engineering design: design and control of a simple robot · engineering design: design and control...

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EngineeringDesign:

DesignandControlofASimpleRobot

ByRobyVelez

Advisor:ErikCheever

Abstract:Thispaperdetailsmyseniordesignproject.Itgoesthroughtheprocessofthecreationofa

simple,crawlingrobot.Itdescribesdifferentcontrolalgorithmsusedtomaketherobotcrawl.Oneofthecontrolalgorithmslookedatwaslearningwithartificialneuralnetworks(ANN)andgeneticalgorithms(GA).TheANNandGAproducedcontrollerswhichreliedoncouplingbetweensensorsand

servosandoscillatorstoproducerobustandfastcrawling.

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1.Introduction.......................................................................................................................................3

2.Hardware ............................................................................................................................................42.1PCB ................................................................................................................................................................4XBEE.......................................................................................................................................................................................6

2.2Chassis..........................................................................................................................................................7

3.Software ........................................................................................................................................... 103.1Servosandpulses .................................................................................................................................. 103.2Timer1andPWMCompare ............................................................................................................... 113.3HandshakingbetweenPICandMATLAB ....................................................................................... 143.4Simulator.................................................................................................................................................. 16crawlingRobot().............................................................................................................................................................17UpdatingPosition..........................................................................................................................................................17Geometry...........................................................................................................................................................................17SimulatedSensors.........................................................................................................................................................19

4.ControlArchitectures .................................................................................................................. 194.1DirectControl ......................................................................................................................................... 194.2DirectProgramming............................................................................................................................. 204.3Learning.................................................................................................................................................... 21ANN .....................................................................................................................................................................................21GeneticAlgorithms .......................................................................................................................................................21NEAT ...................................................................................................................................................................................22

4.4MATLABimplementationofNEAT................................................................................................... 24Neuralnetworksetup..................................................................................................................................................24Activationfunctions .....................................................................................................................................................25

4.5NEATExperiment .................................................................................................................................. 26PortingtoRobot.............................................................................................................................................................28

5.AnalysisofArtificialNeuralNetworks................................................................................... 285.1LocomotionandPatternofActivation ........................................................................................... 295.2DifferenceBetweenPushersandPullers ...................................................................................... 305.3ANNandOscillators .............................................................................................................................. 315.4ExploringPhaseShifts ......................................................................................................................... 325.5PushersbetterthanPullers ............................................................................................................... 34

6.Conclusion ....................................................................................................................................... 35

References............................................................................................................................................ 35

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1.Introduction

Mostmobilerobotsarewheeled.Theyareeasytomakeandeasytocontrol.Theonlyissueisthatthesewheeledrobotsliveinaworldinhabitedbywalkingorganisms.Leggedrobotsaremoredifficulttobuildbecauseoflimitationswithactuatorsandpowerdemands.Theyarealsodifficulttoprogrambecause

theyrequirethecoordinationofmultiplelinkages.Butleggedrobotsofferimmensepossibilitiessuchassearchingthroughacollapsedbuildingwithrubbleforvictims,transportingequipmentoverharshterrainforthemilitary,orworkinginahomeenvironmentassistingpeoplewithdisabilities.

Oneissueinroboticsistryingtomakerobotssmartenoughtoadaptandlearninchanging

environmentsaswellasfindsolutiontoproblemsontheirown.Thishascausedmanyroboticisttodrawinspirationfrombiologicalsystemswhichcanfendforthemselvesinsometimesveryharshandchangingenvironments.Twocomputationmodels/algorithmsinspiredbybiologyareartificialneuralnetworks

andgeneticalgorithms.Artificialneuralnetworksaremodeledafterrealneuralnetworks.Theyconsistofacollectionofinterconnectednodeswhereinformationpropagatesthroughtheconnections,isaltered,andthenshootsouttheend.Geneticalgorithmsareawayofusingevolutiontosearchthrough

asolutionspaceforasolutiontoaproblem.Artificialneuralnetworksandgeneticalgorithmsarebothbiologicallyinspiredandincorporateelementsofadaptionandlearning.

ResearchersinSwitzerlandhavebeenlookingatrobotswhichmovenotbyrollingonwheels,butbyflappingtheirfins(2),crawlingonfourlegs(3),orslitheringlikeasnake(1).Theresearchershavebeen

abletoaccomplishthisthroughtheuseofCentralPatternGenerators.CentralPatternGeneratorsaremodeledoffofatypeofneuralnetwork.Theseneuralnetworksproduceoscillatoryoutputgivennoneoscillatoryinput.CentralPatternGeneratorsandoscillatorymotionhasbeenfoundtobeessentialto

locomotion.Whilethisworkisveryinterestingtheresearchesusedmodelsofneuralnetworks,notactualartificialneuralnetworkstocontroltherobots.

ThepurposeofthisprojectistotrytoemulatetheresearchersfromSwitzerlandandusenotamodelof

aneuralnetwork,butanactualartificialneuralnetworktocontrolthelocomotionofarobot.Usingactualartificialneuralnetworkspreventsconstrainingtotheartificialneuralnetworkstoaparticularmethodforsolvingtheproblem.Theartificialneuralnetworkscouldfindoscillatorstosolvethe

locomotionproblemorcomeupwithsomenovelapproach.Forthemostparttherehasn’tbeenmuchworkonusingactualartificialneuralnetworkstocontrollocomotionwhichistime,andmemorydependentproblemwhichdoesn’thaveinstantfeedback.

Artificialneuralnetworksaregenerallyusedtolearnthroughatrainingalgorithmwhichaltersthe

weightstogettheneuralnetworktoproduceacertainoutputforagiveninput.Howeverartificialneuralnetworkscanbeusedtosolveaproblembyevolvingtheirweightsandtopologywithageneticalgorithm.ThiscanbedonewithanalgorithmknownasNeuroEvolutionofAugmentingTopologies

(NEAT)(4).Thisiswhatwillbeusedinthisprojecttosearchforartificialneuralnetworkstosolvethistask.

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Theevolutionofanartificialneuralnetworkswhichcancontrolacrawlingrobotisthepinnacleofthisproject,buttogetthererequiredmanystepsorstageswhichincludedesignandconstructionofthe

microcontrollerandrobotchassis,creationofthelowlevelservoandcommandprotocols,creationofthehigherlevelcontrolalgorithmswhichincludestheNEATandartificialneuralnetworks,andfinallytheanalysisoftheevolvedneuralnetworks.Thesewillbelaidoutinthefollowsections.

2.HardwareThefirststageofthisprojectconsistedofthecreationoftheactualphysicalrobotandaprotocoltoprogramanddolowlevelcontrol.Thisconsistedofthecreationmicro‐controller,robotchassis,and

commandprotocol.

2.1PCBAprintedcircuitboard(PCB)wasusedtocontroltherobot.AblockdiagramforthePCBisshownbelow.

Figure2.1:BlockDiagramofPrintedCircuitBoard(PCB).

