Distributed consensus in multi-vehicle cooperative control : theory and applications

Information consensus guarantees that robot 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, this monograph 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 effects of range and other restrictions.

The monograph covers introductory, theoretical and experimental material, featuring - an overview of the use of consensus algorithms in cooperative control; - consensus algorithms in single- and double-integrator, and rigid-body-attitude dynamics; - rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance.

Six appendices cover material drawn from graph, matrix, linear and nonlinear systems theories.

Author Notes

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 .

Part I Overview of Consensus Algorithms in Cooperative Control
1 Overview of Consensus Algorithms in Cooperative Control	p. 3
1.1 Introduction	p. 3
1.2 Literature Review: Consensus Algorithms	p. 6
1.2.1 Fundamental Consensus Algorithms	p. 7
1.2.2 Convergence Analysis of Consensus Algorithms	p. 9
1.2.3 Synthesis and Extensions of Consensus Algorithms	p. 15
1.2.4 Design of Coordination Strategies via Consensus Algorithms	p. 17
1.3 Monograph Overview	p. 21
1.4 Notes	p. 22
Part II Consensus Algorithms for Single-integrator Dynamics
2 Consensus Algorithms for Single-integrator Dynamics	p. 25
2.1 Fundamental Algorithms	p. 25
2.2 Consensus Under Fixed Interaction Topologies	p. 28
2.2.1 Consensus Using a Continuous-time Algorithm	p. 28
2.2.2 Consensus Using a Discrete-time Algorithm	p. 38
2.3 Consensus Under Dynamically Changing Interaction Topologies	p. 42
2.3.1 Consensus Using a Continuous-time Algorithm	p. 45
2.3.2 Consensus Using a Discrete-time Algorithm	p. 49
2.3.3 Simulation Results	p. 50
2.4 Notes	p. 52
3 Consensus Tracking with a Reference State	p. 55
3.1 Problem Statement	p. 55
3.2 Constant Consensus Reference State	p. 56
3.3 Time-varying Consensus Reference State	p. 58
3.3.1 Fundamental Consensus Tracking Algorithm	p. 61
3.3.2 Consensus Tracking Algorithm with Bounded Control Inputs	p. 66
3.3.3 Information Feedback to the Consensus Reference State	p. 68
3.4 Extension to Relative State Deviations	p. 71
3.5 Notes	p. 73
Part III Consensus Algorithms for Double-integrator Dynamics
4 Consensus Algorithms for Double-integrator Dynamics	p. 77
4.1 Consensus Algorithm	p. 77
4.1.1 Convergence Analysis Under Fixed Interaction Topologies	p. 79
4.1.2 Convergence Analysis Under Switching Interaction Topologies	p. 91
4.2 Consensus with Bounded Control Inputs	p. 96
4.3 Consensus Without Relative State Derivative Measurements	p. 100
4.4 Notes	p. 103
5 Extensions to a Reference Model	p. 105
5.1 Problem Statement	p. 105
5.2 Consensus with a Reference for Information State Derivatives	p. 106
5.2.1 Consensus with Coupling Between Neighbors' Information State Derivatives	p. 106
5.2.2 Consensus Without Coupling Between Neighbors' Information State Derivatives	p. 109
5.3 Consensus with References for Information States and Their Derivatives	p. 111
5.3.1 Full Access to the Reference Model	p. 112
5.3.2 Leader-following Strategy	p. 113
5.3.3 General Case	p. 114
5.4 Notes	p. 118
Part IV Consensus Algorithms for Rigid Body Attitude Dynamics
6 Consensus Algorithms for Rigid Body Attitude Dynamics	p. 123
6.1 Problem Statement	p. 123
6.2 Attitude Consensus with Zero Final Angular Velocities	p. 124
6.3 Attitude Consensus Without Absolute and Relative Angular Velocity Measurements	p. 128
6.4 Attitude Consensus with Nonzero Final Angular Velocities	p. 131
6.5 Simulation Results	p. 132
6.6 Notes	p. 134
7 Relative Attitude Maintenance and Reference Attitude Tracking	p. 141
7.1 Relative Attitude Maintenance	p. 141
7.1.1 Fixed Relative Attitudes with Zero Final Angular Velocities	p. 141
7.1.2 Time-varying Relative Attitudes and Angular Velocities	p. 142
7.2 Reference Attitude Tracking	p. 143
7.2.1 Reference Attitude Tracking with Attitudes Represented by Euler Parameters	p. 143
