Cellular Actuators. Modularity and Variability in Muscle-Inspired Actuation

374 Pages·2017·23.97 MB·English

by  Jun Ueda

Cellular Actuators

Cellular Actuators
Modularity and Variability in
Muscle-inspired Actuation
Jun Ueda
Georgia Institute of Technology, 771 Ferst Drive,
Atlanta, GA 30332
Joshua A. Schultz
The University of Tulsa, 800 South Tucker Drive,
Tulsa, OK 74104
H. Harry Asada
Massachusetts Institute of Technology, 77 Mas-
sachusetts Avenue, MA 02139
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List of figures
Fig.I Qualitativecomparisonofactuatormaterialsandnaturalmuscle. xxvi
Fig.II Molecularrepresentationandstructureofasarcomere.Imagetakenfrom
[188]andusedwithpermissionunderthecreativecommonslicense. xxix
Fig.III BistableON–OFFControl.©2007SAGEPublications xxxi
Fig.IV BistableON–OFFcontrolofactuatormaterials.©2007SAGEPublications,
modifiedandreprintedwithpermission xxxi
Fig.V Communicationbetweencontrollerandcellularunits. xxxii
Fig.VI Broadcastcontrolandstochasticdecisionmaking. xxxiii
Fig.VII Traditionalcontrolparadigmonacellularactuator:(A)contrastedwith
aparadigmthatoperatesbyrecruitment;(B)usingrecruitmenttakes
advantageofthecellularstructure.(Forinterpretationofthecolorsinthis
figure,thereaderisreferredtothewebversionofthisIntroduction.) xxxiv
Fig.VIII Broadcastfeedback. xxxv
Fig.1.1 Piezoelectricactuatormodel. 2
Fig.1.2 Piezostackactuator.CourtesyofCEDRAT,Inc. 2
Fig.1.3 BenderPiezoActuatororbimetaltypeactuator.CourtesyofPI. 3
Fig.1.4 Moonieactuator:(left)from[182]and(right)courtesyofCEDRAT,Inc. 3
Fig.1.5 Cymbalactuator[60].©1997IEEE,reprintedwithpermission 4
Fig.1.6 Thunderactuator[46].CourtesyofFaceInternationalCorporation. 4
Fig.1.7 ExtensilePZTstrainamplifier:(A)single-cellextendingPZTactuator
model,(B)fabricatedthreecellPZTactuator.©2006IEEE,reprintedwith
permission 5
Fig.1.8 Force–displacementcurveoftheexpandingPZTactuator.©2006IEEE,
reprintedwithpermission 5
Fig.1.9 MEMS–PZTcellularactuator:(A)alargestraincontractingPZTactuator
celldesign,(B)seriallystackedandconnectedPZTactuatorcellsintoa
module.©2006IEEE 6
Fig.1.10 Nestedstructureforexponentialstrainamplification. 7
Fig.1.11 Amplificationprincipleofflextensionalmechanisms[182].©2010IEEE,
reprintedwithpermission 8
Fig.1.12 Generalizednestingforexponentialstrainamplification.Thestrainis
amplifiedbythreelayersofrhombusstrainamplificationmechanisms,with
thefirstlayer,calledanactuatorlayer,consistingofthesmallestrhombi
directlyattachedtotheindividualPZTstackactuators.©2010IEEE,
reprintedwithpermission 10
Fig.1.13 Three-dimensionalnestingfor20%strain.©2010IEEE,reprintedwith
permission 11
Fig.1.14 Schematic assembly of nested rhombus multi-layer mechanism.
