Antonios Tsourdos is a Reader in Autonomous Systems and Control and Head of the Guidance and Control Group at Cranfield. His research areas include UAV Autonomy, UAV Path Planning, Coordinated Guidance, Cooperative Control, UAV Swarm, Autonomous Sensors Network, Sensor and Data Fusion, and Vehicle Health Management. He has authored many scientific research papers and has served as a guest editor for journal special issues on 'multi-vehicle systems cooperative control with applications'; 'advances in missile guidance and control: theory and practice', and cooperative control approaches for multiple mobile robots'. Brian A White, now Professor Emeritus at Cranfield, was until recently Head of the Department of Aerospace, Power and Sensors and also Head of the Guidance and Control Group at Cranfield. His areas of expertise are robust control, non-linear control, estimation, observer applications, inertial navigation, guidance design, soft computing and sensor and data fusion. He has published widely in the control science field, mainly on autopilot design and guidance. He has managed significant contracts in the area of guidance. He has organized and run numerous invited sessions at major control conferences and co-edited a special issue of the IFAC journal Control Engineering Practice on Control in Defence Systems. He has served as associate editor for the IMechE Journal of Aerospace Engineering (Part G), IMechE Journal of Systems and Control Engineering (Part I), and the Journal of Nonlinear Studies.Madhavan Shanmugavel is a Research Officer within the Guidance and Control Group at Cranfield.

• About the Authors ixSeries Preface xiPreface xiiAcknowledgements xiiiList of Figures xvList of Tables xxiNomenclature xxiii1 Introduction 11.1 Path Planning Formulation 21.2 Path Planning Constraints 31.2.1 Flyable Paths: Capturing Kinematics 41.2.2 UAV Inertial Manoeuvre Coordinates 61.2.3 Generation of Safe Paths for Path Planning 71.3 Cooperative Path Planning and Mission Planning 71.4 Path Planning – An Overview 101.5 The Road Map Method 131.5.1 Visibility Graphs 141.5.2 Voronoi Diagrams 141.6 Probabilistic Methods 161.7 Potential Field 161.8 Cell Decomposition 171.9 Optimal Control 181.10 Optimization Techniques 181.11 Trajectories for Path Planning 191.12 Outline of the Book 20References 222 Path Planning in Two Dimensions 292.1 Dubins Paths 302.2 Designing Dubins Paths using Analytical Geometry 312.2.1 Dubins Path: External Tangent Solution 332.2.2 Dubins Path: Internal Tangent Solution 352.3 Existence of Dubins Paths 372.4 Length of Dubins Path 392.5 Design of Dubins Paths using Principles of Differential Geometry 392.5.1 Dubins Path Length 432.6 Paths of Continuous Curvature 452.7 Producing Flyable Clothoid Paths 462.8 Producing Flyable Pythagorean Hodograph Paths (2D) 562.8.1 Design of Flyable Path using 2D PH curve 61References 623 Path Planning in Three Dimensions 653.1 Dubins Paths in Three Dimensions Using Differential Geometry 673.2 Path Length–Dubins 3D 723.3 Pythagorean Hodograph Paths–3D 723.3.1 Spatial PH Curves 733.4 Design of Flyable Paths Using PH Curves 743.4.1 Design of Flyable Paths 75References 784 Collision Avoidance 814.1 Research into Obstacle Avoidance 834.2 Obstacle Avoidance for Mapped Obstacles 854.2.1 Line Intersection Detection 864.2.2 Line Segment Intersection 904.2.3 Arc Intersection 944.3 Obstacle Avoidance of Unmapped Static Obstacles 1034.3.1 Safety Circle Algorithm 1044.3.2 Intermediate Waypoint Algorithm 1044.4 Algorithmic Implementation 1064.4.1 Dubins Path Modification 1074.4.2 Clothoid Path Modification 1074.4.3 PH Path Modification 1104.4.4 Obstacle Avoidance in 3D 112References 1155 Path-Following Guidance 1195.1 Path Following the Dubins Path 1205.2 Linear Guidance Algorithm 1245.3 Nonlinear Dynamic Inversion Guidance 1265.4 Dynamic Obstacle Avoidance Guidance 1325.4.1 UAV Direction Control 1355.4.2 Multiple Conflict Resolution 142References 1456 Path Planning for Multiple UAVs 1476.1 Problem Formulation 1496.2 Simultaneous Arrival 1516.3 Phase I: Producing Flyable Paths 1526.4 Phase II: Producing Feasible Paths 1526.4.1 Minimum Separation Distance 1536.4.2 Non-Intersection Paths 1546.4.3 Offset Curves 1556.5 Phase III: Equalizing Path Lengths 1566.6 Multiple Path Algorithm 1566.7 Algorithm Application for Multiple UAVs 1576.7.1 2D Dubins Paths 1576.7.2 2D Clothoid Paths 1606.8 2D Pythagorean Hodograph Paths 1626.9 3D Dubins Paths 1656.10 3D Pythagorean Hodograph Paths 169References 174Appendix A Differential Geometry 175A.1 Frenet–Serret Equations 177A.2 Importance of Curvature and Torsion 178A.3 Motion and Frames 179References 181Appendix B Pythagorean Hodograph 183B.1 Pythagorean Hodograph 184References 185Index 187

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