Cooperative Path Planning of Unmanned Aerial Vehicles

Cooperative Path Planning of Unmanned Aerial VehiclesAerospace series listCooperative Path Planning of Unmanned Tsourdos et alNovember 2010Aerial VehiclesPrinciples of Flight for PilotsSwattonOctober 2010Air travel and Health: A SystemsSeabridge et alSeptember 2010PerspectiveDesign and analysis of CompositeKassapoglouSeptember 2010Structures: With Applications toAerospace StructuresUnmanned Aircraft Systems: UAVSAustinapril 2010Design, development and deploymentIntroduction to antenna placementMacnamaraapril 2010InstallationsPrinciples of Flight simulationAllertonDctober 200Aircraft Fuel SystemsLangton et alMay 2009The Global Airline IndustryBelobabapril 2009Computational Modelling and Simulation DistonApril 2009of aircraft and the environment: Volume1- Platform Kinematics and SyntheticEnvironmentHandbook of Space TechnologyLey, Wittmannapril 2009HallmannAircraft Performance Theory and Practice SwattonAugust 2008for pilotsSurrogate Modelling in EngineeringForresterAugust 2008Design: A Practical GuideSobester, KeaneAircraft Systems, 3 ra editionMoir seabridge March 2008ntroduction to Aircraft AeroelasticityWright Cooper December 2007And loadsStability and Control of aircraft SystemsLangtonSeptember 2006Military avionics systemsMoir seabridge February 2006Design and Development of AircraftMoir seabridge June 2004SystemsAircraft Loading and Structural LayoutHoweMay 2004Aircraft Display systemsJukesDecember 2003Civil Avionics SystemsMoir seabridge December 2002c。 operative PathPlanning of UnmannedAerial vehiclesAntonios Tsourdos Brian whiteand Madhavan ShanmugavelCranfield Defence and SecurityCranfield University, UKWILEYA John Wiley and Sons, Ltd. PublicationThis edition first published 2011o 2011, John Wiley Sons, LtdRegistered officeJohn wiley sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQUnited KingdomFor details of our global editorial offices for customer services and for information about howto apply for permission to reuse the copyright material in this book please see our website atwww.wlley.comThe right of the author to be identified as the author of this work has been asserted inaccordance with the Copyright, Designs and Patents Act 1988All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,or transmitted, in any form or by any means, electronic, mechanical, photocopying, recordingor otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, withoutthe prior permission of the publisherWiley also publishes its books in a variety of electronic formats. Some content that appears inprint may not be available in electronic booksDesignations used by companies to distinguish their products are often claimed as trademarksAll brand names and product names used in this book are trade names, service marks,trademarks or registered trademarks of their respective owners. The publisher is not associatedwith any product or vendor mentioned in this book. This publication is designed to provideaccurate and authoritative information in regard to the subject matter covered. It is sold on theunderstanding that the publisher is not engaged in rendering professional services. Ifprofessional advice or other expert assistance is required, the services of a competentprofessional should be soughtLibrary of Congress Cataloguing-in-Publication DataTsourdos, antoniosCooperative path planning of unmanned aerial vehicles Antonios Tsourdorian White, Madhavan ShanmugavelP cm.Includes bibliographical references and indexISBN9780-470-74129-0( cloth)1. Drone aircraft- Automatic control. 2. Guidance systems(Flight)3. Airplanes-Piloting-Mathematics. 4. Airplanes-Piloting-Planning5. Airways-Mathematical models I White, Brian, 1947 June 6IL. Shanmugavel, Madhavan. Ill. TitleTL5894.T7820106291325-dc222010026275A catalogue record for this book is available from the British LibraryPrint isbn:978-0-470-74129-0ePDF ISBN:978-0-470-97520-6oBook IsBn:978-0-470-97463-6ePub isbn:978-0-470-97464-3Typeset in 10/12. 5pt Palatino by Laserwords Private Limited, Chennai, IndiaContentsabout the authorsSeries PrefacePrefaceAcknowledgementsX11List of FiguresList of tablesNomenclatureXIII1 Introduction1.1 Path Planning Formulation1.2 Path Planning Constraints1.2.1 Flyable paths: Capturing Kinematics1.2.2 UAV Inertial Manoeuvre Coordinates1.2.3 Generation of Safe Paths for Path Planning12346771.3 Cooperative Path Planning and Mission Planning1. 