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Needle Insertion for Robotic Surgery

Permanent Link: http://ufdc.ufl.edu/UFE0044791/00001

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Title: Needle Insertion for Robotic Surgery
Physical Description: 1 online resource (57 p.)
Language: english
Creator: Laplassotte, Celine
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: control -- needle -- robotics
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Many modern clinical practices involve percutaneous needle insertion. This thesis focuses on modeling and automation aspects related to robotic needle insertion. Medical robotics may offer methods for improving such practices. The first contribution is the development of a controller to ensure that a needle tip tracks a trajectory beginning in a non-contact position and ending within viscoelastic tissue. Through employment of a sliding mode controller and a neural network (NN), the controller guarantees semi-global asymptotic tracking of the desired trajectory. The second contribution is the development of a controller to ensure that a needle tip mounted on a slave robot tracks the trajectory given by the surgeon manipulating the  master robot, in the presence of uncertainties in the user and environment forces. The control development leads to semi-global asymptotic tracking of the desired trajectory using a sliding mode controller and a NN. Lyapunov-based stability analysis and simulations are provided to demonstrate the performance of the control designs throughout the thesis.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Celine Laplassotte.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Dixon, Warren E.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044791:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044791/00001

Material Information

Title: Needle Insertion for Robotic Surgery
Physical Description: 1 online resource (57 p.)
Language: english
Creator: Laplassotte, Celine
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: control -- needle -- robotics
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Many modern clinical practices involve percutaneous needle insertion. This thesis focuses on modeling and automation aspects related to robotic needle insertion. Medical robotics may offer methods for improving such practices. The first contribution is the development of a controller to ensure that a needle tip tracks a trajectory beginning in a non-contact position and ending within viscoelastic tissue. Through employment of a sliding mode controller and a neural network (NN), the controller guarantees semi-global asymptotic tracking of the desired trajectory. The second contribution is the development of a controller to ensure that a needle tip mounted on a slave robot tracks the trajectory given by the surgeon manipulating the  master robot, in the presence of uncertainties in the user and environment forces. The control development leads to semi-global asymptotic tracking of the desired trajectory using a sliding mode controller and a NN. Lyapunov-based stability analysis and simulations are provided to demonstrate the performance of the control designs throughout the thesis.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Celine Laplassotte.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Dixon, Warren E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044791:00001


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NEEDLEINSERTIONFORROBOTICSURGERY By CLINELAPLASSOTTE ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2012

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c 2012ClineLaplassotte 2

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Tomyfamilyandmyfriendsfortheirconstantencouragementandlove 3

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ACKNOWLEDGMENTS Firstofall,IwouldliketothankmyadvisorDr.Dixonforgivingmetheopportunityto workinhislaboratory,NonlinearControlsandRobotics,forthetimehespentwithmeandfor hisvaluableadvicesthathelpedmethroughoutmyproject.Ishallalsothankmyresearchgroup inwhichIwasparticularlywellreceivedandforhavingbroughtupalivelyatmosphereinthe dailywork. Furthermore,IamdeeplygratefultoDr.Collet,Pr.Tran-Son-TayandtheAtlantisprogram forhavingallowedmetotakeparttothisgreatexperiencewhichisstudyinginalargeand well-knownuniversityastheUniversityofFloridaforoneyear.AndIwouldliketothankDr. Bayleforhishelpandthefeedbackhegavemeonmywork. IwouldalsoliketoextendmygratitudetomycommitteememberDr.CarlCraneforthe timeandhelphehasprovided. Finally,Iwouldliketothankmyfamilyandmyfriendsfortheirencouragementandallthe peopleIsharemyworkwithattheUniversityofFlorida. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS....................................4 LISTOFFIGURES.......................................7 ABSTRACT...........................................8 CHAPTER 1INTRODUCTION....................................9 1.1MotivationandProblemStatement.........................9 1.2LiteratureReview..................................9 1.3OutlineandContributions.............................11 2NEEDLEINSERTIONFORCEDESIGN........................13 2.1SoftTissueDeformation..............................13 2.2NeedleInsertionForceModeling..........................13 2.2.1StiffnessForce...............................15 2.2.2FrictionForce................................16 2.2.3CuttingForce................................16 3ROBOTICNEEDLEINSERTIONINTOVISCOELASTICTISSUE..........18 3.1DynamicModel...................................18 3.2ControlDevelopment................................19 3.2.1ControlObjective..............................19 3.2.2Closed-LoopErrorSystem.........................20 3.3StabilityAnalysis..................................24 3.4SimulationResults.................................27 4TELEOPERATEDROBOTFORNEEDLEINSERTIONINTOVISCOELASTIC TISSUE..........................................32 4.1DynamicModel...................................32 4.2ControlDevelopment................................33 4.2.1ControlObjectiveandModelTransformation...............33 4.2.2Closed-LoopErrorSystem.........................35 4.3StabilityAnalysis..................................38 4.4SimulationResults.................................42 5CONCLUSION......................................49 5.1SummaryofResults................................49 5.2RecommendationsforFutureWork........................49 5

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REFERENCES.........................................51 BIOGRAPHICALSKETCH..................................57 6