7.2.2 Reference Attitude Tracking with Attitudes Represented by Modified Rodriguez Parameters	p. 147
7.3 Simulation Results	p. 150
7.4 Notes	p. 152
Part V Consensus-based Design Methodologies for Distributed Multivehicle Cooperative Control
8 Consensus-based Design Methodologies for Distributed Multivehicle Cooperative Control	p. 159
8.1 Introduction	p. 159
8.2 Coupling in Cooperative Control Problems	p. 161
8.2.1 Objective Coupling	p. 162
8.2.2 Local Coupling	p. 162
8.2.3 Full Coupling	p. 162
8.2.4 Dynamic Coupling	p. 163
8.3 Approach to Distributed Cooperative Control Problems with an Optimization Objective	p. 163
8.3.1 Cooperation Constraints and Objectives	p. 164
8.3.2 Coordination Variables and Coordination Functions	p. 165
8.3.3 Centralized Cooperation Scheme	p. 166
8.3.4 Consensus Building	p. 167
8.4 Approach to Distributed Cooperative Control Problems Without an Optimization Objective	p. 169
8.4.1 Coordination Variable Constituted by a Group-level Reference State	p. 170
8.4.2 Coordination Variable Constituted by Vehicle States	p. 172
8.5 Literature Review	p. 174
8.5.1 Formation Control	p. 174
8.5.2 Cooperation of Multiple UAVs	p. 176
8.6 The Remainder of the Book	p. 178
8.7 Notes	p. 178
9 Rendezvous and Axial Alignment with Multiple Wheeled Mobile Robots	p. 181
9.1 Experimental Platform	p. 181
9.2 Experimental Implementation	p. 182
9.3 Experimental Results	p. 184
9.3.1 Rendezvous	p. 185
9.3.2 Axial Alignment	p. 188
9.3.3 Lessons Learned	p. 188
9.4 Notes	p. 189
10 Distributed Formation Control of Multiple Wheeled Mobile Robots with a Virtual Leader	p. 193
10.1 Distributed Formation Control Architecture	p. 193
10.2 Experimental Results on a Multirobot Platform	p. 197
10.2.1 Experimental Platform and Implementation	p. 197
10.2.2 Formation Control with a Single Subgroup Leader	p. 199
10.2.3 Formation Control with Multiple Subgroup Leaders	p. 200
10.2.4 Formation Control with Dynamically Changing Subgroup Leaders and Interrobot Interaction Topologies	p. 201
10.3 Notes	p. 202
11 Decentralized Behavioral Approach to Wheeled Mobile Robot Formation Maneuvers	p. 207
11.1 Problem Statement	p. 207
11.2 Formation Maneuvers	p. 209
11.3 Formation Control	p. 211
11.3.1 Coupled Dynamics Formation Control	p. 211
11.3.2 Coupled Dynamics Formation Control with Passivity-based Interrobot Damping	p. 214
11.3.3 Saturated Control	p. 216
11.4 Hardware Results	p. 219
11.5 Notes	p. 220
12 Deep Space Spacecraft Formation Flying	p. 225
12.1 Problem Statement	p. 225
12.1.1 Reference Frames	p. 226
12.1.2 Desired States for Each Spacecraft	p. 226
12.1.3 Spacecraft Dynamics	p. 228
12.2 Decentralized Architecture via the Virtual Structure Approach	p. 228
12.2.1 Centralized Architecture	p. 228
12.2.2 Decentralized Architecture	p. 229
12.3 Decentralized Formation Control Strategies	p. 232
12.3.1 Formation Control Strategies for Each Spacecraft	p. 233
12.3.2 Formation Control Strategies for Each Virtual Structure Instantiation	p. 234
12.3.3 Convergence Analysis	p. 236
12.3.4 Discussion	p. 239
12.4 Simulation Results	p. 241
12.5 Notes	p. 245
13 Cooperative Fire Monitoring with Multiple UAVs	p. 247
13.1 Problem Statement	p. 247
13.2 Fire Perimeter Tracking for a Single UAV	p. 250
13.3 Cooperative Team Tracking	p. 251
13.3.1 Latency Minimization	p. 251
13.3.2 Distributed Fire Monitoring Algorithm	p. 253
13.4 Simulation Results	p. 257
13.4.1 Fire Model	p. 257
13.4.2 Perimeter Tracking	p. 257
13.4.3 Cooperative Tracking	p. 258
13.5 Notes	p. 260
14 Cooperative Surveillance with Multiple UAVs	p. 265
14.1 Experimental Test Bed	p. 265
14.2 Decentralized Cooperative Surveillance	p. 268
14.2.1 Solution Methodology	p. 269
14.2.2 Simulation Results	p. 271
14.2.3 Flight Tests	p. 273
14.3 Notes	p. 274
A Selected Notations and Abbreviations	p. 279
B Graph Theory Notations	p. 281
C Matrix Theory Notations	p. 285
D Rigid Body Attitude Dynamics	p. 289
E Linear System Theory Background	p. 293
F Nonlinear System Theory Background	p. 295
References	p. 299
Index	p. 317

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