Citation
Cooperative Localization for Autonomous Underwater Vehicles in Strong Ocean Currents

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Title:
Cooperative Localization for Autonomous Underwater Vehicles in Strong Ocean Currents
Creator:
Song, Zhuoyuan
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (86 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering
Mechanical and Aerospace Engineering
Committee Chair:
MOHSENI,KAMRAN
Committee Co-Chair:
CRANE,CARL D,III
Committee Members:
BAROOAH,PRABIR
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Block diagrams ( jstor )
Covariance ( jstor )
Geodetic position ( jstor )
Matrices ( jstor )
Propellers ( jstor )
Robotics ( jstor )
Robots ( jstor )
Sensors ( jstor )
Simulations ( jstor )
Underwater vehicles ( jstor )
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
auv -- localization -- robotics
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Mechanical Engineering thesis, M.S.

Notes

Abstract:
Unavailability of GPS (global positioning system) for underwater navigation has created significant challenges for operation and localization of autonomous underwater vehicles (AUVs). This is more pronounced in dynamic ocean flows where significant background flows exist. In this thesis, a collaborative underwater localization hierarchy is introduced to improve the cooperative performance of a small AUV swarm by utilizing vehicles with bounded localization error as moving references in the presence of dominating background flows. Initially represented in probability theory, the problem is then decomposed into a cooperative localization problem and a dynamic simultaneous localization and mapping problem with moving features. To address the incomplete covariance updating issue, which arises when directly applying the extended Kalman filter in fully distributed systems, the modified extended Kalman filter (MEKF) is proposed and a MEKF based algorithm is discussed in detail. A particle filter based algorithm is implemented for comparative purposes due to its advantages in modeling multimodal non-Gaussian distributions. However, it is shown that the particle filter requires greater computational effort than the MEKF when the number of vehicles is small. Both proposed algorithms are verified in three-dimensional background flow simulations. The divergent behavior of localization error, which appears when using solely cooperative localization, is avoided through the implementation of either the MEKF algorithm or the particle algorithm. Significant decreases in localization error are subsequently observed. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
Local:
Adviser: MOHSENI,KAMRAN.
Local:
Co-adviser: CRANE,CARL D,III.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31
Statement of Responsibility:
by Zhuoyuan Song.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
5/31/2015
Resource Identifier:
908645698 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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COOPERATIVELOCALIZATIONFORAUTONOMOUSUNDERWATERVEHICLESINSTRONGOCEANCURRENTSByZHUOYUANSONGATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2014

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c2014ZhuoyuanSong

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TomydearparentsQingrongSong~BaoyingDu,mymentorDr.KamranMohseni,andmybelovedWenjieZhang

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ACKNOWLEDGMENTS Thisthesiswouldnothavebeenpossiblewithoutthehelpandsupportofmanyfriendsandcolleagues.IwouldliketothankmyadvisorDr.KamranMohseni,whohasbeenstronglysupportingmeeversinceourrstmeetbackin2011.Heenlightenedmywaythroughthetopicselection,problemarticulation,research,publicationsanddeterminingmyPh.D.direction.Hiswiderangeofresearchinterestsbringsdiversitiestoourgroup,whichmakesitpossibleformetondatopicthatmatchesexactlymyinterest.Ireallyappreciateeveryconversationwehadduringthesethreeyears.Healwaysgavemesincereadvicesandledmetothink\outofthebox".Ialsowanttothankhimforspendingsignicantamountoftimeineditingmywritingandgivingmeadvicespatiently.Tome,heisagreatmentor,alifelongfriendandthebesthousepartyhost.IwouldalsoliketothankmyothercommitteemembersDr.CarlD.Crane,IIIandDr.PrabirBarooahfortheirenlighteninginstructionandhelpfulsuggestions.ManythankstoDr.ScottBanks,whogavemeveryhelpfuladviceswhenIrstcametoUF.Iwouldn'thavebeenusedtothestudylifeintheUnitedStatesandfoundmyresearchpositionsoquicklywithouthisgreathelp.ThelifeinUFwouldnothavebeenthesamewithoutthemanygreatpeopleImethere.MostimportantwasBobbyHodgekinsonwhohelpedmeontheCephaloBotcontrolsystemproject.Withouthiseorts,manyofthisworkwouldn'tbepossible.SinceIjoinedthegroup,wesharedmanygreatpersonalandacademicexperiences.Iwishhimandhisfamilythebest.IwouldalsoliketothankDr.MattShieldsforhishelpfulsuggestionsandhelpduringmyresearch.Heisaconsideratefriendandhelpsmealotinovercomingissuesasaninternationalstudent.Withouthisaccompany,myrstconferenceexperiencewouldn'tbethesame.IamalsogladtohaveDr.DouglasLipinski,Dr.MichaelKriegandYimingXuinmygroup.Theirresearchexperiencesinspiredmealot.Ialsowantto 4

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showmygratitudetoallmygroupmembersforbuildingsuchafriendlyandmotivativeatmospheretoworkin.JoiningUFisathingthatisalwaysworthtobeproudof.IgotusedtothecampuslifeeasilyandthepeopleImetherewereniceandresponsible.Allkindsofresourcesprovidedbytheuniversityhelpedmetofeelathome.I'llalwaysrememberthesunshineinFloridaandalwaysbeproudofbeingaFloridaGator.ThewaytoUFwouldnothavebeenpossiblewithoutthesupportsfromthepeopleintheearlystageofmyengineeringcareerwhomIwouldliketothankhere:Prof.GuangweiYufromShanghaiUniversityforbeingmyundergraduateadvisorwhointroducedmetotheworldofengineeringandhelpedmemakethedecisiontopursemygraduatedegreesinUS;Prof.YimingRongfromWorcesterPolytechnicInstituteandTsinghuaUniversityforhisgreathelpinmystudyandgraduateschoolapplicationandRoseOliverM.B.E.forherinstructionandcaringwhenIwasinShanghaiUniversityandalsoforhergreathelpandadvicesinmygraduateschoolapplicationprocess.Finally,Iwouldliketothankmyparentsfortheirself-givingsupportandencouragement,Dr.YizheSun,towhomIwillnevergetachancetoexpressmyappreciation,forhiscontinuoushelpandadvices,andWenjieforherlong-termunderstandingandgreatsupport.Iwishthemallthebest. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 12 CHAPTER 1INTRODUCTION .................................. 13 1.1Robotics ..................................... 13 1.2AutonomousUnderwaterVehicle ....................... 13 1.3Motivation .................................... 14 1.4Methodology .................................. 18 1.5ContributionofthisThesis ........................... 19 1.6ThesisOutline .................................. 20 2HIERARCHICALCOOPERATIVEUNDERWATERLOCALIZATION ..... 22 2.1UnderwaterSLAM ............................... 22 2.2ProbabilisticFormulation ........................... 22 2.3ModiedExtendedKalmanFilter ....................... 29 2.3.1MEKF .................................. 29 2.3.1.1MEKFprediction ....................... 29 2.3.1.2MEKFcorrection ....................... 31 2.3.2MotionModel .............................. 34 2.3.2.1Singlevehiclemotionmodel ................. 34 2.3.2.2Fullstatemodel ........................ 36 2.3.3ObservationModel ........................... 38 2.3.4Intra-AUVDataFusion ......................... 38 2.4ParticleFilter .................................. 39 2.5MatchingMethods ............................... 43 2.6Summary .................................... 45 3SIMULATIONSINBACKGROUNDFLOWS ................... 47 3.1Algorithm-1intheDouble-gyreFlowField .................. 47 3.1.11-DAUVCase .............................. 49 3.1.23-DAUVCase .............................. 49 3.2Algorithm-1intheFlowFieldGeneratedbyFourConvectionCellsAroundaCylinder .................................... 52 3.3Algorithm-1intheFlowFieldGeneratedbyThreeVorticesonaSphereSurface ...................................... 54 6

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3.4Algorithm-2intheFlowFieldGeneratedbyThreeVorticesontheSphereSurface ...................................... 59 4CONCLUSIONSANDFUTUREWORK ...................... 65 ACEPHALOBOT ................................... 67 A.1Overview .................................... 67 A.2MechanicalDesign ............................... 67 A.3EmbeddedSystemDesign ........................... 70 A.3.1VortexRingThruster(VRT)ControlModel ............. 72 A.3.2BuoyancyControlDevice(BCD) .................... 72 A.3.3RearPropellerModel .......................... 73 A.3.4UserInterface(UI)Model ....................... 74 A.3.5PowerDistributionandMonitoring(PDM)Model .......... 74 A.3.6SensorInterfaceBoard(SIB) ...................... 76 A.3.7IntegratedConnectingBoard ...................... 76 A.4ControlSystemSoftwareDesign ........................ 77 A.4.1MotionControl ............................. 78 A.4.2InertialMeasurement .......................... 79 A.4.3DataLogging .............................. 79 A.5Summary .................................... 81 REFERENCES ....................................... 82 BIOGRAPHICALSKETCH ................................ 86 7

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LISTOFTABLES Table page 3-1Timestepportionindierenterrorranges. ..................... 59 A-1Vehiclespecications. ................................. 69 A-2Voltageandcurrentrequirementsofon-boardelectronics. ............. 76 8

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LISTOFFIGURES Figure page 1-1VariouspropelledAUVs. ............................... 15 1-2Variousbuoyancy-drivenAUVs. ........................... 16 1-3AUVsdesignedbyourgroup.Fromtherstgenerationtothefth:Hydro-Bu,RAV,CALAMAR-E,KRAKENandCephaloBot. ................. 17 1-4Diagramofthemother-daughterlocalizationhierarchy. ............. 19 2-1Datastructureofstatevectors,covariancematricesandJacobianmultipliersstoredinDAUV-1(left)andDAUV-3(right)inthecaseofveDAUVsandtwoMAUVs. ..................................... 31 2-2DenitionoftheNEDcoordinatesystem(left)andtheCADmodelofCephaloBot[ 14 { 16 24 ]withlocalandglobalcoordinatesystems(right). ............. 35 2-3DatamatchingCase-1.MorethanoneneighboringDAUVsaredetectedatthesametimeandneighboringDAUVsaremutuallydetectable. ........... 45 2-4DatamatchingCase-2.MorethanoneneighboringDAUVsaredetectedatthesametimebutneighboringDAUVsarenotmutuallydetectable. ......... 46 3-1TheforwardandbackwardFTLEeldsforthetimedependentdouble-gyresystemattimet=0withA=0:1=0:1,!=2=10,andT=)]TJ /F1 11.955 Tf 9.3 0 Td[(15,whichgivesasystemwithanoscillationperiodof10[ 20 ]. .................... 48 3-2Thedouble-gyrevelocityeldattimet=T=4,maximumeastward(rightward)perturbation[ 20 ]. ................................... 49 3-3SimulationofDSLAMusingoneDAUVandoneMAUV. ............. 50 3-4LocalizationerroroftheDAUV. .......................... 50 3-5SimulationofCLandDSLAMusingthreeDAUVs. ................ 51 3-6LocalizationerrorofeachDAUV.DAUV-1(top),DAUV-2(middle),andDAUV-3(bottom). ....................................... 51 3-7AUVs'pathsinthesimulationofoneMAUVandthreeDAUVsintheoweldongeneratedbyfourconvectioncellsaroundacylinder. .............. 53 3-8ComparisonbetweenpureCLandAlgorithm-1withoneMAUVsbasedonlocalizationerrorofthreeDAUVs. ................................ 54 3-9LocalizationerrorofthreeDAUVswhenperformingtheAlgorithm-1withdierentnumbersofMAUVs. ................................. 54 9

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3-103-vortexcongurationonasphere[ 27 ]. ....................... 57 3-11Trajectoriesofthreevorticesandapassiveparticleintheresultingbackgroundoweld. ....................................... 57 3-12NormalizedlocalizationerrorofeachDAUVwhenusezeroMAUVs(top)andtwoMAUVs(bottom)astime(normalized)proceeds. ............... 58 3-13NormalizedlocalizationerrorofDAUV-1ineachaxis.Threeerrorranges,[)]TJ /F1 11.955 Tf 9.3 0 Td[(110)]TJ /F7 7.97 Tf 6.59 0 Td[(3;110)]TJ /F7 7.97 Tf 6.59 0 Td[(3],[)]TJ /F1 11.955 Tf 9.3 0 Td[(0:810)]TJ /F7 7.97 Tf 6.59 0 Td[(3;0:810)]TJ /F7 7.97 Tf 6.59 0 Td[(3]and[)]TJ /F1 11.955 Tf 9.29 0 Td[(0:510)]TJ /F7 7.97 Tf 6.59 0 Td[(3;0:510)]TJ /F7 7.97 Tf 6.58 0 Td[(3],areusetoevaluatetimestepportionsinparticularlocalizationerrorranges. ...... 59 3-14DAUV-1'slocalizationerrorinx-axis,y-axisandz-axis,evaluatedbasedonboththeparticlewiththelargestweightandtheweightedmeanofallparticles. ... 61 3-15LocalizationerrorofeachDAUVwhenperformingtheMEKFalgorithmwithoneMAUVandthreeDAUVs. ............................ 61 3-16LocalizationerrorofeachDAUVwhenperformingthePFalgorithmwithoneMAUVandthreeDAUVsusingdierentnumbersofparticlesforeachvehicle. 62 3-17LocalizationerrorofeachDAUVwhenperformingthePFalgorithmusingoneMAUVandthreeDAUVswithdierentnumberofparticlesforeachvehicle. .. 63 3-18ComputationaltimecomparisonbetweenMEKF-basedalgorithmandPF-basedalgorithmwithdierentnumberofparticles. .................... 64 A-1AUVtestingtank. .................................. 68 A-2The4th-generationofthevortexringthruster. ................... 68 A-3FunctionalprototypeofCephaloBot. ........................ 69 A-4CADmodelofofCephaloBot. ............................ 69 A-5CADmodelofthe7thgenerationoftheVRT. ................... 70 A-6CADmodelofoftheBCD. ............................. 71 A-7Embeddedsystemelectronicsofthecentersectionmountedonbatterypack. .. 71 A-8BlockdiagramoftheVRTcontrolmodel. ..................... 73 A-9BlockdiagramoftheBCDcontrolmodel. ..................... 73 A-10Blockdiagramoftherearpropellermodel. ..................... 74 A-11Blockdiagramoftheuserinterfacemodel. ..................... 75 A-12Blockdiagramofthepowerdistributionandmonitoringmodel. ......... 75 A-13Blockdiagramofthesensorinterfaceboard. .................... 77 10

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A-14Blockdiagramoftheintegratedconnectingboard. ................. 77 A-15TheuserinterfacedesignedforCephaloBot. .................... 78 A-16ThesizeoftheVECTORNAVVN-100surface-mountIMUcomparedwithaquartercoin. ...................................... 79 A-17Dataloggingprocess. ................................. 81 11

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceCOOPERATIVELOCALIZATIONFORAUTONOMOUSUNDERWATERVEHICLESINSTRONGOCEANCURRENTSByZhuoyuanSongMay2014Chair:KamranMohseniMajor:MechanicalEngineeringUnavailabilityofGPS(globalpositioningsystem)forunderwaternavigationhascreatedsignicantchallengesforoperationandlocalizationofautonomousunderwatervehicles(AUVs).Thisismorepronouncedindynamicoceanowswheresignicantbackgroundowsexist.Inthisthesis,acollaborativeunderwaterlocalizationhierarchyisintroducedtoimprovethecooperativeperformanceofasmallAUVswarmbyutilizingvehicleswithboundedlocalizationerrorasmovingreferencesinthepresenceofdominatingbackgroundows.Initiallyrepresentedinprobabilitytheory,theproblemisthendecomposedintoacooperativelocalizationproblemandadynamicsimultaneouslocalizationandmappingproblemwithmovingfeatures.Toaddresstheincompletecovarianceupdatingissue,whichariseswhendirectlyapplyingtheextendedKalmanlterinfullydistributedsystems,themodiedextendedKalmanlter(MEKF)isproposedandaMEKFbasedalgorithmisdiscussedindetail.Aparticlelterbasedalgorithmisimplementedforcomparativepurposesduetoitsadvantagesinmodelingmultimodalnon-Gaussiandistributions.However,itisshownthattheparticlelterrequiresgreatercomputationaleortthantheMEKFwhenthenumberofvehiclesissmall.Bothproposedalgorithmsareveriedinthree-dimensionalbackgroundowsimulations.Thedivergentbehavioroflocalizationerror,whichappearswhenusingsolelycooperativelocalization,isavoidedthroughtheimplementationofeithertheMEKFalgorithmortheparticlealgorithm.Signicantdecreasesinlocalizationerroraresubsequentlyobserved. 12