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LISTOFFIGURES Figure page 2-1Needleinsertionsteps...................................14 3-1Multilayerneuralnetworkforjumpfunctionapproximation...............21 3-2Positionsforthesimulation................................28 3-3Positionoftheneedletip x t ...............................29 3-4Positiontrackingerror e t .................................30 3-5Needleforce f needle asafunctionoftime.........................30 3-6Needleforce f needle asafunctionoftheneedletipposition x t .............31 4-1Trajectoryformasterandslaverobotsfor F 1 = 15sin 1 : 1 t ...............44 4-2Positionerrorbetweenmasterandslaverobotfor F 1 = 15sin 1 : 1 t ...........44 4-3Desiredtrajectory x d 2 andpositionof q 1 + q 2 for F 1 = 15sin 1 : 1 t ............45 4-4Errorbetweenthedesiredtrajectory x d 2 and q 1 + q 2 for F 1 = 15sin 1 : 1 t ........45 4-5Trajectoryformasterandslaverobotsfor F 1 = 8.....................46 4-6Positionerrorbetweenmasterandslaverobotfor F 1 = 8.................46 4-7Desiredtrajectory x d 2 andpositionof q 1 + q 2 for F 1 = 8.................47 4-8Errorbetweenthedesiredtrajectory x d 2 and q 1 + q 2 for F 1 = 8..............47 4-9Needleforce f needle asafunctionoftimefor F 1 = 8...................48 4-10Needleforce f needle asafunctionoftheneedletippositionfor F 1 = 8..........48 7

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AbstractofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience NEEDLEINSERTIONFORROBOTICSURGERY By ClineLaplassotte August2012 Chair:WarrenE.Dixon Major:MechanicalEngineering Manymodernclinicalpracticesinvolvepercutaneousneedleinsertion.Thisthesisfocuses onmodelingandautomationaspectsrelatedtoroboticneedleinsertion.Medicalroboticsmay offermethodsforimprovingsuchpractices.Therstcontributionisthedevelopmentofa controllertoensurethataneedletiptracksatrajectorybeginninginanon-contactposition andendingwithinviscoelastictissue.Throughemploymentofaslidingmodecontroller andaneuralnetworkNN,thecontrollerguaranteessemi-globalasymptotictrackingofthe desiredtrajectory.Thesecondcontributionisthedevelopmentofacontrollertoensurethata needletipmountedonaslaverobottracksthetrajectorygivenbythesurgeonmanipulatingthe masterrobot,inthepresenceofuncertaintiesintheuserandenvironmentforces.Thecontrol developmentleadstosemi-globalasymptotictrackingofthedesiredtrajectoryusingasliding modecontrollerandaNN.Lyapunov-basedstabilityanalysisandsimulationsareprovidedto demonstratetheperformanceofthecontroldesignsthroughoutthethesis. 8

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CHAPTER1 INTRODUCTION 1.1MotivationandProblemStatement Medicalroboticshasgainedpopularityoverthelastdecade.Indeed,surgeonsallaroundthe worldusemanipulatorstoperformsurgicalprocedures.Thedevelopmentoftheseprocedures aremotivatedbyandhaveimprovedduetotherapidadvancementofminimallyinvasive procedures[14].Automatedandteleoperatedsystemshavethepotentialtoimprovethesafety andeffectivenessofsurgeriesbyenhancingvisualization,decreasingbleedingandtransfusion rates,andspeedingrecovery[5]. Manyclinicalpracticesinvolvepercutaneousneedleinsertions.Minimallyinvasive percutaneousproceduresincludebiopsies[6]andbrachytherapy[7]butneedleinsertionis alsousedforproceduressuchasbloodsampling[8],neurosurgery[9],andothers.Inthese procedures,oneorseveralneedlespenetrateintothepatient'sbodytoreachtheplannedtarget. Whileautomatedorteleoperatedneedleinsertionsystemscanleadtovariousadvantages, severalissuesmustbeconsideredincluding:thelackofvisibilityofthetarget,thedifcultaccess tothetarget,andrestrictedmaneuverabilitywiththetool.Forinstance,thetargetmaybeclose toasensitiveorganmandatingtheneedforextracautionandhighprecision.Targetingerrorcan occurduetoimaginglimitations,targetuncertaintiesduetophysiologicalorpatientmotion, humanerrorsduetofatigueorhandtremor,tissuedeformationandneedledeection[10].The efciencyofsuchamedicaltreatmentisveryoftenlinkedtotheaccuracyoftheneedleinsertion andtothecontroloftheinsertionforce.Thedesiredaccuracydependsontheapplicationand usuallyrangesfrommillimetertomicro-millimeter.Givensuchaccuracydemands,roboticand teleoperatedsystemshavebecomeincreasinglypopulartoolstoassistmedicalpersonnel. 1.2LiteratureReview Themodelingofneedleinsertionforceintosofttissuecanfacilitateaccuratesurgical simulationsandrobotictechnologiesappliedtopercutaneoustherapy.Thedevelopmentofsuch modelshasbeenthetopicofmanystudies[1117].Knowledgeofforcesduringneedleinsertion 9

