Formation Control of Multi-Agent Systems: A Graph Rigidity Approach
Marcio de Queiroz, Louisiana State University, USA
Xiaoyu Cai, FARO Technologies, USA
Matthew Feemster, U.S. Naval Academy, USA
A comprehensive guide to formation control of multi-agent systems using rigid graph theory
This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems. Such systems are relevant to a variety of emerging engineering applications, including unmanned robotic vehicles and mobile sensor networks. Graph theory, and rigid graphs in particular, provides a natural tool for describing the multi-agent formation shape as well as the inter-agent sensing, communication, and control topology.
Beginning with an introduction to rigid graph theory, the contents of the book are organized by the agent dynamic model (single integrator, double integrator, and mechanical dynamics) and by the type of formation problem (formation acquisition, formation manoeuvring, and target interception). The book presents the material in ascending level of difficulty and in a self-contained manner; thus, facilitating reader understanding.
Key features:
- Uses the concept of graph rigidity as the basis for describing the multi-agent formation geometry and solving formation control problems.
- Considers different agent models and formation control problems.
- Control designs throughout the book progressively build upon each other.
- Provides a primer on rigid graph theory.
- Combines theory, computer simulations, and experimental results.
Formation Control of Multi-Agent Systems: A Graph Rigidity Approach is targeted at researchers and graduate students in the areas of control systems and robotics. Prerequisite knowledge includes linear algebra, matrix theory, control systems, and nonlinear systems.
Table of Contents
Preface xi
About the Companion Website xiii
1 Introduction 1
1.1 Motivation 1
1.2 Notation 6
1.3 Graph Theory 7
1.3.1 Graph 7
1.3.2 Framework 9
1.3.3 Rigid Graphs 11
1.3.4 Infinitesimal Rigidity 14
1.3.5 Minimal Rigidity 19
1.3.6 Framework Ambiguities 20
1.3.7 Global Rigidity 22
1.4 Formation Control Problems 23
1.5 Book Overview and Organization 26
1.6 Notes and References 28
2 Single-Integrator Model 29
2.1 Formation Acquisition 29
2.2 Formation Maneuvering 35
2.3 Flocking 36
2.3.1 Constant Flocking Velocity 37
2.3.2 Time-Varying Flocking Velocity 38
2.4 Target Interception with Unknown Target Velocity 40
2.5 Dynamic Formation Acquisition 43
2.6 Simulation Results 45
2.6.1 Formation Acquisition 45
2.6.2 Formation Maneuvering 51
2.6.3 Flocking 56
2.6.4 Target Interception 58
2.6.5 Dynamic Formation 63
2.7 Notes and References 66
3 Double-Integrator Model 71
3.1 Cross-Edge Energy 73
3.2 Formation Acquisition 75
3.3 Formation Maneuvering 76
3.4 Target Interception with Unknown Target Acceleration 77
3.5 Dynamic Formation Acquisition 79
3.6 Simulation Results 80
3.6.1 Formation Acquisition 80
3.6.2 Dynamic Formation Acquisition with Maneuvering 81
3.6.3 Target Interception 84
3.7 Notes and References 87
4 Robotic Vehicle Model 91
4.1 Model Description 91
4.2 Nonholonomic Kinematics 93
4.2.1 Control Design 93
4.2.2 Simulation Results 94
4.3 Holonomic Dynamics 97
4.3.1 Model-Based Control 98
4.3.2 Adaptive Control 100
4.3.3 Simulation Results 102
4.4 Notes and References 102
5 Experimentation 107
5.1 Experimental Platform 107
5.2 Vehicle Equations of Motion 110
5.3 Low-Level Control Design 113
5.4 Experimental Results 114
5.4.1 Single Integrator: Formation Acquisition 117
5.4.2 Single Integrator: Formation Maneuvering 118
5.4.3 Single Integrator: Target Interception 126
5.4.4 Single Integrator: Dynamic Formation 128
5.4.5 Double Integrator: Formation Acquisition 132
5.4.6 Double Integrator: Formation Maneuvering 136
5.4.7 Double Integrator: Target Interception 138
5.4.8 Double Integrator: Dynamic Formation 148
5.4.9 Holonomic Dynamics: Formation Acquisition 149
5.4.10 Summary 153
A Matrix Theory and Linear Algebra 159
B Functions and Signals 163
C Systems Theory 165
C.1 Linear Systems 165
C.2 Nonlinear Systems 166
C.3 Lyapunov Stability 168
C.4 Input-to-State Stability 170
C.5 Nonsmooth Systems 171
C.6 Integrator Backstepping 172
D Dynamic Model Terms 175
References 177
Index 187
