Preface xiii
List of Tables xvii
List of Figures xix
Acknowledgments xxv
Part I Formation Control: Fundamental Concepts 1
1 Formation Kinematics 3
1.1 Notation 3
1.2 Vectorial Kinematics 5
1.2.1 Frame Rotation 5
1.2.2 The Motion of a Vector 7
1.2.3 The First Time Derivative of a Vector 11
1.2.4 The Second Time Derivative of a Vector 12
1.2.5 Motion with Respect to Multiple Frames 12
1.3 Euler Parameters and Unit Quaternion 13
2 Formation Dynamics of Motion Systems 17
2.1 Virtual Structure 17
2.1.1 Formation Control Problem Statement 19
2.1.2 Extended Formation Control Problem 22
2.2 Behaviour-based Formation Dynamics 26
2.3 Leader–Follower Formation Dynamics 27
3 Fundamental Formation Control 29
3.1 Unified Problem Description 29
3.1.1 Some Key Definitions for Formation Control 29
3.1.2 A Simple Illustrative Example 30
3.2 Information Interaction Conditions 32
3.2.1 Algebraic GraphTheory 32
3.2.2 Conditions for the Case without a Leader 33
3.2.3 Conditions for the Case with a Leader 35
3.3 Synchronization Errors 36
3.3.1 Local Synchronization Error: Type I 37
3.3.2 Local Synchronization Error: Type II 38
3.3.3 Local Synchronization Error: Type III 40
3.4 Velocity Synchronization Control 42
3.4.1 Velocity Synchronization without a Leader 42
3.4.2 Velocity Synchronization with a Leader 43
3.5 Angular-position Synchronization Control 45
3.5.1 Synchronization without a Position Reference 45
3.5.2 Synchronization to a Position Reference 47
3.6 Formation via Synchronized Tracking 48
3.6.1 Formation Control Solution 1 50
3.6.2 Formation Control Solution 2 51
3.7 Simulations 52
3.7.1 Verification of Theorem 3.12 52
3.7.2 Verification of Theorem 3.13 54
3.7.3 Verification of Theorem 3.14 57
3.8 Summary 60
Bibliography for Part I 61
Part II Formation Control: Advanced Topics 63
4 Output-feedback Solutions to Formation Control 65
4.1 Introduction 65
4.2 Problem Statement 65
4.3 Linear Output-feedback Control 66
4.4 Bounded Output-feedback Control 68
4.5 Distributed Linear Control 71
4.6 Distributed Bounded Control 72
4.7 Simulations 73
4.7.1 Case 1: Verification of Theorem 4.1 73
4.7.2 Case 2: Verification of Theorem 4.5 76
4.8 Summary 78
5 Robust and Adaptive Formation Control 81
5.1 Problem Statement 81
5.2 Continuous Control via State Feedback 83
5.2.1 Controller Development 83
5.2.2 Analysis of Tracker u0i84
5.2.3 Design of Disturbance Estimators 85
5.2.4 Closed-loop Performance Analysis 87
5.3 Bounded State Feedback Control 90
5.3.1 Design of Bounded State Feedback 90
5.3.2 Robustness Analysis 92
5.3.3 The Effect of UDE on Stability 94
5.3.4 The Effect of UDE on the Bounds of Control 94
5.4 Continuous Control via Output Feedback 95
5.4.1 Design of u0i and d^i 95
5.4.2 Stability Analysis 96
5.5 Discontinuous Control via Output Feedback 97
5.5.1 Controller Design 98
5.5.2 Stability Analysis 100
5.6 GSE-based Synchronization Control 102
5.6.1 Coupled Errors 103
5.6.2 Controller Design and Convergence Analysis 105
5.7 GSE-based Adaptive Formation Control 108
5.7.1 Problem Statement 108
5.7.2 Controller Development 109
5.8 Summary 111
Bibliography for Part II 113
