A Guide To using IMU Accelerometer and Gyroscope Devices in Embedded Applications.docx

A Guide To using IMU Accelerometer and Gyroscope Devices in Embedded Applications.docx

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AGuideTousingIMUAccelerometerandGyroscopeDevicesinEmbeddedApplications

Introduction

ThisguideisintendedtoeveryoneinterestedininertialMEMS（Micro-Electro-MechanicalSystems）sensors,inparticularAccelerometersandGyroscopesaswellascombinationIMUdevices（InertialMeasurementUnit）.

ExampleIMUunit:

  Acc_Gyro_6DOF ontopofMCUprocessingunit UsbThumb providingUSB/Serialconnectivity

I'lltrytrytocoverfewbasicbutimportanttopicsinthisarticle:

–whatdoesanaccelerometermeasure

–whatdoesagyroscope（akagyro）measure 

–howtoconvertanalog-to-digital（ADC）readingsthatyougetfromthesesensortophysicalunits（thosewouldbegforaccelerometer,deg/sforgyroscope）

–howtocombineaccelerometerandgyroscopereadingsinordertoobtainaccurateinformationabouttheinclinationofyourdevicerelativetothegroundplane

ThroughoutthearticleIwilltrytokeepthemathtotheminimum.IfyouknowwhatSine/Cosine/Tangentarethenyoushouldbeabletounderstandandusetheseideasinyourprojectnomatterwhatplatformyou'reusingArduino,Propeller,BasicStamp,Atmelchips,MicrochipPIC,etc.TherearepeopleouttherewhobelievethatyouneedcomplexmathinordertomakeuseofanIMUunit（complexFIRorIIRfilterssuchasKalmanfilters,Parks-McClellanfilters,etc）.Youcanresearchallthoseandachievewonderfulbutcomplexresults.Mywayofexplainingthingsrequirejustbasicmath.Iamagreatbelieverinsimplicity.Ithinkasystemthatissimpleiseasiertocontrolandmonitor,besidesmanyembeddeddevicesdonothavethepowerandresourcestoimplementcomplexalgorithmsrequiringmatrixcalculations.

I'lluseasanexampleanewIMUunitthatIdesigned–the Acc_GyroAccelerometer+GyroIMU. We'lluseparametersofthisdeviceinourexamplesbelow.Thisunitisagooddevicetostartwithbecauseitconsistsof3devices:

–LIS331AL（datasheet）–analog3-axis2Gaccelerometer 

–LPR550AL（datasheet）–adual-axis（PitchandRoll）,500deg/secondgyroscope 

–LY550ALH（datasheet）–asingleaxis（Yaw）gyroscope（thislastdeviceisnotusedinthistutorialbutitbecomesrelevantwhenyoumoveonto DCMMatriximplementation）

Togethertheyrepresenta6-DegreesofFreedomInertialMeasurementUnit.Nowthat'safancyname!

Nevertheless,behindthefancynameisaveryusefulcombinationdevicethatwe'llcoverandexplainindetailbelow.

Part1.Accelerometer

Tounderstandthisunitwe'llstartwiththeaccelerometer.Whenthinkingaboutaccelerometersitisoftenusefultoimageaboxinshapeofacubewithaballinsideit.Youmayimaginesomethingelselikeacookieoradonut,butI'llimagineaball:

Ifwetakethisboxinaplacewithnogravitationfieldsorforthatmatterwithnootherfieldsthatmightaffecttheball'sposition–theballwillsimplyfloatinthemiddleofthebox.Youcanimaginetheboxisinouter-spacefar-farawayfromanycosmicbodies,orifsuchaplaceishardtofindimagineatleastaspacecraftorbitingaroundtheplanetwhereeverythingisinweightlessstate.Fromthepictureaboveyoucanseethatweassigntoeachaxisapairofwalls（weremovedthewallY+sowecanlookinsidethebox）.Imaginethateachwallispressuresensitive.Ifwemovesuddenlytheboxtotheleft（weaccelerateitwithacceleration1g=9.8m/s^2）,theballwillhitthewallX-.Wethenmeasurethepressureforcethattheballappliestothewallandoutputavalueof-1gontheXaxis.

Pleasenotethattheaccelerometerwillactuallydetectaforcethatisdirectedintheoppositedirectionfromtheaccelerationvector.Thisforceisoftencalled InertialForceorFictitiousForce .Onethingyoushouldlearnfromthisisthatanaccelerometermeasuresaccelerationindirectlythroughaforcethatisappliedtooneofit'swalls（accordingtoourmodel,itmightbeaspringorsomethingelseinreallifeaccelerometers）.Thisforcecanbecausedbytheacceleration,butaswe'llseeinthenextexampleitisnotalwayscausedbyacceleration.

IfwetakeourmodelandputitonEarththeballwillfallontheZ-wallandwillapplyaforceof1gonthebottomwall,asshowninthepicturebelow:

Inthiscasetheboxisn'tmovingbutwestillgetareadingof-1gontheZaxis.Thepressurethattheballhasappliedonthewallwascausedbyagravitationforce.Intheoryitcouldbeadifferenttypeofforce–forexample,ifyouimaginethatourballismetallic,placingamagnetnexttotheboxcouldmovetheballsoithitsanotherwall.Thiswassaidjusttoprovethatinessenceaccelerometermeasuresforcenotacceleration.Itjusthappensthataccelerationcausesaninertialforcethatiscapturedbytheforcedetectionmechanismoftheaccelerometer.

