[eBook Code] Formation Control of Multi-Agent Systems (eBook Code, 1st)

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