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CHAPTER1INTRODUCTION 1.1RoboticsTheoriginofroboticscanbedatedbacktothethirdcenturyB.C.andearlier,whentheChinesearticerYanShipresentedKingMuofZhou(1023-957BC)withalife-size,human-shapedgureofhismechanicalhandiworkbasedonthedescriptionintheLieZitext[ 26 ].Theconceptofcreatingmachinesthatcanoperateautonomouslygrewalongwiththeevolutionofdierentcivilizations.Buttheresearchintothefunctionalityandpotentialusesofrobotsdidnotgrowsubstantiallyuntilthe20thcentury[ 28 ].Inthe50yearssinceGeorgeDevolandJoeEngelbergerputtherstrobotonthefactoryoorofGeneralMotorsin1961,robotshavefoundtheirwayintosurgeryrooms,scienticlaboratories,battleelds,searchandrescuesituations,Mars,andevenourhomesasvacuumcleaners,toys,andsecurityguards.Today,governments,corporations,andscientistsenvisionroboticsasamajorcomponentoftechnological,economic,andsocialdevelopmentinthe21stcentury.Foreldrobotics,theinventionofautonomousground,aerial,andunderwaterrobotshelpsexpandingthefootprintsofhumanbeingstoextremeareasincludingunderground,outer-spaceanddeepsea.Today'saerialrobotsaremoreandmoreintelligentandcapablesuchthattheyaregraduallytakingoverthejobofworkinginthedirty,dangerousandharshenvironmentforhumanbeings. 1.2AutonomousUnderwaterVehicleThelastfewdecadeshavewitnessedtheemergenceofalargeandevergrowingnumberofdierentautonomousunderwatervehicles(AUVs).Withouttherequirementofhumanoperators,AUVsareabletoexploreareasthatwerepreviouslyhardorimpossibletobeaccessedbyhumanswithsignicantlylowcosts.TherstAUV,the\SpecialPurposeUnderwaterResearchVehicle"(SPURV),wasdevelopedattheAppliedPhysicsLaboratory(APL)attheUniversityofWashingtonasearlyas1957,whichwasusedtostudydiusion,acoustictransmission,andsubmarinewakes.Withthedevelopment 13

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ofadvancedmicroprocessingsystemsandsensorsystems,AUVsarebeingusedmoreandmorecommonlyinoilandgasindustries,oceanographicstudiesandmostrecently,hurricanepredictionandmonitoring.Bythepropulsionmethod,AUVscanbecategorizedaspropelledAUVs,usingpropellersasthemajorpropulsionmethod,e.g.Bluen21byBluenRobotics(Figure 1-1 A),SeabedbyWoodsHoleOceanographicInstitution(WHOI)(Figure 1-1 B)andGaviaAUVsbyTeledyneGavia(Figure 1-1 C),andbuoyancy-drivenAUVs,beingcapableofchangingtheirdisplacedvolumetobecomepositivelyornegativelybuoyantbypumpingoilfromaninternalreservoirtoanoutsidebladder[ 3 ],e.g.SeaExplorerbyALCEM-ACSA(Figure 1-2 A),X-RaybybothAPLandtheMarinePhysicsLab(MPL)atScrippsInstitutionofOceanography(Figure 1-2 B)andSpraybyBluenRobotics(Figure 1-2 C).Since2002,ourgrouphavedesignedvegenerationsofAUVs(Figure 1-3 ).PropelledAUVshaveawiderangeofapplicationsincludingunderwatermapping,shiphullinspection,underwaterpipeinspection,underwatervehicletracking,seabedexploration,wrecksearching,etc..Buoyancy-drivenvehiclesbenetfromtheirlowdragbodydesignandcanmaintainnavigationonminimumenergyconsumption,whichenablethemtotransectseveralthousandskilometersatarelativelowspeed. 1.3MotivationHurricanesaregiant,spirallingtropicalstormsoccurringintheNorthAtlanticOceanortheNorth-EastPacicOcean.Astheincreaseofpopulationincoastalareas,thepotentialdamagebyhurricanesisabigthreattohumanlivesandproperties.HurricaneSandy'sstrikeinOctober2012tookawayatleast253people'slifeinsevencountriesandcausedlossesestimatedat65.6billionUSdollars.Eventhoughttheformationofhurricanesisstillthetopicofextensiveongoingresearchesandisnotfullyunderstood,themainfactorsmaycontributetotheformationareknownastheoceanwatertemperature,airpressureandhumiditynearthesurface.Thegradientdistributionofthesefactorsthroughoutair,oceansurfaceandunderseaareaswillhelpus 14

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ABluen21 BSeabed CGaviaFigure1-1. VariouspropelledAUVs. toobtainabetterunderstandingandforecastofthem.Asaresult,accuratemeasurementsandmonitoringofthesefactorsarethekeystohurricanestudies.Currentlymostofhurricanedatacomefromsatellites,whichisfarlessthanenough.NationalOceanicandAtmosphericAdministration(NOAA)beganaircrafthurricanesurveillancemissionsin1997.Eventhoughbetterdatathansatellitescomefromthesemissions,thehighcostandtheinherentdangertopeople'slivesprohibitdatacollectionatcriticallocationssuchasthehurricaneeyewall,themostdevastatingregion,andtheseaareasunderneath 15

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ASeaExplorer BX-Ray CSprayFigure1-2. Variousbuoyancy-drivenAUVs. thehurricane.TheimplementationofGlobalHawkunmannedaerialvehicle(UAV)lightenedupanewdirectionofweatherforecasting.Meanwhile,theimplementationofAUVshasshownincreasingsuccessandpromiseinmeetingspecicmarinedatacollectionrequirements.MonitoringthechangeofhurricaneformationfactorscanbeachievedbythecollaborationofUAVsandAUVs.LocalizationforsmallAUVsiscrucialinunderwatermissionssuchasoceanographicdatacollection.Nevertheless,underwaterlocalizationhasalwaysbeenachallengingproblemsinceunderwatervehiclescannotdirectlyutilizeGPS(globalpositioningsystem)duetotherapidattenuationofradiofrequencysignalsunderwater.Thisisexasperatedin 16

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ALastfourgenerations BCephaloBotFigure1-3. AUVsdesignedbyourgroup.Fromtherstgenerationtothefth:Hydro-Bu,RAV,CALAMAR-E,KRAKENandCephaloBot. dynamicoceanenvironmentswherethereasignicantbackgroundow;assuch,anumberofrecentstudieshavebeenaimedataddressingthisproblem[ 1 4 41 47 ].Tothebestofourknowledge,theimpactofstrongoceancurrentsontheaccuracyandfeasibilityoflocalizationmethodshasnotbeenconsideredintheseeorts.Inmanyapplications,thebackgroundowshouldnotbetreatedasasmalldisturbanceinputbecausesmall-scaleAUVsarenotcapableofghtingagainstittoapproachlocalizationreferencesandcorrectlocationestimateerror.Eitherignoringorunderestimatingtheimpactofthebackgroundowwillleadtofailuresinlocalizationandmissions.Fluid-basedmissionplanningtechniquesincorporatetheeectsofthebackgroundowintothemethodologyinordertotakeadvantageofthenatureofthehydrodynamicsystem;insteadofexpendinglargeamountsofenergycombatingtheoceancurrents,theAUVmaysimplyglidealongwiththebackgroundowforthemajorityofitsmission.Implementationofthisconceptintocontrolalgorithmsrequiresaconceptualmodelofthelarge-scaleowswhichcanbeusedintrajectoryplanningofthevehicle.LipinskiandMohseni[ 19 ]developedaridgetrackingalgorithmforecientcomputationandextractionofLagrangiancoherentstructures(LCS),whichrepresentsbarrierstotransportofuid 17

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particles.ThederivedalgorithmtracksridgesinthenitetimeLyapunovexponent(FTLE)eldateachtimestep,thenapproximatesthelocationofridgesatthenexttimestepbyadvectingtheLCSforwardwiththeow.Simulationsofthebackgroundowhavebeenutilizedtocharacterizerelationshipsbetweenoptimaltrajectoriesandcoherentstructuresinseveralworks[ 11 18 21 ].AprocedurefortrajectoryplanningbasedonLCSisoutlinedin[ 18 ]and[ 20 ].Theproposedhybridapproachyieldsnearoptimaltrajectoriesinthepresenceofastrongbackgroundowgivenacostfunctionthatcombinesfuelandtimecosts;thesetrajectoriesenableAUVstonavigateinstrongbackgroundoweldswithmoderatefuelusageandrelativelyhighpathfollowingaccuracy.Duringmostoftheirrun-time,AUVsmoveasdriftersandavoidghtingagainsttheow,ensuringbothnavigationaccuracyandendurance. 1.4MethodologyByfollowingtheow-adaptedoptimaltrajectoriesfoundbythemethodin[ 18 ]and[ 20 ],AUVscanmaintainboundedlocalizationerror.ConsideringtheseAUVsasmovinglocalizationreferences,weproposeadistributedmother-daughtercooperativelocalizationhierarchytoimprovethelocalizationofotherlow-cost,less-capableoceanicmeteorologicaldatacollectingAUVsthatsuerfromdead-reckoning(DR)error.Inthisinvestigation,weclassifyAUVsintwocategories:themotherAUVs(MAUVs)andthedaughterAUVs(DAUVs).MAUVsarebetterequippedwithastandardAUVsensorsuite,includinganinertialmeasurementunit(IMU),amagnetometerandaDopplervelocitylog.Theyfollowtheow-basedoptimalpathstomaintainboundedlocalizationerror.Additionalerror-boundingtechniquesarealsoavailableviapre-deployedbeacons;forexample,autonomoussurfacecrafts(ASCs),whichhaveaccesstoGPS,cancommunicatewithMAUVstosustainrelativelymoreaccuratelocalizationestimatesthroughthemovinglong-baseline(MLBL)method[ 5 43 ].Less-capableDAUVsaresmallerinsizeanddonotcarryhigh-accuracysensorsandequipmentduetoinherenthighexpenses.TheseDAUVsaredesignedtobedeployedinlargeamountsasoceanicmeteorologicaldatacollectorsand 18

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Figure1-4. Diagramofthemother-daughterlocalizationhierarchy. navigateinareasfarfromASCs,ifdeployed.TheycanonlyutilizeMAUVsaslocalizationreferencestocorrecttheirDRerrorcausedbyIMUdrifting.Weassumethattheyarealsoequippedwithscope-limitedrangeandbearingsensorstodetectneighboringAUVsandtakeintra-AUVmeasurements.AllAUVsareassumedtohavetwo-waycommunicationcapabilitieswithin-rangeneighboringAUVs.ThegoalofthisworkistodevelopanalgorithmthatimproveslocalizationofDAUVsusingerror-boundedMAUVsasreferencesandsimultaneouslyslowsdowntheincreaseofDAUVs'DRerrorthroughintra-DAUVinteractionswhenMAUVsarenotavailable.AsillustratedinFigure 1-4 ,wheretherearetwoDAUVsandoneMAUV,DAUV-1utilizestheMAUVasareferencetocorrectitslocationestimateatlocation-AandperformsDRduringthetransitionfromlocation-Atolocation-B,whereittakesrelativemeasurementsandobtainslocalizationinformationofDAUV-2intheneighborhoodifDAUV-2hasabetterlocalizationestimate. 1.5ContributionofthisThesisInthisthesis,themother-daughterhierarchyisformulatedusingprobabilitytheoryandthegoalistondajointprobabilitydistributionoflocationsofallAUVs.Thistargetprobabilitydistributionndingproblemisdecomposedintoacooperativelocalization(CL)sub-problemandadynamicsimultaneouslocalizationandmapping(DSLAM)sub-problem.AmodiedextendedKalmanlter(MEKF)isintroducedtoaddresstheincompletecovarianceupdatingissuewhichariseswhenthetraditionalextendedKalmanlter(EKF)isnaivelyappliedtofullydistributedsystems.Consideringthepotential 19

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issuescausedbythelinearizationprocedurewhenapplyingtheMEKFinhighlynonlinearsystems,weadjustthestructureofthetargetprobabilitydistributionanddevelopaparticlelter(PF)basedalgorithmasacomparison.TheabilityofthePFtodescribemulti-modaldistributionsmakesitpossibletotrackmorethanonehypothesizedlocationssimultaneously,whichsignicantlyimprovespredictionaccuracy;however,thePFrequiresrelativelymorecomputationalcomplexitybecauseallparticlesneedtobeupdatedateachtimestep.Simulationresultsinthree-dimensionalbackgroundoweldsshowthatboththeMEKFalgorithmandthePFalgorithmcaneectivelyavoidthedivergentbehaviorofthelocalizationerroroccurringwhenperformingpureCL.TheupperboundofthelocalizationerrorisaectedbyseveralotherfactorsincludingtheinherentlocalizationerrorofreferenceAUVs,intra-vehiclemeasurementnoiselevels,actualAUVpathsundertheinuenceofbackgroundow,etc.ThisworkfocusesoninuencecausedbythenumberofreferenceAUVs.Thisworkhasbeenpublishedfromdierentperspectivesatseveralconferencesincluding:AmericanInstituteofAeronauticsandAstronautics(AIAA)Guidance,Nav-igationandControl(GNC)Conference[ 35 ];IEEE/RSJInternationalConferenceonIntelligentRobotsandSystems(IROS)[ 37 ];IEEEConferenceonDecisionandControl(CDC)[ 36 ];andAmericanControlConference(ACC)[ 38 ].Wealsosubmittedthejournalarticletitled"HierarchicalLocalizationforAutonomousVehicleSwarmsinthePresenceofDominatingBackgroundFlow"forpublication. 1.6ThesisOutlineAsacompletesummaryoftheworkduringthisperiodofstudyandresearch,sometechnicalachievementswillalsobeincluded.Theremainderofthethesisisorganizedasfollows: Chapter2:UnderwaterLocalizationHierarchy.Inthischapter,wesetuptheproblemandrepresentitintermsofprobabilitytheory.ABayesianstructureoftheformulatedproblemisderived.TheMEKFisgeneralizedandappliedtotheproposed 20

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problem.WediscusssolutionstoissuesthatarisewhennaivelyapplyingtraditionalEKFsinfullydistributedsystems.Asacomparison,weprovidethePFbasedalgorithmderivationadjustedforourproblem.Severalpotentialmatchingmethodsarediscussedtoaddressmismatchingbetweenintra-vehiclecommunicationandmeasurements. Chapter3:SimulationsinBackgroundFlows.Simulationsofbothproposedalgorithmsincommonbackgroundowpatternsareperformed,inbothdimensionalandnon-dimensionalmanners,toverifythevalidityoftheproposedalgorithms.Simulationresultsshowglobalboundednessoflow-costAUVs'localizationerrorandperformanceimprovementincomparisonwithpureCLisobserved.EectsofthenumberofreferenceAUVsonlow-costAUVs'localizationerrorarealsoinvestigated. Chapter4:ConclusionandFutureWork.Inthischapter,weconcludethiswork,restateourndingsinsimulationtests,highlightthecontributionofthisworkandprovidesomesuggestionsforimplementationofproposedmethodsinrealapplications.Potentiallimitationsandconcernsarediscussed.Futureworksareenvisionedtoaddressthem. Appendix:CephaloBot.TheappendixincludesanintroductionofthedesignofourfthgenerationAUVCephaloBot.Themechanicaldesign,electronicdesignandnovelvortexringthrusters(VRTs)willbediscussedbriey.Asmycontributiontothedevelopmentofthisvehiclefocusesontheembeddedsystemcontroldesigning,theentireembeddedcontrolsystemwillbeintroducedindetail. 21

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CHAPTER2HIERARCHICALCOOPERATIVEUNDERWATERLOCALIZATION 2.1UnderwaterSLAMSimultaneouslocalizationandmapping(SLAM)asksifitispossibleforamobilerobottoplaceitselfatanunknownpositioninanunknownenvironmentandfortherobottoincrementallybuildaconsistentmapofthisenvironmentandsimultaneouslydetermineitslocationinthemap[ 8 ].Ithasbeenconsideredasthe"holygrail"ofmobilerobotssincetherealizationofSLAMwillmakearobotfullyautonomousinmostpracticalenvironmentsoncepropersensorsareprovided.ThegenesisoftheprobabilisticSLAMproblemcanbedatedbackto1986atIEEERoboticsandAutomationConferenceheldinSanFrancisco,whentheprobabilisticmethodswerebeginningtobeintroducedintoroboticsandarticialintelligence(AI)communities.Overthenextfewyear,anumberofkeyworkswerepublishedbythepioneersincludingSmithandCheeseman[ 32 ]andHughDurrant-Whyte[ 7 ].Amongthem,thekeyelementwastoshowthattheremustbeahighdegreeofcorrelationbetweentherobotpositionestimatesandlandmarks'locationestimatesandsuchacorrelationwouldgrowwithsuccessiveobservations.Thishasbeenconsideredastheconceptualbreak-through.TheSLAMtechniquehasbeenintroducedintounderwaterapplicationsforyears.However,duetoconstrainssuchasthelackoflightanddistinguishablenaturalfeaturesinunderwaterscenario,underwaterSLAMapplicationsareusuallylimited.ThetechniqueintroducedinthisthesisisinspiredbytheoriginalSLAMformulation.Duetothesewell-knownlimitations,theoriginaltechniqueneedstobeadjustedtomeetourrequirements. 2.2ProbabilisticFormulationInordertomathematicallyrepresentthisproblemusingprobabilitytheory,wedenotethecollectionofallMAUVs'locationsattimestepkasMk,whereMk=fM1;k;M2;k;:::;Mm;kgandmisthetotalnumberofMAUVs.Thelocationofthei-thDAUVattimekisdenotedasDi;k.ThelocationcollectionofalltheotherDAUVsat 22