©2013Springer,reprintedwithpermission 11
Fig.1.15 ActuatorcoordinatesystemofPZTstackactuator.©2010IEEE,reprinted
withpermission 13
viii CellularActuators
Fig.1.16 Three-dimensionalstackingofactuatorunits.©2007IEEE,reprintedwith
permission 14
Fig.1.17 Idealizedanalysis.Complianceoftheamplificationmechanismisnot
considered.©2010IEEE,reprintedwithpermission 15
Fig.1.18 Finallayerconnection.©2007IEEE,reprintedwithpermission 16
Fig.1.19 Reconfigurabilityofthecellularactuators.©2007IEEE,reprintedwith
permission 16
Fig.1.20 ModelofPZTstackactuatorconnectedtoaspringload. 18
Fig.1.21 Embodimentofarhombusmechanism. 18
Fig.1.22 Effectofjointcomplianceonfree-loaddisplacement. 19
Fig.1.23 Effectofbeamcomplianceonblockingforce. 19
Fig.1.24 ModelofRhombusMechanismwithFlexibility. 21
Fig.1.25 SimplifiedRepresentationofLumpedParameterModel. 24
Fig.1.26 Recursiveformulaforanestedrhombusmodel. 24
Fig.1.27 Exampleamplificationmechanisms. 26
Fig.1.28 Requirementofinput–outputbidirectionality. 28
Fig.1.29 Designofarhombusmechanismforthe2ndlayer. 29
Fig.1.30 Choiceofaˆ forpositivespringconstants. 30
Fig.1.31 Prototypeactuator:6CEDRATactuatorsareusedforthefirstlayer. 31
Fig.1.32 Snapshotsoffree-loaddisplacement:Twonestedrhombusmechanisms
areconnectedinseries.Eachunitgeneratesapproximately21%effective
straincomparedwithitsoriginallength.©2008ASME,reprintedwith
permission 31
Fig.1.33 Experimentalresult. 32
Fig.1.34 BinaryON–OFFControlExperiment. 33
Fig.1.35 Microgripper.©2012Springer,reprintedwithpermission 33
Fig.1.36 Micromanipulator.©2012Springer,reprintedwithpermission 34
Fig.1.37 (A)Workingprincipleshowingdeformedandundeformedflexuresintwo
planes.(B)A5cellartificialmuscleactuatorbasedonPZT-drivenflexures.
ThephysicalprototypeusestwoNECTokinPZTStacks.©2010IEEE,
reprintedwithpermission 34
Fig.1.38 Fabricationofthecellularactuatorarraysand1-DOFroboticarm. 35
Fig.1.39 MotionofthePZT-driven1-DOFroboticarm. 36
Fig.1.40 Assembledend-effectornestingactuatormodule. 36
Fig.1.41 Assemblyofatweezer-stylepiezoelectricend-effector. 37
Fig.1.42 Schematicmodeloftheend-effectorstructure.©2010JSME,reprintedwith
permission 38
Fig.1.43 Drawingsofthetweezer-styleend-effector.©2010JSME,reprintedwith
permission 38
Fig.1.44 Fabricatedend-effector. 39
Fig.1.45 Motionoftheend-effector.Thedevelopedend-effectorhasareverseaction
mechanism;thetipsclosewhentheactuatorsareenergized. 39
Fig.1.46 Displacementandforceperformance.Circlesareforward(from0to
150[V])andinverse-trianglesarebackward(from150to0[V])directions;
notethat(A)showstheabsolutedisplacementofoneoftheend-points.The
totaldisplacementistwiceofthismeasurement.©2012IEEE,reprinted
withpermission 39
Fig.1.47 Manipulationusingthetweezer-styleroboticend-effector. 40
Listoffigures ix
Fig.1.48 Three-layerrhomboidalamplificationmechanism. 41
Fig.1.49 Roboticvisionsystem.©2015SAGE,reprintedwithpermission 42
Fig.1.50 Pictorialrepresentationofthecameraorientationsystem[219].Thecamera
positionerdrivenbyanantagonisticpairofcellularactuators. 43
Fig.1.51 Singledegree-of-freedommotionofthecameraorientationsystem.
©2013IEEE,reprintedwithpermission 43
Fig.1.52 Muscle-likecomplianceoftheamplificationmechanism:(Left)lumped
parametermodeloftheactuator;(Right)Hill’smusclemodel[294]with
contractileelement(CE)thatproducesforce,serieselement(SE),parallel
element(PE),anddampingelement(DE).ltendon isthelengthofthe
tendon,lmuscle isthelengthofthemuscle,andξ isthepennationangleof
themuscle. 44
Fig.2.1 Anoverlysimplisticunderstandingoftheamplificationprincipleof
arhomboidalstrainamplifyingmechanismthatdoesnotaccountfor
deformationinthepiezoelectricmaterialandtherhomboiditself. 46
Fig.2.2 Arepresentationofatwo-portnetworkmodel.©2013IEEE,reprintedwith
permission 47
Fig.2.3 Free-bodydiagramofaflexiblesegment. 52
Fig.2.4 Doublysymmetricactuatorcomposedofstraightsegments. 53
Fig.2.5 Comparisonofanactuatorwiththesameouterlayeranddifferentnumbers
ofinternalsubunits. 58
Fig.2.6 Activeandinactivesubunitsrepresentedassprings. 59
Fig.2.7 Seriescombinationdisplacementratio. 61
Fig.2.8 Seriescombinationforceratio. 61
Fig.2.9 Multi-layernestedgeometrywithreuseofacompliantmechanism.