AtthecenterofthePCBisamicrocontroller.Themicrocontrollercanbelookedasaminiature‐

processingunit.Itcanbeprogrammedtodocalculations,readsensorsandactuateservos.ThemicrocontrollerusedwasthePIC16F767.ThePIC16F767isasimple,inexpensivemicrocontrollerchosenbecauseithadthemostPWMcomparepins,whichwouldbeusedtocontrolservos,andhada

lotofdigitalandanaloginputs.LikeacentralprocessingunitinarealcomputeraPICcannotworkonitsown.Itneedsperipherals

suchaspower,debugger,andI/Oconnectionsinordertofunction.ThePCBhadtoprovide5voltsforthePIC,7voltstopowertheservos,and3voltsfortheXBEEmodule.TheXBEEmoduleisanintegratedchipthatwillprovidewirelesscommunicationtothePCB.Itwillbediscussedshortly.The

circuitschematicinFigure2.2showshow7voltswerebroughtintothePCBanddropdownto5voltsand3voltsbyvoltagedividers.

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Figure2.2:Powerschematic.

BesidesprovidingpowerthePCBalsoprovidedotherperipheralssuchasadebugger(whichisusedtoprogramthePIC)andI/Oconnections.Figure2.2showstheMultisimschematicfortherestofthePCB.

Figure2.3:Circuitschematic.

MostoftheI/Opins,notusedforpower,debugging,orserialcommunicationbetweenthePICandXBEE,areroutedtothebankofheaderslocatedintheupperrightofFigure2.3.TheheaderbanksprovideaccesstotheI/OpinsforthePICandXBEEaswellasaccesstotheground,the5voltpower

supply,and3voltpowersupply.DesigningtheheadersintothePCBlikethisenablesalotofflexibilityforaddingsensors.

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Infigure2.3,totheleftofthePIC,abankofheadersweremadeforthePWMpinsofthePICandXBEE.Thisiswheretheservoswouldbeconnected.TorightofthePICistheRJ12usedtoconnectand

programthePIC.Adebuggerlikethisisstandardformostmicrocontrollerboards.FinallythePICisconnectedtotheXBEEbywiringtheTXpinofthePICtothedataInpinoftheXBEEandbywiringtheRXpinofthePICtothedataOutpinoftheXBEE.Thesepinsareusedtotransmitserialdatabetween

theXBEEandPIC.Figure2.4showsthecompletedPCBwithallthecomponents.

Figure2.4:CompletedPCB.

XBEETheXBEEmodulescanformverysimple,lowpowernetworksthattransmitserialdata.Theyactlike

wirelesscables.Wirelesscommunicationwithamobilerobotisveryusefulindebuggingandcreatingcontrolarchitecturefairlyquickly.LivecommandscanbesenttotherobotandexecutedinstantaneouslyversuswritingcodetothePIC,compilingit,andthenrunningit.

OneXBEEmodule,calledtheControllerXBEE,wasconnectedtothePICandanothercalledtheBaseXBEE,wasconnectedtoaremotecomputerrunningMATLAB.Thisisseeninfigure2.5.TheController

isaXBEEPROwhiletheBaseisaregularXBEE.ForthemostpartthetwomodulesarethesameexceptthattheXBEEPROis5‐volttolerant.ThiswasessentialsinceitwasreceivingserialdatafromthePICwhichwasrunningoffof5volts.

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Figure2.5:DiagramshowingthewirelesscommunicationbetweentheremotecomputerandPCB.

Theserialport,ontheremotecomputer,isopenedbyMATLABandserialdata,suchasstrings,canbe

sentthroughtheporttotheBaseXBEEmodule.TheBaseXBEEmodulethentransmitstheserialdataoverawirelesscabletotheControllerXBEEmoduleonthePCB.TheControllerXBEEmodulethentransmitstheserialdataintothePICwherethePICcanreadit.ThePICcanalsotransmitserialdatato

theControllerXBEEwhereitissenttotheBaseXBEE.TheBaseXBEEthensendstheserialdatatothecomputerwhereitisreadwithMATLAB

2.2ChassisSincethepurposeofthisprojectwastoexplorelocomotionwithaleggedrobotaverysimpl,yet

interestingdesignwascreated.Therobotiscomposedofa3degreeoffreedom(DOF)armmountedontoawoodenchassis.Thechassisrestsontwocontactsensorsinthefrontandhastotwocastor‐likewheelsinthebackwhichareodometers.Figure2.6showsaconceptdrawingoftherobot.

Figure2.6:Conceptdrawingofrobot.

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Acrawlingrobotwasdesignedinsteadofatraditionallywheeledrobotbecauseacrawlingrobotwouldbemoreinterestingtocontrolwiththelearningalgorithminsteadofawheeledrobot.The

designissimpleinthatthereisonlyonelimbandthingslikebalancearen’tissuesastherobotmoves.Butthedesignstillrequiresthecoordinationofmultiplejointstoproducelocomotionsoitretainsthecomplexityoflocomotionandmanipulatorcontrol.

Linkage3measures13centimeterswiththeendaffecter,andlinkage2measure11centimeters.Theendaffecterisahalfinchpieceofpixelglassmadeintoadiscandboltedontotheendoflinkage3.The

plywoodboard,thatthearmismountedonto,isapieceofquarterinchplywood16by18centimeters.Atthefront,underneaththeplywoodisafoamblockwiththedimension13by3by3.Twocontactsensorsareattachedtoeithersidesofthefoamblock.Therobotrestsonthecontact

sensorsnotthefoamblock.Thefoamblockissimplytheretoallowthecontactsensorstobeattachedtothechassis.Finallyastheendofthechassisaretwocontinuouspotentiometerswithwheelsmountedontotheirshafts.Whentherobotrearsupandliftsthechassisoffthegrounditrollson

thesetwowheels.Figure2.7showsanactualimageoftherobot.

Figure2.7:Imageofrobotchassis.

Therobothasthreeservos.Servoonerotatesthearmwithrespecttobase.Figure2.8isadiagram

fromabovethelimitsofservo1’stravel.

Figure2.8:Topviewoftherobotmeanttoshowtherangeofmotionforservo1.

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Servo2connectslinkage2totheservo1.Servo3connectslinkage2tolinkage3.Figure2.9showsthe

rangeofmotionforservo2andforservo3.

Figure2.9:SideviewoftherobotmeanttoshowtherangeofmotionforServo2and3.

Inordertohavelinkage2and3inalmostthesameplaneServo3isflippedfromServo2.Figure2.10showshowtheServosarecurrentlymounted(left)withthelinkagesinthesameplane,andhowthelinkageslookifServo3wasinthesameorientationasServo2(right).

Figure2.10:Comparisonofthearminaconfigurationwhereitisalignedandwhenitisnotaligned.

ImageontheleftshowstheactualconfigurationofServo3andServo2whichbringsthearmintoalignment,butcausesServo3andServo2tofacedifferentdirection.TheimageontherightshowsapossibleconfigurationofServo3andServo2whichcausesthemtopointinthesamedirection,butthe

armisnotaligned.ThismeansthatifServo2isgivenacommandtorotateclockwise,thatsamecommandwillmakeServo3rotatecounterclockwise.Thisisnotaseriousproblem,butitcomesintoplayduringtheNEATevolutiontests,discussedlater.

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Therobothassixsensors.Theyarelistedinthetablebelow.