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timestepkisD)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k=fDnjn=1;2;;d\n6=iganddisthetotalnumberofDAUVs.ThelocationofDAUV-icanbeestimatedthroughaprobabilisticfunctiongiventhepreviouslocationDi;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1andthecontrolinputuk,whichistheIMUmeasurementfromtimek)]TJ /F1 11.955 Tf 12.46 0 Td[(1totimek.Arelativemeasurementattimekisdenotedaszk.Collectionsofcontrolinputsandrelativemeasurementsaredesignatedasfollows:Uk=fu0;u1;:::;ukg=fUk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;ukg;Zk=fz0;z1;:::;zkg=fZk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;zkg:ThejointposteriorprobabilitydistributionofallAUVs'locationsgiventhemeasurementhistoryandcontrolinputhistorycanberepresentedas P(Di;k;D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k;MkjZk;Uk):(2{1)SimilarrepresentationswereproposedbyWangetal.[ 44 ]intheSLAMwithdetectionandtrackingofmovingobjectsproblemindynamicenvironments.IncontrasttoWangetal.,whoalsoemployedstaticphysicalfeaturestoconstructamapasaglobalreference,hereweonlyutilizeMAUVsasdynamiclandmarks,whichtransformstheMAUV-aidedlocationestimatescorrectionproblemintoaDSLAMproblem.Inthiscontext,multi-DAUVcooperationisastandardCL[ 9 ]problem.ReadersarereferredtoMartinellietal.[ 22 ]andRoumeliotisandBekey[ 31 ]forrelatedworks.Bothliteraturesindicatethenecessityofhavingatleaseonevehiclewithgloballocalizationabilitiestoboundoveralllocalizationerroroftheentirevehiclegroup.TherecursivemotionpropagationandlocalizationupdatingprocessisdescribedinaBayesianlterstructurewiththeMarkovproperty.Forthereader'sreference,ageneralizedformoftheBayesianlterformulationfortheoriginalSLAMproblemispresented,inwhichtherearemultiplestaticlandmarksandtheirlocationsaredenotedasM=fm1;m2;:::;mNg,andonlyonevehiclewhosestateisdenotedasx.Thevehicleupdateitslocationestimationbasedonthecontrolinputu,usuallymeasuredbyproprioceptivesensorssuchasodometerforgroundvehiclesandIMUforaerialor 23

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underwatervehicles.Italsotakesdistanceandorientationmeasurementszrelativetolandmarksatacertainfrequency.ByapplyingBayes'ruleandthelawoftotalprobability,theposteriorprobabilityattimestepkcanbecalculatedasP(xk;Mjzk;uk)=P(zkjxk;M)ZP(xkjxk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;uk)P(xk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Mjzk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)dxk)]TJ /F7 7.97 Tf 6.59 0 Td[(1; (2{2)whereP(xk)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Mjzk)]TJ /F7 7.97 Tf 6.58 0 Td[(1;uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)istheposteriorprobabilityattimestepk)]TJ /F1 11.955 Tf 12.15 0 Td[(1;P(xkjxk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;uk)isthevehicle'smotionmodel;P(zkjxk;M)istheobservationormeasurementmodel;andisanormalizingconstant,ensuringtheprobabilitydistributionsumsto1.InspiredbythedecompositionmethodusedbyWangetal.in[ 44 ],adynamicBayesianlterstructurefortheformulatedproblemisdevelopedbyaddinginthemotionpropagationofMAUVsandinteractionamongDAUVs.Assumingmeasurementsatdierenttimestepsaremutuallyindependent,wecangroupthemas zk=zDk+zMk;(2{3)wherezDkareintra-DAUVsmeasurementsandzMkareDAUV-MAUVmeasurements.Hence,thecollectionofmeasurementsfromtimestep1totimestepkcanbedividedas Zk=ZD;k+ZM;k;(2{4)wherethetimestepindexkasasuperscriptindicatesthatthecorrespondingvariableisacollectionfromtimestep1totimestepk.Accordingly,dividingobservationsintheposteriorprobabilityin( 2{1 )intotwogroupsandperformingnecessaryalgebraic 24

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manipulationsbasedontheMarkovpropertyyieldP(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk;Uk)/P(zMkjDi;k;Mk)P(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)| {z }DynamicSLAMP(zDkjDi;k;D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)P(D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;kjZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)| {z }CooperativeLocalization: (2{5)TheposteriorprobabilitydistributionhasbeenfactorizedintoaDSLAMprobabilitydistributionandaCLprobabilitydistribution.Neitherdistributionisinastandardrecursiveupdatingform.Tointroducetherecursiveupdatingprocess,theposteriorin( 2{5 )canbefurtherfactorizedusingthelawoftotalprobabilitytoobtainP(Di;k;D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k;MkjZk;Uk)=PUpdateCLPPredictionCLPUpdateDSLAMPPredictionDSLAM; (2{6)wherePUpdateCL=P(zDkjDi;k;D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k); (2{7)PPredictionCL=ZP(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;kjD)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1)P(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)dD)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1; (2{8)PUpdateDSLAM=P(zMkjDi;k;Mk); (2{9)PPredictionDSLAM=ZZP(Di;kjuk;Di;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1)P(MkjMk)]TJ /F7 7.97 Tf 6.58 0 Td[(1)P(Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Mk)]TJ /F7 7.97 Tf 6.58 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)dMk)]TJ /F7 7.97 Tf 6.58 0 Td[(1dDi;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1: (2{10)Amoredetailedproofof( 2{5 )and( 2{6 )isprovidedasfollows. 25

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Proofof( 2{5 )and( 2{6 ). BasedonBayes'rule,thetargetposteriorprobabilitydistributioncanberewrittenasP(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk;Uk)/P(zkjDi;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;Mk;Zk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)P(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk): (2{11)Thenormalizationconstantisomittedhereandinfollowingderivations.BasedontheMarkovassumption,theobservationattimestepkdoesnotdependontheobservationhistoryorthecontrolcollection.So( 2{11 )canbefurthersimpliedasP(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk;Uk)/P(zkjDi;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;Mk)P(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk): (2{12)Dividingtheobservationcollectionintotwosub-groupsbasedonthemeasurementindependenceassumptionyieldsP(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk;Uk)/P(zMkjDi;k;Mk)P(zDkjDi;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k)P(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk): (2{13)Forsimplicity,whenwetalkaboutDAUV-i,theinteractionsamongalloftheremainingDAUVsandallMAUVsareignored,suchthatP(Di;k;D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k;MkjZk)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)=P(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk;D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)P(D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;kjZD;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk): (2{14) 26

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SincethejointprobabilityoflocationsofDAUV-iandMAUVsdoesnotdependonthelocationsofD)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k,( 2{14 )canbefurthersimpliedasP(Di;k;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k;MkjZk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)=P(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)P(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;kjZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk): (2{15)Given( 2{13 )and( 2{15 ),separatingthemeasurementprocedureandthemotionupdateprocedureyields( 2{5 ).ForneighboringDAUVsinthesensorrange,themotionupdateprocessisbasedonP(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;kjZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)=ZP(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;kjZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk;D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1)P(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1jZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)dD)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1=ZP(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;kjD)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1)P(D)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1jZD;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)dD)]TJ /F10 7.97 Tf 6.59 0 Td[(i;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1: (2{16)Similarly,thefactorizationofMAUVscanbeexpressedasP(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)=P(Di;kjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk;Mk)P(MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)=ZP(MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)P(Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk;Mk)P(Di;kjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk;Mk;Di;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1)dDi;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1: (2{17)Allstatesandcontrolsattimestepkinthesecondtermoftheintegralin( 2{17 )havenoeectsonthedistributionofDi;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1,so( 2{17 )canbesimpliedasP(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)=ZP(MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)P(Di;kjuk;Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1)P(Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Mk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)dDi;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1: (2{18) 27

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TotakeintoaccountmotionupdateofMAUVs,( 2{18 )canberewrittenbasedonthetheoremoftotalprobabilityasP(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)=ZZP(Di;kjuk;Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1)P(Mk)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.58 0 Td[(1)P(Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Mk)]TJ /F7 7.97 Tf 6.58 0 Td[(1)P(MkjZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk;Mk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)dMk)]TJ /F7 7.97 Tf 6.58 0 Td[(1dDi;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1: (2{19)SincemotionmodelsofMAUVsarenotknownbyDAUV-i,theirmotionupdateisbasedontheprobabilityP(MkjMk)]TJ /F7 7.97 Tf 6.58 0 Td[(1):Wecansimplify( 2{19 )andcombinethesecondandthethirdtermstoobtainP(Di;k;MkjZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)=ZZP(Di;kjuk;Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1)P(MkjMk)]TJ /F7 7.97 Tf 6.58 0 Td[(1)P(Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Mk)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.58 0 Td[(1)dMk)]TJ /F7 7.97 Tf 6.59 0 Td[(1dDi;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1: (2{20)Theformulatedproblemcannallybeexpressedas( 2{6 ). Thejointposteriorprobabilityisdecomposedintotwoseparatedprobabilitydistributions,namely,P(D)]TJ /F10 7.97 Tf 6.58 0 Td[(i;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZD;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.58 0 Td[(1)forCLandP(Di;k)]TJ /F7 7.97 Tf 6.59 0 Td[(1;Mk)]TJ /F7 7.97 Tf 6.59 0 Td[(1jZM;k)]TJ /F7 7.97 Tf 6.58 0 Td[(1;Uk)]TJ /F7 7.97 Tf 6.59 0 Td[(1)forDSLAM. Remark1. CLandDSLAMupdatingprocessescanbeperformedasynchronously.ThisisimportantinthedevelopmentofadistributedalgorithmbecauseoccurrencesofCLandDSLAMarebothrandom.Inaddition,duringeachintra-AUVinteractionphase,thedimensionalitythatneedstobeupdateddecreases,whichiscrucialinreal-timeimplementations.AstraditionalSLAMproblems,therearenoclose-formsolutionstoeitherprobabilitydistributionrecursion.TheextendedKalmanlter(EKF)[ 45 ]hasbeenwidelyusedin 28

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similarestimationproblems.However,foradistributedsystem,directlyimplementingtheoriginalEKFwillleadtomanyissues.WheneachDAUVmaintainsoneEKF,itscovariancematrixcontainstermsthatarerelatedtoallotherAUVs.DuringeachDSLAMorCLmeasurementphase,notalloftheotherAUVscanstayinthecommunicationrangeofthegivenDAUV.Therewillbetermsinthecovariancematrixthatcannotbeupdatedcorrectlyduetothelackofinformation.Toaddressthisissue,weneedtoadjustthetraditionalEKFforthisproblem. 2.3ModiedExtendedKalmanFilterBeforedirectlytargetingtheproblem,werstdiscussthedierencebetweentheMEKFandthetraditionalEKF.Thenafullstatemotionmodelandameasurementmodelareprovided.AnMEKF-basedalgorithmcoordinatingallAUVsispresentedindetail.Todevelopafullydistributedalgorithm,anAUVisnotrequiredtohaveknowledgeofothervehicles'dynamicmodelsortobeabletoestimateothers'locations.TheonlyexceptioniswhenotherAUVswithbetterlocalizationestimatesenterthesensorrangeofthisAUVandbetterlocalizedneighboringAUVstransfertheirlocationestimatestoit. 2.3.1MEKFSimilartotheoriginalEKF,theMEKFconsistsoftwophase,i.e.thepredictionphase,duringwhichvehiclesupdatetheirlocationestimatesbasedonthestatechangemeasuredusingproprioceptivesensors,andthecorrectionphase,duringwhichvehiclesupdatetheirestimatesthroughintra-vehiclemeasurementsandinformationexchange.Detailsaboutthesetwophasesarediscussedinthissection. 2.3.1.1MEKFpredictionThecorrelationrelationshipamongAUVsisimportant.RoumeliotisandBekey[ 31 ]investigatedthepropagationofcovariancematricesintherobotgroupinacentralizedformanddiscussedhowthisproblemcanbedecomposedintoadistributedform.Thecomputationisdistributedtomultiplerobotsbuttheentireestimatedstatevectorandthe 29

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covariancematrixarestillstoredinacentralizedmanner.Inouralgorithm,ontheotherhand,bothdatastorageandcomputationneedtobefullydistributed.EachDAUVhasauniquestatevectorandcovariancematrixdatastructure.Inthiscase,thetermsineachDAUV'sstatevectorandcovariancematrixcannotallbeupdatedsimultaneouslybecausenotalltheotherAUVsareinthecommunicationrange.WeneedtoruleouttermsthatarenotupdatedintheoriginalEKFstructure.Ingeneral,inthecaseofthreevehicles,thecovariancematrixstoredbyVehicle-1canbedescribedas=2666641112132122031033377775;wherecorrelationtermsbetweenVehicle-2andVehicle-3aredroppedo.ThemotionpropagationofVehicle-1canonlypartiallyaectthecovariancematrixtothedegree=266664Fx111FTx1+F!QFT!Fx112Fx11321FTx122031FTx1033377775;whereQisthecovariancematrixofthecontrolinputnoise.Fx1andF!areJacobianmatrices.Afterlstepsofmotionupdateswithoutinformationexchangewithothervehicles,thosenon-trivialcross-correlationtermsinthecovariancematrixturnintok+l1j=Fk+lx1Fk+l)]TJ /F7 7.97 Tf 6.58 0 Td[(1x1Fk+2x1Fk+1x1k1j;j=2;3:Tocompletethepredictionprocess,thesecross-correlationtermsalsoneedtobemultipliedbyFji=Fki+lxjFki+l)]TJ /F7 7.97 Tf 6.58 0 Td[(1xjFki+2xjFki+1xj;orFTji,whichiscalledJacobianmultipliersstoredinvehicle-jforvehicle-i(i=1;2;3).kiisthelasttimestepwhenVehicle-jmeetsVehicle-iandtransmitsinformationtoVehicle-i.Thesemultipliersarealsousedinmotionupdateprocessesofcovariancematricesof 30

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Figure2-1. Datastructureofstatevectors,covariancematricesandJacobianmultipliersstoredinDAUV-1(left)andDAUV-3(right)inthecaseofveDAUVsandtwoMAUVs. Vehicle-2andVehicle-3respectively.Therefore,informationneededtocompletethemotionupdatefromothervehiclesistheirownvariancejjtermsandaccumulatedJacobianmultipliersFj1sincetheirlastmeetwithVehicle-1.Cross-correlationtermsthatareonlyrelevanttovehiclesotherthanVehicle-1aresettozero.ThisisimportantsinceforVehicle-1,theKalmangainusedtoupdateitsownlocationestimatewillincludealltermsofthecovariancematrix.TermsthatarerelatedtoAUVsoutofthecommunicationrangecannotbeupdatedcorrectlyduringeachmeasurementphaseandtheywillintroduceerrorintothelter.ThenewcovariancematrixafterincorporatinginformationfromVehicle-3,forexample,willbe^=266664F1111FT11+F!QFT! F1112F1113FT31 21FT11220F3131FT11 033 377775;whereF31and33arefromVehicle-3andallunderscoredtermsareup-to-datesuchthattheycanbeusedinthecorrectionstep.Figure 2-1 showsdatastructuresinwhichinformationisstoredbytwoparticularDAUVs. 2.3.1.2MEKFcorrectionWhenVehicle-iincorporatesneighboringvehicles'localizationestimates,onlythoseinitssensorrange(denotedbyS)canpotentiallyprovidelocalizationcorrectioninformation. 31

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SeveraltermsinVehicle-i'scovariancematrixthatarerelevanttoneighboringvehiclesoutofthesensorrangecannotbeupdated.Applyingcorrectionequationswithoutrulingoutthesetermswillintroducelargemodelingerror.Toaddressthis,weintroduceaselectionmatrixwithsub-matricesj=8><>:I33forfj=ig[fj6=ijrijSg;033forfj6=ijrij>Sg;wherei=1;2;3,j=1;2;3,andrijisthedistancebetweenVehicle-iandVehicle-j.Thentheselectingmatrixhastheform=266664100020003377775:Wedenethemodiedcovariancematrixtobe^)]TJ /F10 7.97 Tf 0 -11.15 Td[(k+1=^)]TJ /F10 7.97 Tf 0 -11.15 Td[(k+1T;asthecovariancematrixwithonlyfullyupdatedtermsandzeroselsewhere.ThentheMEKFstateestimatecorrectionprocedurecanbecarriedoutbasedon k+1=)]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1+Kk+1[~zk+1)]TJ /F8 11.955 Tf 15.28 0 Td[(h(;0)];(2{21)whereKk+1istheKalmangainwiththeform Kk+1=^)]TJ /F10 7.97 Tf 0 -11.15 Td[(k+1HTH^)]TJ /F10 7.97 Tf 0 -11.15 Td[(k+1HT+Rk+1)]TJ /F7 7.97 Tf 6.59 0 Td[(1;(2{22)followedbythecovariancematrixcorrectionexpressedas ^k+1=^)]TJ /F10 7.97 Tf 0 -11.16 Td[(k+1)]TJ /F8 11.955 Tf 11.95 0 Td[(Kk+1H^)]TJ /F10 7.97 Tf 0 -11.16 Td[(k+1:(2{23) 32

