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This text explores formation control of vehicle systems and introduces three representative systems: space systems, aerial systems and robotic systems

Formation Control of Multiple Autonomous Vehicle Systems offers a review of the core concepts of dynamics and control and examines the dynamics and control aspects of formation control in order to study a wide spectrum of dynamic vehicle systems such as spacecraft, unmanned aerial vehicles and robots. The text puts the focus on formation control that enables and stabilizes formation configuration, as well as formation reconfiguration of these vehicle systems. The authors develop a uniform paradigm of describing vehicle systems' dynamic behaviour that addresses both individual vehicle's motion and overall group's movement, as well as interactions between vehicles.

The authors explain how the design of proper control techniques regulate the formation motion of these vehicles and the development of a system level decision-making strategy that increases the level of autonomy for the entire group of vehicles to carry out their missions. The text is filled with illustrative case studies in the domains of space, aerial and robotics.

 Contains uniform coverage of ´formation´ dynamic systems development

 Presents representative case studies in selected applications in the space, aerial and robotic systems domains

 Introduces an experimental platform of using laboratory three-degree-of-freedom helicopters with step-by-step instructions as an example

 Provides open source example models and simulation codes

 Includes notes and further readings that offer details on relevant research topics, recent progress and further developments in the field

Written for researchers and academics in robotics and unmanned systems looking at motion synchronization and formation problems, Formation Control of Multiple Autonomous Vehicle Systems is a vital resource that explores the motion synchronization and formation control of vehicle systems as represented by three representative systems: space systems, aerial systems and robotic systems.



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 Har