©2013IEEE,reprintedwithpermission 63
Fig.2.10 Boundsondisplacementfigureofmerit. 65
Fig.2.11 Variationinfigureofmeritwithangleandthickness.©2013IEEE,reprinted
withpermission 65
Fig.2.12 Existingactuatorforwhichahigherfreedisplacementisdesired. 66
Fig.2.13 Adding an additional strain amplifying mechanism to amplify the
displacementoftheactuatorinFig.2.12stillfurther. 67
Fig.2.14 Generaloctagonalrhomboidalshapeshowingthegeometricparameters.
The depth into the page of the shape will be denoted b, i.e., the
finalimplementationwillbemachinedfromaplateofthicknessb.
©2013IEEE 71
Fig.2.15 Mechanismcharacteristicsusedinexperiment.Parametersareasin
Fig.2.14.©2013IEEE,reprintedwithpermission 74
Fig.2.16 Firstexperiment(inputfixed).©2013IEEE,reprintedwithpermission 76
Fig.2.17 Secondexperiment(outputfree).©2013IEEE,reprintedwithpermission 76
Fig.2.18 Variationinimmittanceparameters:(A)s1,(B)s2,and(C)s3withgeometry.
©2013IEEE,reprintedwithpermission 78
Fig.2.19 Singledegreeoffreedomroboticjoint.Theagonist(left)isactivatedand
contracts.Theantagonist(right)behavesasapassivestiffness.Thisaffects
therelationshipbetweenappliedloadandjointangle. 82
Fig.2.20 Collapsingoftwo-portnetworks.Eachsquareboxrepresentsatwo-port
network,withavoltageandcurrentattheright-andleft-handports.The
entirehierarchywithinthedashedlinesiscollapsedandreplacedwithits
Nortoncircuit.©2013IEEE,reprintedwithpermission 85
x CellularActuators
Fig.2.21 Two-portrepresentationofantagonisticpairs.Theactiveactuatorisinblack
andhasallbuttheoutermostlayercollapsedandrepresentedbyitsNorton
circuit.Thepassiveactuatorisingrayandiswillbereplacedbyasimple
stiffness.©2013IEEE,reprintedwithpermission 86
Fig.2.22 Convergenceofthevariousstiffnessapproximationsforahypothetical
many-layeredmechanismwithrandomlychosenimmittances.yk is
theinput-fixedapproximationthroughlayerk,andxk istheinput-free
approximation.©2013IEEE,reprintedwithpermission 92
Fig.2.23 PZTstackwithasinglelayerofamplification.©2012IEEE,reprintedwith
permission 96
Fig.2.24 Parameterizationofarhomboidalmechanism.©2012IEEE,reprintedwith
permission 96
Fig.2.25 PZTstackwithtwolayersofamplification.©2012IEEE,reprintedwith
permission 97
Fig.2.26 Parameterspaceregionforatwo-layermechanism. 98
Fig.2.27 Atwo-layeractuatordesignthatmeetsthe8mmdisplacementspecification.
Thisdesignwasrejectedinfavorofathree-layermechanismbecausethe
“bow-tie”shapewasnotasgoodofauseofspaceandposedmanufacturing
difficulties. 98
Fig.2.28 Customstrainamplifierforthetwo-layeractuatorthatamplifiesaseries
chainof16CédratAPA50XSamplifiedpiezoelectricstacks. 98
Fig.2.29 PZTstackwiththreelayersofamplification. 100
Fig.2.30 Blockedforcevariationwithgeometry. 102
Fig.2.31 Secondlayereffectonblockedforce. 102
Fig.2.32 Hill-typemodel. 106
Fig.2.33 Explanationofincidencematrixcomponentsforalayerbasedactuator
arraytopology:OutgoingconnectionsarerepresentedbyGandincoming
connectionsarerepresentedbyH. 108
Fig.2.34 Examplesof(A)alayerbasedactuatorarraystructureand(B)anon-layer
basedactuatorstructure.Thelayerbasedarrayhastwocellsoneachpath
betweenarrayendpointswhilethenon-layerbasedarrayhasonepathwith
oneandonewithtwo.Withidenticalcells,thenon-layerbasedarraywould
likelygenerateinternalcompressiveforces. 108
Fig.2.35 Examplearraytopologies.©2011SAGEPublications,reprintedwith
permission 109
Fig.2.36 Exampleofbuildingafingerprintfromanactuatorarraytopology. 109
Fig.2.37 Incidencematrixrepresentationofafingerprint. 110
Fig.2.38 Frontsectionautogenerationexample.©2011SAGE,reprintedwith
permission 111
Fig.2.39 Autogenerationprocesstreeforgeneratingfingerprintsforarrayswith
4cells.Thethirdrowineachrepresentationshowsunallocatedcells
remaining. 112
Fig.2.40 Automaticallygenerated23topologiesfor5cells.©2011SAGE,reprinted
withpermission 112
Fig.2.41 Automaticallygeneratedtopologiesandcomputationaleffortfor1–9
cells. 113
Fig.2.42 Exampletransitionsbetweenidenticaltopologies. 115
Fig.2.43 Robustnessmeasure:“minimumcelllosstouncontrollability”=3. 117
Listoffigures xi
Fig.2.44 Dynamicmodelingofathree-layerhierarchicalactuatorarray. 118
Fig.2.45 Forceattheendofthepiezoelectricbasedcamerapositioneractuatorarray
underisometriccontraction. 118
Fig.3.1 Referencecommandgoingfrom0to3unitsactiveafterbeingputthrougha
ZVshaperwitha63msdelay. 123
Fig.3.2 Vectordiagramshowingimpulsesrepresentedasphasorsinthecomplex
plane.Thevectordiagramsfortwofrequenciesaresuperimposedontopof
oneanother.Thelowerfrequencyisshownwiththesolidarrows,thehigher
ofthetwoasthedashedarrows.ThephaseoftheimpulseA1,φ1,isshown
explicitly.Tobeavibrationsuppressingcommand,bothsetsofimpulses
mustsumtozerointhecomplexplane. 125
Fig.3.3 Illustrationofall-ONall-OFFcontrolforamovefrom0to4unitsON
(greendenotestheONstateinboththeplotandtheillustration).(For
interpretationofthereferencestocolorinthisfigurelegend,thereaderis
referredtothewebversionofthissection.) 127
Fig.3.4 Close-upviewofthetwo-layercantileveredactuatorusestovalidatethe
DSVSmethod. 131
Fig.3.5 Significantvibrationmodesofthecellularactuator.©2012IEEE,reprinted
withpermission 132
Fig.3.6 Flowchartdepictingalgorithmtodetermineswitchingpattern.©2012IEEE,
reprintedwithpermission 134
Fig.3.7 VenndiagramillustratingthevariousDiscreteSwitchingVibration
SuppressionCommands. 136
Fig.3.8 Diagramofhowarbnovib2f.mfindsacommandthatmeetsthegoalyg
andsuppressesthetwomodesofvibration.©2012IEEE,reprintedwith
permission 138
Fig.3.9 MSDSVSexperimentalsetup.©2012IEEE,reprintedwithpermission 141
Fig.3.10 Frequencyresponseofcellularactuator.©2012IEEE,reprintedwith
permission 142
Fig.3.11 Variouscommandstoposition1. 143
Fig.3.12 Variouscommandstoposition2. 143
Fig.3.13 Variouscommandstoposition3. 144
Fig.3.14 Variouscommandstoposition4. 144
Fig.3.15 Variouscommandstoposition5. 144
Fig.3.16 Variouscommandstoposition6. 145
Fig.3.17 Responsetocommandstoposition6. 145
Fig.3.18 Residualoscillation,largestFFTcomponent. 146
Fig.3.19 RMSoscillation,normalizedbymovedistance.©2012IEEE,reprinted
withpermission 146
Fig.3.20 Framesfromhigh-speedvideoshowingthemotionoftheactuator:
(A)actuatorbeforethecommandisapplied,(B)maximumexcursionwhen
all6inputsareactivatedatonce,(C)actuatoratmaximumexcursionunder
anMSDSVScommandfromposition0to6,and(D)actuatoratmaximum
excursionunderAllON/AllOFFcontrolfromposition0to6. 147
xii CellularActuators
Fig.3.21 Oscilloscopecaptureofthecellularactuatorreceivingasinusoidalinput.
