Combining Methods of Mathematical Optimization and Artificial Intelligence for Autonomous UAV

171 Pages·2017·3.66 MB·English

by  Henning Andre Åsgård

Combining Methods of Mathematical
Optimization and Artificial Intelligence for
Autonomous UAV Mission Planning and
Execution
Henning Andre Åsgård
Master of Science in Cybernetics and Robotics
Submission date: July 2017
Supervisor: Tor Arne Johansen, ITK
Norwegian University of Science and Technology
Department of Engineering Cybernetics

i
Abstract
In this thesis, different solutions for autonomous mission planning and execution aimed at
Unmanned Aerial Vehicles (UAV) is investigated using methods of Artificial Intelligence
(AI) and Mathematical Optimization. Different configurations of these solutions is then im-
plemented as an Autonomous Mission Planning and Execution (AMPE) system in order to
test the online performance of the complete system, and the different individual models that
composesthesystem. Inspiredby[26]thesystemisdividedintomoduleshandlingtheplan
in different levels of refinement in a hierarchical manner. Where applicable, modules will
be tested and compared when implemented by AI and Mathematical Optimization and the
advantages and disadvantages will be discussed. The system should be able to plan with a
certainamountofresourcesinmind,continuouslyupdatetheplanusingstatefeedback,and
perform the plan by using the plans current actuator inputs. In order to keep clear goals for
the the AMPE system, it is designed with a specific case in mind. Both the implemented
capabilitiesandthediscussionofresultswillfocusonoff-shoredatagatheringfromsensors
where the distances causes the required bandwidth impossible to achieve for direct commu-
nication. SeveralUAVswillcooperateinordertocollectthedatabycreatingadelay-tolerant
communicationnetwork,andwillseektodosoinsomeoptimalmanner. Thedifferentlevels
of the planning problem will be solved using Nonlinear Model Predictive Control (NMPC),
Mixed Integer Linear Programming (MILP) and domain models for EUROPA. The tools
ACADO, AMPL, EUROPA and T-REX will be used to implement the AMPE system with
parallel, synchronous deliberation of the planning levels. Simulations will be performed
whichshowsthatusingtheMILPoptimizationwithdataflowconstraintsarenoteapplicable
forarealworldsystemasituseshourstosolveaplan. However,byfindingplansinastatic
mission,theEUROPAsolverswillshowthatitismuchmoreefficientandwaysofcombining
EUROPAandMILPinthefuturewillbediscussed. Simulationsisdonetoshowre-planning
capabilities when the mission is affected by poor flight dynamics, dynamic resource con-
sumption and dynamically positioned nodes. In the end we will see how this system can
be quite easily expanded so that the case of this thesis is only a specialization of a much
broader domain of problems solvable by a more general system. A system where a mission
problem would be defined as a top-level nddl domain model, and then solved automatically
throughouttheAMPEpipeline. Thethesiswillconcludewithhowasystembasedonpurely
MathematicalOptimizationisill-fittedforreal-timedemands,andhowAIandMathematical
Optimizationcanbecombinedforautonomousmissionplanningandexecution.
ii
Abstrakt
I denne oppgaven vil forskjellige løsninger for autonom oppdragsplanlegging og utførelse
siktet mot ubemannede fly bli utforsket ved a˚ bruke matematisk optimalisering og kunstig
intelligens. Forskjellige konfigurasjoner for disse løsningene er sa˚ implementert til et au-
tonomtsystemfora˚ testedenonlineytelsentildetkomplettesystemet,ogtildeindividuelle
modulene som utgjør systemet. Inspirert av [26] vil systemet bli delt inn i moduler som
behandler planen i forskjellige grovhetsgrader pa˚ en hierarkisk ma˚te. Der det er mulig vil
modulerblitestetogsammenlignetmedhverandrena˚rdeerimplementertmedkunstigintel-
ligensogmatematiskoptimalisering,ogfordelerogulempervilblidiskutert. Systemetsskal
kunneplanleggemedenbestemtmengdetilgjengeligeressurser,kontinuerligoppdaterepla-
nen ved a˚ bruke status tilbakemeldinger, og gjennomføre planen ved a˚ bruke de na˚værende
kontrolverdieneiplanenforflykontroll. Fora˚ holdeklarema˚lforsystemetvildetbliutviklet
forenspesifikkcase. Ba˚dedenimplementertefunksjonaliteten,ogdiskusjonenavresultater
vil fokusere pa˚ off-shore datasamling fra sensorer hvor avstandene er for store for direkte
kommunikasjon. Flere fly vil samarbeide for a˚ samle data ved a˚ skape et forsinkelsestol-
erant rele´nettverk, og vil prøve a˚ gjøre sa˚ pa˚ en optimal ma˚te. De forskjellige delene av
planleggingenvilbligjennomførtveda˚ brukeNonlinearModelPredictiveControl(NMPC),
Mixed Integer Linear Programming (MILP) og domenemodeller for EUROPA. Verktøyene
ACADO, AMPL, EUROPA og T-REX vil bli brukt for a˚ implementere systemet med paral-
lellsynkronoverveielseavplanleggingsniva˚ene. Simuleringervilbligjennomførtsomviser
at MILP optimaliseringen med dataflyt begrensninger kan ikke brukes for systemer i den
virkelige verden da den er treg og kan bruke flere timer pa˚ a˚ finne en løsning. Ved a˚ finne
planer for et statisk oppdrag vil EUROPA løseren vise at den er mye kjappere enn MILP
modulen, og ma˚ter for a˚ kombinere EUROPA og MILP vil bli diskutert. Simuleringer er sa˚
gjort for a˚ vise re-planleggingsevnene til systemet na˚r oppdraget er pa˚virket av da˚rlig fly-
dynamikk, dynamisk ressursbruk, og dynamisk plasserte noder. Til slutt vil vi se hvordan
dette systemet kan utvides til a˚ takle et mye bredere spekter av oppdrag. Oppgaven vil kon-
kluderemedatetsystembasertrentpa˚matematiskoptimaliseringvilpasseda˚rligforekte-tid
systemer, og hvordan kunstig intelligens og matematisk optimalisering kan kombineres for
