Positioning Algorithms for Surveillance Using Unmanned Aerial Vehicles

159 Pages·2011·2.22 MB·English

Link¨opingStudiesinScienceandTechnology
ThesisNo. 1476
Positioning Algorithms for
Surveillance Using Unmanned
Aerial Vehicles
by
Per-Magnus Olsson
SubmittedtoLink¨opingInstituteofTechnologyatLink¨opingUniversityinpartial
fulfilmentoftherequirementsfordegreeofLicentiateofEngineering
DepartmentofComputerandInformationScience
Link¨opinguniversitet
SE-58183Link¨oping,Sweden
Link¨oping2011
ISBN 978-91-7393-200-4, ISSN 0280–7971
Printed by LiU-Tryck, 2011
Copyright ' Per-Magnus Olsson 2011
Electronic version available at :
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-66060
Positioning Algorithms for Surveillance Using
Unmanned Aerial Vehicles
by
Per-MagnusOlsson
April2011
ISBN978-91-7393-200-4
Link¨opingStudiesinScienceandTechnology
ThesisNo. 1476
ISSN0280–7971
LiU–Tek–Lic–2011:15
ABSTRACT
Surveillanceisanimportantapplicationforunmannedaerialvehicles(UAVs). Thesensed
informationoftenhashighpriorityanditmustbemadeavailabletohumanoperatorsas
quickly as possible. Due to obstacles and limited communication range, it is not always
possibletotransmittheinformationdirectlytothebasestation. Inthiscase,otherUAVs
canformarelaychainbetweenthesurveillanceUAVandthebasestation. Determining
suitablepositionsforsuchUAVsisacomplexoptimizationprobleminandofitself,and
ismadeevenmoredifficultbycommunicationandsurveillanceconstraints.
TosolvedifferentvariationsoffindingpositionsforUAVsforsurveillanceofonetarget,
two new algorithms have been developed. One of the algorithms is developed especially
forfindingasetofrelaychainsofferingdifferenttrade-offsbetweenthenumberofUAVs
andthequalityofthechain. Theotheralgorithmistailoredtowardsfindingthehighest
qualitychainpossible,givenalimitednumberofavailableUAVs.
Finding the optimal positions for surveillance of several targets is more difficult. A
study has been performed, in order to determine how the problems of interest can be
solved. Itturnsoutthatveryfewoftheexistingalgorithmscanbeusedduetothechar-
acteristics of our specific problem. For this reason, an algorithm for quickly calculating
positionsforsurveillanceofmultipletargetshasbeendeveloped. Thisenablescalculation
of an initial chain that is immediately made available to the user, and the chain is then
incrementallyoptimizedaccordingtotheuser’sdesire.
ThisworkhasbeensupportedbyCUGS(theSwedishNationalGraduateSchoolinCom-
puter Science), LinkLab (www.linklab.se), the Swedish National Aeronautics Research
ProgramNFFP04–S4203andNFFP05–01263,theELLIITExcellenceCenteratLinko¨ping-
Lund for Information Technology, the Swedish Foundation for Strategic Research (SSF)
Strategic Research Center MOVIII, the Center for Industrial Information Technology
CENIIT(grantnumber06.09)andtheLinnaeusCenterforControl,Autonomy,Decision-
making in Complex Systems (CADICS), funded by the Swedish Research Council (VR).
DepartmentofComputerandInformationScience
Link¨opinguniversitet
SE-58183Link¨oping,Sweden

Acknowledgements
This thesis would not have been possible without the support of co-workers
and friends. Especially I would like to thank:
Mysupervisors, professorPatrickDohertyandassociateprofessorJonas
Kvarnstr¨om for guidance in research as well as in writing of this thesis.
My co-researchers Kaj Holmberg and Oleg Burdakov for many valuable
discussions.
ThecolleaguesatAIICSandespeciallyOlovAndersson, FredrikHeintz,
David Land´en, Martin Magnusson and Piotr Rudol for spending time read-
ing this thesis as well as earlier papers.
Anne Moe for guiding me through the bureaucratic maze of graduate
studies.
Otherfriends,toonumeroustomentionbyname,forencouragementand
inspiration.
Linda for being the world’s best girlfriend.

