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Series editors E.D. Sontag g M. Thoma·A. Isidori·JH. van Schuppen Published titles include Stability and Stabilization of Infinite Dimensional Systems with Applications Robust Control (second edition) Zheng-Hua Luo, Bao-Zhu Guo and Omer Morgul Jurgen Ackermann Nonsmooth Mechanics(second edition) Flow Control by Feedback Bernard brogliato ole morten aamo and miroslav krstic Nonlinear Control Systems II Learning and Generalization(Second edition) Alberto isidori Mathukumalli vidyasagar L, -Gain and Passivity Techniques in nonlinear Constrained control and estimation Control Graham C. Goodwin, Maria M. seron and jose a Arjan van der Schaft De dona Control of linear Systems with Regulation and Randomized Algorithms for Analysis and Control Input Constraints of Uncertain Sy Ali Saberi, Anton A. 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Perdon Functional adaptive Control Polynomial and Rational matrices Simon g. fabri and visakan kadirkamanathan Tadeusz kaczorek Positive 1d and 2D Systems Simulation-based Algorithms for Markov decision Tadeusz kaczorek Processes Hyeong Soo Chang, Michael C. Fu, Jiaqiao Hu and Identification and Control Using Volterra Models Steven i. marcus Francis J. doyle ill, ronald K Pearson and Bobatunde a Ogunnaike Iterative Learning Control Hyo-Sung Ahn, Kevin L. Moore and Yang Quan Chen Non-linear Control for Underactuated mechanical Systems Isabelle Fantoni and Rogelio Lozano Wei ren and randal w. beard Distributed Consensus in Multi-vehicle Cooperative Control Theory and Applications ②s pringer Wei ren phD Randal w. beard PhD Department of Electrical and Computer Department of Electrical and Computer Engineering Engineering Utah State University Brigham Young University Logan,UT84322-4120 Provo, UT84602 USA USA ISBN978-1-84800-0148 e-ISBN978-1-84800-015-5 DOI10.10071978-1-84800-015-5 Communications and Control Engineering Series ISSN 0178-5354 British Library Cataloguing in Publication Data Ren, Wei Distributed consensus in multi-vehicle cooperative control theory and applications. - Communications and control engineering 1. Digital control systems 2. Automatic control Mathematics 3 Algorithms I. Title Il. beard, Randal w. 62989015181 ISBN-13:9781848000148 Library of Congress Control Number: 2007934265 C 2008 Springer-Verlag London Limited Apart from any fair dealing for the purposes of research or private study, or criticism or review,as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the ublishers The use of registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free ge ne al use The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made Cover design: LE-TEX Jelonek, Schmidt Vockler GbR, Leipzig, Germany Printed on acid-free paper 987654321 nger. com This work is dedicated to My wife, Fei Cheng, and My parents, Hongyi Ren and Liying Wang Wei ren My wife, Andre Randal w. beard Preface Recent advances in miniaturizing of computing, communication, sensing, and actuation have made it feasible to envision large numbers of autonomous ve- hicles(air, ground, and water) working cooperatively to accomplish an ob jective. Cooperative control of multiple vehicle systems has potential impact in numerous civilian, homeland security, and military applications. Potential civilian applications include monitoring forest fires, oil fields, pipelines, and tracking wildlife. Potential homeland security applications include border pa trol and monitoring the perimeter of nuclear power plants. For the military applications include surveillance, reconnaissance, and battle damage assess ment. However, for all of these applications, communication bandwidth and power constraints will preclude centralized command and control This book addresses the problem of information consensus, where a team of vehicles must communicate with its neighbors to agree on key pieces of information that enable them to work together in a coordinated fashion. The problem is particularly challenging because communication channels have lim ited range and experience fading and dropout. The study of information flow and sharing among multiple vehicles in a group plays an important role in understanding the coordinated movements of these vehicles. As a result, a critical problem for cooperative control is to design appropriate distributed algorithms such that the group of vehicles can reach consensus on the shared information in the presence of limited and unreliable information exchange and dynamically changing interaction topologies Our interest in distributed consensus algorithms and their applications was motivated by our research efforts in cooperative control of multiple vehi- cle systems and, in particular, teams of unmanned air vehicles. Air vehicles are constantly moving and consequently their ability to communicate is dynami cally changing. In addition, in current military scenarios involving unmanned air vehicles, large assets like the Predator may have two-way communic tion capabilities, but micro