Distributed Consensus in Multi-Vehicle Cooperative Control

by Ren, Wei; Beard, Randal W.

• ISBN13: 9781848000148
• ISBN10: 1848000146
• Format: Hardcover
• Copyright: 2007-11-01
• Publisher: Springer Nature

Summary

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.

Author Biography

Wei Ren is an assistant professor in the Department of Electrical and Computer Engineering at Utah State University. He received his Ph.D. degree in electrical engineering from Brigham Young University, Provo, UT, in 2004. From October 2004 to July 2005, he was a research associate in the Department of Aerospace Engineering at the University of Maryland, College Park, MD. His research has been focusing on cooperative control for multiple autonmous vehicles and autonomous control of robotic vehicles. He is a member of the IEEE Control Systems Society and AIAA. Randal W. Beard received the B.S. degree in electrical engineering from the University of Utah, Salt Lake City in 1991, the M.S. degree in electrical engineering in 1993, the M.S. degree in mathematics in 1994, and the Ph.D. degree in electrical engineering in 1995, all from Rensselaer Polytechnic Institute, Troy, NY. Since 1996, he has been with the Electrical and Computer Engineering Department at Brigham Young University, Provo, UT, where he is currently an associate professor. In 1997 and 1998, he was a Summer Faculty Fellow at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA. In 2006 and 2007 he was a visiting research fellow at the Air Force Research Laboratory, Munitions Directorate, Eglin AFB, FL. His primary research focus is autonomous control of miniature air vehicles and multivehicle coordination and control. He is currently an associate editor for the IEEE Control Systems Magazine and the Journal of Intelligent and Robotic Systems.