SensorName

Description

3PositionSensors

MadefrommonitoringapinoffoftheServocontrolboard.TheyindicatetheangleofeachServo,butarequitenoisy.Theyrangefromavalueof80to400.

1ForceSensor

Mountedattheendofthearm.TheServosarenotverystrongsothesensorwascalibratedtobeverysensitive,whichresultsitinnotbeingabletodistinguishawiderangeofdifferentforce.Therobotprettymuchknowsifitistouchingthegroundornot.Itiseither1023whenthearmisoffthegroundandaround600whenthearmisonetheground.

1ContactSensor

Twocontactsensorsaremountedoneithersideofthefoamonthebottomofthechassis.Therobotrestsofthem.Theyarewiredtogetherandactasonecontactsensor.Theyreporta1ifoneofthemisreleasedandazerootherwise.

1Odometer Whentherobotrollsforwarditisrollingforwardontwowheelsmountedatthebackofthechassis.Thetwowheelsaremadeupofcontinuouspotentiometerswhichreadachangingvoltageastheyturn.OnlyoneOdometerreadingisread.Thisisusedtomeasurehowfartherobothasmoved.Itreadsavaluefrom0to1023.Ifthepotentiometerswiperreaches1023butcontinuestorollitwillrolloverto0andincrementnormally.Ifthepotentiometerreads0andcontinuestorollbackwardsitwillrolloverto1023andcontinuesdecrementingnormally.

Table2.1:Sensorsoftherobot.

3.SoftwareOncethemicrocontrollerandchassiswerebuiltcodewaswrittenforthePICandMATLABwhichactuatedtheServosandcreatedacommand/communicationprotocolbetweentheremotecomputer

andthePCB.Servosneedaspecificprotocoltoworkproperlyandthecommunication/codingprotocolwilldeterminehoweasyitistowritecontrolalgorithms.

3.1ServosandpulsesServosworkbysendingthempulsewidths.PulsewidthscanbegeneratedbyaPICholdingapinhighfor

asetamountoftimeandthensettingitlow.Thepulsescanbelaunchesatsetperiods.ThisisshowninFigure3.1.

Figure3.1:Illustrationofpulseswidths.Alteredimagetakenfrom.

http://www.servocity.com/html/how_do_servos_work_.html

Forservosthepulseshavetohaveaperiodof20millisecondsandwidthsrangingfrom500microsecondsto2500microseconds.Thewidthofthepulsedeterminesthepositionoftheservo.ThisisshowninFigure3.2.

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Figure3.2:Imageofhowpulsewidthscorrespondtopositionoftheservos.Imagealteredandtakenfromhttp://www.servocity.com/html/how_do_servos_work_.html

3.2Timer1andPWMCompareInordertoproduceandvarythepulsewidthsTimer1andthePWMcomparefunctionsofthePICare

used.AninternalclockregulatestheoperationofthePIC.Thisinternalclock(Fosc)issimplyaninternal(orforsomePICsexternal)oscillatorthatoscillatesandsendspulsesatcertainfrequencies.Timer1isa16bitcounterwhichincrementsonceeveryfourclockcycles.BecauseTimer1isa16bitnumber,onceit

countsupto65535itrestartsat0andbeginscountingupagain.ThisiscalledanoverflowandisshowninFigure3.3.

Figure3.3:DiagramillustratingthefillingandoverflowingofTimer1.

ThePICcanbemadetolaunchaninterruptwheneverthishappens.Aninterruptisanoperationthat

canbetriggeredbyanumberofthingssuchasaregisteroverflowing,acompareevent,orachangeofanexternalinput.WhenaninterruptistriggeredthePICputswhateveritisdoingonholdanddoeswhatevercodeisassignedtotheinterrupt.

Overflow Reset

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ThecountofTimer1canbesettosomeInitialCount(IC)afteritoverflows.Timer1willthencountupfromthisInitialCountuntilitreaches65535andoverflowsagain.BecauseTimer1incrementsatafixed

ratethetimebetweenoverflowscanbealteredbythroughtheInitialCountvalue.ThisisillustratedinFigure3.4.

Figure3.4:DiagramwithdescribeshowtheInitialCountcanbecalculatedtoproduceanoverflowafterasetaboutoftime.

WithFoscequalto8MhzandanInitialCountof60535Timer1willoverflowandlaunchaninterrupt

every20ms.TheinterruptwillpullthepinsconnectedtotheServoshigh.Servo3isconnectedtopinc1.Servo2isconnectedtopinc2.Servo1isconnectedtopinb3.

That’sonepartoftheservoactuation.ThesecondusesthePIC’sPWMcomparefunction.ThePIChasthreeinternalvariablescalledCCP_1,CCP_2,andCCP_3.ThePICcanbemadetolaunchinterrupts

wheneveroneofthesevaluesequalsthecurrentvalueofTimer1.TheinterruptswillpullthepinsconnectedtotheServoslow.ThisisshowninFigure3.5.

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Figure3.5:IllustrationofhowthefillingofTimer1launchestheinterruptsofCCP_1,CCP_2,andCCP_3.

Thewidthofthepulsecanbecalculatedas:

Thepulsewidthdeterminesthepositionoftheservo.TheequationbelowsolvesfortheCCPvalueto

produceacertainpulsewidth.

ThismeanstheServoscanbecontrolledbychangingtheCCPvalues.

InsummarysettingTimer1tosomeInitialCountafteritoverflowsdeterminesthetimeuntilthenext

overflowwhenaninterruptwillbelaunched.Theinterruptwillhappenevery20msandwillpullpinsc1,c2,andb3high.ThecomparefunctionofthePICcanbeusedtolaunchinterruptsandpullthepinsc1,c2,andb3low.ThetimebetweenTimer1settingapinhighandaCCPinterruptsettingitlow

correspondstotheCCPvalue.Thiswillproduceapulseacertainwidthevery20mswhichcanbeusedtocontrolaservo.

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3.3HandshakingbetweenPICandMATLABThepurposeofequippingthePCBwithawirelessfunctionwastobeabletoactuatetheservosbytypingcommandstringsintoMATLAB’scommandline.MATLABwouldprintthestringstotheserialportwhichwouldthensendthestringtothePCBviathewirelessserialconnection.Thisisincontrastto

writing,compiling,anddebuggingcoderightoffthePIC.Figure3.6showsaflowchartcomparingthetwoprogrammingapproaches.

Figure3.6:FlowchartcomparingwritingcodetothePICversussendingcommandsoverwirelesscable.

SendingcommandfromMATLABclearlylookseasierandfaster.Inordertodothisaprotocolwas

developedsothatthePICwouldunderstandthecommandstringssentbyMATLABandMATLABwouldunderstandthecommandstringssentbythePIC.

MATLABwouldsendstringstothePIC.ThePICwasprogrammedtolookforthe‘#’symboltosignifythebeginningofacommand,parsetheservowordsinblocksoffour,andexecutetheproperactionbased

onthecommandandservowords.Thecommandstringshavetheformof:

# 1 0 0 0 2 0 0 0 3 0 0 0 0 0 2 0

Signifiesthebeginningofa

command

Firstfourdigitsrelatetoservo1.

Secondsetoffourdigitsrelateto

servo2.