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Theselectionmatrixltersouttermsthatcannotbeupdatedinthecovariancematrixtoguaranteethevalidityoftheupdatestep.Thefollowingexampleshowstheeectoftheselectionmatrixindetail.Inthethreevehiclescase,whenVehicle-3isobservedbyVehicle-1,thecovariancematrixbeforecorrectionandthecorrespondingselectionmatrixstoredbyVehicle-1are)]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1=2666641112132122031033377775andk+1=266664I303030303030303I3377775;whichgives )]TJ /F10 7.97 Tf 0 -8.27 Td[(k+1=k+1)]TJ /F10 7.97 Tf 0 -8.27 Td[(k+1Tk+1=266664110313030303310333377775:(2{24)IfweuseasimpleCartesianmeasurementmodel,(dx;dy;dz),tosimplifytheformofHforabetterexplanation,theinnovationcovariancematrixcanbecomputedasSk+1=H)]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1HT+Rk+1=11)]TJ /F8 11.955 Tf 11.95 0 Td[(13)]TJ /F8 11.955 Tf 11.95 0 Td[(31+33+Rk+1; (2{25)whereH=[)]TJ /F8 11.955 Tf 9.29 0 Td[(I303I3]andalltermsareupdatedcorrectly.ThentheKalmangaincanbecalculatedas Kk+1=^)]TJ /F10 7.97 Tf 0 -11.16 Td[(k+1HTS)]TJ /F7 7.97 Tf 6.59 0 Td[(1k+1=26666413)]TJ /F8 11.955 Tf 11.96 0 Td[(110333)]TJ /F8 11.955 Tf 11.96 0 Td[(31377775S)]TJ /F7 7.97 Tf 6.59 0 Td[(1k+1:(2{26)Finally,wehave Kk+1H)]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1=266664X1103X13030303X3103X33377775;(2{27) 33

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whereallXtermsonlyinclude11,13,31,33,andRk+1.Sothecorrectionprocessonlyaectscorrespondingtermsin)]TJ /F10 7.97 Tf 0 -8.27 Td[(k+1andonlythosecorrectlyupdatedtermsareusedinthecorrectionstep. 2.3.2MotionModel 2.3.2.1SinglevehiclemotionmodelUnlikemostgroundSLAMapplications,AUVsneedtobemodelledinthreedimensionswithsixdegreeoffreedoms(DOFs).Proprioceptivesensorsonvehicles,commonlyIMUs,providechangesinpositioninareal-timemanner.IMUsarewidelyusedinaeronauticandunderwaterapplications.Nowadays,theyarecommerciallyavailableinverysmalldimensionswithhighaccuracy.Theycommonlyhavethree-axisaccelerometerstoaidtheDRlocationestimation,three-axisgyrosformeasuringangularratesandcalculatingorientation,andmagnetometers.EventhoughintrinsicltersthatarebuiltinIMUsdecreasemeasurementnoisetosomedegrees,noisecannotbetotallyeliminatedandallIMUssuerfromdrifting.SinceDRisanerroraccumulationprocedure,anexteriorglobalreferencemustbeprovidedtocompensatethedriftinlongdistancenavigation.Manyo-the-shelfIMUsprovidethree-axisorientationinEuleranglesorinquaternions.Inthiswork,wendittobeconvenienttodirectlyusetheyaw,pitch,rollanglesinTait-Bryanconventions.WeassumeallAUVssharethesameNorth-East-Down(NED)earthxedcoordinatesystem,denotedasG,andEuleranglesinthissystemaredenedas(;; ),asillustratedinFigure 2-2 .ThecoordinatesystemattachedtothevehicleisdenotedasA.TheorientationofAwithrespecttotheNEDisdenedastheresultofthreeconsecutiverotationsaboutthex-axis,they-axis,andthez-axisbyangles ,,and,respectively.ThentherotationmatrixcanbeexpressedasGAR=266664cccss )]TJ /F1 11.955 Tf 11.95 0 Td[(sc csc +ss scsss +cc ssc )]TJ /F1 11.955 Tf 11.95 0 Td[(cs )]TJ /F1 11.955 Tf 9.3 0 Td[(scs cc 377775; 34

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Figure2-2. DenitionoftheNEDcoordinatesystem(left)andtheCADmodelofCephaloBot[ 14 { 16 24 ]withlocalandglobalcoordinatesystems(right). wherewehaves=sin()andc=cos()forsimplicity.Intuitively,giventherotationmatrixGARfromframe-Gtoframe-A,andtherotationmatrixABRfromframe-Atoframe-B,therotationmatrixfromframe-Gtoframe-Bcanbecomputedas GBR=GARABR:(2{28)IntheEuclidianspace,thesix-DOFsinglevehiclestatevectorattimestepkcanbeexpressedasxk=pTkoTkT=xkykzkkk kT;wherepk=[xkykzk]Tisthevehicle'slocationandok=[kk k]TistheorientationinEulerangles.Inoriginaltwo-dimensionalSLAMproblemsandmostothermobileroboticapplications,odometersandinertiasensormeasurementsareoftenutilizedascontrolinputstothevehicle'sdynamicmodel.Althoughthethree-dimensionalrotationcannotbeintuitivelyexpressedintermsofchangesinEuleranglesbecausetheyarecoupled,IMUscandirectlyprovidethemostrecentEuleranglesmeasurementsrelativetotheNEDcoordinatesystem.HereweuseEuleranglemeasurementsasorientationcontrolinputsandtheintegrationofthree-axisaccelerationstoexpressthevehiclevelocity.Therefore,thecontrolinputdrivesthevehiclefromstatexktostatexk+1canbeexpressed 35

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ask+1=xk+1yk+1zk+1k+1k+1 k+1T;andsuchaninputisassumedtobecorruptedbynoise.Giventhedenitionsabove,thesinglevehiclemotionmodelcanbesummarizedas xk+1=f(xk;k+1;k+1);(2{29)andthenoise-freemodelisintheformx)]TJ /F10 7.97 Tf 0 -8.27 Td[(k+1=f(xk;k+1;0)=Ik+1+I)]TJ /F8 11.955 Tf 8.8 -9.68 Td[(Ixk+Gk+1RIk+1t; (2{30)whereI=264033033033I33375;I=264I33033033033375;I=264I33033375T:Again,thesuperscript\)]TJ /F1 11.955 Tf 9.3 0 Td[("indicatesthatthecorrespondingvariableistheestimationbeforeincorporatingintra-AUVmeasurements.TherotationmatrixGk+1RdescribesthecurrentorientationrelationshipbetweentheNEDcoordinatesystemandthelocalcoordinatesystemofthevehicle. 2.3.2.2FullstatemodelLet'sexplaintheimplementationoftheMEKFwithrespecttoDAUV-1.Inadditiontothesix-DOFsinglevehiclemotionmodel,foreachoftheMAUVsandDAUVsotherthanDAUV-1(eitherinoroutofthesensorrange),athree-DOFstatevectordescribingeachvehicle'slocationisnecessary.ThefullstatevectorofDAUV-1canbewrittenas=xTD1pTD2pTDdpTM1pTM2pTMmT;whosedimensionisL1andL=6+3(d)]TJ /F1 11.955 Tf 12.37 0 Td[(1)+3m.DierentfromtheoriginalstaticSLAMproblem,the\landmarks"hereareMAUVs.Again,forDAUV-1,otherAUVs'motionmodelsandmovingpathsareunknown.Asaresult,correspondingstatesoftheseAUVsstoredinDAUV-1canonlybeupdatedwhentheyenterthesensorrangeand 36

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providetheirownlocationestimates.ThetotalcontrolinputvectorisalsoaL1vectorwiththeformu=TD1pTD2pTDdpTM1pTM2pTMmT;wherepDi(i=2;3;;d)andpMj(j=1;2;;m)arelocationestimatesoftheotherAUVsrespectively,updatedonlywhentheyenterthesensorrange.ThisdoesnotaectthevalidityofthisexpressionifonlythelocationofDAUV-1isofinterest.LocationsoftheotherAUVsaretrivialunlesstheyareusedinthelocalizationestimatecorrectionprocessofDAUV-1.Giventhedenitionsuptonow,thefullstatemotionmodelcanbewrittenintheform )]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1=f(k;uk+1;!k+1);(2{31)where!k+1isthefullstatecontrolnoisewiththemean0andthecovariancematrixQk+1.SameastheoriginalEKF,theMEKFlinearizesthenonlinearmotionmodelusingTaylorseriesexpansionandthemotionpredictionofDAUV-1isbasedon )]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1=ITL)]TJ /F2 11.955 Tf 8.8 -9.69 Td[(ILk+Gk+1RILuk+1t+ICuk+1;(2{32)whereIL=I3303(L)]TJ /F7 7.97 Tf 6.59 0 Td[(3);IC=26666403303303(L)]TJ /F7 7.97 Tf 6.59 0 Td[(6)033I3303(L)]TJ /F7 7.97 Tf 6.59 0 Td[(6)0(L)]TJ /F7 7.97 Tf 6.58 0 Td[(6)30(L)]TJ /F7 7.97 Tf 6.59 0 Td[(6)30(L)]TJ /F7 7.97 Tf 6.59 0 Td[(6)(L)]TJ /F7 7.97 Tf 6.58 0 Td[(6)377775:In( 2{32 ),thersttermtranslatesDAUV-1toanewlocationandthesecondtermupdatesvehicleorientationbasedonEuleranglemeasurements.TherotationmatrixusesupdatedEulerangles.Asmentionedabove,AUVs'motionmodelsandpathsarenotknownbyoneanothersoDAUV-1cannotestimatethelocationsoftheothers.Suchamotionupdatingprocesswillberepeatedateachtimestep,duringwhichthecovariance 37

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matrixalsoupdatesbasedon )]TJ /F10 7.97 Tf 0 -8.28 Td[(k+1=FkFT+F!Qk+1FT!;(2{33)wheretheJacobianmatricesarecalculatedasF=@f(k;uk+1;!k+1) @kandF!=@f(k;uk+1;!k+1) @!k+1: 2.3.3ObservationModelDAUV-1takesrangeandbearingmeasurementsrelativetoneighboringAUVsinitssensorscopeeverybtimesteps.Aconvenientwaytoexpressthosemeasurementsisinsphericalcoordinatesas[rnnn]T.Eachmeasurementisa31vectorintheform zn=sarccosznD1 satan2ynD1 xnD1T;(2{34)forfnjn2[D2;;Dd;M1;;Mm]\rnSg,wheres=p xnD12+ynD12+znD12,SistherangeofthesensorandxnD1=xn)]TJ /F5 11.955 Tf 12.24 0 Td[(xD1.Thenthemeasurementmodelcanbewrittenas ~zk+1=h)]TJ /F18 11.955 Tf 5.48 -9.68 Td[()]TJ /F10 7.97 Tf 0 -8.27 Td[(k+1;k+1=zT2;k+1zT3;k+1zTd+m;k+1T+k+1;(2{35)wherek+1isthemeasurementnoise,whichisalsoassumedtobewhiteGaussiannoisewiththemean0andthecovariancematrixRk+1. 2.3.4Intra-AUVDataFusion DAUV-MAUVDataFusion.SinceMAUVsnavigatealonguid-basedoptimalpathstosustaingoodlocalizationandMLBLcanpotentiallyfurtherboundlocalizationerror,MAUVsalwayshavebetterlocalizationaccuracythanDAUVs.Duringthemeasurementphase,DAUVsrstsearchforMAUVsforlocalizationcorrection.InthecasethatmorethanoneMAUVisdetectedinthesensorrange,theywillallbeused.MessagestransmittedamongAUVsaretaggedsuchthatonecanidentifytheAUVit'stalkingto.MAUVs'locationestimatesrequiredbyDAUVsaretransmittedalongwith 38

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theirvariancetermsjj(j=1;2;:::m)andtheaccumulatedJacobianmultiplierFjisincetheirlastmeet.Meanwhile,acquiredoceanicmeteorologicalmeasurementdatacanbetransferredtoMAUVs,whohavelargerstoragespaces.AftertheinteractionwithatleastoneMAUV,DAUVshavelocalizationaccuracynoworsethanotherDAUVs.Inthiscase,thegivenDAUVwillnalizethelocalizationcorrectionphase.However,whenMAUVsarenotdetected,theintra-DAUVinteractionmayhavesignicanteectsonDAUVs'localizationperformance. Intra-DAUVDataFusion.CLtakesplacewhentwoDAUVsenterintothesensorrangeofeachother.ThisprocessneedstobeconsideredcarefullybecauseeachDAUVhaslocalizationestimatesindierentaccuracyandnotallintra-DAUVinteractionsarehelpful.ItisbelievedthatthemeasurementusedbyaparticularAUVformorethanonceleadstoinconsistentorovercondentestimates[ 2 ].Toavoidthis,DAUVsdonottakerelativemeasurementswithrespecttothesameneighboringDAUVduringtwoconsecutivemeasurementphases.Meanwhile,eachDAUVtakesrelativemeasurementsandcommunicateswithatmostoneneighboringDAUVinthesensorrangeduringeachmeasurementphase.WhenmultipleneighboringDAUVsaredetectedsimultaneously,aproperselectingtechniqueisnecessarytoensurethatthebestlocalizedneighboringDAUVischosen.Withabsolutelocalizationerrorunknown,onereasonablealternativeisthevarianceoflocationestimates,whichdescribesthedegreeofspreadingoutoftheestimatedistribution.Inthethree-dimensionalcase,forexample,wechoosethetraceofthevarianceofDAUV-n,i.e.trace(nn),evaluatedbyDAUV-nitself.Algorithm-1brieydescribestheMEKF-basedlocalizationprocess. 2.4ParticleFilterSincetheirintroductionin1993[ 10 ],particlelters(PFs)havebeenappliedinestimationproblemstocomplementthedeciencyofKalmanltersinnon-linearnon-Gaussiancases.InPFs,theprobabilitydistributionisrepresentedbyasetof\particles"insteadoftherawandcentralmoments,i.e.themeanandvariance,which 39

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Algorithm1MEKF-basedalgorithmrunningoneachDAUV 1: repeatAlltimesteps 2: procedureMotionUpdate 3: forallDAUVsdo 4: Predictstatevectorsandcovariancematrices 5: UpdateallJacobianmultipliers 6: endfor 7: endprocedure 8: ifMeasurementtakesplace,then 9: procedureDataexchange&correction 10: forallDAUVsdo 11: ifpMAUVsinthesensorrangethen 12: forj=1topdo 13: Dataexchanging,relatedtermsupdating,MEKFcorrectionandJacobianmultiplierresetting. 14: endfor 15: elseifqDAUVsinthesensorrangethen 16: FindtheneighboringDAUVwiththesmallestvariancetrace. 17: Dataexchanging,relatedtermsupdating,MEKFcorrectionandJacobianmultiplierresetting. 18: else 19: Donothing 20: endif 21: endfor 22: endprocedure 23: endif 24: untilend enablesthemtodescribemulti-modalnon-Gaussiandistributions.Withoututilizinganylocallinearizationtechniquesorcrudefunctionapproximationmethods,PFstbetterinsystemswithhighnonlinearity.ComputationalcomplexityofPFsdependmostlyonthenumberofparticles,whichcanbeadjustedbasedontheapplication.Manyinvestigationshavebeendoneinregardstosolvingsingle-robotlocalizationproblemsusingPFs[ 6 ].Theyhavealsobeenappliedinmulti-robotlocalizationproblems[ 9 29 ],SLAMproblems[ 25 ]andunderwaterlocalizationproblems[ 3 ].Inthiswork,neitherpredeterminedmapsordistinguishablestaticfeaturesareavailable.WeneedtoderiveaPFstructurebasedonthetargetposteriorprobability. 40

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UnliketheMEKF-basedalgorithm,inPFs,DAUVsdonottrackMAUVs'locationchangesthroughincorporatingtheirJacobianmultipliersduringeachDSLAMcorrectionphase.Asaresult,locationsofMAUVscanbeconsideredasanothersetofgivenparameters,similartothemeasurementhistoryZkandcontrolinputhistoryUk.Moreover,thePFtrackstheentirepathhistoryofagivenDAUV.ForanyDAUV-i,theposteriorprobabilitydistributioncanbeexpressedasP(Dki;Dk)]TJ /F10 7.97 Tf 6.59 0 Td[(ijMk;Zk;Uk);inwhich,again,thesuperscriptkindicatesthatthecorrespondingparameterisacollectionfromtimestep1totimestepk.Basedonthechainruleofconditionalprobability,thisposteriordistributioncanbecalculatedthroughP(Dki;Dk)]TJ /F10 7.97 Tf 6.58 0 Td[(ijMk;Zk;Uk)=P(DkijMk;Zk;Uk)P(Dk)]TJ /F10 7.97 Tf 6.59 0 Td[(ijDki;Mk;Zk;Uk): (2{36)IflocationsofDAUV-iandallMAUVsarecalculatedorestimated,giventhemeasurementhistoryandcontrolhistory,locationhistoriesoftherestoftheDAUVscanbeindependentlydetermined,suchthat P(Dk)]TJ /F10 7.97 Tf 6.59 0 Td[(ijDki;Mk;Zk;Uk)=DdYn=D1n6=Di(nkjDki;Mk;Zk;Uk):(2{37)In( 2{36 ),thersttermcanbefurtherdecomposedbasedontheBayes'ruletoyield P(DkijMk;Zk;Uk)=P(MkjDki;Zk;Uk)P(DkijZk;Uk) P(MkjZk;Uk);(2{38)whereP(DkijZk;Uk)istheposteriorprobabilityofDAUV-i'spathbasedonitsmotionmodel.WedeneweightsofparticlesdrawnfromtheparticlesetofthemotionmodelasWMDi=P(MkjDki;Zk;Uk) P(MkjZk;Uk):TheseweightsaredeterminedfromthediscrepanciesbetweenMAUVs'locationscalculatedfromtheirmotionmodel,asexpressedbythedenominator,andestimated 41