4 Path Planning -An Overview101.5 The Road Map method131.5. 1 Visibility graphs141.5.2 Voronoi Diagrams14Contents1.6 Probabilistic methods161.7 Potential field161.8 Cell decomposition1.9 Optimal Control181.10 Optimization Techniques181.11 Trajectories for Path Planning191.12 Outline of the bookReferences222 Path Planning in Two Dimensions2.1 Dubins paths302.2 Designing dubins paths using analytical geometry312.2.1 Dubins path: External Tangent Solution332.2.2 Dubins Path Internal Tangent Solution2.3 Existence of Dubins paths372.4 Length of Dubins Path392.5 Design of Dubins Paths using Principles of DifferentialGeometry392.5.1 Dubins path length432.6 Paths of Continuous Curvature452.7 Producing Flyable Clothoid Paths462.8 Producing Flyable Pythagorean Hodograph Paths(2D562.8.1 Design of Flyable Path using 2D PH curve61References623 Path Planning in Three dimensions653.1 Dubins Paths in Three Dimensions Using DifferentialGeometry3.2 Path Length -Dubins 3D3. 3 Pythagorean Hodograph Paths-3D723.3.1 Spatial PH Curves3.4 Design of Flyable Paths Using PH Curves743.4.1 Design of Flyable Paths75References4 Collision avoidance814.1 Research into obstacle avoidance4. 2 Obstacle Avoidance for Mapped Obstacles4.2.1 Line Intersection detection86Contents4.2.2 Line segment Intersection4.2.3 Arc Intersection944.3 Obstacle Avoidance of Unmapped Static Obstacles1034.3.1 Safety Circle Algorithm1044.3.2 Intermediate Waypoint algorithm1044.4 Algorithmic Implementation4.4.1 Dubins path modification1074.4.2 Clothoid Path Modification1074.4.3 PH Path Modification1104.4.4 Obstacle Avoidance in 3D112References1155 Path-Following Guidance1195.1 Path Following the Dubins Path1205.2 Linear Guidance algorithm1245.3 Nonlinear dynamic Inversion guidance1265.4 Dynamic Obstacle Avoidance guidance1325.4.1 UAV Direction Control1355.4.2 Multiple Conflict Resolution142References1456 Path Planning for Multiple uavs1476.1 Problem formulation1496.2 Simultaneous arrival1516.3 Phase I: Producing Flyable Paths1526.4 Phase Il: Producing Feasible paths1526.4.1 Minimum Separation distance1536.4.2 Non-Intersection paths1546.4.3 Offset Curves1556.5 Phase Ill: Equalizing path lengths1566.6 Multiple Path Algorithm1566.7 Algorithm Application for Multiple UAVs1576.7.1 2D Dubins Paths1576.7.2 2D Clothoid Paths1606.8 2D Pythagorean Hodograph paths1626.9 3D Dubins paths1656.10 3D Pythagorean Hodograph Paths169References174vilContentsAppendix a differential geometry175A 1 Frenet-Serret equations177A2 Importance of Curvature and Torsion178A 3 Motion and frames179References181Appendix B Pythagorean Hodograph183B. 1 Pythagorean Hodograph184References185Index187About the authorsAntonios Tsourdos was appointed Head of the Autonomous SystemsGroup at cranfield university in 2007. He obtained a Phd on nonlinearRobust Flight Control Design and Analysis from Cranfield University in1999. He was a member of the Team Stellar, the winning team for the UKMoD Grand Challenge(2008). He has served as an Editorial Board Memberfor the Proceedings of the Institution of Mechanical engineers, Part G: Journalof Aerospace engineering, the International Journal of Systems Science, the IEEETransactions on Instrumentation and Measurement, the International Journal onAdvances in Intelligent Systems and the international journal mathematics inEngineering, Science and Aerospace(MESA). He is a member of the AIDISAutonomous Systems Strategy group and the a&d Ktn National Technical Committee on Autonomous Systems. He is also a member of the iFacTtechnical Committee on Aerospace Control, the IFAC Technical Committee on Networked Systems, the alaa Technical committee on guidanceControl Navigation the Ieee Control System Society Technical Committeeon Aerospace Control (TCaC)and the IEEE Technical Committee on AerialRobotics and Unmanned aerial vehiclesBrian White obtained a BSc degree in Engineering from the University ofLeicester, followed by an MSc and PhD from UMIST, Manchester, in 1974He has worked in the aerospace industry for the company mbda, workingon novel guidance techniques for missile systems, including one of the firstdevelopments of Kalman filters for integration into guidance systems. He hassince been a faculty member of the school of Engineering at the universityof Bath and at Cranfield University where for many years he was headof the Department of Aerospace, Power and Sensors. While in the post, hebuilt up a strong department in Aerospace Systems and also led the control