Thirdsetoffourdigitsrelateto

servo3.

Teeltherobothowtoexecutethecommand.

Table3.1:Commandstringprotocol.

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Currently3typesofcommandshavebeendeveloped.

Command Description

0010 AddsthevaluesindicatedforeachservototheCCPvalueassignedtothespecificservosensor.Effectivelymakestheservogotothepositioncorrespondingtothosevalues.

0020 Printthepositionreadingfrompotentiometer.Ignoreservowords.

0030 IncrementthevaluesforCCP_1,CCP_2,andCCP_3bythevaluesineachservoword.Indicateanegativeincrementbyprecedingaservowordwith‘n’.Forexamples‘#0200n500n1000030’meansincrementthefirstservoby100anddecrementthesecondandthirdservoby500and

300respectively.Thelargestnegativecommandisn999.

xxxx Anythingnotthethreecommandsshownabovewillsimplybeignored.

Table3.2:Commandtypeoptions.

ThefollowingcodeopensaserialportandincrementsServo1by500anddecrementsServo2by200.

ThefollowingcoderequeststhePICtotransmitinformationonitssensors.

WhenthePICreceivesa‘0020’commanditqueriesitssensorsandsendsthembacktoMATLABistheformatof:

# 0 2 7 0 0 0 8 0 0 4 0 0 0 9 0 0 0 0 0 1 0 5 4 0 0 0 1 0

BeginningofCommand

PositionofServo1

PositionofServo2

PositionofServo3

ForceSensor

ContactSensor

OdometerReading

MessagefromPIC

Table3.3:FormatforthePICsendingsensorinformationbacktoMATLAB.

Tostreamlinethesendingandreceivingofcommandandmessagestringsafunctioncalled

sendCommandStringwaswritten.Itisdefinedas:

[serialHndl,sensorReadings,message,success]=

sendCommandString(serialHndl,[servoWord1,servoWord2,servoWord3,commandWord]);

>>s=serial(‘COM1’,’BaudRate’,13400);%Openstheserialport

>>fprintf(s,’#0500n20000000030’);

>>fprintf(s,’#0100n20000000020’);

>>reponse=fscanf(s,’%s’,29);

0000000030’);

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serialHndl Handlefortheserialobject.

sensorReading Arraywiththesensorvalues.Thisarrayisfullofzerosunlessa20commandissent.

Message MessagefromthePIC

Success Flagwhichindicatesifthecommunicationwassuccessful.

servoWord Insteadoftyping‘0020’or‘n200’thevalues20or‐200canbetypedin.

commandWord Insteadoftype‘0020’or‘0010’typing20or10wouldwork.

Table3.4:ParametersforthesendCommandStringfunction.

ThecommunicationbetweenMATLABandthePICisoverawirelesscommunicationandhassomelag.

Onaveragethelagbetweensendingsaya‘0020’andreceivingareplyfromthePICwas0.02seconds.Thiswillcomeintoplayindesigningthesimulator.

3.4SimulatorAsimple2DsimulatorwascreatedinMATLABinanticipationofhavingtorunmultipleevolutionrunswiththerobot.Ascreenshotisshowninfigure3.7.

Figure3.7:Screenshotofthesimulator.

Ideallyevolutionwouldbedoneontheactualrobot,butthisisslow,cancausedamagetotherobot,andrequiressomeonetocontinuouslywatchtherobot.Thesimulatorcreatedisfairlysimple,butfortheamountoftimeitcapturesalloftherelevantaspectsoftherobotneededtoproduceacceptable

evolutionruns

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crawlingRobot()

ThecornerstoneofthesimulatorisasimulatedrobotobjectcalledcrawlingRobot().Thesimulatedrobothasthesameattributesandphysicalcharacteristicsastherealrobot.Ithasparametersforthecurrentvaluesofallitssensors,currentlocationofitsphysicalbody,andvaluesforinternalvariables

presentintherealrobotsuchastheCCPvalues.

UpdatingPosition

MATLABtalkstothesimulatedrobotthesamewayittalkstotherealrobot.ItusesthesendCommandStringfunction,butpassesinahandletothecrawlingRobotinsteadoftheserialport.Oncethecommandstringsaresenttothesimulatedrobotitupdatesitsservolocations,physical

position,andsensorvalues.WhenthecommandstringisdecipheredtheCCPvaluesofthesimulatedrobotareupdatedaccordingly.TheCCPvaluesrepresentthedesiredlocationoftheServos.ThesimulatedrobotcannotautomaticallysetitsservolocationstotheanglesspecifiedbytheCCPvalues.

Thiswouldmeanthattheservosmovedinstantaneouslytowheretheyweretoldtogo.Theservoshaveamaxangularspeed.Thecurrentlocationoftheservos,whichisencodedina

variablecalledsPos,approachesthedesiredlocationoftheServosataspeedequaltothemaxspeedoftheservos.Theupdatedlocationoftheservosaftereachupdatecycleiscalculatedfromthemax

angularvelocityandtheelapsetimefromthelastupdate.Theelapsedtimebetweenupdatesissetto0.02seconds.ThisdoesnotreflecthowlongtheMATLABcodetakestoupdatethesimulatedrobot.0.02istheaveragelagincommunicationbetweenMATLABandtherealrobot.Becausetheshortest

elapsetimebetweenMATLABqueryingtherealrobotforsensorvaluesorsendingaservocommandis0.02secondsthenthiscanbeusedasthetheoreticalelapsetimebetweenupdatecycles.

GeometryOncethepositionoftheservosisknowntheorientationofallthepointsoftherobotcanbecalculated.Thisisthenusedtodeterminewhatthesensorsvaluesshouldbe,ifacollisionhasoccurred,oriftherobothasmovedany.Thesimulatedrobothastwodifferentstateswhichplotand

updatedifferently.Thesimulatedrobotrestsandcrawlsoveravirtualground.Ifthechassisofthesimulatedrobotison

thegroundandtheendaffecterisn’t,thejointsofthesimulatedrobotarecalculatedbyusingthebackofthechassisasthereferenceandfigure3.8.Inthisreferencetheta1,whichistheanglebetweenthechassisandtheground,is0.

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Figure3.8:Diagramwhichillustratestheanglesusedtodrawtherobot.Thereferencelocationisthebackofthechassis.

Whentheendaffectertouchesthegrounditispinnedthereandtherobotissaidtobeofftheground.

Inthisstatethegeometryplotsdifferent.Inthisstatethereferencepointistheendaffecterandallthepointsplotinreferencetothat.Thismeansthatthebackpointoftherobotcanmove.Thesimulatedrobotisoutofthisstateifthechassistouchesthegroundagain.Itwillthengobacktousing

thebackoftherobot,whateverlocationitisat,asthereferencelocation.

Figure3.9:Diagramwhichillustratestheanglesusedtodrawtherobot.Thereferencelocationistheend

affectr.

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SimulatedSensorsOncethegeometryofthesimulatedrobotisknown,afteranupdatecycleiscomplete,thesimulatedsensorscanbeupdated.ThesimulatedrobothasthesamesensorsastherealrobotwhicharelistedinTable2.1.