Part III Formation Control: Case Studies 115
6 Formation Control of Space Systems 117
6.1 Lagrangian Formulation of Spacecraft Formation 117
6.1.1 Lagrangian Formulation 117
6.1.2 Attitude Dynamics of Rigid Spacecraft 118
6.1.3 Relative Translational Dynamics 120
6.2 Adaptive Formation Control 122
6.3 Applications and Simulation Results 123
6.3.1 Application 1: Leader–Follower Spacecraft Pair 123
6.3.1.1 Simulation Condition 123
6.3.1.2 Control Parameters 123
6.3.1.3 Simulation Results and Analysis 124
6.3.2 Application 2: Multiple Spacecraft in Formation 124
6.4 Summary 130
7 Formation Control of Aerial Systems 131
7.1 Vortex-induced Aerodynamics 131
7.1.1 Model of the Trailing Vortices of Leader Aircraft 134
7.1.2 Single Horseshoe Vortex Model 135
7.1.3 Continuous Vortex Sheet Model 137
7.2 Aircraft Autopilot Models 138
7.2.1 Models for the Follower Aircraft 139
7.2.2 Kinematics for Close-formation Flight 140
7.3 Controller Design 140
7.3.1 Linear Proportional-integral Controller 140
7.3.2 UDE-based Formation-flight Controller 142
7.3.2.1 Formation Flight Controller Design 143
7.3.2.2 Uncertainty and Disturbance Estimator 144
7.4 Simulation Results 147
7.4.1 Simulation Results for Controller 1 147
7.4.2 Simulation Results for Controller 2 148
7.5 Summary 154
8 Formation Control of Robotic Systems 157
8.1 Introduction 157
8.2 Visual Tracking 159
8.2.1 Imaging Hardware 159
8.2.2 Image Distortion 160
8.2.3 Color Thresholding 163
8.2.4 Noise Rejection 163
8.2.5 Data Extraction 165
8.3 Synchronization Control 167
8.3.1 Synchronization 167
8.3.2 Formation Parameters 168
8.3.3 Architecture 169
8.3.4 Control Law 169
8.3.5 Simulations 170
8.3.5.1 Constant Formation along Circular Trajectory 171
8.3.5.2 Time-varying Formation along Linear Trajectory 173
8.4 Passivity Control 176
8.4.1 Passivity 176
8.4.2 Formation Parameters 176
8.4.3 Control Law 177
8.4.4 Simulation 178
8.5 Experiments 181
8.5.1 Setup 181
8.5.2 Results 182
8.5.2.1 Constant Formation along Circular Trajectory 182
8.5.2.2 Time-varying Formation along Linear Trajectory 183
8.6 Summary 186
Bibliography for Part III 189
Part IV Formation Control: Laboratory 191
9 Experiments on 3DOF Desktop Helicopters 193
9.1 Description of the Experimental Setup 193
9.2 MathematicalModels 196
9.2.1 Nonlinear 3DOF Model 196
9.2.2 2DOF Model for Elevation and Pitch Control 199
9.3 Experiment 1: GSE-based Synchronized Tracking 201
9.3.1 Objective 201
9.3.2 Initial Conditions and Desired Trajectories 202
9.3.3 Control Strategies 203
9.3.4 Disturbance Condition 203
9.3.5 Experimental Results 204
9.3.6 Summary 208
9.4 Experiment 2: UDE-based Robust Synchronized Tracking 208
9.4.1 Objective 208
9.4.2 Initial Conditions and Desired Trajectories 208
9.4.3 Control Strategies 209
9.4.4 Experimental Results and Discussions 210
9.4.5 Summary 215
9.5 Experiment 3: Output-feedback-based Sliding-mode Control 216
9.5.1 Objective 216
9.5.2 Initial Conditions and Desired Trajectories 216
9.5.3 Control Strategies 217
9.5.4 Experimental Results and Discussions 217
9.5.5 Summary 222
Bibliography for Part IV 223
Part V Appendix 225
Bibliography for Appendix 237
Index 239