Table of Contents

Overview of Consensus Algorithms in Cooperative Control
Overview of Consensus Algorithms in Cooperative Control	p. 3
Introduction	p. 3
Literature Review: Consensus Algorithms	p. 6
Fundamental Consensus Algorithms	p. 7
Convergence Analysis of Consensus Algorithms	p. 9
Synthesis and Extensions of Consensus Algorithms	p. 15
Design of Coordination Strategies via Consensus Algorithms	p. 17
Monograph Overview	p. 21
Notes	p. 22
Consensus Algorithms for Single-integrator Dynamics
Consensus Algorithms for Single-integrator Dynamics	p. 25
Fundamental Algorithms	p. 25
Consensus Under Fixed Interaction Topologies	p. 28
Consensus Using a Continuous-time Algorithm	p. 28
Consensus Using a Discrete-time Algorithm	p. 38
Consensus Under Dynamically Changing Interaction Topologies	p. 42
Consensus Using a Continuous-time Algorithm	p. 45
Consensus Using a Discrete-time Algorithm	p. 49
Simulation Results	p. 50
Notes	p. 52
Consensus Tracking with a Reference State	p. 55
Problem Statement	p. 55
Constant Consensus Reference State	p. 56
Time-varying Consensus Reference State	p. 58
Fundamental Consensus Tracking Algorithm	p. 61
Consensus Tracking Algorithm with Bounded Control Inputs	p. 66
Information Feedback to the Consensus Reference State	p. 68
Extension to Relative State Deviations	p. 71
Notes	p. 73
Consensus Algorithms for Double-integrator Dynamics
Consensus Algorithms for Double-integrator Dynamics	p. 77
Consensus Algorithm	p. 77
Convergence Analysis Under Fixed Interaction Topologies	p. 79
Convergence Analysis Under Switching Interaction Topologies	p. 91
Consensus with Bounded Control Inputs	p. 96
Consensus Without Relative State Derivative Measurements	p. 100
Notes	p. 103
Extensions to a Reference Model	p. 105
Problem Statement	p. 105
Consensus with a Reference for Information State Derivatives	p. 106
Consensus with Coupling Between Neighbors' Information State Derivatives	p. 106
Consensus Without Coupling Between Neighbors' Information State Derivatives	p. 109
Consensus with References for Information States and Their Derivatives	p. 111
Full Access to the Reference Model	p. 112
Leader-following Strategy	p. 113
General Case	p. 114
Notes	p. 118
Consensus Algorithms for Rigid Body Attitude Dynamics
Consensus Algorithms for Rigid Body Attitude Dynamics	p. 123
Problem Statement	p. 123
Attitude Consensus with Zero Final Angular Velocities	p. 124
Attitude Consensus Without Absolute and Relative Angular Velocity Measurements	p. 128
Attitude Consensus with Nonzero Final Angular Velocities	p. 131
Simulation Results	p. 132
Notes	p. 134
Relative Attitude Maintenance and Reference Attitude Tracking	p. 141
Relative Attitude Maintenance	p. 141
Fixed Relative Attitudes with Zero Final Angular Velocities	p. 141
Time-varying Relative Attitudes and Angular Velocities	p. 142
Reference Attitude Tracking	p. 143
Reference Attitude Tracking with Attitudes Represented by Euler Parameters	p. 143
Reference Attitude Tracking with Attitudes Represented by Modified Rodriguez Parameters	p. 147
Simulation Results	p. 150
Notes	p. 152
Consensus-based Design Methodologies for Distributed Multivehicle Cooperative Control
Consensus-based Design Methodologies for Distributed Multivehicle Cooperative Control	p. 159
Introduction	p. 159
Coupling in Cooperative Control Problems	p. 161
Objective Coupling	p. 162
Local Coupling	p. 162
Full Coupling	p. 162
Dynamic Coupling	p. 163
Approach to Distributed Cooperative Control Problems with an Optimization Objective	p. 163
Cooperation Constraints and Objectives	p. 164
Coordination Variables and Coordination Functions	p. 165
Centralized Cooperation Scheme	p. 166
Consensus Building	p. 167
Approach to Distributed Cooperative Control Problems Without an Optimization Objective	p. 169
Coordination Variable Constituted by a Group-level Reference State	p. 170
Coordination Variable Constituted by Vehicle States	p. 172
Literature Review	p. 174
Formation Control	p. 174
Cooperation of Multiple UAVs	p. 176
The Remainder of the Book	p. 178
Notes	p. 178
Rendezvous and Axial Alignment with Multiple Wheeled Mobile Robots	p. 181
Experimental Platform	p. 181
Experimental Implementation	p. 182
Experimental Results	p. 184
Rendezvous	p. 185
Axial Alignment	p. 188
Lessons Learned	p. 188
Notes	p. 189
Distributed Formation Control of Multiple Wheeled Mobile Robots with a Virtual Leader	p. 193
Distributed Formation Control Architecture	p. 193
Experimental Results on a Multirobot Platform	p. 197
Experimental Platform and Implementation	p. 197
Formation Control with a Single Subgroup Leader	p. 199
Formation Control with Multiple Subgroup Leaders	p. 200
Formation Control with Dynamically Changing Subgroup Leaders and Interrobot Interaction Topologies	p. 201
Notes	p. 202
Decentralized Behavioral Approach to Wheeled Mobile Robot Formation Maneuvers	p. 207
Problem Statement	p. 207
Formation Maneuvers	p. 209
Formation Control	p. 211
Coupled Dynamics Formation Control	p. 211
Coupled Dynamics Formation Control with Passivity-based Interrobot Damping	p. 214
Saturated Control	p. 216
Hardware Results	p. 219
Notes	p. 220
Deep Space Spacecraft Formation Flying	p. 225
Problem Statement	p. 225
Reference Frames	p. 226
Desired States for Each Spacecraft	p. 226
Spacecraft Dynamics	p. 228
Decentralized Architecture via the Virtual Structure Approach	p. 228
Centralized Architecture	p. 228
Decentralized Architecture	p. 229
Decentralized Formation Control Strategies	p. 232
Formation Control Strategies for Each Spacecraft	p. 233
Formation Control Strategies for Each Virtual Structure Instantiation	p. 234
Convergence Analysis	p. 236
Discussion	p. 239
Simulation Results	p. 241
Notes	p. 245
Cooperative Fire Monitoring with Multiple UAVs	p. 247
Problem Statement	p. 247
Fire Perimeter Tracking for a Single UAV	p. 250
Cooperative Team Tracking	p. 251
Latency Minimization	p. 251
Distributed Fire Monitoring Algorithm	p. 253
Simulation Results	p. 257
Fire Model	p. 257
Perimeter Tracking	p. 257
Cooperative Tracking	p. 258
Notes	p. 260
Cooperative Surveillance with Multiple UAVs	p. 265
Experimental Test Bed	p. 265
Decentralized Cooperative Surveillance	p. 268
Solution Methodology	p. 269
Simulation Results	p. 271
Flight Tests	p. 273
Notes	p. 274
Selected Notations and Abbreviations	p. 279
Graph Theory Notations	p. 281
Matrix Theory Notations	p. 285
Rigid Body Attitude Dynamics	p. 289
Linear System Theory Background	p. 293
Nonlinear System Theory Background	p. 295
References	p. 299
Index	p. 317
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