Thegreensignalisfromafunctiongenerator,theyellowisthehighvoltage
signalacrossthePZTstackfromtheamplifier.Thebluecurveisthe
displacementofthecellularactuator,measuredbytheOptoNCDTlaser
positionsensor.Noticethatalthoughtheinputvoltageissinusoidal,the
displacementisnot.(Forinterpretationofthereferencestocolorinthis
figurelegend,thereaderisreferredtothewebversionofthissection.) 148
Fig.3.22 Energyconsumptionpermove.©2012IEEE,reprintedwithpermission 150
Fig.3.23 SensitivityplotforAllON/AllOFFcontrolandMSDSVS.©2012IEEE,
reprintedwithpermission 151
Fig.3.24 Responsewhencommandandplantfrequencymismatched. 152
Fig.3.25 Splitshotsinkersattachedtothecellularactuatortoshifttheresonant
frequencyofthefirstmode. 152
Fig.3.26 Cellularactuatorresponsewhenthenaturalfrequencyischangedbyadding
masstotheactuator.©2012IEEE,reprintedwithpermission 153
Fig.3.27 Singlecell. 154
Fig.3.28 AggregateMarkovmodel. 155
Fig.3.29 ProbabilitydistributionfordifferentN. 156
Fig.3.30 Broadcast feedback for a cellular control system with distributed
decision-makingunits. 157
Fig.3.31 Compensationfortheerrorbyclosed-loopcontrol. 158
Fig.3.32 Singlecellwithunilateraltransitioncontrol. 161
Fig.3.33 Stabletransitionprobabilities. 163
Fig.3.34 Simulationsnapshots:(white)ONcell,(black)OFFcell. 165
Fig.3.35 Simulationresults:stepresponse. 166
Fig.3.36 Simulationresults:sinusoidaltrajectorytracking. 167
Fig.3.37 Distributionofthecelllength.©2007IEEE,reprintedwithpermission 169
Fig.3.38 Stabletransitionprobabilities.©2007IEEE,reprintedwithpermission 170
Fig.3.39 SimulationresultsforN = 25withnon-uniformtransitionprobability.
©2007IEEE,reprintedwithpermission 170
Fig.3.40 SimulationresultsforN =25withnon-uniformcelllength.©2007IEEE,
reprintedwithpermission 170
Fig.3.41 SimulationresultsforN =1000withnon-uniformcelllength,non-uniform
transitionprobability,and20%ofdeadcells.©2007IEEE,reprintedwith
permission 171
Fig.3.42 Input–outputcharacteristicsofhystereticmaterials.©2011ASME,Wood,
L.,reprintedwithpermission 173
Fig.3.43 Coordinatedcontrolofmultitudeofcellularunits.©2011ASME,Wood,
L.,reprintedwithpermission 173
Fig.3.44 HysteresisloopcontrolofSMAactuatorunit. 175
Fig.3.45 Statetransitionofhysteresisloopcontrol. 175
Fig.3.46 Mappingoftransitionprobabilityprofilesonhysteresisloop. 176
Fig.3.47 Broadcastfeedbackwithlocalizedstochasticrecruitment(BFSR)forSMA
cellularactuatorarray.©2006IEEE,reprintedwithpermission 177
Fig.3.48 Centralizedbinary-schemerecruitment(CBR).©2006IEEE,reprintedwith
permission 179
Fig.3.49 Binaryrecruitment.©2006IEEE,reprintedwithpermission 179
Fig.3.50 Centralizedsequentialrecruitmentofuniformsegments(CSR). 179