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canhelptoidentifyandmodeldifferenttissuetypes.Humanbiologicaltissuesareknown toexhibitnonlinearpropertiesandconsistofinhomogeneousstructures.TheHunt-Crossley model[18]hasbeenconrmedasbeingsuitablefordescribingthepropertiesofviscoelastic tissues[19],especiallywhensmalldeformationsareinvolved[20].HuntandCrossleyshowed thatitispossibletoobtainabehaviorthatisinbetteragreementwiththephysicalintuitionifthe dampingcoefcientismadedependentonthebody'srelativepenetration.Nevertheless,some studiespresumealineartissuemodel,especiallyforcomputationalperformance[21].Oneofthe keyissuesisthattheinsertionforcevariesfromonepatienttoanother.Forthesametissue,the insertionforcecanbedifferentdependingontheage,thegender,orthebodymassofthepatient. Evenforonepatient,theinsertionforceneededforonetissuecanvary,forexample,ifthetissue isdiseased.Moreover,acquiringdatafrombiologicaltissuesanddevelopingappropriatemodels forapplicationinsimulationorrobot-assistedsurgeryisdifcultduetotissuedeformation, inhomogeneity,nonlinearity,andopacity[2224].Asaresult,itisnecessarytodesigntheneedle insertionforcesothatitaccountsfortheuncertaintyintissuecomposition. Inmedicalrobotics,ateleoperatedsystemconsistsofaslaverobotwhichtracksthemotion ofamasterrobotcommandedbyasurgeon,oftenwiththeassistanceofmedicalimaging.Many clinicalapplicationsbenetfromteleoperatedsystems.Exampleproceduresrangesfromteleechography[25,26]tominimallyinvasivesurgery[1,4,5,27,28].Teleoperatedsystemshavethe abilitytoreducethemorbidityofclinicalproceduresbyimprovingthesterileeld,decreasing bleeding,andreducingrecoverytime.However,sincetheclinicianisremovedfromdirect contactwiththepatient,researcheffortshavefocusedonmethodstoprovideimprovedforce reection,compensateforrobotic/tissueuncertainties,andimprovethestabilityandpassivityof thesystem. Thegoalofteleoperationsystemsistoachievepassivityandtransparencywhilemaintaining stability.Passivityisrelatedtoenergydissipation,apassivesystemconsumesenergyanddoes notproduceenergy.Toachieveidealtransparency,theslaverobothastoexactlyreproducethe positiontrajectoryofthemastermanipulator,andthemasterrobothastoaccuratelydisplaythe 10

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environmentforcetothehuman.Manybilateralcontrolarchitectureshavebeendevelopedto reachthesetwoaims[2933].Linearcircuittheory[34]andlinearrobustcontroltheory[35,36] havebeenstudiedinthepast.Someworkshavealsobeendonefornonlinearsystemsusing adaptivecontrol[3740],howeverthesedesignsneedexactmodelknowledge.Someprevious workshighlightedthestabilityandsafeoperationoftheteleoperatorusingthepassivityconcept asin[36,4143].Themethodproposedin[44]makestheteleoperatedsystempassiveusing ctitiousenergystorage.Researchesthataimtoachieveidealtransparencyusuallyrequire knowledgeabouttheenvironmentinputsasin[35],orestimatetheimpedanceoftheslaverobot asin[45].In[46],anadaptivecontrollerisdesignedforteleoperatedsystemswithparametric uncertaintiesinthemasterandslaverobotsdynamics.Timedelaymayalsobeanissue.In[47], abilateralteleoperatorprovidesrobuststabilityagainstconstantdelaybutdoesnotguarantee positiontracking. 1.3OutlineandContributions Chapter 1 servesasanintroduction,thatprovidesmotivation,problemstatement,literature review,andcontributionsofthethesis. Chapter 2 providesabackgrounddiscussiononsofttissuedeformation.Thischapter presentsalsoanovelneedleinsertionforcemodelingforviscoelastictissue.Theforcemodeling isdesignedasthesumofastiffnessforce,africtionforce,andacuttingforce[48].Thesethree forcesarecarefullychosentobeasclosetotherealityaspossible.Thestiffnessforceisdesigned usingtheHunt-Crossleymodel.Thefrictionforceismodeledasin[49].Thecuttingforceis modeledasaconstant. Chapter 3 detailsthedesignofanautomatedcontrollerthatensuressemi-globalasymptotic trackingofatrajectoryforwhichtheneedletipmovesfromanon-contactpositionintoviscoelastictissue.Thestudyisbasedonpreviousworks[5052],wheretheobjectivewastodesign acontrollerforarobotinteractingwithanuncertainHunt-Crossleyviscoelasticenvironment andundergoinganon-contacttocontacttransitionbuttherobotdidnotgointotheviscoelastic environment. 11

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Chapter 4 describesthedevelopmentofateleoperatedcontrollertoensurethataneedle tipmountedonaslaverobottracksthetrajectorygivenbythesurgeonmanipulatingthemaster robot,andgoingfromanon-contactpositionintoviscoelastictissue.Thestudyisbasedona previouswork[53],wheretheobjectivewastodesigntwocontrollersforateleoperatorsystem thattargetscoordinationofthemasterandslavemanipulatorsandpassivityoftheoverallsystem. Asin[53],thereisnoneedtoknowtheuserandenvironmentforcesinthispaper.However,the controldevelopmentusedin[53]isnotapplicableinthecaseofadiscontinuousneedleinsertion force.Then,thecontrollerisdesignedusingaslidingmodetermandneuralnetworkmethod. Chapter 5 givessomeconcludingcommentsandrecommendationsforfuturework. 12

