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Flexible Robot Manipulators Modelling, simulation and control Edited by M.O. Tokhi and A.K.M. Azad TheInstitutionofEngineeringandTechnology PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom ©2008TheInstitutionofEngineeringandTechnology Firstpublished2008 ThispublicationiscopyrightundertheBerneConventionandtheUniversalCopyright Convention.Allrightsreserved.Apartfromanyfairdealingforthepurposesofresearch orprivatestudy,orcriticismorreview,aspermittedundertheCopyright,Designsand PatentsAct,1988,thispublicationmaybereproduced,storedortransmitted,inany formorbyanymeans,onlywiththepriorpermissioninwritingofthepublishers,orin thecaseofreprographicreproductioninaccordancewiththetermsoflicencesissued bytheCopyrightLicensingAgency.Inquiriesconcerningreproductionoutsidethose termsshouldbesenttothepublishersattheundermentionedaddress: TheInstitutionofEngineeringandTechnology MichaelFaradayHouse SixHillsWay,Stevenage Herts,SG12AY,UnitedKingdom www.theiet.org Whiletheauthorsandthepublishersbelievethattheinformationandguidancegivenin thisworkarecorrect,allpartiesmustrelyupontheirownskillandjudgementwhen makinguseofthem.Neithertheauthorsnorthepublishersassumeanyliabilityto anyoneforanylossordamagecausedbyanyerrororomissioninthework,whether sucherrororomissionistheresultofnegligenceoranyothercause.Anyandallsuch liabilityisdisclaimed. 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BritishLibraryCataloguinginPublicationData Flexiblerobotmanipulators:modelling,simulationandcontrol.-(IETcontrolseries) 1.Manipulators(Mechanism)2.Manipulators(Mechanism)-Automaticcontrol I.Tokhi,M.O.II.Azad,AbulIII.InstitutionofEngineeringandTechnology 629.8’92 ISBN978-0-86341-448-0 TypesetinIndiabyNewgenImagingSystems(P)Ltd,Chennai PrintedintheUKbyAthenaeumPressLtd,Gateshead,Tyne&Wear Abbreviations AB Articulatedbody ACC Adaptivecompositecontroller ACU Armcomputerunit A/D Analogue/digital ADAM Aerospacedual-armflexiblemanipulator AMM Assumedmodesmethod ANN Artificialneuralnetwork ARMAX Autoregressivemovingaveragewithexogeneousinputs ARX Autoregressivewithexogenousinputs AVC Activevibrationcontrol BC Boundarycondition CACE Computeraidedcontrolengineering CCD Chargecoupleddevice CDT Contactdynamicstoolkit CLIK Closed-loopinversekinematics CMFC Centralisedmodel-freecontroller CMM Coordinatemeasuringmachine CI Compositeinertia CRB Compositerigidbody CSA CanadianSpaceAgency D/A Digital/analogue DFM Duisburgflexiblemanipulator DMFC Decentralisedmodel-freecontroller DNA DirectNyquistarray DOF Degreeoffreedom DSP Digitalsignalprocessing EAP Electroactivepolymer EBRC Energy-basedrobustcontroller ERLS Equivalentrigidlinksystem EVA Extravehicularactivity FD Finitedifference FE Finiteelement xxii Flexiblerobotmanipulators FMA Forcemomentaccommodation FMS Flexiblemanipulatorsystem FRF Frequencyresponsefunction GA Geneticalgorithm GOCF Generalizedobservabilitycanonicalform GUI Graphicaluserinterface HC Hardcomputing HLS Hardware-in-the-loopsimulation IIR Infiniteimpulseresponse IMSC Independentmodalspacecontrol INA InverseNyquistarray I/O Input/output ISS InternationalSpaceStation ISTE Integralsquaredtimederror JBC Joint-basedcollocated LED Light-emittingdiode LHP Lefthalfofs-plane LMS Leastmeansquares LPDC Localproportional,derivativecontrol LQ Linearquadratic LQG LinearquadraticGaussian LQR Linearquadraticregulator LRMS Long-reachmanipulatorsystem MAM Manualaugmentedmode MBS Mobilebasesystem MDR MacDonaldDettwilerSpaceandAdvancedRoboticsLtd. MDSF Manipulatordevelopmentandsimulationfacility MF Membershipfunction MIMO Multi-inputmulti-output MIQ Machineintelligencequotient MLFM Multi-linkflexiblemanipulator MLP Multi-layeredperceptron MNN Modularneuralnetwork MOTS MSSoperationandtrainingsimulator MPIPD MultivariablePI–PD MPO Modelpredictedoutput MPP Multivariablepole-placement MRO MSSroboticsoperator MSL MechatronicSimulinklibrary MSS Mobileservicingsystem MTF Matrixtransferfunction NARMAX Non-linearautoregressivemovingaveragewithexogeneousinputs NARX Non-linearautoregressivewithexogeneousinputs NB Negativebig NN