is assumed that the agents are subjected to limited communication constraints, and exchange relative information according to a time-invariant undirected graph. The feedback control laws to achieve these collective motions are obtained by using Lyapunov theory and LaSalles invariance principle. Simulations are given to illustrate the theoretical findings.
References
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Journal ArticleDOI
TL;DR: In this article, the authors review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto's work to Crawford's recent contributions.

2,795 citations


Additional excerpts

  • ...Also, ∣ṙc− ṙre f ∣∣ = 1 only if θk = θc, ∀ k [7], [34]....

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BookDOI
01 Jan 2008
TL;DR: In this article, the authors present a survey of the use of consensus algorithms in multi-vehicle cooperative control, including single-and double-integrator dynamical systems, rigid-body attitude dynamics, rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance.
Abstract: The coordinated use of autonomous vehicles has an abundance of potential applications from the domestic to the hazardously toxic. Frequently the communications necessary for the productive interplay of such vehicles may be subject to limitations in range, bandwidth, noise and other causes of unreliability. Information consensus guarantees that vehicles sharing information over a network topology have a consistent view of information critical to the coordination task. Assuming only neighbor-neighbor interaction between vehicles, Distributed Consensus in Multi-vehicle Cooperative Control develops distributed consensus strategies designed to ensure that the information states of all vehicles in a network converge to a common value. This approach strengthens the team, minimizing power consumption and the deleterious effects of range and other restrictions. The monograph is divided into six parts covering introductory, theoretical and experimental material and featuring: an overview of the use of consensus algorithms in cooperative control; consensus algorithms in single- and double-integrator dynamical systems; consensus algorithms for rigid-body attitude dynamics; rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance. Notation drawn from graph and matrix theory and background material on linear and nonlinear system theory are enumerated in six appendices. The authors maintain a website at which can be found a sample simulation and experimental video material associated with experiments in several chapters of this book. Academic control systems researchers and their counterparts in government laboratories and robotics- and aerospace-related industries will find the ideas presented in Distributed Consensus in Multi-vehicle Cooperative Control of great interest. This text will also serve as a valuable support and reference for graduate courses in robotics, and linear and nonlinear control systems.

2,720 citations

Journal ArticleDOI
05 Mar 2007
TL;DR: This paper addresses the design of mobile sensor networks for optimal data collection by using a performance metric, used to derive optimal paths for the network of mobile sensors, to define the optimal data set.
Abstract: This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored

920 citations

Book
01 Jan 1970
TL;DR: This book discusses systems of Linear Equations and Matrices and its applications in vector spaces, as well as some of theorems on how to model ellipsoidal spaces and the role of Eigenvalues in these spaces.
Abstract: The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition.Learning Tools CD-ROM will be automatically packaged free with every new text purchased from Houghton Mifflin.Section 3.4, now named Introduction to Eigenvalues, has been broken into two separate sections to provide more emphasis on the early introduction of eigenvalues. The new Section 3.5, Applications of Determinants, covers the Adjoint of a Matrix; Cramer' s Rule; and the Area, Volume, and Equations of Lines and Planes.All real data in exercises and examples have been updated to reflect current statistics and information.This edition features more Writing Exercises to reinforce critical-thinking skills and additional multi-part True/False Questions in the end-of-section and chapter review exercise sets to encourage students to think about mathematics from different perspectives.Additional exercises involving larger matrices have been added to the exercise sets where appropriate. These exercises will be linked to the data sets found on the web site and the Learning Tools CD-ROM.Eduspace is Houghton Mifflin' s online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. The Larson Elementary Linear Algebra course features algorithmic exercises and test bank content in question pools.

792 citations


Additional excerpts

  • ...by using the property 〈z1,cz2〉= c〈z1,z2〉, where c ∈R [32]....

    [...]

  • ...U̇(θ ) = N 〈 ṙc− ṙre f ,− N N ∑ k=1 ieiθk 〈 ṙc− ṙre f , ieiθk 〉〉 (17) Since 〈z1,z2 + z3〉= 〈z1,z2〉+〈z1,z3〉 for z1,z2,z3 ∈C [32], U̇(θ ) in (16) is rewritten as...

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