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CHAPTER2 NEEDLEINSERTIONFORCEDESIGN 2.1SoftTissueDeformation Realisticmodelingofsofttissuedeformationduringneedleinsertioncanbeusedand improvedfortrainingandplanningtoreduceerrorsbetweendesiredandactualplacementof theneedletip.Thismodelingiscomplexbecauseoftheinhomogeneous,nonlinear,anisotropic, elasticandviscouspropertiesofsofttissue.Todetermineandunderstandtheseproperties,it isessentialtodosomemeasurementsonsofttissue[54].Manyultrasonicmethodshavebeen developedformeasuringbiomechanicalpropertiesofsofttissues[55,56]. Skinandsofttissueexhibitparticularproperties[57,58].Thecharacteristicsubstances ofthiskindoftissuearethecollagen,elastinandgroundsubstance[59].Atsmallstrains, elastinconfersstiffnesstothetissueandstoresmostofthestrainenergy.Thecollagenbers arecomparativelyinextensibleandareusuallyloose.Softtissueshavethepotentialtoundergo bigdeformationsandstillcomebacktotheinitialcongurationwhenunloaded.Thenonlinear stress-strainrelationshipresultsinforcenotbeinglinearlyproportionaltodisplacement[60].For computationalefciency,however,manyresearchersassumeasimplelineartissuemodel. 2.2NeedleInsertionForceModeling Theforcemodelingusedinthisstudyisinspiredby[48],whereanexperimentalprocedure foracquiringdatafromexvivotissueisgivenandtheneedleinsertionforceisdesignedasthe sumofastiffnessforce,africtionforce,andacuttingforce.Inthisstudy,thestiffnessforceis designedusingthenonlinearviscoelasticHunt-Crossleymodel.Thefrictionforceismodeled asin[49].Thismodeloffersanaccuraterepresentationofnonlinearfrictioneffects.Thecutting forcerequiredtoslicethroughtissueismodeledasaconstantdependingontheneedlesizeand onthetissueproperties[48]. Aneedleinsertionprocedurecanbedividedintothreestages.Therststageisafree-space motionandoccursbeforetheneedletouchesthetissue.Thesecondstageistheneedle-tissue viscoelasticinteractionandoccurswhen x t 2 R ,thepositionoftherobotend-effectoratthe 13

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Figure2-1.Needleinsertionsteps needletip,rangesbetween x t t 2 R ,thepositionoftheviscoelastictissue,and x m t 2 R ,the positionofthemaximallydeformedtissuesurfacebeforepuncture.Thelaststageistheinsertion throughthetissue,whichoccurswhen x t isgreaterthan x m t .Thedynamicsofthetissue dependsonforcesfromsurroundingtissueandorgans,physiologicalmovements,etc.,which resultintheevolutionof x t t overtime.Figure2-1illustrateseachstage. Theforce f needle x ; x isdiscontinuousbecauseofthetransitionbetweenneedle-tissue contactandinsertionthroughthetissue.Theneedleinsertionforcecanbemodeledas[48] 14

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f needle L 1 f stiffness + L 2 f friction + L 2 f cutting ; where L 1 x ; x t ; x m and L 2 x ; x m 2 R arefunctionswhichswitchatcontactandperforation, respectively,denedas L 1 8 > > < > > : 1 x t x x m 0 otherwise ; L 2 8 > > < > > : 1 x m < x 0 otherwise : 2.2.1StiffnessForce Thestiffnessforcecorrespondstoaviscoelasticinteractionbetweenthetissueandthe needletip[61].Thisinteractionoccursbeforethepuncture.Theneedlecompressesthesoft tissueuntilthepunctureofthesurface.In2,thestiffnessforce f stiffness x ; x 2 R is describedbytheHunt-Crossleymodelas[18] f stiffness ld n + m dd n ; where l 2 R istheunknowncontactstiffnessoftheviscoelasticmass, m 2 R istheunknown dampingcoefcient, n 2 R istheunknownHertziancompliancecoefcient,and d t 2 R isthe localdeformationofthetissue,denedas d x )]TJ/F54 11.9552 Tf 10.95 0 Td [(x t : Theviscoelasticforce f stiffness x ; x dependsonthelocaldeformationofthetissue,whilethe positionofthetissueisthesumofthedeformationandthepositionofthetissueunderthe pressureofphysiologicalmotionorneedletip. 15