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locationsbasedonthelocationofDAUV-iandDAUV-MAUVmeasurements,representedbythenumerator.Meanwhile,termsintheproductin( 2{37 )canberewritteninasimilarmannerbyusingBayes'ruleandthechainruletoyield P(nkjDki;Mk;Zk;Uk)=WMnWDinP(nkjZk;Uk);(2{39)whereWMnandWDinareweightsofparticlesdrawnfromtheparticlesetfromthemotionmodelofnandWMn=P(Mkjnk;Zk;Uk) P(MkjZk;Uk);WDin=P(Dkijnk;Mk;Zk;Uk) P(DkijMk;Zk;Uk):Thecompletedposteriorprobabilitycalculationcanbeexpressedas P(Di;Dk)]TJ /F10 7.97 Tf 6.59 0 Td[(ijMk;Zk;Uk)=WMDiP(DkijZk;Uk)DdYn=D1n6=DiWMnWDinP(nkjZk;Uk):(2{40)Byobserving( 2{40 ),onecannoticethat,foreachDAUV,theupdatingcanbeaccomplishedbyusingonePF.Eachparticlestoresapathestimateanditsweight:Particle-l:fDk;[l]i;w[l]k;Dig:Intra-DAUVmeasurementsandDAUV-MAUVmeasurementsareincorporatedbyassigningdierentweightstoparticles.Ingeneral,theweightofParticle-lofDAUV-iattimestepkiscalculatedbasedonw[l]k;Di/1 p 2Rkexp)]TJ /F1 11.955 Tf 10.5 8.09 Td[(1 2(zk)]TJ /F1 11.955 Tf 12.01 .17 Td[(^zk)TR)]TJ /F7 7.97 Tf 6.59 0 Td[(1k(zk)]TJ /F1 11.955 Tf 12.02 .17 Td[(^zk);whereRkisthecovarianceofthemeasurementnoise.Algorithm-2describesthestructureofthePF-basedalgorithm.DuringCLcorrectionphases,wechoosetheDAUVwhoseparticlesethasthesmallestvarianceasthebestlocalizedneighboringDAUV. 42

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Algorithm2PF-basedalgorithmrunningonDAUVs 1: repeatAlltimesteps 2: procedureMotionUpdate 3: forallDAUVsdo 4: forallParticlesdo 5: Retrieveaposefromthepaicleset 6: Predictthenewpose 7: endfor 8: endfor 9: endprocedure 10: ifMeasurementtakesplacethen 11: procedureDataexchange&Update 12: forallDAUVsdo 13: forallParticlesdo 14: ifpMAUVsinsensorrangethen 15: forj=1topdo 16: ReceivethelocationestimatefromMAUV-jandcalculateweightw[l]k;Di 17: endfor 18: elseifqDAUVsinsensorrangethen 19: ReceivethelocationestimateofthebestlocalizedneighboringDAUVandcalculatetheweightw[l]k;Di 20: else 21: Donothing 22: endif 23: endfor 24: endfor 25: endprocedure 26: procedureResampling 27: forallDAUVsdo 28: Samplethesameamountofparticleswhereeachparticleissampledwithaprobabilityproportionaltow[l]k;Di 29: endfor 30: endprocedure 31: endif 32: untilend 2.5MatchingMethodsInmulti-AUVcooperation,matchingmethodsareveryimportantowingtothefactthatincorrectdataassociationwillcauseundesiredconsequences[ 42 ].HerewefocusonthedataassociationproblemwhenmultipleneighboringDAUVsare 43

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detectedsimultaneouslybyaparticularDAUV.WhenallDAUVshavethesamemeasurementsensorscopes,mutualdetectionoccursatthesametime.Weassumethatthemeasurementdelaycanbeignoredandthecommunicationrangeisnotlessthanthemeasurementscope.ItisalsoassumedthatallDAUVsaresynchronized,theytakemeasurementsatthesamefrequencyanddatabeingexchangedaresentoutassoonasneighboringDAUVsaredetected.Inthiscase,theself-locationestimatefromtheotherDAUVisevaluatedatthetimestepwhentheintra-DAUVmeasurementtakesplace,eventhoughtheremayexistcommunicationdelays.WhenmorethanoneneighboringDAUVsaredetectedsimultaneouslybyagivenDAUV,dataassociationisrequiredtodeterminethecorrespondencerelationshipbetweenmeasurementsanddatasentbyneighboringDAUVs.InthecaseshownbyFigure 2-3 ,DAUV-2andDAUV-3aredetectedbyDAUV-1.Basedontheprecedingpartofthetext,DAUV-1receivesdatafrombothneighboringDAUVs.WedenotethemeasurementstakenbyDAUV-1relativetotheothersas1r12and1r13.DAUV-3takesmeasurementsrelativetoDAUV-2,denotedas3r32.AssumeIMUsonallDAUVsarecalibratedwithrespecttothesameinertialframeandthemagnitudeofallmeasurementsjrijjaremuchlargerthanthelocalizationerrorofeachDAUV.TherotationmatrixbetweenthelocalcoordinatexedtoDAUV-1andthelocalcoordinatexedtoDAUV-3,called13R,canbecalculatedwhenIMUEuleranglemeasurementstakenbyDAUV-3aresenttoDAUV-1.Toguaranteecorrectdataassociation,3r32isalsorequiredtobesenttoDAUV-1,suchthat 1~r12=1r13+13R3r32:(2{41)If1~r121r12,thisisthecorrectmatching.AnothermoregeneralmatchingmethodappliestothecasediscussedaboveaswellasthecasewhenneighboringDAUVsarenotnecessarilymutuallydetectable(Figure 2-4 ).Inthiscase,themeasurement3r32isnotavailable.However,sinceIMUsusedbyallDAUVsarecalibratedwithrespecttothesameinertialframeF,positionvectorsofall 44

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Figure2-3. DatamatchingCase-1.MorethanoneneighboringDAUVsaredetectedatthesametimeandneighboringDAUVsaremutuallydetectable. threeDAUVsinthisframecanbeexpressedbyFp1,Fp2andFp3respectively.TheyareestimatedbyeachcorrespondingDAUV.Fp2andFp3aresenttoDAUV-1whenDAUV-2andDAUV-3detectit.Giventhisinformation,DAUV-1isabletocalculateestimatedpositionrelationshiprelativetoneighboringDAUVsasF~r12andF~r13.Theseexpectedmeasurementscanbecalculatedas1~r12=F1R)]TJ /F7 7.97 Tf 6.58 0 Td[(1(F~r12)]TJ /F6 7.97 Tf 9.3 4.94 Td[(Fp1);1~r13=F1R)]TJ /F7 7.97 Tf 6.58 0 Td[(1(F~r13)]TJ /F6 7.97 Tf 9.3 4.93 Td[(Fp1);whereF1RcanbeobtainedfromIMUEuleranglemeasurementstakenbyDAUV-1.Thecorrectmatchingshouldapproximatelymeet1~r121r12and1~r131r13: 2.6SummaryBoththeMEKF-basedalgorithmandthePF-basedalgorithmarefullydistributed.ForeachDAUV,allcomputationneededisperformedbyitself.Duringeachupdatingstage,termsthatarerelatedtoirrelevantvehiclesdonotaectthecomputation.Withthedesignedmatchingtechnique,bothalgorithmsareapplicableforgroupsofheterogeneousAUVs.Oneshouldnoticethattheproposedlocalizationmethodsdonothavespecic 45

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Figure2-4. DatamatchingCase-2.MorethanoneneighboringDAUVsaredetectedatthesametimebutneighboringDAUVsarenotmutuallydetectable. requirementsonthepathofeitherMAUVsorDAUVs,whichmakesitpossibletoapplythemtoawiderangeofscenario. 46

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CHAPTER3SIMULATIONSINBACKGROUNDFLOWSUnlikegroundoraerialcounterparts,underwatervehicles,especiallyinsmallsizes,areoftennotcapableenoughtoghtagainstnaturalenvironmentalforcesinordertonavigatefreelyandapproachlocalizationreferencestocorrectlocalizationestimation.Duetolimitedon-boardpowerandactuationcapability,movingalongthebackgroundowasdriftersasmuchaspossibleisthebestwaytoguaranteebothsafetyandeciency.Totesttherobustnessoftheproposedalgorithms,backgroundowpatternsincluding2-Ddouble-gyre,owonthecylindersurfacegeneratedby3-Ddouble-gyreandowonthespheregeneratedbythreemovingvorticesareusedinfollowingsimulationtests.Alltheseowpatternsaresimpliedoranalogousmodelsofpracticaloceancurrents.Thereforesimulationsinthesescenariowillsomehowreectthepracticalperformanceofouralgorithms. 3.1Algorithm-1intheDouble-gyreFlowFieldThedouble-gyrephenomenainlarge-scaleoceancirculationistypicalofthenorthernmid-latitudeoceanbasins.Itisquitedominantandpersistentinoceansandconsistsofasub-polarandasub-tropicalgyres.Thetimedependentdouble-gyreisanoscillatingperturbationtotwocounter-rotatinggyres.It'satypeofoceancirculationwhoseseveralmainfeatureshavebeenidentiedbyanalyzingtheobservationaldataaswellasbynumericalsimulationsbySpeichandGhil[ 40 ],Jiangetal.[ 12 ],andSpeichetal.[ 39 ].Thedouble-gyreexamplehasbeenusedextensivelyinotherapplicationsandischosensinceitiswellunderstoodandbearssomeresemblancetooceangyres.Theowisgivenbythestreamfunction(x;y;t)=Asin(f(x;t))sin(y); (3{1) 47

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AForward BBackwardFigure3-1. TheforwardandbackwardFTLEeldsforthetimedependentdouble-gyresystemattimet=0withA=0:1=0:1,!=2=10,andT=)]TJ /F1 11.955 Tf 9.3 0 Td[(15,whichgivesasystemwithanoscillationperiodof10[ 20 ]. andthevelocityeldisgivenbyu=)]TJ /F5 11.955 Tf 10.5 8.09 Td[(@ @y; (3{2)v=@ @x: (3{3)Thenthevelocityeldforthetimedependentdouble-gyresystemcanbecalculatedasu=)]TJ /F5 11.955 Tf 9.3 0 Td[(Asin(f(x))cos(y); (3{4)v=Acos(f(x))sin(y)@f @x; (3{5)wheref(x;t)=a(t)x2+b(t)x; (3{6)a(t)=sin(!t); (3{7)b(t)=1)]TJ /F1 11.955 Tf 11.96 0 Td[(2sin(!t): (3{8)AcasewithchosenparametersisshowninFigure 3-1 .AsnapshotofthevelocityeldcanbeseeninFigure 3-2 48

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Figure3-2. Thedouble-gyrevelocityeldattimet=T=4,maximumeastward(rightward)perturbation[ 20 ]. 3.1.11-DAUVCaseInthiscase,oneDAUVisusedtotesttheperformanceoftheDSLAMportionoftheMEKF-basedalgorithm.OneMAUVmovesalongthebackgroundowasthelocalizationreference,ormovinglandmarkfortheDAUV.ActualpathsandpathestimatesareshowninFigure 3-3 .TheDAUVpredictsitslocationusingIMUdataandupdatestheestimatebyobservingtheMAUV(redcross).ThelocalizationuncertaintygrowswhentheMAUV(pathshownasbluedashline)isoutofthesensorrange.Theestimatedpath(darksolidline)deviatesfromtheactuallypath(pinkdotdashline).WhentheMAUVentersthesensorrangeoftheDAUV,theestimatedpathgetscorrected.Theresidualiscausedbyobservationnoise,whichistherelativemeasurementuncertainty.Figure 3-4 showslocalizationerroroftheDAUV.Theyvaluesindicatepatherrormeanofthevehicleateachtimestep.Magnitudesoferrorbarsarethesquarerootsofsumsofcovariancesinxandydirections.BoththemeanandthecovarianceincreasewhenvehicleperformsDRanddecreasewhenobservationsaretaken. 3.1.23-DAUVCaseTheperformanceoftheentirealgorithmisthentestedusingthreeDAUVsandoneMAUVinthedouble-gyreenvironment.Actualpathsandpathestimatesareshownin 49

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Figure3-3. SimulationofDSLAMusingoneDAUVandoneMAUV. Figure3-4. LocalizationerroroftheDAUV. Figure 3-5 .Solidlinesrepresentestimatedpathsofeachvehicle.Relativeobservationsaretakenwhenvehiclesentersensorrangesofeachother.Theserelativemeasurementsamongvehiclesslowdowntheerrorincrease.Figure 3-6 showslocalizationerrorofDAUV-1,DAUV-2andDAUV-3respectively.Comparedwiththeone-DAUVcase,theerrorincreasingrateismuchsmallerduetorelativeobservationsandthelocalizationestimatesexchangingamongDAUVs.Inthesimulationtimerange,thefusionofCLandDSLAMboundslocalizationerroratasatisfactorylevel. 50

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Figure3-5. SimulationofCLandDSLAMusingthreeDAUVs. Figure3-6. LocalizationerrorofeachDAUV.DAUV-1(top),DAUV-2(middle),andDAUV-3(bottom). 51

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3.2Algorithm-1intheFlowFieldGeneratedbyFourConvectionCellsAroundaCylinderInthissimulation,weconsideranextensionofthedouble-gyreoweldinathree-dimensionspace.Athree-dimensionextensionofthedouble-gyreisconstructedbyLekienandRossin[ 17 ]usingfourRayleigh-Benardconvectioncellswrappingaroundacylinder.Thetwo-dimensionmodelofRayleigh-BenardconvectioncellsisintroducedbySolomonandGollub[ 33 34 ].Theoriginalstreamfunctionisgivenas (x;y;t)=sin((1)]TJ /F5 11.955 Tf 11.96 0 Td[(g(t)))sin(y):(3{9)Thecylinderisparameterizedby )]TJ /F7 7.97 Tf 6.59 0 Td[(1:[0;4]h)]TJ /F5 11.955 Tf 10.5 8.08 Td[( 2; 2i!R3;(3{10) (1;2)7!(cos1 2;sin1 2;2 ):(3{11)Theresultingstreamfunctionisrepresentedas (1;2;t)=sin(1)]TJ /F5 11.955 Tf 11.96 0 Td[(g(t))sin(2+ 2);(3{12)whereg(t)isanoscillatingfunctionandaquasiperiodicrollmotionisusedheregiven g(t)=0:3sin(4t)+0:1sin(2t):(3{13)Inthissimulation,wechoosetheradiusofthecylinderas1500minordertoinvestigatetheboundednessofDAUVs'localizationerrorwhenapplyingtheMEKF-basedalgorithm.Figure 3-7 showspathsofoneMAUVandthreeDAUVsinthisoweld.AllAUVsaretreatedasdriftersasasimplication.MAUVsareassumedtohaveabsolutelocationerrorof[)]TJ /F1 11.955 Tf 9.3 0 Td[(1m;1m].TheaveragenavigationspeedofallDAUVsisaround5m/swiththeuncertaintyof[)]TJ /F1 11.955 Tf 9.3 0 Td[(0:1m=s;0:1m=s]ineachdirection.Themotionupdatingrateissetto1Hzandthemeasurementrateis0:1Hz.Themeasurementsensorrangeandthecommunicationrangearebothsetto100mandmeasurementerrorisboundedby 52

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Figure3-7. AUVs'pathsinthesimulationofoneMAUVandthreeDAUVsintheoweldongeneratedbyfourconvectioncellsaroundacylinder. [)]TJ /F1 11.955 Tf 9.3 0 Td[(1m;1m].TheperformancecomparisonbetweenpureCLandAlgorithm-1isshowninFigure 3-8 .DivergingdeviationsofestimatedpathsfromactualpathscanbeobservedfromFigure 3-8 A.Withoutlocalizationcorrection,DAUVs'localizationerrordivergesquickly,whichwillfurtherleadtomissionfailures.WhenanMAUVisaddedinasanoisymovinglocalizationreference,DAUVsareabletoavoidlargedeviations(Figure 3-8 B).Althoughdeviationsfromactualpathsstillexist,especiallywhenanMAUVisnotintheirsensorranges,DAUVscancontinuecollectingvaluabledatawhenlocalizationerrordropsinacceptableranges.EectsofthenumberofMAUVsareinvestigatedinFigure 3-9 .ByincreasingthenumberofMAUVs,weprovideDAUVsmoreopportunitiestoperformDSLAMcorrectionwithMAUVs.Decreasesinlocalizationerrorupperboundscanbeobserved.Meanwhile,asDAUVsmeetMAUVsmorefrequently,theeectofintra-DAUVCLbecomesmoresignicant.WhenaparticularDAUVnishesDSLAMcorrectionwithatleastone 53