Contents
1 Introduction 1
1.1 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Related Work 7
2.1 UAVs As Relays . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Single Target . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Multiple Targets . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Area Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Ad-hoc Networks and Wireless Sensor Networks. . . . . . . . 12
3 The Relay Positioning Problems 15
3.1 Problem Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Definitions of the Single Target Relay Problems . . . . . . . . 16
3.3 Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 Transmission Quality. . . . . . . . . . . . . . . . . . . 19
3.3.2 Position Visibility . . . . . . . . . . . . . . . . . . . . 20
3.3.3 Minimum Free Angle Between Positions . . . . . . . . 21
3.3.4 Minimum Distance to Obstacles . . . . . . . . . . . . 23
3.3.5 Surveillance Cost Functions . . . . . . . . . . . . . . . 23
3.4 Reachability Functions . . . . . . . . . . . . . . . . . . . . . . 24
3.5 Problem Properties . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Continuous Solution Methods . . . . . . . . . . . . . . . . . . 27
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Environment Representation and Discretization 31
4.1 Discretization and Graph Creation . . . . . . . . . . . . . . . 31
4.2 Fixed-Size Grids . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Octrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
ix
4.4 Expanded Geometry Graphs . . . . . . . . . . . . . . . . . . 35
4.5 Voronoi Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 37
4.6 Discretization Methods Used in Motion Planning . . . . . . . 38
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Relay Positioning Algorithms for Single Target Problems 41
5.1 Existing Algorithms for the STR-ParetoLimited Problem . 42
5.2 A New Label-Correcting Algorithm . . . . . . . . . . . . . . . 44
5.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . 44
5.2.2 Algorithm Details . . . . . . . . . . . . . . . . . . . . 46
5.2.3 Correctness Proof . . . . . . . . . . . . . . . . . . . . 50
5.2.4 Time Complexity . . . . . . . . . . . . . . . . . . . . . 52
5.2.5 Improved Preprocessing . . . . . . . . . . . . . . . . . 52
5.2.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 A New Dual Ascent Algorithm . . . . . . . . . . . . . . . . . 54
5.3.1 Algorithm Details . . . . . . . . . . . . . . . . . . . . 55
5.3.2 Theoretical Properties . . . . . . . . . . . . . . . . . . 57
5.3.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.4 Performance Improvements . . . . . . . . . . . . . . . 60
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6 Relay Positioning for Multiple Targets 65
6.1 Definition of the Multiple Target Relay Problems . . . . . . . 65
6.2 Relation to Steiner Tree Problems . . . . . . . . . . . . . . . 67
6.2.1 Continuous Steiner Trees . . . . . . . . . . . . . . . . 67
6.2.2 Discrete Steiner Trees . . . . . . . . . . . . . . . . . . 68
6.3 Adapting the Cheapest Path Heuristic . . . . . . . . . . . . . 78
6.3.1 Theoretical Properties . . . . . . . . . . . . . . . . . . 80
6.3.2 Extensions . . . . . . . . . . . . . . . . . . . . . . . . 81
6.4 Calculating Pareto-optimal Relay Trees For Two Targets. . . 83
6.4.1 Determining the Set of Pareto-optimal Relay Trees . . 85
6.4.2 Duplicate Edges in the Relay Tree . . . . . . . . . . . 86
6.5 Improving Relay Trees . . . . . . . . . . . . . . . . . . . . . . 87
6.5.1 Reduced Trees . . . . . . . . . . . . . . . . . . . . . . 89
6.5.2 Choosing Subtrees for Optimization . . . . . . . . . . 89
6.5.3 Different Tree Structures . . . . . . . . . . . . . . . . 94
6.5.4 Collisions Between Trees . . . . . . . . . . . . . . . . . 95
6.5.5 Algorithm Details . . . . . . . . . . . . . . . . . . . . 97
6.5.6 Time Complexity . . . . . . . . . . . . . . . . . . . . . 99
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7 Implementation and Experimental Results 103
7.1 Software Architecture . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Problem Setup for Empirical Testing . . . . . . . . . . . . . . 107
7.3 Pareto-Optimal Relay Chains . . . . . . . . . . . . . . . . . . 110
7.4 Optimal Chains Using At Most M UAVs . . . . . . . . . . . 114
7.5 Relay Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8 Discussion 127
8.1 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . 128