Neuralnetwork Listofabbreviations xxiii NRT Non-real-time NS Negativesmall ODE Ordinarydifferentialequation OLS Orthogonalleastsquares OPDE Ordinarypartialdifferentialequation ORU Orbitalreplacementunit OSA One-step-ahead OTCM Orbitaltoolchange-outmechanism OTCME ORUtoolchange-outmechanismemulator PB Positivebig PD Proportional,derivative PDE Partialdifferentialequation PI Proportional,integral PID Proportional,integral,derivative PR Probabilisticreasoning PRBS Pseudo-randombinarysequence PS Positivesmall PSD Powerspectraldensity PZT LeadZirconateTitanate(piezoelectricceramicmaterial) RAC Resolved-accelerationcontrol RBF Radialbasisfunction RC Resistance–capacitance RFM Realflexiblemanipulator RFR Rigid–flexible–rigid RH Routh–Hurtwiz RHP Righthalfofs-plane RLS Recursiveleastsquares RMRC Resolved-motion-ratecontrol RMS Remotemanipulatorsystem RTAI Real-timeapplicationinterface RTW Real-timeworkshop RVDT Rotaryvariabledifferentialtransformer SC Softcomputing SCEFMAS SimulationandControlEnvironmentforFlexibleManipulator Systems SHM Sharedmemory SIM Dynamicsimulator SISO Single-inputsingle-output SLFM Single-linkflexiblemanipulator SM Symbolicmanipulation SMG Symbolicmodelgenerator SMP SystemformonitoringandmaintainingMSSroboticsoperators performance SMT STVFtest-bed SMT-SIM SMTdynamicsimulator xxiv Flexiblerobotmanipulators SPDM Specialpurposedextrousmanipulator SSRMS Spacestationremotemanipulatorsystem STVF SPDMtestverificationfacility TLFM Two-linkflexiblemanipulator USB UniversalSerialBus VR Visualrenderer VRM Virtualrigidmanipulator VSC Variablestructurecontrol ZN Ziegler–Nichols ZPETC Zerophaseerrortrackingcontroller ZV Zerovibration ZVD Zerovibrationandderivative 1D One-dimensional 1DOF One-degree-of-freedom 2D Two-dimensional 2DOF Two-degrees-of-freedom 3D Three-dimensional Notations a Thicknessofbeam b Widthofbeamandofsmartmaterial a,b,c Constants,parameters,coefficientsofpolynomials i i i a Absolutelinearaccelerationvectorofpointpexpressedinthebody p referenceframe a ,a Absolutelinearaccelerationvectorofthebodyreferenceframeand n k ofthecrosssectionreferenceframe,expressedinthebody referenceframe a Matrixelement ij A Cross-sectionalarea A Generalizedaccelerationvectorofbodyreferenceframen n A,B,C Systemstatematrices bm Biasonthejthneuronofthemthlayer j B ,(cid:2)B Abodyanditssurfaceinthereferenceundeformedconfiguration no no B∈R3 Magneticfluxdensityvector cM ∈R6×6 Symmetricmatrixofelasticstiffnesscoefficientsofthebeam cS ∈R6×6 Symmetricmatrixofelasticstiffnesscoefficientsofthesmartmaterial c Thicknessofuppersurfacesmartmaterialpatch 1 cM Stiffnessofthebeam 11 cS Stiffnessofthepiezoelectricmaterial 11 c Thicknessoflowersurfacesmartmaterialpatch 2 c Stiffnessperunitlengthofthebeam L1 c Stiffnessperunitlengthofthesmartmaterial L2 C,C Kineticenergy,capacitance n C Actuatorvoltageconstant a C Sensorvoltageconstant s d Constant d Componentsofthedisplacementgradientstrainvector i d Piezoelectricchargeconstant 31 D Dampingmatrix D Displacementgradientstrainvectoratabeamcrosssection xxvi Flexiblerobotmanipulators D(x,t)∈R3 Electricaldisplacementatlocationxandtimet e Error e˙ Changeinerror e ,e ,e Unitvectorsalongtheaxisofthecrosssectionreferenceframe, 1 2 3 expressedinthebodyreferenceframe E ,E ,E Unitvectorsalongtheaxisofthebodyreferenceframe,expressed 1 2 3 intheinertialreferenceframe E Youngmodulus E ActuatinglayerYoung’smodulus a E Systemkineticenergy K E Systempotentialenergy P E∈R3 Electricalfieldintensityvector E[.] Expectation f NaturalfrequencyinHz n f Forceperunitareaappliedonthesurfaceofabeam s fn,fnˆ Forceperunitareaappliedonthebaseandtipofabeam f(cid:2)B¯no Forceperunitareaappliedonthelateralfacesofabeam excludingtheedgesofthefirstandlastcrosssection F(t) Forcefunction F ,M Resultingexternalforceandmomentappliedattheoriginofthe n n bodyreferenceframe F(cid:2)B¯no ,M(cid:2)B¯no Resultingexternalforceandmomentperunitlengthappliedatthe originofthecrosssectionreferenceframe Fnˆ ,Mnˆ Resultingexternalforceandmomentappliedatthe originofthetipcrosssectionreferenceframe FM ∈R6 Simplifiedstressvectorofthebeam FS ∈R6 