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APerformingpureCL BPerformingAlgorithm-1Figure3-8. ComparisonbetweenpureCLandAlgorithm-1withoneMAUVsbasedonlocalizationerrorofthreeDAUVs. AAlgorithm-1withtwoMAUVs BAlgorithm-1withthreeMAUVsFigure3-9. LocalizationerrorofthreeDAUVswhenperformingtheAlgorithm-1withdierentnumbersofMAUVs. MAUV,itcanactasasub-optimalMAUVduringCLsuchthattheeectofDSLAMspreadstroughtheDAUVswarm. 3.3Algorithm-1intheFlowFieldGeneratedbyThreeVorticesonaSphereSurfaceWethenconsideranothercommonglobal-scaleowpatterngeneratedbyNmovingvorticesonthesurfaceofasphere.Thisowpatterniswidelyusedingeophysicaluiddynamicswhenconsideringlarge-scaleatmosphericoroceanographicowswithcoherentstructuresthatpersistoveralongperiodoftimeandmoveoverlargedistances.Thisowpatterncanbeappliedasasimpliedmodelofglobaloceancurrentsbyignoring 54

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interactionswithlands[ 27 ].Inthismodel,oceanvorticesaresimulatedwithmovingpointvortices.Theresultingowpatterncanbeusedinmeteorologicalstudiesincludinghurricanesimulationsandoceancurrentsimulations[ 30 ].Inthiswork,wefocusonaspecialsolutiondiscussedbyKidambiandNewtonin[ 13 ],wherethreevorticesareusedforsimplicitywithoutlossofgenerality.Figure 3-10 showsthebasicgeometryassociatedwiththe3-vortexcongurationonasphere.Thecenterofvorticityvectorforthesystemisgivenby c=M )]TJ /F5 11.955 Tf 11.23 8.2 Td[(;(3{14)where M=NXi=1)]TJ /F10 7.97 Tf 7.31 -1.79 Td[(ixi(3{15)isthemomentofvorticity,and)]TJ /F2 11.955 Tf 173.63 0 Td[(PNi=1)]TJ /F10 7.97 Tf 7.32 -1.8 Td[(iisthetotalcirculation.Theanglebetweencandnisdenotesasandthechorddistancebetweentwovorticesarelij.VorticestravelundertheimpactofothersandtheirtravelingvelocitiescanbeexpressedintheCartesiancoordinatesystemas _xi=1 4RNXj6=i)]TJ /F10 7.97 Tf 7.31 -1.8 Td[(jxjxi R2)]TJ /F8 11.955 Tf 11.95 0 Td[(xixj;(3{16)wherexiisthelocationofvortex-i,)]TJ /F10 7.97 Tf 14.46 -1.79 Td[(jisthecirculationofvortex-jlocatedatxj,Nisthetotalnumberofvortices,andRistheradiusofthesphere.Alternatively,thevelocityeldcanalsobeexpressedas _x=1 4RNXj6=i)]TJ /F10 7.97 Tf 7.31 -1.79 Td[(j2(xjxi) l2ij;(3{17)where l2ij2(R2)]TJ /F8 11.955 Tf 11.96 0 Td[(xixj)=jjxi)]TJ /F8 11.955 Tf 11.96 0 Td[(xjjj2:(3{18)Inthisspecialcase,allcirculationsareassumedtobeconstant)]TJ /F7 7.97 Tf 333.58 -1.79 Td[(1=)]TJ /F7 7.97 Tf 20.5 -1.79 Td[(2=)]TJ /F1 11.955 Tf 9.3 0 Td[()]TJ /F7 7.97 Tf 7.31 -1.79 Td[(3=)-342(=1,suchthat l212=l223+l231andl223l231 l212=const.(3{19) 55

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Afterseveralmathematicalmanipulations,chorddistancescanbecalculatedas l12=2Rcos2ut 2+sin220sin2ut 21=2;(3{20) l23="l12(l12p l212)]TJ /F1 11.955 Tf 11.96 0 Td[(4R2sin220) 2#1=2;(3{21) l31="l12(l12p l212)]TJ /F1 11.955 Tf 11.96 0 Td[(4R2sin220) 2#:(3{22)where u=)-166(cos20 2R2(3{23)and0isthevalueofatt=0.Finally,formulasforCartesiancoordinatesofvorticesare: x1=)]TJ /F5 11.955 Tf 10.5 8.09 Td[(l23 l212l23q 4R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l212sin20sinut 2+2Rl31cosut 2;(3{24) y1=l23 l212l23q 4R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l212cosut 2)]TJ /F1 11.955 Tf 11.96 0 Td[(2Rl31sin20sinut 2;(3{25) z1=1 2R(2R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l223);(3{26) x2=l31 l212)]TJ /F5 11.955 Tf 9.3 0 Td[(l31q 4R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l212sin20sinut 2+2Rl23cosut 2;(3{27) y2=l31 l212l31q 4R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l212cosut 2+2Rl23sin20sinut 2;(3{28) z2=1 R(2R2)]TJ /F5 11.955 Tf 11.96 0 Td[(l231);(3{29) x3=q 4R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l212cosut 2;(3{30) y3=q 4R2)]TJ /F5 11.955 Tf 11.96 0 Td[(l212sin20sinut 2;(3{31) z3=1 2R(2R2)]TJ /F5 11.955 Tf 11.95 0 Td[(l212):(3{32)MoredetailsontheformulationoftheN-vortexproblemcanbefoundin[ 27 ].Wenon-dimensionalizetheproblemwithrespecttotheradiusofEarthR=6:371106mandthecirculation)-316(=8106m2=s.IfafullypassiveAUVisplacedatthenorth 56

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Figure3-10. 3-vortexcongurationonasphere[ 27 ]. Figure3-11. Trajectoriesofthreevorticesandapassiveparticleintheresultingbackgroundoweld. poleofthesphere,theresultingtrajectoryundertheimpactofthebackgroundowisshowninFigure 3-11 .Again,allAUVsareassumedtobetotallyow-driven.InitiallocationsofallDAUVsarechosenrandomlyonthesphere.ThemeasurementfrequencyisselectedbasedonTH=TM=33:3,whereTHisthehydrodynamictime-scale,whichcanbedeterminedfromthelength-scaleandthecirculation-scale,andTMisthemeasurementtime-scale.TwosimulationsareperformedbyusingzeroMAUVstoevaluatepureCLandusing 57

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twoMAUVstoevaluatethecombinationofCLandDSLAM.TheperformanceofpureCLisshownbyFigure 3-12 (top).LocalizationerrorofallDAUVsincreaseastheynavigate,eventhoughCLslowsdownthespeedoferrorincreasingthroughintra-DAUVmeasurementsanddataexchange.ErrorwillkeepincreasingandeventuallyallDAUVswillfailinlocalization.ThenweaddtwoMAUVsintothesimulation.ThesetwoMAUVshaveabsolutelocalizationerrorintherangeof[)]TJ /F1 11.955 Tf 9.3 0 Td[(1:510)]TJ /F7 7.97 Tf 6.59 0 Td[(5;1:510)]TJ /F7 7.97 Tf 6.59 0 Td[(5]andtheirinitiallocationsarealsorandomlychosen.LocalizationerrorofallthreeDAUVsisshowninFigure 3-12 (bottom).Muchbetterperformanceisobservedandlocalizationerrorisbounded.AlthoughlocationestimatecorrectionswithMAUVsdonothappenallthetime,divergingspeedsoferroraresmallercomparedtothenon-MAUVcase.ThisisanotherevidencethateectsofDSLAMspreadintheDAUVswarm. Figure3-12. NormalizedlocalizationerrorofeachDAUVwhenusezeroMAUVs(top)andtwoMAUVs(bottom)astime(normalized)proceeds. Inapplicationssuchasoceanographicdatacollection,theaccuracyoflocalizationplaysanimportantroleinthevalueofcollecteddata.Althoughexactunderwater 58

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AErrorinx-axis BErroriny-axis CErrorinz-axisFigure3-13. NormalizedlocalizationerrorofDAUV-1ineachaxis.Threeerrorranges,[)]TJ /F1 11.955 Tf 9.3 0 Td[(110)]TJ /F7 7.97 Tf 6.59 0 Td[(3;110)]TJ /F7 7.97 Tf 6.59 0 Td[(3],[)]TJ /F1 11.955 Tf 9.3 0 Td[(0:810)]TJ /F7 7.97 Tf 6.59 0 Td[(3;0:810)]TJ /F7 7.97 Tf 6.59 0 Td[(3]and[)]TJ /F1 11.955 Tf 9.3 0 Td[(0:510)]TJ /F7 7.97 Tf 6.59 0 Td[(3;0:510)]TJ /F7 7.97 Tf 6.59 0 Td[(3],areusetoevaluatetimestepportionsinparticularlocalizationerrorranges. Table3-1. Timestepportionindierenterrorranges. RangesBasedonBasedonBasedonBasedon10)]TJ /F7 7.97 Tf 6.59 0 Td[(3x-errory-errorz-erroroverallerror [)]TJ /F1 11.955 Tf 9.3 0 Td[(1:0;1:0]99.8%99.3%100.0%99.1%[)]TJ /F1 11.955 Tf 9.3 0 Td[(0:8;0:8]98.5%97.7%99.2%95.4%[)]TJ /F1 11.955 Tf 9.3 0 Td[(0:5;0:5]92.4%87.4%95.1%77.1% localizationisextremelydiculttoachieve,moderate-levellocalizationerrorissometimesacceptablesincemanyoceanographiccharactersdonotchangerapidlyoversmalldistances,ifatall.WeevaluateabsolutelocalizationerrorofDAUV-1ineachaxis.Givendierentlocalizationerrorranges,portionsoftimesteps,duringwhichthelocalizationerrorisboundedbythegivenranges,areanalyzedinTable 3-1 .Theseerrorrangescanbechosenbasedonspatialdistributionpropertiesoftheoceanographiccharactersbeingmeasuredinpracticalapplications.Thelargertheportionis,themoremeaningfulthecollecteddatawillbe. 3.4Algorithm-2intheFlowFieldGeneratedbyThreeVorticesontheSphereSurfaceUnderthesamesetupasthenon-dimensionalN-vortexoweldsimulationforAlgorithm-1,wefurthertestthePF-basedalgorithm.ThreeDAUVsandtwoMAUVsfollowthesamepathsasinthesimulationsforAlgorithm-1.EachDAUVmaintainsone 59

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PFwithftyparticles.Asacomparison,DAUV-1'sabsolutelocalizationerrorineachdirectionisevaluatedinbothFigure 3-14A andFigure 3-14B .Figure 3-14A evaluateslocalizationerrorbasedontheparticlewiththelargestweight.Sinceweightsreectlikelihoodofvehiclelocationsrepresentedbyparticles,theparticlewiththelargestweightrepresentsthemostlikelylocationgivenbothDAUV-1'smotionmodelanditsintra-AUVmeasurementswithrespecttoneighboringAUVs.Figure 3-14B evaluateslocalizationerrorbasedonweightedmeansofallparticlesateachtimestep.Smallererrorboundsareobservedcomparedtousingtheheaviestweightedparticle.Thisdoesnotcontradictthefactthatweightedparticlesarebetterthantherstmomentinrepresentingtheprobabilitydistributioninthisproblemsincetheweightedmeantakesweightsofparticlesintoconsiderationandputspreferencesintoparticularlocations.Inthecasewhenambiguityarises,whichresultsinmulti-modaldistributions,thePFcantrackmorethanonehypothesizedlocationsandswitchlocationestimatesamongmultiplehighprobabilitylocationsbasedonintra-AUVmeasurementswithoutlag.Moreover,thePFfocusescomputationandmemoryontrackingDAUVs'locationhypothesis.IntheMEKF,however,mosttermsinbothfullstatevectorsandcovariancematricescannotbeupdatedtimelybutstillarekepttoguaranteetheconsistencyofdimensions.Togetacloserlookattheperformancedierencebetweenbothalgorithms,werenethemotionupdatingperiodto0.0005,setDAUVmeasurementfrequencytobeevery10timestepsandsimulatebothalgorithmsunderthesamenoisesettings.Figure 3-15 presentslocalizationerrorofMAUVsrunningtheMEKFalgorithm.Figure 3-15A showslocalizationerrorofeachofthethreeDAUVswhenthereisnoMAUVandintra-AUVinteractionisdisabled.DRerrorkeepsincreasingastimeevolvesandDAUVswillnallybecomelost.TheperformanceofCLisshowninFigure 3-15B whereinteractionamongthreeDAUVsisenabled.TheincreasingoflocalizationerrorofeachvehicleissloweddownanderrortrendsofthreeDAUVsareverysimilarduetotheirestimationexchange.However,theiroveralllocalizationerrorstillkeepsincreasingduetothelackofglobal 60

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AMostweighted BWeightedmeanFigure3-14. DAUV-1'slocalizationerrorinx-axis,y-axisandz-axis,evaluatedbasedonboththeparticlewiththelargestweightandtheweightedmeanofallparticles. ADR BCL CCL&DSLAMFigure3-15. LocalizationerrorofeachDAUVwhenperformingtheMEKFalgorithmwithoneMAUVandthreeDAUVs. references.FinallyinFigure 3-15C ,oneMAUVisaddedintothesimulationandallDAUVs'localizationerrordecreasessignicantlyandiskeptbounded,whichisduetoinformationbroughtinbytheerrorboundedMAUV.Underthesamesetup,weapplythePFalgorithm.SimilarerrordivergingbehavoirisobservedinFigure 3-16A ,wherethereisnoMAUV,interactionamongDAUVsisdisabledandoneparticleisusedforeachDAUV.AsweenableCLandusetenparticlesforeachDAUV,muchbetterbutstilldivergingestimationerrorisresultedasshowninFigure 3-16B .ComparedwiththeMEKFalgorithm,CLinPFyieldsmuchsmoother 61

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ADRwithN=1 BCLwithN=10 CCL&DSLAMwithN=10Figure3-16. LocalizationerrorofeachDAUVwhenperformingthePFalgorithmwithoneMAUVandthreeDAUVsusingdierentnumbersofparticlesforeachvehicle. errortrends.ThisisouttothefactthatthePFalgorithmguaranteesthatonlybetterlocalizedDAUVsareconsideredasreferencesforothersinCL.IntheMEKF,instead,everyDAUVistreatedasareferencebyothersinCLsincetheyarehomogeneousinthissimulationandtheircovariancematricesarethesame.FinallyinFigure 3-16C ,allDAUVs'localizationerrorisboundedasseenintheMEKFcase.AlthoughthePFalgorithmachievessimilarperformanceastheMEKFalgorithm,onemayhavenoticedthatthelatteroutperformstheformerintermsoflocalizationerrorupperbounds,whichisbecausethenumberofparticlesisfairlysmalltocapturecorrectvehiclelocations.Asweincreasethenumberofparticlesto50and100(Figure 3-17 ),thePFalgorithmyieldssimilarorevenbetterresultsthantheMEKFalgorithm.Ingeneral,it'satrade-obetweendesiredlocalizationerrorboundsandthecomputationalcost.Althoughdecreasingthenumberofparticleswillimprovethecomputationaleciency,smallnumbersofparticleswillleadtoparticledeprivation,whichwillfurtherleadtoincorrectestimation.IntheMEKFalgorithm,eachDAUVperformsestimationcorrectionwithnomorethanoneneighboringAUV,eitherMAUVorDAUV,andeachDAUVpartiallytracksthestatusofalltheotherAUVs,whichmakesitscomputationalcomplexityroughlyproportionaltod2.InthePFalgorithm,sinceeachparticleneeds 62

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AN=50 BN=100Figure3-17. LocalizationerrorofeachDAUVwhenperformingthePFalgorithmusingoneMAUVandthreeDAUVswithdierentnumberofparticlesforeachvehicle. tobeupdatedandcorrectedwithnomorethanoneneighboringAUV,thecomputationcomplexityisproportionaltoNd.Figure 3-18 comparesthetimeusedbyAlgorithm-1andAlgorithm-2withusingdierentnumbersofparticles.Ingeneral,Algorithm-1outperformsAlgorithm-2withsmallnumberofparticles.ThelatterstartstomatchtheperformanceofAlgorithm-1whenthenumberofparticlesgoesbeyond30alongwiththeincreasingoftherunningtime.Asaresult,asthenumberofDAUVsincreases,thePFalgorithmcangeneratebetterperformancewithsimilarcomputationaleortastheMEKFalgorithm.Whenon-boardcomputationalresourcepermits,ThePFalgorithmwithlargernumbersofparticlescanprovidebetterlocalizationperformance. 63

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Figure3-18. ComputationaltimecomparisonbetweenMEKF-basedalgorithmandPF-basedalgorithmwithdierentnumberofparticles. 64