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2.2.2FrictionForce Thefrictionforceoccursinsidethetissueafterthepunctureandalongtheneedleshaft. Frictionisanaturalphenomenonthatcanbefoundinmanymechanicalapplicationshowever itsmodelingisnotentirelyunderstood.In2,thefrictionforce f friction x 2 R ismodeled accordingto[49]as f friction g 1 tanh g 2 x )]TJ/F23 11.9552 Tf 10.949 0 Td [(tanh g 3 x + g 4 tanh g 5 x + g 6 x ; where g i 2 R ,for i = 1 ; 2 ;::: 6,areunknownpositiveconstants.Themodelin2exhibitsthe followingproperties: 1.itissymmetricabouttheorigin, 2.ithasastaticcoefcientoffriction,givenby g 1 + g 4 3.itincludestheStribeckeffect,givenbytanh g 2 x )]TJ/F23 11.9552 Tf 10.949 0 Td [(tanh g 3 x 4.ithasaviscousdissipationterm,givenby g 6 x 5.ithasaCoulombicfrictioncoefcientintheabsenceofviscousdissipation,givenby g 4 tanh g 5 x See[49]and[62]forfurtherdetails. 2.2.3CuttingForce Alsoin2,thecuttingforce f cutting 2 R representstheforcerequiredfortheneedleto penetrateintothetissue.Thisforceonlydependsontheneedlesizeandonthetissueproperties andisdenedas f cutting c ; where c 2 R isaunknownpositiveconstant. Remark 2.1 Inmanyneedleinsertionapplications,thedifferentparametersofthestiffnessforce, frictionforceandcuttingforce,denedpreviouslyin2,2and2,havetobeknown. Theidenticationoftheneedleinsertionforcecanbeperformedbeforetheoperationusing ex 16

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vivo testsasin[48].Foramedicalintervention, exvivo testscannotbedoneonapatientbut theseparameterscanbedeterminedduringtheintervention.In[11],anapproachforestimating needleforceisgivenbutitisnoteasilyapplicableformedicalproceduresbecauseoftheneed toputmarkersonthesurface.[22]describesanonlineestimationtodetermineHunt-Crossley parameters.Forthecontrolanalysisdevelopedinthefollowingchapters,theseparametersare assumedtobeuncertain. 17

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CHAPTER3 ROBOTICNEEDLEINSERTIONINTOVISCOELASTICTISSUE Thischapterdescribesthedevelopmentofanautomatedcontrollertoensurethataneedle tiptracksadesiredtrajectorybeginninginanon-contactpositionandendingwithinviscoelastic tissue. 3.1DynamicModel Thedynamicmodelforaone-degree-of-freedomtranslationrobotinteractingwitha viscoelasticenvironmentis M x x + h x + f needle x ; x = F : In3, x t ; x t ; x t 2 R denotetheplanarCartesianposition,velocity,andacceleration oftherobotend-effectorattheneedletip,respectively, M x 2 R denotestheuncertaininertia, h x 2 R denotesuncertainconservativeforces, f needle x ; x 2 R ,introducedinChapter2, denotestheinteractionforcebetweentherobotattheneedletipandtheviscoelastictissueduring theneedleinsertionprocedure,and F t 2 R denotestheforcecontrolinput. Remark. Thisstudyhasbeendevelopedforaone-degree-of-freedomtranslationrobotbutcould beextendedtotheresolutionofaredundancymanipulatorsproblem[63]. Thefollowingpropertyandassumptionsareappliedinthecontroldevelopment. Property1. Thefollowingrelationshipsarevalidforall x 2 R [64]: x tanh x tanh x 2 ; j tanh x j 1 : Assumption3.1. Therobot,tissue,andmaximaltissuesurfacepositions, x t x t t ,and x m t ,introducedinChapter2,andthecorrespondingvelocities, x t and x t t ,aremeasurable. Further,itisassumedthattherobottrajectory x t isboundedduetothegeometryoftherobot. 18

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Remark 3.1 Thepositionofthemaximallydeformedtissuesurfacebeforepuncture x m t canbe measuredusingthetechniquedescribedin[65]. Assumption3.2. Thelocaldeformationoftheviscoelasticmaterialduringcontact d x ; x t denedin2,isassumedtobebounded;hence, d n canbeupperboundedas d n d n ; where d n 2 R isaknownpositiveboundingconstant. Assumption3.3. Thedampingconstant m ,in2,isassumedtobeupperboundedas m m ; where m 2 R isaknownpositiveboundingconstant. 3.2ControlDevelopment 3.2.1ControlObjective Thecontrolobjectiveistoensurethattheone-degree-of-freedomtranslationrobottracks adesiredposition,denotedby x d t 2 R ,whichbeginsinfreespaceandendswithinthe viscoelastictissue.Thecontrollerisdesignedsuchthattheforcerequiredtoachievethis objectiveisboundedbyanarbitrarysmallvalue,whichisdesiredforproceduralsafety.A positiontrackingerrorandalteredtrackingerroraredesignedtoquantifythecontrolobjective as e x d )]TJ/F54 11.9552 Tf 10.949 0 Td [(x ; r e + a e ; where e t 2 R representsthepositionerrorattheneedletip, r t 2 R isalteredtrackingerror thatfacilitatesthesubsequentcontroldevelopment,and a 2 R isapositiveconstantcontrolgain. 19