autonomoppdragsplanleggingogløsning.
Contents
I Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Structureofthisthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Previouswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Assumptionsandscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 TheAMPEsystemhighleveloverview . . . . . . . . . . . . . . . . . . . 6
1.7 Agentsandmodules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.8 Externallibrariesandequipment . . . . . . . . . . . . . . . . . . . . . . . 7
II Methods of implementation 9
2 Derivingalinearandnon-linearmodelfortheX-8UAV 11
2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Referenceframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 NEDframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Bodyframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Vehicleframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Statevector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.1 Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
iii
iv CONTENTS
2.6 Nonlinearequationsofmotion . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 Linearizedequationsofmotion . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.1 Trimconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 ConceptsandterminologyofdeliberativecontrolbyEUROPAandT-REX 23
3.1 TerminologyofT-REXandEuropa . . . . . . . . . . . . . . . . . . . . . . 23
4 TheAMPEsystemimplementation 25
4.1 Modularizing the system for hierarchical synchronous planning and execu-
tionusingT-REX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 TheAMPEsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 Systemdefinitions . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 AgentsandTeleo-reactors . . . . . . . . . . . . . . . . . . . . . . 29
4.2.3 Timelinesandpredicates . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.4 Implementationcustomizedforlocalsimulations . . . . . . . . . . 32
4.3 Flowdiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5 ThemodulesoftheAMPEsystem 35
5.1 Planningacrudeoverallmission-TheupperlevelmoduleusingEUROPA . 35
5.1.1 EUROPAandthenewdomaindescriptionlanguage . . . . . . . . . 36
5.1.2 Thenddlmodelformulation . . . . . . . . . . . . . . . . . . . . . 37
5.2 Planningacrudemissionpathusingmixedintegerlinearprogramming . . . 47
5.2.1 Motivationandconsiderations . . . . . . . . . . . . . . . . . . . . 47
5.2.2 Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2.3 MixedIntegerLinearProgramingprinciplesandformulation . . . . 48
5.2.4 TheMILPproblemformulation . . . . . . . . . . . . . . . . . . . 49
5.2.5 Resourcesconstraints . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2.6 Solveralgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.7 Implementing The MILP crude path planner using AMPL, CPLEX
andAMPLAPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 RefiningasystemdynamicsdependentpathusingModelPredictiveControl 61
5.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.3 Modelpredictivecontrolprinciple . . . . . . . . . . . . . . . . . . 61
5.3.4 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3.5 MPCforUAVcontrol . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.6 Theobjectivefunctionandconstraints . . . . . . . . . . . . . . . . 64
CONTENTS v
5.4 Thenavigatormodule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6 Handlingexternalforces 69
6.1 Optimizationofpathwithconsiderationofwind . . . . . . . . . . . . . . . 69
6.2 Implementedutilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.1 Europanddlmodeldebug-tool . . . . . . . . . . . . . . . . . . . . 70
6.2.2 MILPmodeldebug-tool . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.3 MPCdebug-tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.4 UDPservice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
III Simulations and results 73
7 Simulationsandequipment 75
7.1 Themissiondefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.2 Simulationandsystemparameters . . . . . . . . . . . . . . . . . . . . . . 76
8 Simulatingstaticmissions 79
8.1 SimulatingastaticmissionusingEUROPA . . . . . . . . . . . . . . . . . 79
8.1.1 Expandingtodynamicplanning . . . . . . . . . . . . . . . . . . . 79
8.2 SimulatingastaticmissionusingMILPanddataflowconstraints . . . . . . 80
8.2.1 Expandingtodynamicplaning . . . . . . . . . . . . . . . . . . . . 81
8.3 Re-planingcapabilitiesinastaticmission . . . . . . . . . . . . . . . . . . 81
9 Simulatingdynamicmissions 97
9.1 Simulatingamissionwithdynamicresourcesconsumption . . . . . . . . . 97
9.2 Simulatingamissionwithdynamicnodepositions . . . . . . . . . . . . . 102
9.3 Externalsimulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
IV Discussion and conclusion 121
10 Discussion 123
10.1 MILPperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
10.2 EUROPAperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
10.3 MPCperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
10.4 Applicabilityinreal-timeoperations . . . . . . . . . . . . . . . . . . . . . 125
10.5 Notesonstability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.6 AcombinedsystemofMILPandEUROPA . . . . . . . . . . . . . . . . . 127
vi CONTENTS
11 Futurework 129
12 Conclusion 131
13 Bibliography 133
V Appendix III
Appendices V
A UAVmodelconstantsandparameters V
A.1 UAVlinearmodelconstants . . . . . . . . . . . . . . . . . . . . . . . . . VI
A.2 TheX8flying-wingparameters . . . . . . . . . . . . . . . . . . . . . . . . VII
A.3 TheX8flying-wingtrimcondition . . . . . . . . . . . . . . . . . . . . . . VIII
B EUROPAnddlmodel XI
C AMPLmodel XIX
Part I
Introduction
1