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CHAPTER4CONCLUSIONSANDFUTUREWORKThisworkintroducesadistributedcooperativelocalizationhierarchyforautonomousunderwatervehicles(AUVs)basedontherecentndinginoptimizedpathplanninginstrongbackgroundowelds.Thefeasibilityofimprovingtheperformanceofcooperativelocalizationbyusingseveralmobilelocalizationerrorboundedreferencesisveried.Theproposedproblemisdecomposedintoadynamicsimultaneouslocalizationandmapping(DSLAM)sub-problemwithmovingreferencesandacooperativelocalization(CL)sub-problem.DSLAMutilizeslocalizationerrorboundedmotherAUVs(MAUVs)asreferencestobounddivergingerrorinCL.Meanwhile,CLspreadstheeectofDSLAMamongthedaughterAUVs(DAUVs)swarm.ThemodiedextendedKalmanlter(MEKF)isproposedinordertoavoidincorporatingtermsthatarenotupdatedinstatevectorsandcovariancematricesandguaranteethatnecessarytermsareupdatedcorrectly.TotracklocationchangesofotherAUVs,theJacobianmultiplierisintroducedtocompletethemotionupdateprocess.AnMEKF-basedalgorithmisdeveloped.Asacomparison,wethenadjusttheprobabilityrepresentationoftheproblemanddecomposeitintoaformatthatissuitableforapplyingtheparticlelter(PF),whichhastheadvantageofmodellingmulti-modalnon-GaussiandistributionsbutrequiresmorecomputationalcomplexitycomparedwiththeMEKF.Simulationsinseveralbackgroundowpatternsareconducted:atwo-dimensiondouble-gyreoweld,anextensionofthedouble-gyreoweldinthree-dimensionspacebywrappingfourconvectioncellsaroundacylinderandtheoweldgeneratedbythreemovingvorticesonthesurfaceofasphere.InsimulationsfortheMEKFbasedalgorithm,withoutusingMAUVs,pureCLwiththreeDAUVsresultsinlocalizationerrordivergence.WhenoneMAUVisaddedin,DAUVs'localizationerrorisboundedandtheboundsdecreaseasweincreasethenumberofMAUVs.TheimportanceoflocalizationerroronthevalidityofcollecteddataisalsodiscussedaccordingtooneDAUV'slocalization 65

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errorineachdirection.Thecomparisonbetweenthetwoproposedalgorithms,theMEKF-basedalgorithmandthePF-basedalgorithm,showsthatthelaterfocusesmostofthecomputationaleortsinmoremeaningfulhypothesistrackingandyieldsbetteroverallperformanceintermsoflocalizationerrorbounds.Insteadofconsideringimpactsofthebackgroundowassmalldisturbancesorsimplyignoringthem,weincorporatetheminthelocalizationalgorithmdevelopmentasthedominatingpathplanningfactor.TheroleofthebackgroundowinAUVapplicationsshouldbefurtherre-evaluated.Ifproperlyutilized,itcanpotentiallybenetAUVs'performanceinnavigationandlocalization.Withmoreaccurateoceancurrentmodellingandsimulations,informationthatcanbeextractedfromthebackgroundowwillchangethewayweaddressunderwaterlocalizationproblems. 66

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APPENDIXACEPHALOBOT A.1OverviewCephaloBotisourfthgenerationAUVbuiltbytheInstituteforNetworkedAutonomousSystemsattheUniversityofFlorida,whichisacontinuationoftheworkdonebythegrouppreviouslyattheUniversityofColorado.TheentireAUVisredesignedwhilemaintainingthenoveltechnologiesofpreviousgenerations.Itisusedinmulti-vehiclecooperationresearches[ 35 ],bio-inspiredvehiclecontrol[ 46 ]aswellasthedevelopmentofbiologicallyinspiredvortexringthrusters(VRTs)[ 16 23 ].Thegoalofthegroupistohavemultiplelow-cost,massproducible,easilyoperable,individuallyexpandablevehicleswithcapabilityofintercommunicationandsimilarperformancefromvehicletovehicle.Theavailable15foottall,26footdiameter(60,000gallon)testingtank(Figure A-1 )providesagoodtestingledforsmallandhighlymaneuverablevehicles.Theabilitytorunmultiplevehiclesinanindoortesttankallowsfortestingalgorithmsinacontrolledlaboratoryenvironment.ComingfromthenaturalpropulsionofCephalopodaandjellysh,thebio-inspiredVRT(Figure A-2 )isdesignedtoprovidehigh-accuracy,low-speedmanueveringtounderwaterrobots,whichhasaminimaleectontheforward-dragproleofthevehicle,generatingcontrolforcesbysuccessiveingestionandexpulsionofjetsofwaterfromacavitymountedinthehullofthevehicle[ 15 16 ].InthisAppendix,abriefintroductiontothemechanicaldesign,electronicsystemdesignandtheembeddedcontrolsystemdesignofCephaloBotisprovided[ 14 ]. A.2MechanicalDesignCephaloBothasfourVRTs,twoactivebuoyancycontroldevices(BCDs)andonerearpropellertocovermanageabilitiesinallsixDOFs(Figure A-3 ).MoredetailsaboutthisAUVarelistedinTable A-1 .CephaloBotisseparatedintothreehullsections.Figure A-4 showstheCADmodelofthevehicle,whereitiseasiertoseethesectionsseparatedbysyringeringseals.ThefrontsectionhastwoVRTsandoneBCD.Thebacksectionalso 67

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FigureA-1. AUVtestingtank. FigureA-2. The4th-generationofthevortexringthruster. hastherearpropellermotor.Theprimarybatteriesandalltheelectronicsexceptformotorcontrolarehousedinthecentersection.Anadditionalpayloadsectionmaybeaddedtoincludeadditionalsensors,devices,and/orbatteries.Regulatedpoweranddigitalcommunicationlinesinterfacethepayloadtothecentersection.Whenassembled,the0.15m(6in)diameter,0.92m(36in)longvehicleweightsaneutrallybuoyant16kg(36lb).TheBCDscanchangethebuoyancyby1%tosubmergeorsurface,and2kgofinternalballastisadjustabletobalancethepitchofthevehicle. 68

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TableA-1. Vehiclespecications. ItemSpecication Mass16kg(36lb)Dimensions0.15m0.92m(6"36")Actuators4Vortexringthrusters,2Activebouyancy,RearpropellerEndurance12-25hours(dependingonmotoroperation,communication)SensorsIMU(3-axisaccelerometer,gyroscope,magnetometer),Depth(relativepressure),Acousticpositioning(relativetopinger)CommunicationsEthernet(whentethered),802.11g,XBee,AcousticModemProcessingNISingleBoardRIO(FPGA,Real-timemicroprocessor),PICmicrocontrollersSoftwareLabVIEWTM,embeddedC FigureA-3. FunctionalprototypeofCephaloBot. TheVRTisbio-inspiredbyjellyshandsquidpropulsion.Itwasdevelopedbythegroupandprovideslowspeedmaneuveringjetswhilestillallowingthevehicletomaintainastreamlineshape[ 15 16 23 24 ].TheseventhgenerationVRTsusedontheCephaloBotprovidethrustforswayandyawmodesofthevehiclebyusingbio-inspiredvortexrings FigureA-4. CADmodelofofCephaloBot. 69

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studiedinthegroup.TheseVRTsarecurrentlythesmallestvolumeVRTsascomparedtoanypreviousdesigniterations.Thevortexringactuationisprovidedbyarubbercavity,pistoncrank-armassemblyandafaceplatewithaspecicoutletdiameter.Thepurposeoftherubbercavityistomovewaterwhileconsistentlysealingtheinsideofthevehicle. FigureA-5. CADmodelofthe7thgenerationoftheVRT. BCDsareusedtomechanicallyadjustvehiclebuoyancyallowingforprecisedepthandpitchcontrolduringvehicleoperation.Theyareexposedtowaterthroughtwocylindricalinlets.AsshowninFigure A-6 ,eachBCDrequiresbi-directionalmotorcontrol,andanabsolutepositionoftheplungerthatcontrolsthepercentbuoyancyofthevehicle.Themotorhasa298:1gearratio,andcanthereforebeunpoweredwhilemaintainingthepositionoftheplungerevenwithwaterpressureapplied.Thevehicleistrimmedsuchthatitisneutrallybuoyantwhentheplungerisinthecenter.Movingtheplungerupordownchangestheamountofwaterinsidethevehicle,resultingina1%changeinbuoyancy. A.3EmbeddedSystemDesignTheembeddedsystemofCephaloBotwascustomdesignedbyPeterKleinetal.[ 14 ].ThisAUVneedstobeusedinworkingtowardsthegoalofhavingheterogeneousmultiplevehiclesensornetworkingcooperationbetweenthewaterandairmediums.Toachievethis,thevehiclerequiresairandwatercommunication,sparecomputationpower,andtheabilitytoquicklyaddnewsensors.Tomakeitfeasibletotestmultiplevehicles,eachonemustberobustandeasytohandleandoperate.Theembeddedsystemisseparated 70

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FigureA-6. CADmodelofoftheBCD. intomultipleprintedcircuitboards(PCBs).Apowerdistributionboardhandlesvoltageregulationandbatterycharging.Aninterfaceboardconnectson-boarddeviceswiththepowerboardandtheprocessingdevice.SmallerPCBsarelocatedthroughoutthevehicletoprovidespecicfunctionalitysuchasmotorcontrol,userinterface,orsimplywirerouting.Figure A-7 showselectronicslocatedinthecentersection,whereeverythingexceptformotorscontrollersandtheuserinterfaceislocated. FigureA-7. Embeddedsystemelectronicsofthecentersectionmountedonbatterypack. TheprimaryprocessingdeviceonCephaloBotisaNationalInstrumentssingle-boardRIO(sbRIO)9602.Ithasanon-board400MHzprocessorrunningreal-timeLabVIEWTMsoftware,128MBofRAM,256MBofash,a40MHz2MgateFPGAproviding110 71

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digitalI/Opins.ThecombinationofmicroprocessorsandtheFPGAwasproveneectiveinthepreviousgenerationvehiclewhereaCompactRIOwasused.Allofthelow-levelcommunication,interface,andcontroltasksarehandledontheFPGAleavingmicroprocessorsopentoperformhighlevelmissioncontrol.Inreal-timeapplications,the400Mhzreal-timeprocessorislittleusedbythebasesystem,andthereforeprovidessignicantcomputationalpowertotheresearcher. A.3.1VortexRingThruster(VRT)ControlModelTheVRTcontrolmodelisdesignedtoprovidemotorcontrolofVRTactuators.Figure A-8 showsthestructureoftheVRTcontrolmodel.Duetotherenovatedmechanicaldesign,thisgenerationofVRTactuatorhasgreatlyincreasedineciency.A12V,8.7WFAULHABER2232-012SRmicro-motorisusedtodrivetheVRT.Theprimarybatteryvoltageis14.8Vandthemotorworksunder12V.Itrequirestheleastamountofvoltageconversion.Beingabletocontrolthemotortoadesiredspeedrequiresadevicetothrottlethemotorandadevicetomeasuretheactualspeedofthemotor.AnintegratedH-bridgechipMC33926waschosenbecauseitincludesallrequiredfeatures.AsimplePWMsignalandadirectionsignalareallthechipneedsasinputsandithandlesalltherest.Evenacurrentfeedbackisprovidedtoallowformonitoringtheapproximatedcurrentdraw.TheFAULHABER2232-012SRalsohasanintegratedencoderproviding512countsperrevolutionofthemotor.An8-bitmicro-controllertakestheencoderinputandsendsaPWMsignaltotheH-bridge.Themicro-controllercommunicatesoverI2CwiththesbRIOtochangethespeedofthemotorandtoprovidefeedback.AtemperaturesensorisalsoplaceddirectlyunderneaththeH-bridgechiptoallowasimpleformoftemperaturecheck. A.3.2BuoyancyControlDevice(BCD)TheelectronicssolutionfortheBCDcontrolmodelisverysimilartotheonefortheVRT(Figure A-9 ).TheBCDhastwocavitiesthatlledwithwatertoadjustthebuoyancyofthevehicleby1%.Asaresult,theBCDmotorneedstobeabletoturnin 72

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FigureA-8. BlockdiagramoftheVRTcontrolmodel. bothdirectionsandthewaterlevelinthecavityneedstobeknown.ThesameH-bridgeasfortheVRTcanbeused.However,themotorchosendoesnothaveanon-boardencoder.TheencoderontheVRTmotorisincrementalandthereforewouldforgetwhereitwaswhenthedevicelostpower.A298:1gearratiogreatlyincreasesthetorqueofthemotortoenableittopushwateroutofthevehicleatdepth.Apotentiometer(anadjustableresistor)providestheencoding.Dependingontherotationofthepotentiometer,aknownvoltagewillbeoutputwhen5Visappliedacrossthepotentiometer,andthisvoltageismeasuredbythemicro-controller. FigureA-9. BlockdiagramoftheBCDcontrolmodel. A.3.3RearPropellerModelTherearpropellermodelprovidesmotorcontrolfortherearpropeller.Therearpropellermotorturnsinbothdirectionsatvariablespeeds.Thespeedismeasurableandcanbeusedtoassumeathrustoutput,correspondingtoaspeedofthevehicle.The 73

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samemicro-controllerandH-bridgechipastheVRTandBCDareused.Becausethemotorwillbespinningquickly,anormalquadratureencoderisusedoverapotentiometer(Figure A-10 ). FigureA-10. Blockdiagramoftherearpropellermodel. A.3.4UserInterface(UI)ModelThissimpleUImodelistobeusedbydiversandoperatorssothattheycanquicklydeterminethestatusofthevehicleandwhatpartofthemissionthevehicleistryingtoaccomplish(Figure A-11 ).Tothisextent,theUImodelincorporatestwohighbrightnessLEDsforimportantstatusinformation.TheLEDscanbeprogrammedtoshowleakstatusandkillswitchstatus.SeverallowerpowerLEDsarealsoprovidedforotherinformation,e.g.thesystempowerstatus.Adual7-segmentdisplayshowswhichstatethevehicleisin.Withtwodigits0-9,99statescanbeshown.Inadditional,blinkingandnon-standardcongurationscanincreasethisnumber.Aleaksensorisalsoincorporatedintothisboard.Ifthetwoleadsoftheleaksensorareconnectedbywater,asignalwillbesentfromthemicro-controllertothecentersectionsignallingaleak.Thecentersectionshouldthentellthevehicletosurface,anddisableallsystemswiththehopethattheymaybedriediftheygetwetwhilenoelectricityisowing. A.3.5PowerDistributionandMonitoring(PDM)ModelThePDMmodelprovidespowertovehiclesystemsandregulatesitsvoltagetowhateverisrequiredbyotherelectronics.Italsochargesandmonitorstheon-boardbatterypack.Table A-2 showsthevoltageandcurrentrequirementsofthevariouselectronicslocatedonthevehicle.Basedonthesevoltagerequirements,lithiumpolymer 74

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FigureA-11. Blockdiagramoftheuserinterfacemodel. batteriesarechosensincethesebatterieshavebeenusedonthepreviousvehiclewithgoodsuccesswithoutsafetyissues.Figure A-12 showsthelayoutofpowerdistribution.Asourceselectorallowsthesystemtorunothewalladapter(whichalsochargesthebatteries),ortwoseparatebatterypacks.AlmostallofthevoltageconversionisdoneusingDC-DCswitchingmodules.Thesemoduleshavebuiltinswitches,regulators,etc.andonlyneedexternalcapacitorsandinductors.Ananalogmultiplexerisusedtoinputvoltageandcurrentmeasurementstothemicro-controlleronthePDMformonitoringthesafetyofthesystem. FigureA-12. Blockdiagramofthepowerdistributionandmonitoringmodel. 75

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TableA-2. Voltageandcurrentrequirementsofon-boardelectronics. ComponentVoltage(V)Current(A)Power(W) 802.11Bridge90.43.6Xbeeradio3.30.30.99Acoustic50.10.5EthernetSwitch50.0010.005sbRIO200.255OpenLog50.010.05Micro-controller50.010.05ADC50.0010.005Batterycharger16.8/202.1536.12IMU50.0650.325Pressure90.010.09GPS3.30.150.495Temperature50.0010.005Leak50.0010.005VRT(4)5/120.01/0.526.24Buoyancy(2)5/120.01/0.89.65Rearpropeller5/120.01/224.05 A.3.6SensorInterfaceBoard(SIB)TheSIB(Figure A-13 )isdesignedtoeliminatecustomwiringbecausecustomwiringincreasesthetimerequiredtoassemblethevehicleandmayintroducemistakeswhenwiredincorrectly.TheSIBmountstheIMU,wirelessconnection,GPS,andthesbRIO.ThePDMisconnectedtotheSIBwhichroutesthepowerintothecorrectDB9connectors.Theseconnectorsthenconnecttotheintegratedconnectingboard(ICB)onthefrontandback.TheSIBalsoconnectstothepayloadbay. A.3.7IntegratedConnectingBoardICBsinbothfrontandbacksectionaretoprovideanerrorfreemethodofconnectingthevarioussmallerPCBslocatedinthefrontandbacktotheSIBlocatedinthecentersection.TheboardsalsoincludealeaksensorthatiswiredintothePDMmicro-controllerprovidingaveryfastresponsetimebecausetheleaksensorstateisnottransmittedoverI2C.ADB9serialconnectorisusedtoconnectthefrontandbacktothecentersectionofthevehicle.ThefrontthenconnectstotheUI,twoVRTboards,andaBCDboard.ThebackconnectstotherearpropellerboardinsteadoftheUIboard,butisotherwisethe 76

