Flexible Robot Manipulators - Modelling, Simulation and Control

569 Pages·2008·8.799 MB·English

by  Tokhi, M.O., Azad, A.K.M.(eds.)

Flexible Robot
Manipulators
Modelling, simulation and control
Edited by
M.O. Tokhi and A.K.M. Azad
TheInstitutionofEngineeringandTechnology
PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom
©2008TheInstitutionofEngineeringandTechnology
Firstpublished2008
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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