Cooperative Path Planning of Unmanned Aerial Vehicles

Contents

About the Authors

Series Preface

Preface

Acknowledgements

List of Figures

List of Tables

Nomenclature

1 Introduction

1.1 Path Planning Formulation

1.2 Path Planning Constraints

1.2.1 Flyable Paths: Capturing Kinematics

1.2.2 UAV Inertial Manoeuvre Coordinates

1.2.3 Generation of Safe Paths for Path Planning

1.3 Cooperative Path Planning and Mission Planning

1.4 Path Planning – An Overview

1.5 The Road Map Method

1.5.1 Visibility Graphs

1.5.2 Voronoi Diagrams

1.6 Probabilistic Methods

1.7 Potential Field

1.8 Cell Decomposition

1.9 Optimal Control

1.10 Optimization Techniques

1.11 Trajectories for Path Planning

1.12 Outline of the Book

References

2 Path Planning in Two Dimensions

2.1 Dubins Paths

2.2 Designing Dubins Paths using Analytical Geometry

2.2.1 Dubins Path: External Tangent Solution

2.2.2 Dubins Path: Internal Tangent Solution

2.3 Existence of Dubins Paths

2.4 Length of Dubins Path

2.5 Design of Dubins Paths using Principles of Differential Geometry

2.5.1 Dubins Path Length

2.6 Paths of Continuous Curvature

2.7 Producing Flyable Clothoid Paths

2.8 Producing Flyable Pythagorean Hodograph Paths (2D)

2.8.1 Design of Flyable Path using 2D PH curve

References

3 Path Planning in Three Dimensions

3.1 Dubins Paths in Three Dimensions Using Differential Geometry

3.2 Path Length–Dubins 3D

3.3 Pythagorean Hodograph Paths–3D

3.3.1 Spatial PH Curves

3.4 Design of Flyable Paths Using PH Curves

3.4.1 Design of Flyable Paths

References

4 Collision Avoidance

4.1 Research into Obstacle Avoidance

4.2 Obstacle Avoidance for Mapped Obstacles

4.2.1 Line Intersection Detection

4.2.2 Line Segment Intersection

4.2.3 Arc Intersection

4.3 Obstacle Avoidance of Unmapped Static Obstacles

4.3.1 Safety Circle Algorithm

4.3.2 Intermediate Waypoint Algorithm

4.4 Algorithmic Implementation

4.4.1 Dubins Path Modification

4.4.2 Clothoid Path Modification

4.4.3 PH Path Modification

4.4.4 Obstacle Avoidance in 3D

References

5 Path-Following Guidance

5.1 Path Following the Dubins Path

5.2 Linear Guidance Algorithm

5.3 Nonlinear Dynamic Inversion Guidance

5.4 Dynamic Obstacle Avoidance Guidance

5.4.1 UAV Direction Control

5.4.2 Multiple Conflict Resolution

References

6 Path Planning for Multiple UAVs

6.1 Problem Formulation

6.2 Simultaneous Arrival

6.3 Phase I: Producing Flyable Paths

6.4 Phase II: Producing Feasible Paths

6.4.1 Minimum Separation Distance

6.4.2 Non-Intersection Paths

6.4.3 Offset Curves

6.5 Phase III: Equalizing Path Lengths

6.6 Multiple Path Algorithm

6.7 Algorithm Application for Multiple UAVs

6.7.1 2D Dubins Paths

6.7.2 2D Clothoid Paths

6.8 2D Pythagorean Hodograph Paths

6.9 3D Dubins Paths

6.10 3D Pythagorean Hodograph Paths

References

Appendix A Differential Geometry

A.1 Frenet–Serret Equations

A.2 Importance of Curvature and Torsion

A.3 Motion and Frames

References

Appendix B Pythagorean Hodograph

B.1 Pythagorean Hodograph

References

Index