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3.2.2Closed-LoopErrorSystem Premultiplyingthelteredtrackingerror r t in3bytherobotinertiamatrix M x takingthetimederivativeoftheresultingexpression,andusing3and3yieldsthe followingopen-looproboterrorsystem: M r = M e + M x d + h + f needle )]TJ/F54 11.9552 Tf 10.95 0 Td [(F + M a e + M a e )]TJ/F23 11.9552 Tf 15.372 2.379 Td [( Mr : Usingthedenitionoftheneedleforce f needle denedin2,2,2,and2,the expressionin3becomes M r = f + M e + L 2 g 1 tanh g 2 x )]TJ/F23 11.9552 Tf 10.949 0 Td [(tanh g 3 x + L 2 g 4 tanh g 5 x + L 2 g 6 x + L 2 c )]TJ/F54 11.9552 Tf 10.949 0 Td [(F + M a e )]TJ/F23 11.9552 Tf 15.373 2.379 Td [( Mr ; where f t 2 R isanauxiliarynonlinearanddiscontinuousfunctiondenedas f M x d + M a e + h + L 1 ld n + m dd n : Basedontheuniversalfunctionapproximationpropertyandresultsfrom[66]forapproximation ofjumpfunctions,thediscontinuousfunction f t in3canbeapproximatedbyathree-layer input,hidden,andoutputneuralnetworkNNas f = W T 1 s )]TJ/F54 11.9552 Tf 4.878 -9.69 Td [(V T 1 y + W T 2 j )]TJ/F54 11.9552 Tf 4.877 -9.69 Td [(V T 2 y + e y ; wheretheNNinput y t isdenedas y t = 1 x t xer dd d T 2 R 7 W 1 ; W 2 2 R N + 1 and V 1 ; V 2 2 R 7 N areidealNNweights, N 2 R isthenumberofhiddenlayerneuronsof theNN, s )]TJ/F54 11.9552 Tf 4.877 -9.689 Td [(V T 1 y = s 2 R N + 1 isasigmoidactivationfunction, j )]TJ/F54 11.9552 Tf 4.878 -9.689 Td [(V T 2 y = j 2 R N + 1 isasigmoid jumpapproximationfunction,and e y 2 R isthefunctionalreconstructionerroroftheNN. Theweights V 2 areknown,givenbythedesigneranddependingonthelocationofthejumps. Figure3-1showstheaugmentedmultilayerneuralnetworkforjumpfunctionapproximation. 20

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Figure3-1.Multilayerneuralnetworkforjumpfunctionapproximation. Thesubsequentstabilityanalysisindicatesthat,providedsomesufcientgainconditionsare satised,if y 0 isinacompactset,then y t remainsinacompactset 8 t Property2. BoundednessoftheIdealWeightsTheidealweightsareassumedtoexistandto beboundedbyknownpositivevaluessothat k V i k 2 F = tr V T i V i V iB ; k W i k 2 F = tr W T i W i W iB ; where i = 1 ; 2, V iB and W iB arepositiveconstants, k k F istheFrobeniusnormofamatrix,and tr isthetraceofamatrix. Theestimatefor f t ,denotedas f t 2 R ,isdenedas f W T 1 s )]TJ/F23 11.9552 Tf 7.597 -7.311 Td [( V T 1 y + W T 2 j )]TJ/F54 11.9552 Tf 4.878 -9.69 Td [(V T 2 y ; where W 1 t ; W 2 t 2 R N + 1 and V 1 t 2 R 7 N aretheestimatesoftheidealweightsandare generatedbyintegratingtheadaptiveupdatelaws 21

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W 1 = proj )]TJ/F55 11.9552 Tf 5.476 -9.69 Td [(G w 1 s r )]TJ/F55 11.9552 Tf 10.949 0 Td [(G w 1 s 0 V T 1 yr ; V 1 = proj )]TJ/F55 11.9552 Tf 5.476 -9.69 Td [(G v 1 yr W T 1 s 0 ; W 2 = proj G w 2 j r ; where G w 1 ; G w 2 2 R N + 1 N + 1 and G v 1 2 R 7 7 areconstant,positivedenite,diagonal, gainmatrices, s 0 2 R N + 1 N denotesthepartialderivativeof s = s )]TJ/F23 11.9552 Tf 7.598 -7.311 Td [( V T 1 y withrespectto itsargument,and proj denotesasmoothprojectionoperator[67,68].Basedonthefact that W 1 t and W 2 t areboundedbytheprojectionoperator,and s and j arebounded activationfunctions,then f t canbeupperboundedas f k ; where k 2 R isaknownpositiveconstant. Basedon3andthesubsequentstabilityanalysis,therobotcontrolforceinputis designedas F = f + k p tanh w e + b sgn r ; where k p ; w ; b 2 R arepositiveconstantcontrolgains.Thesmoothsaturationfunction tanh in3isusedtosaturatethetermsinthecontrollertolimitthecontrolforceduringcontact andpenetration.Using3,3,andtheNNprojectionboundsin[64],thecontrolforcein 3canbeboundedas j F j k + k p + b : Using3,3,and3,theexpressionin3canberewrittenas 22