Theservopositionsensorsarecalculatedafterthefinalpositionofthearmandchassisareknownafter

theupdatecycle.Sincetherealpositionsensorsarenoisey,oncethesensorvalueiscalculatedbasedontheorientationoftheservoGaussiannoisewithastandarddeviationof2isaddedtothevalues.

Whenthesimulatedchassisisonthegroundthecontactsensorreads0.Whenthesimulatedchassisisoffthegroundthecontactsensorreads1.Theforcessensorsattheendofthearmreads400plusarandomnumber~N(0,100)whenitisincontactwiththegroundorchassisandreads990plusarandomnumber~N(0,30)otherwise.Thisagainreflectsthefactthatthereissomenoisewiththeforcesensorreading.Whenthebackofthechassismovesthesimulatortakesthatdisplacementsandcalculateshowmanyturnstheodometerhasmade.Thisisusedtofigureoutwhatthenewodometerreading.Thesimulatedodometerliketherealonerollsoverfrom1023to0.

4.ControlArchitecturesOncetherobotwasfullycompleteddifferentcontrolalgorithmswereexplored.Whilethegoalofthis

projectwastoexploreddifferentlearningalgorithmstwoclassicalcontrolapproacheswerelookedat.LookingatDirectControlandDirectProgramminghelptodebuggingsomeaspectsoftherobotdesignandgainanintuitionabouthowhardtheproblemis.

4.1DirectControlDirectControlreferstorobotsormachinesbeingoperatedbyhumans.TheoperationofconstructionequipmentorunderwaterROV’scanbeseenasthedirectcontrolofrobots.Directcontrolisverysimpletoimplementandwasusedasatestbedtoseeiftherobotcouldactuallycrawl.

ThreepotentiometerswerefedintothePIC.ThepotentiometerscansendacontinuousvoltageintothePICfrom0to5volts.ThePICreadthisvalueinasa10bitnumberandchangesthepulsewidth,

throughtheCCPvalues,foreachservoaccording.0voltscorrespondtoapulsewidthof500microsecondsand5voltscorrespondtoapulsewidthof2500microseconds.Therewasonepotentiometerforeveryservo.

Byturningtheknobsahumanoperatorcanmovethearmoftherobottogetittocrawl.Thiswasnotaneasytaskandtooksometimetolearnhowtocoordinatetheservosandlinkages.Timeseries

imagesoftherobotcrawlingforwardandbackwardareshowninFigure4.1andFigure4.2.CCPvaluesaccordingly.

Figure4.1:Timeseriespicturesoftherobotbeingcontrolledtocrawlforward.

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Figure4.2:Timeseriespicturesoftherobotbeingcontrolledtocrawlbackwards.

4.2DirectProgrammingUsingthecommandfunctionscreatedinMATLAB,codewaswrittenwhichqueriedthesensorsofthe

robotandactuatedtheservos.Thegoalwastocontroltherobotandhaveitcrawlforward.AflowchartforhowtheprogramworkedisshowninFigure4.3.

Figure4.3:Flowchartshowingtheoperationofthedirectprogrammingcode.

TheflowchartshowninFigure4.3showsaverydeterministalgorithmwhichsimplygoesfromonestatetoanother.Theonlyfeedbackoccursbetweenstates2and3wherelinkage2willrotateCWorCCW

dependingiftherobotisonthegroundornot.Servo3and2arenotwellcoordinatedtooneanother.Theyareactuallycoordinatedtothecontactsensor.Thisapproachproducedacrawlingrobot,butitcrawledfairlyslowly.

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4.3LearningOnceDirectControlandDirectProgrammingweredonesuccessfullylearningwaslookedat.Inordertoexplorelearningtwotoolsfrommachinelearningwereused,artificialneuralnetworks(ANN),and

geneticalgorithms(GA).TheANNaregoingtobeusedtocontroltherobot.Theyaregoingtomanagetheinteractionbetweentheinputsandoutputs.AGAwillbeusedtotunetheweightsandtopologyoftheANNtodoatask.Forthesesetofexperimentsthetaskistogettherobottomovesomedistance,

eitherforwardsorbackwards.

ANNFigure4.3showsaANNwhichsolvesAND.ThecapabilitiesofthisANNdependontheweightsandtopology.Inordertoproduceacrawlingrobottherightweightsandtopologyneedstobefound.

Figure4.3:Exampleofaartificialneuralnetwork.

GeneticAlgorithmsGeneticalgorithmsaretypeofsearchalgorithminspiredbybiology.Theyarebasedontheideaof

evolution.AgeneticalgorithmwillbeusedtofindtherightweightsandtopologyfortheANN.Foragivenproblem,suchtheonepresentedinFigure4.4,thesolutionsarebrokenintogenotypes.

Figure4.4:Applicationofgeneticalgorithmtoanavigationproblem.

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Herethegoalisgetthegreenrobotfromthestartlocationtothegoallocation.Thesequenceofstepsittakescanbeencodedintoagenotype.Thesuccessorthefitnessofthisgenotypecanbe

evaluatedbyhowclosethegreenrobotgetstothegoalsquare.Inageneticalgorithmapopulationofrandomgenotypesiscreatedandtheirfitnessisevaluated.The

fitnessfunctionisdifferentforeachtask.Herethefitnessfunctionishowclosethegreenrobotgetstothegoal.Aftereachgenotypeisevaluatedtheoneswiththehighestfitnessareallowedtocrossandproduceoffspringasshowninfigure4.5.Alsothereisachanceformutationoftheoffspring.

Figure4.5:Illustrationofreproductionwithageneticalgorithm.

Ifthisisdonemanytimesovermanygenerationsthefitnessofthepopulationwillslowlyriseuntila

solutionisfoundasshowninFigure4.5.

NEATNEATwhichstandsfortheNeuroEvolutionofAugmentingTopologies,isageneticalgorithmwhich

evolvesneuralnetworks.Theneuralnetworksareencodedusingtheirconnections.Arraysaremadewhichencodethestrengthofeachconnection,thefromandtonodes,itsinnovationnumber,andwhetherornottheconnectionisdisabled.

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MutationsinNEATaltertheweightsoftheconnectionsaswellasaddmoreconnectionsandnodes.Thisishowthetopologiesoftheneuralnetworksarealtered.Figure4.7illustrateshowconnections

andnodesareaddedtothenetworks.

Figure4.7:DiagramillustratinghowmutationworksinNEAT.TakenfromthepaperonNEAT(4).

Addinganewconnectionisfairlysimple.Thereisnotlimittowhereconnectionscanbeadded.Nodesareaddedwithinconnections.Node6inFigure4.7isaddedinthemiddleoftheconnectionbetween

nodes3and4.Theconnectionanditsweightbetween3and4isreassignedtobebetween3and6andanewconnectionisaddedbetweennodes6and4.

Thealgorithmkeepsarecordofalltheconnectionscreated,andgivesthemanumberbasedontheirorder.Notethattheinnovationnumbersarenottheorderthatconnectionsarecreatedwithinan

individualneuralnetwork.Theyareatheorderconnectionsarecreatedinreferencetotheentireevolutionrun.NEATusestheseinnovationsnumberstolineupthegenotypesoftheneuralnetworksandperformcrossover.Thisisshowninfigure4.8.