WhilethismodelisnotexactlyhowaMEMSsensorisconstructeditisoftenusefulinsolvingaccelerometerrelatedproblems.Thereareactuallysimilarsensorsthathavemetallicballsinside,theyarecalledtiltswitches,howevertheyaremoreprimitiveandusuallytheycanonlytellifthedeviceisinclinedwithinsomerangeornot,nottheextentofinclination.

Sofarwehaveanalyzedtheaccelerometeroutputonasingleaxisandthisisallyou'llgetwithasingleaxisaccelerometers.Therealvalueoftriaxialaccelerometerscomesfromthefactthattheycandetectinertialforcesonallthreeaxes.Let'sgobacktoourboxmodel,andlet'srotatethebox45degreestotheright.Theballwilltouch2wallsnow:

Z-andX-asshowninthepicturebelow:

Thevaluesof0.71arenotarbitrary,theyareactuallyanapproximationforSQRT（1/2）.Thiswillbecomemoreclearasweintroduceournextmodelfortheaccelerometer.

Inthepreviousmodelwehavefixedthegravitationforceandrotatedourimaginarybox.Inlast2exampleswehaveanalyzedtheoutputin2differentboxpositions,whiletheforcevectorremainedconstant.Whilethiswasusefulinunderstandinghowtheaccelerometerinteractswithoutsideforces,itismorepracticaltoperformcalculationsifwefixthecoordinatesystemtotheaxesoftheaccelerometerandimaginethattheforcevectorrotatesaroundus.

Pleasehavealookatthemodelabove,Ipreservedthecolorsoftheaxessoyoucanmakeamentaltransitionfromthepreviousmodeltothenewone.Justimaginethateachaxisinthenewmodelisperpendiculartotherespectivefacesoftheboxinthepreviousmodel.ThevectorRistheforcevectorthattheaccelerometerismeasuring（itcouldbeeitherthegravitationforceortheinertialforcefromtheexamplesaboveoracombinationofboth）.Rx,Ry,RzareprojectionoftheRvectorontheX,Y,Zaxes.Pleasenoticethefollowingrelation:

R^2=Rx^2+Ry^2+Rz^2     （Eq.1）

whichisbasicallytheequivalentofthe Pythagoreantheoremin3D.

RememberthatalittlebitearlierItoldyouthatthevaluesofSQRT（1/2）~0.71arenotrandom.Ifyouplugthemintheformulaabove,afterrecallingthatourgravitationforcewas1gwecanverifythat:

1^2=（-SQRT（1/2））^2+0^2+（-SQRT（1/2））^2

simplybysubstitutingR=1,Rx=-SQRT（1/2）,Ry=0,Rz=-SQRT（1/2）in Eq.1

Afteralongpreambleoftheorywe'regettingclosertoreallifeaccelerometers.ThevaluesRx,Ry,Rzareactuallylinearlyrelatedtothevaluesthatyourreal-lifeaccelerometerwilloutputandthatyoucanuseforperformingvariouscalculations.

Beforewegettherelet'stalkalittleaboutthewayaccelerometerswilldeliverthisinformationtous.Mostaccelerometerswillfallintwocategories:

digitalandanalog.DigitalaccelerometerswillgiveyouinformationusingaserialprotocollikeI2C,SPIorUSART,whileanalogaccelerometerswilloutputavoltagelevelwithinapredefinedrangethatyouhavetoconverttoadigitalvalueusinganADC（analogtodigitalconverter）module.IwillnotgointomuchdetailabouthowADCworks,partlybecauseitissuchanextensivetopicandpartlybecauseitisdifferentfromoneplatformtoanother.Somemicrocontrollerwillhaveabuilt-inADCmodulessomeofthemwillneedexternalcomponentsinordertoperformtheADCconversions.NomatterwhattypeofADCmoduleyouuseyou'llendupwithavalueinacertainrange.Forexamplea10-bitADCmodulewilloutputavalueintherangeof0..1023,notethat1023=2^10-1.A12-bitADCmodulewilloutputavalueintherangeof0..4095,notethat4095=2^12-1.

Let'smoveonbyconsideringasimpleexample,supposeour10bitADCmodulegaveusthefollowingvaluesforthethreeaccelerometerchannels（axes）:

AdcRx=586

AdcRy=630

AdcRz=561

EachADCmodulewillhaveareferencevoltage,let'sassumeinourexampleitis3.3V.Toconverta10bitadcvaluetovoltageweusethefollowingformula:

VoltsRx=AdcRx*Vref/1023

Aquicknotehere:

thatfor8bitADCthelastdividerwouldbe255=2^8-1,andfor12bitADClastdividerwouldbe4095=2^12-1.

Applyingthisformulatoall3channelsweget:

VoltsRx=586*3.3V/1023=~1.89V（weroundallresultsto2decimalpoints）

VoltsRy=630*3.3V/1023=~2.03V

VoltsRz=561*3.3V/1023=~1.81V

Eachaccelerometerhasazero-gvoltagelevel,youcanfinditinspecs,thisisthevoltagethatcorrespondsto0g.Togetasignedvoltagevalueweneedtocalculatetheshiftfromthislevel.Let'ssayour0gvoltagelevelisVzeroG=1.65V.Wecalculatethevoltageshiftsfromzero-gvoltageasfollows:

:

DeltaVoltsRx=1.89V–1.65V=0.24V

DeltaVoltsRy=2.03V–1.65V=0.38V

DeltaVoltsRz=1.81V–1.65V=0.16V

WenowhaveouraccelerometerreadingsinVolts,it'sstillnoting（9.8m/s^2）,todothefinalconversionweapplytheaccelerometersensitivity,usuallyexpressedinmV/g.LetssayourSensitivity=478.5mV/g=0.4785V/g.Sensitivityvaluescanbefoundinaccelero