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M r = W T 1 s + W T 2 j + e y )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W T 1 s )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W T 2 j )]TJ/F54 11.9552 Tf 10.949 0 Td [(k p tanh w e )]TJ/F52 11.9552 Tf 10.949 0 Td [(b sgn r + M e + L 2 g 1 tanh g 2 x )]TJ/F23 11.9552 Tf 10.949 0 Td [(tanh g 3 x + L 2 g 4 tanh g 5 x + L 2 g 6 x + L 2 c + M a e )]TJ/F23 11.9552 Tf 15.373 2.379 Td [( Mr : UsingtheTaylorseriesexpansion[66],theterm s = s )]TJ/F23 11.9552 Tf 13.508 0.52 Td [( s canbewrittenas s = s 0 V 1 T y + O V 1 T y 2 ; where W 1 t 2 R N + 1 and V 1 t 2 R 7 N areestimateerrorsoftheidealweightsandaredened as W 1 = W 1 )]TJ/F23 11.9552 Tf 14.374 2.379 Td [( W 1 ; V 1 = V 1 )]TJ/F23 11.9552 Tf 13.072 2.379 Td [( V 1 ; W 2 = W 2 )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W 2 : Aftersomealgebraicmanipulations,theexpressionin3canbeexpressedas M r = W T 1 s + W T 1 s 0 V T 1 y )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W T 1 s 0 V T 1 y + W T 2 j + D )]TJ/F54 11.9552 Tf 10.95 0 Td [(k p tanh w e )]TJ/F52 11.9552 Tf 10.949 0 Td [(b sgn r )]TJ/F23 11.9552 Tf 12.145 8.094 Td [(1 2 Mr )]TJ/F54 11.9552 Tf 10.949 0 Td [(kr )]TJ/F54 11.9552 Tf 10.949 0 Td [(e ; where k 2 R isapositiveconstant,thestatevector z 2 R 2 isdenedas z e ; r e t r t T and D z 2 R isdenedas D = W T 1 s 0 V T 1 y + W T 1 O )]TJ/F23 11.9552 Tf 7.597 -7.311 Td [( V T 1 y 2 + e y + L 2 g 1 tanh g 2 x )]TJ/F23 11.9552 Tf 10.949 0 Td [(tanh g 3 x + L 2 g 6 x + M e )]TJ/F23 11.9552 Tf 12.145 8.093 Td [(1 2 Mr + L 2 g 4 tanh g 5 x + L 2 c + M a e + kr + e : Using3,3,and[69],anupperboundfor D z canbedeterminedas j D j z + r k z k k z k ; 23

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where r 2 R isapositive,globallyinvertiblefunction,and z 2 R isaknownpositiveconstant. 3.3StabilityAnalysis Theorem3.1. Thecontrollergivenin3ensuressemi-globaltrackinginthesensethat e t 0 ast ; providedcontrolgainsareselectedsufcientlylargeseethesubsequentstabilityanalysis. Proof. Let D R 3 beadomaincontaining v t = 0,where v t 2 R 3 isdenedas v t z T t p Q t T ; andtheauxiliaryfunction Q t 2 R isdenedas Q t 1 2 tr )]TJ/F23 11.9552 Tf 7.598 -7.31 Td [( V T 1 G )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 v 1 V 1 + 1 2 tr )]TJ/F23 11.9552 Tf 8.901 -7.31 Td [( W T 1 G )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 w 1 W 1 + 1 2 tr )]TJ/F23 11.9552 Tf 8.901 -7.31 Td [( W T 2 G )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 w 2 W 2 : Since G 1 v G w 1 and G w 2 areconstant,symmetric,andpositivedenitematrices,itisstraightforwardthat Q t 0. Let V v ; t : D [ 0 ; R beaLipschitzcontinuousregularpositivedenitefunction denedas V 1 2 Mr 2 + 1 2 e 2 + k p w ln cosh w e + Q ; whichsatisesthefollowinginequalities: U 1 v V v ; t U 2 v ; wherethecontinuouspositivedenitefunctions U 1 v ; U 2 v 2 R aredenedas U 1 v h 1 k v k 2 ; U 2 v h 2 k v k 2 ; where h 1 ; h 2 2 R areknownpositiveconstants. 24

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Thedifferentialequationsoftheclosedloopdynamicsgivenin3arecontinuousexcept insets f v j x = x t g and f v j r = 0 g .UsingFilippov'sdifferentialinclusion[70],theexistenceof solutionscanbeestablishedfor v = f v ,where f v 2 R 3 denotestheright-handsideofthe closed-looperrorsignals.UnderFilippov'sframework,ageneralizedLyapunovstabilitytheory canbeusedtoestablishstrongstabilityoftheclosed-looperrorsystem.Thegeneralizedtime derivativeof3existsalmosteverywherea.e.,and V v 2 a : e : V v where V = x 2 V v K r e 1 2 Q )]TJ/F23 6.9738 Tf 8.162 3.532 Td [(1 2 Q T ; where V isthegeneralizedgradientof V v [71], K [ ] isdenedas[72,73] K [ f ] d > 0 m = 0 cof B x ; d )]TJ/F55 11.9552 Tf 10.949 0 Td [( ; where m = 0 denotestheintersectionofallsets ofLebesguemeasurezero, co denotesconvex closure,and B x ; d = u 2 R 3 jk u )]TJ/F54 11.9552 Tf 10.949 0 Td [(v k < d .Since V v isaLipschitzcontinuousregular function V = V T K r e 1 2 Q )]TJ/F23 6.9738 Tf 8.163 3.533 Td [(1 2 Q T Mre k p w tanh w e 2 Q 1 2 T K r e 1 2 Q )]TJ/F23 6.9738 Tf 8.162 3.533 Td [(1 2 Q T : Using3,3,and3,theexpressionin3becomes V r D )]TJ/F52 11.9552 Tf 10.949 0 Td [(b j r j )]TJ/F54 11.9552 Tf 10.95 0 Td [(kr 2 )]TJ/F52 11.9552 Tf 10.949 0 Td [(a e 2 )]TJ/F54 11.9552 Tf 10.651 0 Td [(tanh w e k p a e : Using3and3,theexpressionin3canbeupperboundedas V a : e : r k z k j r jk z k )]TJ/F56 11.9552 Tf 10.949 0 Td [( b )]TJ/F52 11.9552 Tf 10.949 0 Td [(z j r j )]TJ/F54 11.9552 Tf 10.949 0 Td [(kr 2 )]TJ/F52 11.9552 Tf 10.95 0 Td [(a e 2 )]TJ/F54 11.9552 Tf 12.145 8.284 Td [(k p a w j tanh w e j 2 : Letthecontrolgain k in3bedenedas k k 1 + k 2 ; 25