Figure4.8:IllustrationsofhowcrossoverworksinNEAT.TakenfromthepaperonNEAT(4).

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Theinnovationnumbersgiveaframeworkfortakinggeneticinformationfromonepartandmixingitwiththeotherparent.Theconnectionscanbeverycomplexandintricate.Justpickingandswapping

connectionsfromthetwoparentstothemakeachilddoesn’tpreservetheoriginalstructurewhichcontributedtothehighfitnessoftheparents.Usingtheinnovationnumberstoperformcrossoverkeepsthegeneralstructureofeachparent,butallowsamixingofthegeneticinformation.Fromabiological

standpointthisissimilartoonlycrossinggeneswithacommonhistory.Allthegenesassociatedwiththevertebrateofhumansshareasimilarhistorywhileallthegenesassociatedwiththeopposablethumbsofhumansalsoshareacommonhistoryduringevolution.Youwouldwanttocrossthegenesfor

thumbstogetherandthegenesforspinestogether.

4.4MATLABimplementationofNEAT

NEATwasoriginallydevelopedbyKennethStanley.HisimplementationwasoriginallywritteninC++.Ithassincebeenportedtovariouslanguagessuchaspython,Java,andMATLAB.AMATLABimplementationofNEATwasusedforthisproject.ItcanwithasampleexperimentwhichsolvedXOR.

NeuralnetworksetupTheimplementationofXORloadedinputsintotheinputlayeroftheneuralnetworkandwaiteduntil

thevaluesfullypropagatedthroughthenetworkbeforereturningtheoutputs.Itwaiteduntiltheoutputvalueswerestable.Itseemsbiologicallyunrealistictoexpectactivationstoreachtheoutputlayeratthesametimeeventhoughtheytakedifferentlengthsofpathsthroughtheneuralnetwork.Thisalsostops

activationsfromreachingtheoutputwithdifferentdelays.

Thepropagationcodewaschangedtodothefollowing.Eachtimestepthealgorithmgoesthrougheachconnectionandincrementstheactivationofthenodeitisgoingtobytheweightoftheconnectiontimestheactivationofthenodetheconnectioniscomingfrom.Oncealltheconnectionsareallowedto

sendtheirinformationtheoutputisevaluatedandthenextroundofinputsentersthenet.Thecodedoesnotsitthereandwaituntilthevaluesattheoutputnodereachasteadystatebeforeloadinginthenextsetofinputs.

Theneuralnetworksfortheseexperimentshave6inputsnodes,twooutputnodes,andonebias.An

initialneuralnetworkisshowninFigure4.9.Theinputnodesarefullyconnectedtotheoutputnodes.Theconnectionsweightsrangefrom‐1to1.

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Figure4.9:Initialnetworksetup.

Thesixinputstotheneuralnetwork,fromlefttoright,arethepositionofservo1,2,3.Thereadingfromtheforcesensor,thereadingfromtheodometer,andthecontactsensor.Thetwooutputsgotoservo2andservo3.Thevaluesfromtheoutputnodeswouldbesenttotherobotas‘0030’commands.

ThismeansthatthevalueoutputfromtheneuralnetworkwillincrementordecrementtheCCPvaluesforServos2and3bysomeamount.Thenextsectionontheactivationfunctiongoesintomoredetailonhowtheactivationattheoutputcontrolstheservos.

ActivationfunctionsTheactivationfortheinputnodesinlinearfunctionof1.Thatistheinputvaluesaresimplypassedthe

straighttotheoutput.Beforethesensorsvaluesaresentintotheinputnodestheyarescaledlinearlytobetween0.1and0.9.Forthepositionsensorsthismeanstheyarescalefrom80to400.Fortheforcesensorandodometertheyarescaledfrom0to1023.Andforthecontactsensoritisscaledfrom0to1.

Theactivationofthehiddenandoutputnodesissigmoidfunctioncenteredat0.5.

Figure4.10:Sigmoidfunctionusedastheactivationfunctionofthehiddenandoutputnodes.Imagetakenfrom11http://en.wikipedia.org/wiki/Sigmoid_function

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Withtheequation

Theinputtoeachnodewasscaledtobebetween‐6and6withtheformula

TheweightCapfortheconnectionsis1becausetheweightscanrangefrom‐1to1.Theactivationfunctionofeachhiddenandoutputnodeisthen

Ifannodefeedingintoanoutputnodeorhiddennodewasfiringatthehighestactivationpossible,whichis1,andtheweightbetweenthatnodeandtheoutputorhiddennodewasatitsmaximumpositivevaluethentheactivationoftheoutputorhiddennodewouldbe1.Ifannodefeedingintoan

outputnodeorhiddennodewasfiringatthelowactivationpossible,whichis0,andtheweightbetweenthatnodeandtheoutputorhiddennodewasatitsmaximumnegativevaluethentheactivationoftheoutputorhiddennodewouldbecloseto0.Allotheractivationsarescaledfromthis.

Theactivationoftheoutputnodesrangesfrom0to1.Aswassaidearlier,theoutputnodeswouldsend

theservowordsforsendinga‘0030’commandtotherobot.Thevalues0and1arescaledlinearlybetween‐999and999beforebeingsenttotherobot.‐999and999arethelargestcommandsthatcanbesenttotherobotwitha‘0030’.Witha‘0030’commandtheoutputnodesareincrementingor

decrementingtheservosbysomevalueeverytimestep.Theyareessentiallysettingthespeedofservo2andServo3.

4.5NEATExperimentTheevolutionexperimentswerenotrunontherealrobot.Thiswouldhavetakenalotoftimeandwouldhaveprobablyresultsintherobotdestroyingitself.Someinitialrunswererunontheactual

physicalrobot.Intheserunstherobotslearnedtohitthemselvestherebyusingtheinertiaoftheimpactandtheirarmtomovebackwards.

Insteadofrunningexperimentsontherealrobotthesimulatordescribedinsection3.4wasused.Thetaskforthisrobotwastomove.Itsfitnesswashowmuchnetdisplacementitgainedin450timesteps.

Thedisplacementismeasuredbythevirtualodometeratthebackofthesimulatedrobot.

Threesetsoffourexperimentswererunwithdifferentmutationrates.MostoftheparametersfromtheXORexperimentswerekept.Theonesalteredatlistedbelow.Theonlydifferencebetweenthethreesetsoffourexperimentsarethemutationrates.

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ParameterName Value Description

Population_size 30 number_input_nodes 6

number_output_nodes 2

Initial.kill_percentage 0.5Percentageofbottomperformerseliminatedeverygeneration.

selection.pressure 1.95Determinesselectivepressuretowardsmostfitindividualofspecies

mutation.probability_add_node

0.07(Run23‐27)0.03(Run28‐31)0.05(Run31‐35)

mutation.probability_add_connection

0.09(Run23‐27)0.05(Run28‐31)0.07(Run31‐35)

mutation.probability_recurrency 0.05

stagnation.threshold 2500 Thresholdtojudgeifaspeciesisinstagnation.Table4.1:ParametersusedfortheevolutiontrialsthataredifferentfromtheXORsampleexperiment.

