modeling cellular actuator arrays

156 Pages·2013·7.52 MB·English

MODELINGCELLULARACTUATORARRAYS
AThesis
Presentedto
TheAcademicFaculty
by
DavidL.MacNair
InPartialFulfillment
oftheRequirementsfortheDegree
DoctorofPhilosophyinthe
TheGeorgeWoodruffSchoolofMechanicalEngineering
GeorgiaInstituteofTechnology
December2013
Copyright(cid:13)c 2013byDavidL.MacNair
MODELINGCELLULARACTUATORARRAYS
Approvedby:
Dr. JunUeda,Advisor Dr. MikeStilman
GeorgiaWWoodruffSchoolofMechanical SchoolofInteractiveComputing
Engineering GeorgiaInstituteofTechnology
GeorgiaInstituteofTechnology
Dr. Kok-MengLee Dr. JeannetteYen
GeorgiaWWoodruffSchoolofMechanical SchoolofBiology
Engineering GeorgiaInstituteofTechnology
GeorgiaInstituteofTechnology
Dr. HarveyLipkin DateApproved: August2013
GeorgiaWWoodruffSchoolofMechanical
Engineering
GeorgiaInstituteofTechnology
ACKNOWLEDGEMENTS
This material is based upon work supported by the National Science Foundation under Grant
No. ECCS-0932208
iii
TABLEOFCONTENTS
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LISTOFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LISTOFSYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
I INTRODUCTIONANDLITERATURESURVEY . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 TraditionalActuationDrawbacks . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 BiologicalAdvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 NaturalMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.4 ArtificialMusclesforRehabilitationandQuality-of-Life . . . . . . . . . 7
1.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 NaturalMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 MuscleOptimalityCriteria . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3 BiologicalMuscleStructure . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.4 StochasticEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.5 GraphTheoreticModeling . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 ResearchGoals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
II ARRAYSTRUCTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 ConnectingStructures(Masses) . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 IncidenceMatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Fingerprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.1 FingerprintDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2 FingerprinttoIncidenceMatrixRelationship . . . . . . . . . . . . . . . . 24
2.4.3 FingerprintAutogeneration . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 IncidenceMatrixIdentityandSimilarityTransforms . . . . . . . . . . . . . . . . 28
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2.5.1 IncidenceMatrixIdentityTransforms . . . . . . . . . . . . . . . . . . . 29
2.5.2 IncidenceMatrixSimilarityTransforms . . . . . . . . . . . . . . . . . . 31
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
III DYNAMICMODELING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 Hill-TypeCellModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 GeneralLinearDynamicCellEquations . . . . . . . . . . . . . . . . . . . . . . 37
3.3 State-SpaceStateVectorandInputVector . . . . . . . . . . . . . . . . . . . . . 40
3.4 GeneralDynamicSystemModelingMethod . . . . . . . . . . . . . . . . . . . . 41
3.5 Hill-TypeArrayExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 DynamicNumericalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.6.1 AlgorithmComparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.7 GeneralLinearDynamicEquationsProof . . . . . . . . . . . . . . . . . . . . . . 63
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
IV OUTSIDEDYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1 OutsideDynamicsProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.1 ρDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1.2 ΛDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.3 ΨDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1.4 ΞDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2 RemovalofDuplicateStates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 OutsideDynamicsExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.1 ρComponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.2 ΛComponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.3 ΨComponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.4 ΞDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.4 HierarchicalActuatorArrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5 NumericalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
V STATICMODELING,SIGNALDISTRIBUTION,ANDNON-LINEARCELLS . 102
5.1 StaticModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.1.1 StaticForceFunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
v
5.2 Forward-LoopSignalDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.1 ProbabilisticSignalDistribution . . . . . . . . . . . . . . . . . . . . . . 105
5.3 StaticProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4 Non-LinearCells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.4.1 Non-LinearDerivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.4.2 Non-LinearNumericalExample . . . . . . . . . . . . . . . . . . . . . . 112
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
VI EXPERIMENTALVALIDATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.1 StaticSolenoidArrayExperiment . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.1.1 ExperimentalSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.2 SolenoidArrayExperimentalResults . . . . . . . . . . . . . . . . . . . . 117
6.1.3 StaticandStochasticAnalysis . . . . . . . . . . . . . . . . . . . . . . . 117
6.2 DynamicSMAExperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.1 DampedSMAArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.2 DynamicSMAArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2.3 DampedSMAArrayExperimentalResults . . . . . . . . . . . . . . . . . 124
6.2.4 DynamicSMAArrayExperimentalResults . . . . . . . . . . . . . . . . 125
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
VII CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.2.1 RelateIncidenceMatrixtoActuatorArrayProperties . . . . . . . . . . . 132
7.2.2 ExpandCoverageofDynamicTheory . . . . . . . . . . . . . . . . . . . 132
7.2.3 Multi-DegreeofFreedomSystems . . . . . . . . . . . . . . . . . . . . . 133
7.2.4 UnderstandingNaturalMotion . . . . . . . . . . . . . . . . . . . . . . . 133
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
vi
LISTOFTABLES
1 CellReferenceVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2 CellEffectVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 StateVectorVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 InputVectorVariables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5 ModelingEquationGuide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6 GeneralArrayVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7 ComparisonofpresenteddynamicsmethodandMatlab’sSimMechanicsenvironment. 60
8 ExampleActuatorArrayProperties. . . . . . . . . . . . . . . . . . . . . . . . . . 110
vii
LISTOFFIGURES
1 Example actuator array (robotic muscle). An actuator array is made from many
small interconnected traditional actuation units (cells) which can combine to carry
greaterloads,achievegreaterdisplacement,andexhibithigherrobustnessthantheir
constituentactuators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Issueswithtraditionalmotor-drivenroboticdevicesincludelackofflexibilitywhich
canleadtodamageorinjury. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Serieselasticactuatorexample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 Multi-actuator examples. Left: Redundant actuation in reconfigurable robotics.
Center: Increased load capacity in parallel robotics applications. Right: Increased
displacementwithoutsacrificingaccuracywithmicro-macroactuators. . . . . . . . 5
5 GraphTheoreticmodelingExample. . . . . . . . . . . . . . . . . . . . . . . . . . 14
6 ResearchGoals. Motivationsarehighlightedbycircleswhileitemsthisworkcovers
arehighlightedwithrectangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7 Hill-Typemodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
8 Explanationofincidencematrixcomponents. Outgoingconnectionsarerepresented
byGandincomingconnectionsarerepresentedbyH. . . . . . . . . . . . . . . . 23
9 Examples of (a) a layer based actuator array approach and (b) a non-layer based
actuatorarray. Thelayerbasedarrayhastwocellsoneachpathbetweenarrayend-
pointswhilethenon-layerbasedarrayhasonepathwithoneandonewithtwo. With
identicalcells,thenon-layerbasedarraywouldlikelygenerateinternalcompressive
forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10 Exampleofbuildingafingerprintfromanactuatorarraytopology. . . . . . . . . . 24
11 Exampleofbuildingafingerprintfromanactuatorarraytopology. . . . . . . . . . 25
12 Frontsectionautogenerationexample. . . . . . . . . . . . . . . . . . . . . . . . . 26
13 Autogenerationprocesstreeforgeneratingfingerprintsforarrayswith4cells. The
thirdrowineachrepresentationshowsunallocatedcellsremaining. . . . . . . . . . 27
14 Automaticallygenerated23topologiesfor5cells. . . . . . . . . . . . . . . . . . . 28
15 Automaticallygeneratedtopologiesandcomputationaleffortfor1-9cells. . . . . . 29
16 Exampletransitionsbetweenidenticaltopologies. . . . . . . . . . . . . . . . . . . 30
17 DampedHill-TypeCellModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
18 Graphicalrepresentationoftheprocesstogeneratethedynamicequationsofmotion
foranactuatorarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
19 Graphicalrepresentationoftheexampleactuatorarraywiththefingerprintgivenin
(51). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
viii
20 IsometricandDisplacementtrialsconductedfornumericactuatorarraytests. . . . 60
21 ShapedInputandStepInputusedfornumericalsimulation. . . . . . . . . . . . . . 61
22 Isometric and displacement numeric trials for a 6 cell damped Hill-Type model
actuatorarray. Theleftgraphshowstheisometricforceattherightendpointofthe
array. The right graph shows the displacements of all cells in the array when the
arrayisconnectedtoaload. ThetopologyforthiscellisgiveninFig. 19 . . . . . 61
23 Isometric and displacement numeric trials for a 14 cell damped Hill-Type model
actuatorarray. Theleftgraphshowstheisometricforceattherightendpointofthe
array. The right graph shows the displacements of all cells in the array when the
arrayisconnectedtoaload. ThetopologyforthiscellisgiveninFig. 10 . . . . . 62
24 Isometric and displacement numeric trials for a 100 cell damped Hill-Type model
actuatorarray. Theleftgraphshowstheisometricforceattherightendpointofthe
array. The right graph shows the displacements of all cells in the array when the
