Cooperative Path Planning of Unmanned Aerial Vehicles

An invaluable addition to the literature on UAV guidance and cooperative control, Cooperative Path Planning of Unmanned Aerial Vehicles is a dedicated, practical guide to computational path planning for UAVs. One of the key issues facing future development of UAVs is path planning: it is vital that swarm UAVs/ MAVs can cooperate together in a coordinated manner, obeying a pre-planned course but able to react to their environment by communicating and cooperating. An optimized path is necessary in order to ensure a UAV completes its mission efficiently, safely, and successfully. Focussing on the path planning of multiple UAVs for simultaneous arrival on target, Cooperative Path Planning of Unmanned Aerial Vehicles also offers coverage of path planners that are applicable to land, sea, or space-borne vehicles. Cooperative Path Planning of Unmanned Aerial Vehicles is authored by leading researchers from Cranfield University and provides an authoritative resource for researchers, academics and engineers working in the area of cooperative systems, cooperative control and optimization particularly in the aerospace industry.

About the Authors ix Series Preface xi Preface xii Acknowledgements xiii List of Figures xv List of Tables xxi Nomenclature xxiii 1 Introduction 1 1.1 Path Planning Formulation 2 1.2 Path Planning Constraints 3 1.2.1 Flyable Paths: Capturing Kinematics 4 1.2.2 UAV Inertial Manoeuvre Coordinates 6 1.2.3 Generation of Safe Paths for Path Planning 7 1.3 Cooperative Path Planning and Mission Planning 7 1.4 Path Planning – An Overview 10 1.5 The Road Map Method 13 1.5.1 Visibility Graphs 14 1.5.2 Voronoi Diagrams 14 1.6 Probabilistic Methods 16 1.7 Potential Field 16 1.8 Cell Decomposition 17 1.9 Optimal Control 18 1.10 Optimization Techniques 18 1.11 Trajectories for Path Planning 19 1.12 Outline of the Book 20 References 22 2 Path Planning in Two Dimensions 29 2.1 Dubins Paths 30 2.2 Designing Dubins Paths using Analytical Geometry 31 2.2.1 Dubins Path: External Tangent Solution 33 2.2.2 Dubins Path: Internal Tangent Solution 35 2.3 Existence of Dubins Paths 37 2.4 Length of Dubins Path 39 2.5 Design of Dubins Paths using Principles of Differential Geometry 39 2.5.1 Dubins Path Length 43 2.6 Paths of Continuous Curvature 45 2.7 Producing Flyable Clothoid Paths 46 2.8 Producing Flyable Pythagorean Hodograph Paths (2D) 56 2.8.1 Design of Flyable Path using 2D PH curve 61 References 62 3 Path Planning in Three Dimensions 65 3.1 Dubins Paths in Three Dimensions Using Differential Geometry 67 3.2 Path Length–Dubins 3D 72 3.3 Pythagorean Hodograph Paths–3D 72 3.3.1 Spatial PH Curves 73 3.4 Design of Flyable Paths Using PH Curves 74 3.4.1 Design of Flyable Paths 75 References 78 4 Collision Avoidance 81 4.1 Research into Obstacle Avoidance 83 4.2 Obstacle Avoidance for Mapped Obstacles 85 4.2.1 Line Intersection Detection 86 4.2.2 Line Segment Intersection 90 4.2.3 Arc Intersection 94 4.3 Obstacle Avoidance of Unmapped Static Obstacles 103 4.3.1 Safety Circle Algorithm 104 4.3.2 Intermediate Waypoint Algorithm 104 4.4 Algorithmic Implementation 106 4.4.1 Dubins Path Modification 107 4.4.2 Clothoid Path Modification 107 4.4.3 PH Path Modification 110 4.4.4 Obstacle Avoidance in 3D 112 References 115 5 Path-Following Guidance 119 5.1 Path Following the Dubins Path 120 5.2 Linear Guidance Algorithm 124 5.3 Nonlinear Dynamic Inversion Guidance 126 5.4 Dynamic Obstacle Avoidance Guidance 132 5.4.1 UAV Direction Control 135 5.4.2 Multiple Conflict Resolution 142 References 145 6 Path Planning for Multiple UAVs 147 6.1 Problem Formulation 149 6.2 Simultaneous Arrival 151 6.3 Phase I: Producing Flyable Paths 152 6.4 Phase II: Producing Feasible Paths 152 6.4.1 Minimum Separation Distance 153 6.4.2 Non-Intersection Paths 154 6.4.3 Offset Curves 155 6.5 Phase III: Equalizing Path Lengths 156 6.6 Multiple Path Algorithm 156 6.7 Algorithm Application for Multiple UAVs 157 6.7.1 2D Dubins Paths 157 6.7.2 2D Clothoid Paths 160 6.8 2D Pythagorean Hodograph Paths 162 6.9 3D Dubins Paths 165 6.10 3D Pythagorean Hodograph Paths 169 References 174 Appendix A Differential Geometry 175 A.1 Frenet–Serret Equations 177 A.2 Importance of Curvature and Torsion 178 A.3 Motion and Frames 179 References 181 Appendix B Pythagorean Hodograph 183 B.1 Pythagorean Hodograph 184 References 185 Index 187