Figure4.11showsthemaxfitnessversusgenerationforthethreesetsoffourexperiments.Theyareclearlyverysimilarwhichmeansthatthemutationratesisnotaffectinghowfasttheneuralnetworksarebecomingfit.Atleastnotattheratestested.Thereforefromhereonthethreesetsofdatawillbe

lumpedtogetherandtreatedthesame.

Figure4.11:Fitnessforthedifferentmutationrates.

Theaveragemaxandmeanfitnessareshowninfigure4.12.

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Figure4.12:Combinedfitnessforallexperiments.

Thefigures4.11and4.12showthattheneuralnetworkswereabletosolvethetaskandevolvecrawling

behavior.Theevolutionrunsarerepeatableandstable.Everyrunproducedresults.

TwodifferenttypesofANNevolved.SomeANNevolvedwhichmadethesimulatedrobotmovebackwards(pushers)andsomeANNevolvedwhichmadethesimulatedrobotmoveforwards(pullers).ForthemostpartmostoftheevolutionrunsproducebackwardorpushingANN.Thedifference

betweenthetwotypesofbehaviorsandwhyonewasmorepreferredthantheotherisdiscussedinthenextsection.

PortingtoRobotSomeofthebestneuralnetworkswereportedontotherealrobot.Quantitativelyit’shardtocomparetheperformanceoftheANNontherealrobotwiththeANNonthesimulatedrobotsothedistance

traveledintherealworldwasn’tcomparedtothedistancetraveledontherealrobot.

QualitativelytheANNworkedbeautifullyontherealrobot.ThepushingandpullingANNmaketherealrobotmoveincrediblefast.ThesesolutionsgoaboutfourtimesasfastastheDirectProgrammingsolution.VideosoftheANNportedtotherealrobotcanbefoundonYouTubebysearchingfor

“crawlingrobot,Lola,NEAT”

5.AnalysisofArtificialNeuralNetworksNEATwassuccessfulatevolvingANNtoproducecrawlingmotion,buthowaretheANNproducingthe

crawlingmotion?HowaretheANNsuccessfullycoordinationthemotionofServo2andServo3?TheanalysisoftheANNrequiredwritingcodewhichplottedtheANNandshowedhowtheinformationwaspropagatingthroughtheANN.Thisanalysisyieldedsomeveryinterestingresultswhichtiebackintothe

earlierdiscussiononlocomotionandoscillators.

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5.1LocomotionandPatternofActivationAfterthetaskswerecompletedtheartificialneuralnetworkswereanalyzedinordertounderstandhowtheyproducedthecrawlingmotion.Thefollowingimagesshowscreenshotsofthesimulatedrobot

alongsideitsartificialneuralnetwork.Theimagesgostepbystepandshowhowthepatternofactivationofthenodesproduces,inthiscase,pushingmovement.

Figure5.1:SimulatedrobotandANNatt=0.

Att=0bothoutputnodesproducelowactivation.Thisinturnwillcauselinkage3torotatecounter

clockwiseandlinkage2torotateclockwiseasshowninfigure5.1.Thearmwilldoastretchingoutmotionuntilitmakescontactwiththeground.


Att=3thearmmakescontactwiththeground,liftingthechassisofftheground.Thesixthinputnode,

whichcorrespondstothecontactsensorlocatedatthebottomoftherobot,goesfromlowactivation(black)tohighactivation(orange).Astheanimationcontinuestheactivationwillspreadfrominput6tooutput1,tothehiddennode,tooutput2asindicatedbythearrowsinfigure5.2.NEAThas

strengthenedtheseweightsoverthecourseofevolution.

t=0

t=3

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Att=6theactivationofthetwooutputsisnowhigh.Thiscauseslinkage3torotateclockwiseandlinkage2torotatecounterclockwiseasshowniffigure5.3.Noteittooktwotimestepsfortheactivationfromspreadfromoutput1tooutput2.Thismeansthatlinkage2changeddirections(rotate

counterclockwise)twotimestepsbeforeoutput2.


Att=10thechassismakescontactwiththegroundandinput6getspulledlowasshowninfigure5.4.Theactivationwillnowtravelthroughtheartificialneuralnetworkthesamewayitdidbetweent=3andt=6.Thiswillbringtherobotintoastateseenatt=0,andthemotionwillrepeat.

Thisisanexampleofhowoneoftheartificialneuralnetworkswascontrollingthesimulatedrobotand

makingitpushbackwards.Aftermoreanalysisitwasdiscoveredthatallthepushershadasimilarflowofactivation.

5.2DifferenceBetweenPushersandPullersTheANNanalyzedinsection5.1showsatypicalANNwhichgeneratedpushingmotion.ANNwhichgeneratedpullingmotionalsoevolvedduringtheexperiments.Fundamentallythereisn’tmuch

differencebetweenpushingANNandpullingANN.Figure5.5showsexamplesoftwoANN.OnerepresentsthesimplestpushingANNandonerepresentsthesimplestpullingANN.

t=6

t=10

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Figure5.5:SimpleillustrationofhowpullingANNdifferedfrompushingANN.TheANNontheleftisapushing

ANN.TheANNontherightisapullingANN.

Asseeninfigure5.5theonlydifferencebetweenpushingANNandpullingANNisthedelayinfiringoutput1andoutput2withrespecttothecontactsensor(input6).ForpushingANNontheleft,output

1willfireonetimedelayafterthecontactsensorfiresandoutput2withfire1plussomedelay,equaltothenumberofhiddennodesbetweenoutput1andoutput2,afterthecontactsensor.ForpullingANNontheright,output2willfireonetimedelayafterthecontactsensorfiresandoutput1withfire1plus

somedelay,equaltothenumberofhiddennodesbetweenoutput2andoutput1,afterthecontact.

5.3ANNandOscillatorsTofurtherelaborateonthedifferencebetweenthepushingandpullingANNandtolinktothediscussionofneuralnetworks,oscillators,andcentralpatterngeneratormentionedintheintroduction,

theactivationofthecontactsensor,output1,andoutput2wasplottedversustimestep.TwoANNandtheplotoftheiractivationsversustimeareshowninfigure5.6andfigure5.7.

Figure5.6:AverysimplepushingANNandaplotofitsactivationversustimesteps.

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Figure5.7:AverysimplepullingANNandaplotofitsactivationversustimesteps.

ForthepushingANNshowninfigure5.6thedashedline,whichcorrespondstooutput2,firestwotimestepsafterthesolidline,whichcorrespondstothecontactsensor.Thedottedline,whichcorrespondstooutput1,firesonetimestepsafterthesolidline,whichcorrespondstothecontactsensor.Output2

issaidtohaveaphaseshiftoftwowhileoutput1issaidtohaveaphaseshiftofonefromthecontactsensor.

Forthepulling.ForthepullingANNshowninfigure5.7thedashedline,whichcorrespondstooutput2,firesonetimestepsafterthesolidline,whichcorrespondstothecontactsensor.Thedottedline,which

correspondstooutput1,firestwotimestepsafterthesolidline,whichcorrespondstothecontactsensor.Output2issaidtohaveaphaseshiftofonewhileoutput1issaidtohaveaphaseshiftoftwofromthecontactsensor.