air vehicles may have only the ability to receive commands. Therefore, we were motivated to study distributed coordination Preface problems where the communication network is noisy, limited, time-varying and possibly unidirectional No, Of course, coming into consensus, or agreement, is not the only issue. Each mber of the team must act to achieve the team objective using the best available information. The interplay between communications/consensus and control introduces significant challenges that are only beginning to be un derstood. In much of the current research on cooperative control, either the consensus problem is studied in the absence of an application, or the coop- erative control problem is studied under the assumption of full and reliable communication Our objective in writing this research monograph is to summarize our work in cooperative control using distributed consensus algorithms. The monograph is roughly divided into two parts. In the first half of the book( Chapters 1-7) we describe theoretical results on distributed consensus algorithms where the dynamics of the information state evolve according to first- and second-order dynamics and according to rigid body attitude dynamics. The consensus algo rithms require only neighbor-to-neighbor interaction, which minimizes power consumption, increases stealth, and improves the scalability and robustness of the team. The second half of the book( Chapters 8-14)describes our attempts to apply the theory to a variety of applications in cooperative control, includ ing formation keeping for wheeled mobile robots and spacecraft and cooper ative perimeter tracking and timing for a team of unmanned air vehicles. We maintainawebsitehttp://www.engineering.usu.edu/ece/faculty/wren/ book/consensus at which can be found sample simulation and experimental videos and other useful materials associated with the book The results in this book and particularly the results in Chapters 8-14 would not have been possible without the efforts and support of our col- leagues and students. In particular, we are indebted to Professor Tim Mclain at Brigham Young University for his leadership in the area of cooperative control for unmanned air vehicles and for countless discussions on consensus and other applications of cooperative control. We are also indebted to Profes sor Ella atkins at the University of michigan and Professors Yang Quan Chen and Mac McKee at Utah State University for many fruitful discussions on research ideas. e also acknowledge the efforts of Nathan Sorensen, Yongcan Cao, Haiyang Chao, William Bourgeous, and Larry Ballard at Utah State Uni- versity, and Derek Kingston, Jonathan Lawton, Brett Young, David Casbeer, Ryan Holt, Derek Nelson, Blake Barber, Stephen griffiths, David Johansen and Andrew Eldridge at Brigham Young University. We are thankful to our editor Oliver Jackson for his interest in our project and his professionalism In addition, we acknowledge Ieee, John wiley sons, Elsevier, AIAA, and Taylor francis for granting us the permission to reuse materials from our publications copyrighted by these publishers in this book. The last section of each chapter gives a detailed list of the references used in the chapter. Finally, we gratefully acknowledge the support of our research on consensus algorithms and cooperative control by the Utah Water Research Laboratory and Com Preface munity/University Research Initiative as well as National Science Foundation under Information Technology Research Grant CCR-0313056, NASA under STTR Contract No. NNA04AA19C. Air Force Office of Scientific Research under award no.F49550-04-0209.F49620-01-1-0091.andF49620-02C-0094 and Defense Agency Research Projects Agency under Grant NBCH1020013 Utah State University, Logan, Utah Wei ren Brigham Young University, Provo, Utah Randal w. beard September 2007 Contents Part I Overview of Consensus Algorithms in Cooperative Control 1 Overview of Consensus Algorithms in Cooperative Control 3 1.1 Introduction 1.2 Literature Review: Consensus algorithms 6 1.2.1 Fundamental Consensus Algorithms 1.2.2 Convergence Analysis of Consensus Algorithms.... 9 1.2.3 Synthesis and Extensions of Consensus algorithms 1.2.4 Design of Coordination Strategies via Consensus algorithms 17 1.3 Monograph Overview 21 otes 22 Part II Consensus Algorithms for Single-integrator Dynamics 2 Consensus Algorithms for Single-integrator dynamics 25 2.1 Fund tal algorithms 25 2.2 Consensus Under Fixed Interaction Topologies........ 28 2.2. 1 Consensus Using a Continuous-time algorithm 2.2.2 Consensus Using a Discrete-time Algorithm 38 2.3 Consensus Under Dynamically Changing Interaction Topologies 42 2.3.1 Consensus Using a Continuous-time algorithm 45 2.3.2 Consensus Using a Discrete-time Algorithm 49 2.3.3 Simulation results 50 2. 4 Notes 3 Consensus Tracking with a Reference State 55 3.1 Problem Statement 55 3.2 Constant Consensus Reference State 56 3.3 Time-varying Consensus Reference State 58


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