arrayisconnectedtoaload. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
25 Displacement numeric trial for a 200 cell damped Hill-Type model actuator array.
The left graph shows the displacements of all cells in the array when the array is
connectedtoaload. Therightgraphshowsthestructureofthearray. . . . . . . . . 63
26 Displacement numeric trial for a 600 cell damped Hill-Type model actuator array.
The left graph shows the displacements of all cells in the array when the array is
connectedtoaload. Therightgraphshowsthestructureofthearray. . . . . . . . . 63
27 Displacementnumerictrialfora1000celldampedHill-Typemodelactuatorarray.
The left graph shows the displacements of all cells in the array when the array is
connectedtoaload. Therightgraphshowsthestructureofthearray. . . . . . . . . 64
28 Left: Dynamic Hill-Type cell model based on Miga NanoMuscle 714 SMA actu-
ators and lightly damped pen springs. Further details of the model are given in
chapter6. Right: Floating-pointquantizedactuationofannon-uniformactuatorarray. 64
29 Camera positioner based on piezoelectric (PZT) actuators shown as an example of
amulti-layerhierarchicalactuatorarray. . . . . . . . . . . . . . . . . . . . . . . . 78
30 SimMechanics model used to evaluate the piezoelectric based camera positioner
actuatorarrayunderisometriccontraction. . . . . . . . . . . . . . . . . . . . . . . 99
31 Force at the end of the piezoelectric based camera positioner actuator array under
isometriccontraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
32 RobustnessMeasure: MinimumCellLosstoUncontrollability=3. . . . . . . . . . 104
33 Exampleactuatorarraysanalyzedusingthefingerprintmethod . . . . . . . . . . . 108
34 ForceprobabilitydensityfunctionforactuatorarrayD. . . . . . . . . . . . . . . . 109
35 Normalizedforcefunctionforallarraytopologies . . . . . . . . . . . . . . . . . . 109
36 Forcevarianceofexamplearraysusingnormalizedforcefunction . . . . . . . . . 110
37 Forcevarianceofexamplearraysusingnormalizedforcefunction . . . . . . . . . 112
ix
38 Forcevarianceofexamplearraysusingnormalizedforcefunction . . . . . . . . . 112
39 Experimentalactuatorarraysusedtovalidatethetheorypresentedinthisthesis. . . 114
40 Solenoidactuatorarrayexperimentalsetup. . . . . . . . . . . . . . . . . . . . . . 115
41 Solenoidactuatorarraycontroldiagram . . . . . . . . . . . . . . . . . . . . . . . 116
42 Coupling among solenoid actuator array units. Units with the same number were
treatedasbelongingtothesamecell. . . . . . . . . . . . . . . . . . . . . . . . . . 116
43 Solenoid actuator array experimental results. (a) shows the mean force generated,
whichwashighlylinear. (b)showsthevarianceintheforcewhichwasclosetothe
valuescalculatedusingthefingerprintmethod.. . . . . . . . . . . . . . . . . . . . 118
44 Molecular representation and structure of a sarcomere. Image taken from [60] and
usedwithpermissionunderthecreativecommonslicense. . . . . . . . . . . . . . 120
45 Siliconerubberbasedactuatorarray. . . . . . . . . . . . . . . . . . . . . . . . . . 120
46 Biologicalsimilarityofthesiliconerubberbasedactuatorarraycell. . . . . . . . . 122
47 Physical6cellarrayactuatorusedforexperimentalvalidation. . . . . . . . . . . . 124
48 MigaNanoMuscle704SMAactuatorcellmodel. . . . . . . . . . . . . . . . . . . 125
49 Comparisonof4cellactuatorarrayphysicalsystemandsimulatedresults. . . . . . 126
50 Comparisonof6cellactuatorarrayphysicalsystemandsimulatedresults. Allcells
wereactivatedfor3secondsandthendeactivated. . . . . . . . . . . . . . . . . . . 127
x