3comparing control strategies for automomous line-tracking robots.pdf

COMPARINGCONTROLSTRATEGIESFORAUTONOMOUSLINETRACKINGROBOTSLUISALMEIDA,ALEXANDREMOTA,PEDROFONSECAIDA,ALEX,PJTIAPTDEPARTAMENTODEELECTRONICAETELECOMUNICA5ESUNIVERSIDADEDEAVEIRO,P3810AVEIRO,PORTUGALTEL35134370859FAX35134381128ABSTRACTAUTONOMOUSMOBILEROBOTICSISAVERYEXCITINGAREAFORSTUDENTSPARTICULARLYFORTHOSEWHOATTENDCOURSESONELECTRONICSTHEAUTHORSHAVEBEENINVOLVEDINSEVERALACTIVITIESINTHISAREATOGETHERWITHSTUDENTSOFTHEUNIVERSITYOFAVEIROINPARTICULAR,ONEOFSTICHACTIVITIESISTOBUILDROBOTSTOFOLLOWALINEDRAWNONTHEJLOORINORDERTODOTHISEFFICIENTLYASIMULATORHASBEENIMPLEMENTEDANDUSEDTOTESTTHEINFLUENCEOFDIFFERENTCONTROLAPPROACHESTHISARTICLEPRESENTSABRIEFDESCRIPTIONOFTHEMATLABBASEDROBOTMODELANDLINETRACKINGSIMULATORITTHENCOMPARESSEVERALDRFFERENTCONTROLAPPROACHESINTERMSOFRESTILTINGINTEGRALABSOLUTEERRORIAEANDINTEGRALSQUAREDERRORISE,EASINESSOFTUNINGANDCOMPLEXIFYOFTHERESPECTIVECODETHECOMPAREDAPPROACHESAREPROPORTIONAL,PROPORTIONALDERIVATIVE,PROPORTIONALINTEGRALDERIVATIVE,FZZY,TABLEBASEDFUZZY,SELFORGANISINGFIIZZYANDNEURALNETINVERSEMODELBASED1INTRODUCTIONBUILDINGAUTONOMOUSROBOTSISANINTERDISCIPLINARYACTIVITYANDTHUSHASAGREATPEDAGOGICALVALUEWITHTHISFACTINMINDTHEAUTHORSHAVEBEENSUPPORTINGSTUDENTTEAMSFROMTHEUNIVERSITYPFAVEIROTOPARTICIPATEINANANNUALEVENTTHATTAKESPLACESINFRANCEWHERE,BASICALLY,AUTONOMOUSMOBILEROBOTSHAVETOFOLLOWALINE,AMONGSTOTHERTASKSTOBETTERUNDERSTANDTHEBEHAVIOUROFTHELINETRACKINGROBOTANDTOSHOWSTUDENTSHOWDIFFERENTSCIENTIFICCONCEPTSFROMPHYSICS,GEOMETRY,ELECTRONICS,INSTRUMENTATIONANDCONTROLAREINTEGRATEDWHENBUILDINGSUCHAROBOT,THEAUTHORSHAVEDEVELOPEDANANALYTICAL0780344847198I100001998IEEE542MODELOFTHELINEFOLLOWINGROBOTLTHEMODELTAKESINTOACCOUNTSEVERALREALWORLDCONSTRAINTSANDALLOWSTOPREDICTTHEMOVEMENTOFTHEROBOTBASEDONTHEELECTRICALVOLTAGESAPPLIEDTOTHEMOTORSALSOINLTHEAUTHORSHAVEDESCRIBEDTHEGEOMETOFTHELINETRACKINGPROCESSWHICHWASUSEDTOBUILDASIMULATORTHISALLOWEDTODETERMINETHEPATHOFTHEROBOTASWELLASTHERELATIONSHIPBETWEENTHISPATHANDTHEREFERENCEPATHTHATTHEROBOTISTOFOLLOWTHESIMULATORISAVALUABLETOOLTOCOMPAREDIFFERENTCONTROLAPPROACHES,ASWELLASDIFFERENTSENSORLAYOUTS,PRIORTOTHEROBOTCONSTRUCTIONTHISALLOWSFORBETTERDECISIONSCONCERNINGTHEPHYSICALPROPERTIESOFTHEROBOTBEFOREACTUALLYBUILDINGITINTHENEXTSECTIONTHISARTICLEPRESENTSABRIEFDESCRIPTIONOFTHEROBOTMODELANDOFTHESIMULATORINSECTION3SEVERALCONTROLAPPROACHESARECOMPARED,NAMELYPROPORTIONAL,PROPORTIONALDERIVATIVE,PROPORTIONALINTEGRALDERIVATIVE,FUZZY,TABLEBASEDFUZZY,SELFORGANISINGFUZZYANDNEURALNETINVERSEMODELBASEDCONCLUSIONSAREDRAWNINSECTION4WHICHALSOINCLUDESSOMECOMMENTSCONCERNINGONGOINGWORK2SIMULATINGTHEROBOT21THEROBOTMODELTHEROBOTSWHICHHAVEBEENBUILTBYTHESTUDENTSINTHEACTIVITIESMENTIONEDBEFOREARENORMALLYSIMPLEFIG1MOTIONISACHIEVEDBYUSINGTWOINDEPENDENTDCELECTRICMOTORSTHATDRIVEONEWHEELEACHDIFFERENTIALDRILEI5USEDTOSTEERTHEROBOTONEORTWOEXTRACASTERWHEELSAREAMC98COIMBRAUSEDTOKEEPTHEROBOTHORIZONTALLYTHEDEVIATIONOFTHEROBOTFROMTHEREFERENCEPATHISMEASUREDBYASETOFSENSORSPLACEDAHEADOFTHEROBOTWHICHARE,NORMALLY,INFRAREDLIGHTDETECTORSTYPICALLY,CLOSEDLOOPCONTROLOFTHEWHEELSVELOCITYHASNOTBEENDONETHEVELOCITYOFEACHWHEELISCONTROLLEDINDIRECTLYBYAPPLYINGVOLTAGESTOTHEMOTORSTHISOPTIONMAYDECREASETHEPERFORMANCEOFTHETRACKINGALGORITHMBUTSIMPLIFIESTHEFINALTUNINGREMEMBERTHATTHEUSEOFCLOSEDLOOPWHEELSPEEDCONTROLWOULDREQUIRETHETUNINGOFTWOEXTRAINDEPENDENTLOOPSFIGURE1THEBASICROBOTTHESECHARACTERISTICSHAVEBEENUSEDTODERIVEAMODELFORTHELINETRACKINGROBOTFIG2TOIMPROVEITSACCURACYTHEMODELTAKESINTOACCOUNTINERTIAMASSMANDMOMENTOFINERTIAA,FRICTIONCOEFFICIENTSFORTRANSLATIONALBYANDROTATIONALB,MOVEMENTS,ELECTRICMOTORSPARAMETERSTHERESISTANCERANDTHEMOTORCONSTANTKM,ADDITIVENOISEINTHESENSORREADINGSANDPHYSICALLIMITATIONSOFTHEROBOTSUCHASTHELENGTHOFTHELINESENSORS5ANDTHEMAXIMUMVOLTAGETHATCANBEAPPLIEDTOTHEMOTORSV“THEMODELISDESCRIBEDINLANDALLOWSTOCALCULATEBOTHLINEARVANDANGULAR0VELOCITIESOFTHEROBOTBASEDONTHEVOLTAGESAPPLIEDTOTHEMOTORSVOWAVERAGE,ANDV,DIFFERENTIAL22THELINETRACKINGSIMULATORTHEROBOTMODELREFERREDTOABOVE,WASCOMPLEMENTEDWITHAGEOMETRICANALYSISOFTHELINETRACKINGPROBLEMTHISPROBLEMFALLSWITHINTHEGENERALPATHTRACKINGPROBLEMWHICHHASBEENTREATEDINTHELITERATURE,EG2INPARTICULAR,THESIMULATORPRESENTEDINTHISARTICLEFOLLOWSAREACTIVEAPPROACHTOTRACKANUNKNOWNLINEASOPPOSEDTOTHEPLANNINGAPPROACHOFTRACKINGAPATHPREVIOUSLYPLANNEDANDTHUS,KNOWNINADVANCEINLAGEOMETRICANALYSISISALSOSHOWNTHATALLOWSTOCALCULATETHENEXTDEVIATIONFROMTHELINEEBASEDONTHEPRESENTDEVIATION,WHEELSVELOCITIESANDANGULARPOSITIONOFTHEROBOTRELATIVETOTHELINETHEROBOTISUSEDASREFERENTIALHOWEVER,INORDERTOBETTERDEFINETHEREFERENCETRAJECTORYANDTOVISUALISETHEROBOTTRAJECTOQ,ANOTHERMODELWASBUILTINWHCHTHEROBOTPOSITIONWASREFERREDTOANABSOLUTEREFERENTIALINTHISGEOMETRICMODEL,THENEXTDEVIATIONFROMTHELINEEISCALCULATEDBASEDONTHEROBOTABSOLUTEPOSITIONANDTHEWHEELSVELOCITIESKNOWINGTHEROBOTPOSITIONXO,YO,ARITISPOSSIBLETOCALCULATETHEINTERSECTIONOFTHESENSORARRAYWITHTHELINEXEY,WHICHTHENALLOWSTOCALCULATETHEDEVIATIONEFIG3THERESULTINGDEPENDENCYOFERELATIVETOTHEPOSITIONOFTHEROBOTISNONLINEARTHEVELOCITIESAREUSEDTOCALCULATETHEROBOTDISPLACEMENTDZ,DA,DURINGANINFINITESIMALTIMEINTERVAL200WASFOUNDTHATBESTRESULTSWEREOBTAINEDWITHK,TOOANDKP380FIGURE8SHOWSTHEDEVIATIONOBTAINEDALONGTHEREFERENCEPATHWITHTHESEVALUESTHEABSOLUTEMAXIMUMDEVIATIONIS23MMANDTHEIAEIS66ANOTEWORTHREFERRINGISTHEFACTTHATTHECONTROLLERISCAPABLEOFCONVERGINGTOZERODEVIATIONOVERSTRAIGHTSEGMENTSBUTINCURVESWITHCONSTANTRADIUS,THEDEVIATIONCONVERGESTOANONZEROVALUESINCETHEANGLEOFTHEREFERENCEPATHISCONSTANTINSTRAIGHTSEGMENTSSTEPINPUTANDINCREASESCONSTANTLYINCURVESWITHFIXEDRADIUSRAMPINPUTTHELINETRACKINGROBOTCANBECONSIDEREDASATYPE1SYSTEMTHESAMEHAPPENSWITHTHEPROPORTIONALCONTROLLER33PROPORTIONALINTEGRALDERIVATIVETHISTYPEOFCONTROLLER,KNOWNASPID,RESULTSFROMTHEPREVIOUSONEBYADDINGANINTEGRALTERMTOTHEACTUATINGSIGNALTHISALLOWSTOBRINGTHEDEVIATIONTOZEROOVERANYPARTOFTHELINE,EITHERSTRAIGHTORCURVETHEDEBLATION00,02004006008001000002TIMESAMPLINGINTONALSFIGURE8USINGAPDCONTROLLERWITHKP400ANDK380545CANBEKEPTVERYSMALLWHENTHERIGHTPARAMETERSAREUSEDALTHOUGHITALWAYSINCREASESINTHEBEGINNINGANDENDINGOFANYCURVETHECONTROLLEROUTPUTISVDL,KPEKDCEKIIEWITHKP200,KP200ANDK,LOOITWASPOSSIBLETODECREASETHEIAE78ANDTHEMAXIMUMABSOLUTEERROR25MMNOATTEMPTWASDONETOFINDTHEBEST3VALUESANYWAYTHERESULTSAREBETTERTHANWITHTHENONOPTIMISEDPDCONTROLLERALTHOUGHCONTROLLERSOFTHISTYPENORMALLYACHIEVEAGOODPERFORMANCE,THETUNINGOFTHE3CONSTANTSISVERYDIFFICULTTHEUSEOFNONOPTIMALCONSTANTSMAYCAUSEACONSIDERABLEDEGRADATIONINPERFORMANCE34FUZZYLOGICAPPROACHTHEFUZZYLOGICAPPROACHCANBEANALTERNATIVETOTHEPREVIOUSSTRATEGIESALTHOUGHITISMORECOMPLEXTHANEITHERP,PDORPIDAPPROACHES,ITISSTILLRELATIVELYEASYTOIMPLEMENTSINCEITISBASEDONINTUITIVERULESEXPLICITLYGIVENBYTHEPROGRAMMER4INTHISCASEAFUZZYINCREMENTALCONTROLLERWITHNORMALISEDUNIVERSESOFDISCOURSEANDGAUSSIANMEMBERSHIPFUNCTIONSISUSED51THECONTROLLERINPUTSARETHETRAJECTORYERROREANDITSDERIVATIVECETHECONTROLLEROUTPUTISTHEDIFFERENTIALVOLTAGEVDIPTHEFUZZYCONTROLSURFACECANBEDEPICTEDONFIGURE9NOTETHENONLINEARSURFACEANDTHEGRADIENTNEARTHECENTERTWOAPPROACHESWERETRIEDWITHTHLSTYPEOFCONTROLLERRULEBASEDANDTABLEBASEDALGORITHMTHEFIRSTONEUSESFUNCTIONSFROMTHEMATHWORKSFUZZYLOGICTOOLBOXTHESECONDISONLYA2DLOOKUPTABLETHERESULTSAREIDENTICALINTERMSOFIAE,ISEANDMAXIMUMABSOLUTEERRORSOMEBETTERRESULTSWEREOBTAINEDADDINGALINEARINTEGRALTERMTOTHEFUZZYALGORITHMSEETABLE1FOR11FIGURE9FUZZYCONTROLSURFACEDETAILSHOWEVERTHERESULTSWEREALITTLEBITMOREMODESTTHANTHEONESOBTAINEDWITHTHEOPTIMISEDPDCONTROLLERTRYINGTOIMPROVETHESERESULTSLEADTOTHEUSEOFASELFORGANISINGFUZZYCONTROLLER35SELFORGANISINGFUZZYAPPROACHTHESELFORGANISINGFUZZYCONTROLLERSOCUSESSOMEKINDOFPERFORMANCEMEASURETOUPDATETHERULEBASETHEMOSTCOMMONAPPROACHHASAHIERARCHICALSTRUCTUREINWHICHTHELOWERLEVELISATABLEBASEDCONTROLLERTHEHIGHERLEVELMONITORSTHEERRORANDTHECHANGEINERRORANDMODIFIESTHETABLE,WHENNECESSARY,THROUGHAMODIFIERALGORITHM6THEPERFORMANCEMEASUREMENTISCARRIEDOUTUSINGEXPRESSION2PISTHEPERFORMANCEMEASUREORTHEPENALTY,THATISADDEDTOTHECONTROLTABLE,EISTHEERRORANDCEISTHECHANGEINERRORKCEISATIMECONSTANTANDGPISTHELEARNINGRATEFACTORSTARTINGWITHATABLESIMILARTOTHEONEUSEDONTHETABLEBASEDCONTROLLERITISPOSSIBLE,AFTER10TRAININGSESSIONSOFONEFULLREFERECEPATHEACH,TOIMPROVETHEOVERALLPERFORMANCEUPTOTHEONEOBTAINEDWITHTHEOPTIMISEDPDCONTROLLERFIGURE10SHOWSTHEIAEEVOLUTIONALONGTHE10TRAININGSESSIONSNOTETHATTHETRAININGOCCURS“ONLINE“WHILETHEROBOTISACTUALLYMOVINGALONGTHELINEASWELLASWITHTHESIMPLEFUZZYAPPROACHES,THEADDITIONOFANINTEGRALACTIONTOTHESOCALLOWSTOACHIEVEEVENBETTERRESULTSASCANBESEENINTABLE136NEURALNETWORKSAPPROACHKNOWINGTHATTHEROBOTMODELPREDICTSNONLINEAR,IAEEVOLDONTRAPCTONMSFIGURE10SELFORGANISINGCONTROLLERIAEEVOLUTION546STABLE,DYNAMICBEHAVIOURLEADTOTHEIDEAOFUSINGSOMEKINDOFNEURALNETWORKAPPROACHINORDERTOIMPLEMENTADIRECTINVERSECONTROLALGORITHMTHEINVERSEMODELWASIDENTIFIEDBYTHEUSEOFA2LAYERFEEDFORWARDNETWORKWITH4INPUTS,8HIDDENNONLINEARNEURONSANDALINEAROUTPUTNEURONTHENETWORKWASTRAINEDOFFLINEWITHTHELEVENBERGMARQUARDTMETHOD7AND,AFTER5000EPOCHS,ITWASPOSSIBLETOGETA“GOOD“INVERSEMODELWITHTHEOBTAINEDNETWORKADIRECTINVERSECONTROLSCHEMEWASIMPLEMENTEDSITHERESULTSOBTAINEDTHISWAYARETHEBESTONESAMONGTHECOMPAREDCONTROLSTRATEGIESASCANBESEENINTABLE14CONCLUSIONSTABLE1PRESENTSTHERESULTSOBTAINEDWITHEACHCONTROLLINGAPPROACHTWOMAINSORTSOFCONTROLLERSWEREUSED,THOSECAPABLEOFLEARNINGSOC,SOCIANDNNANDTHEREMAININGONESFROMTHESELATTERONESITISPOSSIBLETOSEETHATTHEUSEOFFUZZYCONTROLLERSDOESNOTBRINGALONGANIMMEDIATEBENEFITASIMPLE“HANDTUNED“PDCONTROLLERPERFORMSBETTERWHENANINTEGRALCOMPONENTISADDEDTOTHEFUZZYCONTROLLERS,THEIRPERFORMANCEISIMPROVEDUPTOTHEONEOFTHEPDCONTROLLERHOWEVER,THEV,PARAMETERISSTILLSUPERIORINTHEPDAPPROACHNOTICETHATADIFFERENCEOF003MSYIELDSADIFFERENCEOF10SAFTER30MOPTIMALLYTUNINGAPDCONTROLLERISEITHERVERYDIFFICULTHIGHLYTIMECONSUMINGOREVENIMPOSSIBLEWHENTHEREISNOANALYTICALMODELOFTHEROBOTANDTHETUNINGHASTOBEDONEWITHTHEREALROBOTTHEPIDAPPROACHISALSODIFFICULTTOTUNEAND,INMANYCASES,THERESULTINGPERFORMANCEMAYEVENBEWORSETHANFORTHEPDTHETUNINGOFTHEFUZZYCONTROLLERSISEASIERTOACHIEVESINCEITISEMBEDDEDINTHEINTUITIVERULESEXPLICITLYGIVENBYTHEPROGRAMMERRULEBASEDAPPROACHORINTHETABLETABLE1COMPARINGDIFFERENTCONTROLSTRATEGIESTOTRACKANUNKNOWNLINECONTROLLZRIAEISEVMEANEMAX/IAE/PP15103303000491PDPDOPTIMIZEDPIDFUZZYFUZZYIFUZZYTABLEFUZZYTABLEISOC10EPOCHSSOCI15EPOCHSNNSO00EPOCHS9501403200333766007030002356780090310025481080210310051289501402900373710702103100532995013029003437660070310024566200603000215952004031002166BUILTFROMSUCHRULESTABLEBASEDAPPROACHCONCERNINGTHECONTROLLERSCAPABLEOFLEARNING,THESOCPRESENTSAGOODSTRATEGYTOIMPROVEPERFORMANCEWITHARELATIVELYLOWCOMPUTATIONALCOSTBESIDES,ITSONLINELEARNINGCAPABILITYASWELLASITSSPEEDOFLEARNINGMAKEITVERYATRACTIVETHENEURALNETBASEDAPPROACHISVERYPOWERFULBUTVERYTIMECONSUMINGOFFLINETRAININGANDREQUIRINGLARGECOMPUTATIONALRESOURCESFLOATINGPOINTCALCULATIONSTHUS,ITISNOTWELLSUITEDTOBEUSEDWITHLOWPROCESSINGPOWERMICROCONTROLLERSTHEAUTHORSARECURRENTLYWORKING,TOGETHERWITHSTUDENTS,INTHECONSTRUCTIONOFANEWLINETRACKI