Simplifiedstressvectorofthesmartmaterial g Numberofgenerationingeneticalgorithms g Gravitationalaccelerationvectorexpressedinthebodyreference frame g Maximumnumberofgenerationingeneticalgorithms max g Piezoelectricstressconstant 31 G Green–Lagrangestraintensor G HalfYoungmodulus,G =E/2 G Green–Lagrangestrainvectoratabeamcrosssection b G(s) Transferfunction(continuous) h∈R6×3 Couplingcoefficientsmatrix h Couplingparameterperunitvolumeofthepiezoelectricmaterial 12 h Couplingparameterperunitlengthofthesmartmaterialrobot L H(x,t)∈R3 Magneticfieldintensityatlocationxandtimet H Depth/heightofarm/link H(jω) Frequencyresponsefunction Hnω ,Hnv RotationandtranslationJacobianmatricesofjointn i Constants,index,polynomial/modelorder Listofnotations xxvii I Areamomentofinertia I Identitymatrix I Hubinertia h Ip Inertiaassoci(cid:2)atedwithpay(cid:3)load I Totalinertia I +l3ρA/3 T h j Constants,index,polynomial/modelorder,unitimaginarynumber J Costfunction J Jexpressedinthebodyreferenceframe k J,I ,I Torsionalandbendinggeometricmomentsofinertia. 2 3 J ElasticrotationJacobianofthekthcrosssection Rek J Secondmomentofinertiatensorofrigidbodynexpressedinthe n bodyreferenceframe J ElastictranslationJacobianofthekthcrosssection Tk k Constant,index J Geometricalmomentsofinertiatensorofacrosssectionrelativeto k andexpressedinthecrosssectionreferenceframe K Controloutputscalingfactor c K Stiffnessmatrix K Vectorofbendingcurvaturesexpressedinthecrosssection k referenceframe K Elementalstiffnessmatrix n k Piezoelectricelectromagneticcouplingconstant 31 K ,K ,K ComponentsofK .K isthetorsionalstrain,andK andK arethe 1 2 3 k 1 2 3 bendingstrains K ,K,K Proportional,integral,derivativeparametersinPIDcontrol p i d K DerivativegaininPDcontrol v l Elementallength L Lengthofarm/link L Lagrangian g m TotalnumberofNNsinanMNN m Payloadatend-point 3 M Massmatrix M Elementalmassmatrix n M Massmatrixofflexiblebeamn en M (x,t) Localmomentinducedinbeambypiezoelectricactuatinglayer a M Payloadmass p m Elementsofmassmatrix ij n Constant,numberofelements,numberofmodes N Constant,numberofsamples N Coriollisandcentrifugalforcetermsofbodyn n N¯ Generalizedforcevectorcontemplatingnon-linearinertialforces, en linearelasticforcesandthegeneralizedexternalforcesappliedon theboundaryofthebeam N(x),N (x) Shapefunctionvector a O OriginofCartesiancoordinatesystem xxviiiFlexiblerobotmanipulators {O ,X Y Z } Inertialreferenceframe I I I I {O ,X Y Z } Bodynreferenceframe n n n n {O ,X Y Z } Beamcrosssectionk referenceframe k k k k OX Y LocalreferenceframewithaxisOX tangentialtothebeamat 1 1 1 thebase OX Y Fixedbaseframe 0 0 p Constant,pole P Crossoverprobability c P Mutationprobability m P Dynamiccrossoverprobability cd P Dynamicmutationprobability md P,P Potentialenergy n q Globalvectoroftheelasticgeneralizedcoordinatesofabeam en q Vectorofpurebendingdisplacementandpuretorsionangle Kn generalizedcoordinates qϕ Vectorofpuresheardisplacementgeneralisedcoordinates n qnω ,qnv Vectorsofangularandlinearpositionparametersofjointn Q(t),Q (t) Nodaldisplacementvector a Q(t) Totalchargeinsensinglayer q(x,t) Chargedistributioninsensinglayer q (t) Time-dependentgeneralizedcoordinates i r PositionvectorofpointPexpressedinthefixedbaseframe r Referenceinput r Positionvectorofbodyreferenceframenrelativetoandexpressed n intheinertialreferenceframe r Positionvectorofmaterialpointprelativetoandexpressedinthe p inertialreferenceframe rn−1,n Vectordescribingthepositionofbodynrelativetobodyn−1, expressedinbodyn−1referenceframe R Rotationmatrixfromtheinertialreferenceframetobody n nreferenceframe R Rotationmatrixfrombodynreferenceframetocrosssection ek k referenceframe Rn/n−1 Orthogonalrotationmatrixexpressingtherotationofbodynrelative tobodyn−1 s Laplacevariable S∈R6 Simplifiedstrainvector t Time(continuous) t, t Tangentvectortothebeamneutralfibreexpressedinthebody k referenceframe,andexpressedinthecrosssectionreferenceframe t ,t ,t Respectivethicknessesofpiezoelectricactuator,beamand a b c piezoelectricsensor T Totalelapsedtimeofthedesiredtrajectory T Generalizedcontrolforcevectoratjointn n u Plantinput,controloutput