ForbothpushingandpullingANNtheoutputnodesareentrainedtothecontactsensor.The

fundamentaldifferencebetweenpullingandpushingANNarethephaseshiftsofoutput1andoutput2withrespecttothecontactsensor.PushingANNseemtohavethephaseshiftofoutput2greaterthanthephaseshiftofoutput1whilepullingANNseemtohavethephaseshiftofoutput1greaterthanthe

phaseshiftofoutput2.

5.4ExploringPhaseShiftsToexplorethisideafurtheraMATLABscriptwaswrittenwhichplantsthesimulatedrobot’sarm,tostarttheoscillation,andthenvariedthephaseshiftsforoutput1and2.Thesimulatedrobotwas

allowedtomovefor450timestepsanditsfitnesswasrecorded.Theresultsforthistestareshownintable5.1.

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PhaseShiftOutput2 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0Output1

1.0 15.7 109.8 193.8 218.7 238.3 258.2 235.7 254.1 268.8 293.1

2.0 ‐99.5 9.6 112.8 172.6 177.2 227.1 222.7 226.0 245.7 255.83.0 ‐224.7 ‐91.1 11.9 111.5 149.3 177.9 194.8 224.5 223.1 225.14.0 ‐297.0 ‐207.0 ‐58.7 46.2 92.1 152.2 156.8 195.8 201.9 217.45.0 ‐284.2 ‐226.8 ‐161.2 ‐39.5 41.8 105.5 121.3 171.1 184.7 198.16.0 ‐112.4 ‐305.7 ‐227.5 ‐139.5 ‐27.1 30.7 63.6 142.8 160.9 182.07.0 ‐19.2 ‐129.5 ‐286.3 ‐180.5 ‐93.6 ‐27.9 12.9 56.1 131.6 158.58.0 ‐20.1 ‐61.9 ‐159.2 ‐257.4 ‐146.4 ‐79.9 ‐30.8 15.5 85.9 125.29.0 ‐13.8 ‐17.4 ‐63.6 ‐282.1 ‐216.6 ‐158.1 ‐104.1 ‐22.5 37.6 90.9

10.0 ‐15.1 ‐16.3 ‐6.5 ‐125.0 ‐228.6 ‐220.0 ‐151.4 ‐87.8 1.2 32.1Table5.1:Thistableshowsthefitnessvaluesforagivenphaseshiftcombination.

Thehorizontalandverticalaxesontheedgesindicatethephaseshiftordelaybetweeneitheroutput1andthecontactsensororoutput2andthecontactsensor.Thevaluesintheboxesshowthefitness(incentimeters)thatthesimulatedrobotachievedafter450.Thenegativevaluesgrayedoutindicatedthat

thesimulatedrobotmovedbackwards.Table5.1confirmsthepreviousassertionthatpushingANNoccurwhenthephaseshiftofoutput2isgreaterthanthephaseshiftofoutput1.

Table5.1showsthatthechangingofthephaseshiftcangreatlychangethefitness.Thiswasseenin

someoftheevolutiontrialswheretherewerehugespikesoffitness.Figure5.8showsthefitnessversusgenerationofoneoftheevolutionruns.

Figure5.8:Fitnessversusgenerationforexperiment29.Showsthesharpincreasesinfitnessduetoinnovations.

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Thehugespikeatgeneration50occurredbecausesomeinnovationintheevolution(additionofconnection,node,orchangingofweight)producedanANNwithagoodsetofphaseshifts.Thesame

thinghappensataroundgeneration80.

5.5PushersbetterthanPullersTheadditionofconnections,hiddennodes,andthechangingweightsarerandomeventswhichoccurduringtheevolutionprocess.TherateoftheseeventsarecontrolledbythemutationratessetintheNEATalgorithm.Figure5.9showstwoANNwithsimilarlevelsofcomplexity.Theybothhaveanextra

nodeandtwoextraconnectionsnotfoundintheoriginalANNsetup.

Figure5.9:TwoANNwiththesamelevelofcomplexity.TheoneontheleftispushingANNandtheoneontherightisapullingANN.

TheANNonthelefthasaphaseshiftof[1,3]andbasedonTable5.1wouldhaveafitnessofaround‐224.7.TheANNontherighthasaphaseshiftof[3,1]andafitnessofaround193.8.LookingatTable5.1thistrendisfairlyconsistentwithafewexceptions.ForacertainlevelofcomplexitythepushingANNgo

fasterthanthepullingANN.ThisbecomesobviouswhenlookingatthepatternofactivationsofapushingandpullingANNinfigure5.10.Figure5.10showsthesameoscillatorsinfigure5.6and5.7exceptzoomedout.ItcanbeseenthatthepushingANNundergoesmoreoscillationsorcycles,in100

timesteps,thanthepullingANN.ThismeansthepushingANNgetsmorestrokesinthanthepullingANNwhichiswhytheyareonaveragefasterthanthepullingANN.

Figure5.10:Zoomedoutimagesoftheplotsoftheactivationsshowninfigure5.7and5.8.

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ThisisonepossibleexplanationforwhypushingANNaremorecommon,duringtheevolutiontrials,thanpullingANN.Forthesamelevelofcomplexity,thepushingANNareinherentlyfasteranddominate

thepopulationscausingtheextinctionofthepullingANN.

TheincreasednumberofcyclesforapushingANN,whencomparedtoapullingANN,ismostlikelycausedbythegeometryoftherobot.Alterationstotherobot’schassiswerenotexploredinordertotrytoseeifthepullingbehaviorcouldbemadebetterthanthepushingbehavior.

6.ConclusionInthisprojectafairlysimple,yetorthodoxrobotwascreatedquickly.Itprovedtobeveryrobustand

easytoworkwith.Classicengineeringandcomputerscienceapproachestoprogrammingandcontrolwereappliedtotherobotandsatisfactoryresultswereobtained.Controlwaslearningandadaptationusingartificialneuralnetworksandgeneticalgorithmswasthenexploredwithgreatsuccess.This

projectshowedthefeasibilityofamethodlikelearningwithartificialneuralnetworksandgeneticalgorithmstocontrolamobilerobot.

TheANNandGAproducedveryrobustandinterestingsolutionstotheproblem.It’snothardtoimaginetakingtheunderstandinggainedfromtheanalysisoftheANNandreverseengineeringthesolution.

Thatis,takethisideaofthecouplingofinputsandoutputsandoscillatorstohandcodeasolutionwhichwouldworkaswellastheevolvedANN.Theselearningapproacheshaveshownaviablewaytoprogramarobotandlearnnewwaystoconceptualizethecontrolofamobilerobot.

References1.Crespi,A.J.."AmphiBotI:anamphibioussnake‐likerobot."RoboticsandAutonomousSystems

50(2008):163‐175.

2.Crespi,A.J.."Controllingswimmingandcrawlinginafishrobotusingacentralpatterngenerator."AutonomousRobots25(2008):3‐13.

3.Crespi,A.J.."Fromswimmingtowalkingwithasalamanderrobotdrivenbyaspinalcordmodel”SCIENCE315(2007):1416‐1420.

4.Stanley,Kenneth.“Competivecoevolutionthroughevolutionarycomplexification.”JournalofArtifical

IntelligenceResearch,vol21.2004

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