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FigureA-13. Blockdiagramofthesensorinterfaceboard. same.EachofthesesmallerboardsinthefrontandbacksectionsisconnectedtotheICBwithapolarized6-pinconnector(Figure A-14 ). FigureA-14. Blockdiagramoftheintegratedconnectingboard. A.4ControlSystemSoftwareDesignThesoftwareonCephaloBotconsistsofthelowlevelsoftware:motorcontrollers,localcommunicationbetweensystems,powerdistributionandmonitoring,andsensorreading;andthehighlevelsoftware:vehiclecontrol,missionplanning,anduserinterface.Ingeneral,MotorcontrollingprogramsarewrittenonPIC18F(45/25)K22fortheBCDandVRTmotors.LocalcommunicationisdoneusingtheI2Cprotocol.CommunicationlinesexistbetweenthemotorcontrollersandthesbRIO,andbetweenthepowerregulationboardandthesbRIO.ThesbRIOisthemasterandallPICsareslaves.ThepowerregulationsoftwarerunsonaPIC18F45K22.SensorsarereadbydigitalI/Osonthe 77

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sbRIOthroughmultiplecommunicationprotocolsinthesameVIincludingI2CandSPI(SerialPeripheralInterface).ThissectionfocusesonthehighlevelvehiclecontrolsoftwareandtheuserinterfacedesigndoneinLabVIEWTM.ThehighlevelcontrolsoftwareisdevelopedbasedonaNationalInstrumentSB-RIO9602inLabVIEWTM.AsimpleversionoftheuserinterfaceisshowninFigure A-15 FigureA-15. TheuserinterfacedesignedforCephaloBot. A.4.1MotionControlThe\Control"sectioncommandsallfourVRTs,twoBCDs,therearpropellerandtheUImodel.Allparameterscanbemanuallyinput.Akeyboardnavigationcontrolfunctionisbuiltintotheprogramtofacilitatethecontrolduringtests.ForVRTs,thevelocitysettingisseparatedfromtheH-bridgeenablingtopreventpotentialmotordamagecausedbyimpropersettings.Eachslavehasauniqueaddresssuchthatallof 78

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themcanbecommandedsimultaneously.CommunicationbetweenthesbRIO(master)andslavesisachievedutilizingtheI2Cprotocol. A.4.2InertialMeasurementAVECTORNAVVN-100IMUisusedtotakeaccelerationandorientationmeasurements(Figure A-16 ).ItwasthesmallestAttitudeandHeadingReferenceSystem(AHRS)onthemarketthenandtherstavailableinthesurfacemountpackage.Ithasabuilt-inKalmanltertodecreasemeasurementnoise.BothEuleranglesandquaternionsareavailablefororientationmeasurements.Thecontrolsystemreadsyaw/pitch/rollangles,three-axismagnetic,three-axisaccelerationsandthree-axisangularratesdirectlyfromtheIMUregister.TheonlydownsideofthisIMUisthatitdoesnotsupporttheI2Cprotocol.Asaresult,anSPIprotocolisimplementedinLabVIEWTMtointerfacetheIMUwiththesbRIO. FigureA-16. ThesizeoftheVECTORNAVVN-100surface-mountIMUcomparedwithaquartercoin. A.4.3DataLoggingWhenthevehicleisnavigatingunderwater,wirelessconnectionwillnotbeavailable.Anon-boarddatastorageisnecessarytologIMUoutputdataforpost-missionanalysis.OpenLogisanopen-sourcedataloggerthatwasdesignedtorecordserialinputstoatextleonaninsertedMicro-SDcardformattedwithanFAT32le-system.Thisdatalogger 79

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iseasytousedifsetproperly.However,theFPGAavailableontheSB-RIOhassomelimitationsintermsofhandlingthisdataloggingprocess: FPGAscannotreadormanipulateoatingpointnumbersduetotheirhardwarelimits; FPGAscannotread,manipulate,orstorestrings; FPGAsdonothaveanindependent,real-worldtimereferencewhentheyarenotconnectedtoone; FPGAscannotgroupelementsinanyformatotherthaninan1-dimensionalarrayofxedsizes.Inmostserialcommunicationprotocols,suchasSPIandI2C,receptionofdatatypicallyrequiresaclocklineinadditiontothedataline.However,OpenLogdoesnothaveapinforaclockline,andcompensatesforthisbyallowingthebaudratevalueinthecongurationletobemanipulated.SerialdataissenttoOpenLogin10-bitsizedpackets.Thersttwobitsofeachpacketarethestartbitstruethenfalse,followedbythe8bitsthatdeterminethevaluebeingsenttoOpenLog.Thereisnorequirementforastopbitfollowingbytetransmission.EachbytereadbyOpenLogisan8-bitsignedinteger,andcanthereforerepresentavaluefrom-128to127.EverybyteOpenLogreceivesonitsseriallineisrepresentedintheloglebythevalue'sASCIIrepresentation.Therefore,thenalloglecontainsastringoftheASCIIcharacters,eachrepresentingabyteOpenLogreceived.Figure A-17 illustratesthedataloggingprocess.TheIMUisconguredtooutputasetoftwelve32-bitoatingpointnumbersforeachreadcommandsenttotheIMU.ThesevaluesgettemporarilystoredinanarraysoadesktoplevelVIcandisplaythesevaluestothedriver.Fromhere,samplinginformationgetstransmittedtoOpenLog.SincedataisstoredinOpenLogasASCIIcharacters,thedatasenttoOpenLogmustbebrokendownintoindividualbytes.TherstitemsenttoOpenLogisthetimeatwhichtheIMUwassampledin32-bitunsignedintegerrepresentation.Therst8bitsofthis32-bitunsignedintegeraresenttoOpenLogandthecorrespondingASCIIcharacterisrecorded,followed 80

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bythesecond,third,andfourthsetsof8bits.Then,thearrayofdatavaluesfromtheIMUissenttoOpenLog.The32-bitoatingpointnumbersinthisarrayaresentsimilarlytohowthetimeintegerwassent;therst8bitsaresentandrecorded,followedbythesecond,third,andfourthsetsof8bitsforeachnumberinthearrayofIMUoutputs.OnceallofthedataforagivenIMUsamplinghasbeentransferredtoOpenLog,theloopiteratestorefreshtheIMUsample. FigureA-17. Dataloggingprocess. A.5SummaryFurtherworkneedstobedoneonCephaloBotincludingnishingthePDMmodel,somecommunicationmodelssuchastheacousticmodel,andahigherlevelautonomousnavigationcontrolsystem.Meanwhile,potentialimprovementscanbeappliedonthebodyshapedesignofthevehicletofurtherreducethedragandfacilitatetheassemblingandleaktesting.Furthermore,asmallerbutmorepowerfulversionofsbRIO,thesbRIO-9612,iscurrentlyavailable,whichhasbetterconnectivitybutonlyalmosthalfofthesize,makingitpossibletofurtherreducethevehicle'sdimensionandimprovefunctionalityinlaterdevelopment. 81

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REFERENCES [1] Aulinas,Josep,Petillot,YvanR.,Llad,Xavier,Salvi,Joaquim,andGarcia,Rafael.\Vision-basedunderwaterSLAMfortheSPARUSAUV."Proceedingsofthe10thIn-ternationalConferenceonComputerandITApplicationsintheMaritimeIndustries(COMPIT).Berlin,Germany,2011,171{181. [2] Bahr,A.,Walter,M.R.,andLeonard,J.J.\Consistentcooperativelocalization."RoboticsandAutomation,2009.ICRA'09.IEEEInternationalConferenceon.2009,3415{3422. [3] Bahr,Alexander.CooperativeLocalizationforAutonomousUnderwaterVehicles.Ph.D.thesis,MassachusettsInstituteofTechnology,Cambridge,MA,USA,2009.AAI0821762. [4] Bahr,Alexander,Leonard,JohnJ.,andFallon,MauriceF.\Cooperativelocalizationforautonomousunderwatervehicles."TheInternationalJournalofRoboticsResearch28(2009).6:714{728. [5] Curcio,J.,Leonard,J.,Vaganay,J.,Patrikalakis,A.,Bahr,A.,Battle,D.,Schmidt,H.,andGrund,M.\Experimentsinmovingbaselinenavigationusingautonomoussurfacecraft."OCEANS,2005.ProceedingsofMTS/IEEE.vol.1.2005,730{735. [6] Dellaert,F.,Fox,D.,Burgard,W.,andThrun,S.\MonteCarlolocalizationformobilerobots."RoboticsandAutomation,1999.Proceedings.1999IEEEInterna-tionalConferenceon.vol.2.1999,1322{1328vol.2. [7] Durrant-Whyte,H.F.\Uncertaingeometryinrobotics."RoboticsandAutomation,IEEEJournalof4(1988).1:23{31. [8] Durrant-Whyte,HughandBailey,Tim.\Simultaneouslocalisationandmapping(SLAM):PartItheessentialalgorithms."IEEERoboticsandAutomationMagazine2(2006):99{110. [9] Fox,Dieter,Burgard,Wolfram,Kruppa,Hannes,andThrun,Sebastian.\Aprobabilisticapproachtocollaborativemulti-robotlocalization."AutonomousRobots8(2000).3:325{344. [10] Gordon,N.J.,Salmond,D.J.,andSmith,A.F.M.\Novelapproachtononlinear/non-GaussianBayesianstateestimation."IeeProceedingsFRadarandSignalProcessing140(1993). [11] Inanc,T.,Shadden,S.C.,andMarsden,J.E.\Optimaltrajectorygenerationinoceanows."AmericanControlConference,2005.Proceedingsofthe2005.2005,674{679. [12] Jiang,Shi,Jin,Fei-fei,andGhil,Michael.\Multipleequilibria,periodic,andaperiodicsolutionsinawind-driven,double-gyre,shallow-watermodel."JournalofPhysicalOceanography25(1995).5:764{786. 82

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[13] Kidambi,RangachariandNewton,PaulK.\Motionofthreepointvorticesonasphere."PhysicaD:NonlinearPhenomena116(1998):143{175. [14] Krieg,M.,Klein,P.,Hodgkinson,R.,andMohseni,K.\AHybridclassunderwatervehicle:bioinspiredpropulsion,embeddedsystem,andacousticcommunicationandlocalizationsystem."MarineTechnologySocietyJournal:SpecialEditiononBiomimeticsandMarineTechnology45(2011).4:153{164. [15] Krieg,M.andMohseni,K.\Thrustcharacterizationofpulsatilevortexringgeneratorsforlocomotionofunderwaterrobots."IEEEJ.OceanicEngineering33(2008).2:123{132. [16] |||.\Dynamicmodelingandcontrolofbiologicallyinspiredvortexringthrustersforunderwaterrobotlocomotion."IEEETrans.Robotics26(2010).3:542{554. [17] Lekien,F.andRoss,S.D.\Thecomputationofnite-timeLyapunovexponentsonunstructuredmeshesandfornon-Euclideanmanifolds."Chaos20(2010):017504. [18] Lipinski,D.andMohseni,K.\Cooperativecontrolofateamofunmannedvehiclesusingsmoothedparticlehydrodynamics."Tech.rep.,AIAAGuidance,Navigation,andControlConference,Toronto,Ontario,Canada,2010. [19] |||.\AridgetrackingalgorithmanderrorestimateforecientcomputationofLagrangiancoherentstructures."Chaos20(2010):017504(9pp.).Doi:10.1063/1.3270049. [20] |||.\Amaster-slaveuidcooperativecontrolalgorithmforoptimaltrajectoryplanning."IEEEInternationalConferenceonRoboticsandAutomation.Shanghai,China,2011,3347{3351.PaperWeA212.2. [21] |||.\Feasibleareacoverageofahurricaneusingmicro-aerialvehicles."AIAAScitech2014.AIAApaper2014-0894.NationalHarbor,Maryland,2014. [22] Martinelli,A.,Pont,F.,andSiegwart,R.\Multi-robotlocalizationusingrelativeobservations."IEEEInternationalConferenceonRoboticsandAutomation(ICRA).2005,2797{2802. [23] Mohseni,K.\Zero-masspulsatileJetsforunmannedunderwatermaneuvering."AIAApaper2004-6386,Chicago,Illinois,2004.3rdAIAAUnmannedUnlimitedTechnicalConference,WorkshopandExhibit. [24] |||.\Pulsatilevortexgeneratorsforlow-speedmaneuveringofsmallunderwatervehicles."OceanEngineering33(2006).16:2209{2223. [25] Montemerlo,M.,Thrun,S.,andSiciliano,B.FastSLAM:Ascalablemethodforthesimultaneouslocalizationandmappingprobleminrobotics.SpringerTractsinAdvancedRobotics.Springer,2007. 83

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[26] Needham,J.andWang,L.ScienceandCivilisationinChina:Volume2,HistoryofScienticThought.HistoryofScienticThought.CambridgeUniversityPress,1956. [27] Newton,P.K.TheN-VortexProblem:AnalyticalTechniques.No.v.145inAppliedMathematicalSciences.Springer,2001. [28] Nocks,L.Therobot:Thelifestoryofatechnology.GreenwoodTechnographiesSeries.GreenwoodPublishingGroup,Incorporated,2007. [29] Prorok,A.,Bahr,A.,andMartinoli,A.\Low-costcollaborativelocalizationforlarge-scalemulti-robotsystems."RoboticsandAutomation(ICRA),2012IEEEInternationalConferenceon.2012,4236{4241. [30] Ross,N.Thedynamicsofpoint-vortexdataassimilation.Ph.D.thesis,UniversityofColoradoatBoulder,2008. [31] Roumeliotis,StergiosI.andBekey,GeorgeA.\Distributedmultirobotlocalization."IEEETransactionsonRoboticsandAutomation18(2002):781{795. [32] Smith,RandallC.andCheeseman,Peter.\Ontherepresentationandestimationofspatialuncertainly."Int.J.Rob.Res.5(1986).4:56{68. [33] Solomon,T.H.andGollub,J.P.\Chaoticparticletransportintime-dependentRayleigh-Benardconvection."Phys.Rev.A38(1988):6280{6286. [34] |||.\PassivetransportinsteadyRayleighBenardconvection."PhysicsofFluids(1958-1988)31(1988).6:1372{1379. [35] Song,Z.andMohseni,K.\Cooperativeunderwaterlocalizationinoceancurrents."ProceedingsofAIAAGuidance,Navigation,andControl(GNC)Conference.2013-5111.Boston,MA,2013. [36] |||.\Fluid-basedcooperativeunderwaterlocalization."52ndIEEEConferenceonDecisionandControl.Florence,Italy,2013,2300{2305. [37] |||.\Hierarchicalunderwaterlocalizationindominatingbackgroundowelds."IntelligentRobotsandSystems(IROS),2013IEEE/RSJInternationalConferenceon.Tokyo,Japan,2013,3356{3361. [38] |||.\ADistributedLocalizationHierarchyForAnAUVSwarm."AmericanControlConference(ACC).2014.Toappear. [39] Speich,S.,Dijkstra,H.,andGhil,M.\Successivebifurcationsinashallow-watermodelappliedtothewind-drivenoceancirculation."NonlinearProcessesinGeo-physics2(1995).3/4:241{268.URL http://www.nonlin-processes-geophys.net/2/241/1995/ [40] Speich,S.andGhil,M.\Interannualvariabilityofthemid-latitudeoceans:Anewsourceofclimatevariability."SistemaTerra3(1994).3:459. 84

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[41] Tan,Hwee-Pink,Diamant,Roee,Seah,WinstonK.G.,andWaldmeyer,Marc.\Asurveyoftechniquesandchallengesinunderwaterlocalization."OceanEngineering38(2011).14-15:1663{1676. [42] Thrun,S.andLiu,Y.\Multi-robotSLAMwithsparseextendedinformationlters."RoboticsResearch15(2005):254{266. [43] Vaganay,J.,Leonard,J.J.,Curcio,J.A.,andWillcox,J.S.\Experimentalvalidationofthemovinglongbase-linenavigationconcept."AutonomousUnderwaterVehicles,2004IEEE/OES.2004,59{65. [44] Wang,Chieh-Chih,Thorpe,Charles,andThrun,Sebastian.\Onlinesimultaneouslocalizationandmappingwithdetectionandtrackingofmovingobjects:Theoryandresultsfromagroundvehicleincrowdedurbanareas."IEEEInternationalConferenceonRoboticsandAutomation(ICRA).2003,842{849. [45] Welch,GregandBishop,Gary.\AnintroductiontotheKalmanlter."Tech.rep.,UniversityofNorthCarolinaatChapelHill,ChapelHill,NC,USA,1995. [46] Xu,Y.andMohseni,K.\Bioinspiredhydrodynamicforcefeedforwardforautonomousunderwatervehiclecontrol."Mechatronics,IEEE/ASMETransactionsonPP(2013).99:1{11. [47] Zhou,Yi,Chen,Kai,He,Jianhua,Chen,Jianbo,andLiang,Alei.\Ahierarchicallocalizationschemeforlargescaleunderwaterwirelesssensornetworks."HighPerfor-manceComputingandCommunications,2009.HPCC'09.11thIEEEInternationalConferenceon.June,470{475. 85

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BIOGRAPHICALSKETCH ZhuoyuanSongwasborninacommonfamilyinAnyang,Henan,China.HereceivedtheB.S.EdegreeinMechanicalandMechatronicEngineeringfromShanghaiUniversity,Shanghai,Chinain2011.HeiscurrentlyworkingtowardthePh.D.degreeinMechanicalEngineeringattheUniversityofFlorida,Gainesville,FL,USA.Hisresearchinterestsincluderobotics,multi-agentcollaboration,underwaterlocalizationandoceancurrentadaptedSLAM. 86