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where k 1 ; k 2 2 R areknownpositiveconstants.Using3andthegaincondition b > z ; theexpressionin3canbeupperboundedas V a : e : )]TJ/F66 11.9552 Tf 24.567 9.69 Td [()]TJ/F54 11.9552 Tf 5.475 -9.69 Td [(k 1 r 2 )]TJ/F52 11.9552 Tf 10.95 0 Td [(r k z k r k z k )]TJ/F54 11.9552 Tf 10.949 0 Td [(k 2 r 2 )]TJ/F52 11.9552 Tf 10.949 0 Td [(a e 2 : Completingthesquaresontheterminparenthesesin3yields V a : e : r k z k 2 4 k 1 k z k 2 )]TJ/F54 11.9552 Tf 10.949 0 Td [(k 2 r 2 )]TJ/F52 11.9552 Tf 10.949 0 Td [(a e 2 : Theexpressionin3canbefurtherupperboundedas V a : e : )]TJ/F52 11.9552 Tf 23.239 0 Td [(l k z k 2 + r k z k 2 4 k 1 k z k 2 ; where l = min f k 2 ; a g isaknownpositiveconstant.Finally,giventhegaincondition l > r k z k 2 4 k 1 ; theexpressionin3becomes V a : e : )]TJ/F54 11.9552 Tf 22.641 0 Td [(U v ; where U v = J k z k 2 ,forsomepositiveconstant J 2 R isacontinuouspositivesemi-denite functionsuchthat D n v 2 R 3 j k v k r )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 2 p l k 1 o : Theexpressionsin3and3canbeusedtoshowthat V v ; t 2 L ;hence, e t ; r t and Q t 2 L in D .Giventhat e t ; r t 2 L in D ,itcanbeproventhat e t 2 L in D from3.Since e t ; r t 2 L in D ,theassumptionthat x d t ; x d t existandarebounded 26

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canbeusedtoconcludethat x t ; x t 2 L in D .Similarly,itcanbeshownthat r t 2 L in D .Since e t ; r t 2 L in D ,thedenitionsfor U v and z t canbeusedtoprovethat U v isuniformlycontinuousin D Let S D denotesasetdenedasfollows: S v t D U 2 v t < h 1 r )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 2 p l k 1 2 : [74]cannowbeinvokedtostatethat k z t k 2 0 ast 8 v 0 2 S : Basedonthedenitionof v t in3,3canbeusedtoshowthat j e t j 0 ast 8 v 0 2 S : 3.4SimulationResults Thedevelopedcontrollerissimulatedforasystemwhosedynamicmodelisgivenby m x + b x + f needle x ; x = F ; where F t and f needle x ; x areintroducedin3, m = 0 : 152 kg b = 1 : 426 N s m )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 ,which correspondtotheneedleinsertionrobotdescribedin[75].Thedifferentpositionandparameter valuesarechosentoagreewithadirectinsertionintotheliver.Theinitialneedletippositionis supposedtobeat x = 0for t = 0.Forsakeofsimplicity,itisassumedthatthetissueposition x t doesnotdependontimeanditsvalueisxedto x t = 20 mm .Thepositionofthemaximally deformedtissuesurfacebeforepunctureischosenas x m = 36 mm ,whichmeansthattheneedle progresses16mmwhileincontactwiththeliverbeforethepunctureoccurs.Thedesiredposition ischosenas x d = 60 mm ,whichcorrespondto40 mm intotheliver.Figure3-2showsthechoice ofthedifferentpositionsforthatsimulation.Theparametersfor f stiffness x ; x f friction x ,and 27

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Figure3-2.Positionsforthesimulation f cutting ,introducedinChapter2,arechosenas l = 0 : 2 N m )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 ; m = 5 : 5 N s m )]TJ/F23 8.9664 Tf 6.967 0 Td [(2 ; n = 1 : 5 ; g 1 = g 4 = 0 : 1 N ; g 2 = g 3 = g 5 = 0 : 2 s m )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 ; g 6 = 0 : 5 N s m )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 ; c = 0 : 94 N : Theparametersin3areselectedusingresultsfromexperimentsonliver[48,65].The controllergainsintroducedin3andthecontrolgain a introducedin3areselectedas k p = 5 ; w = 1 ; b = 2 ; a = 10 : ThenumberofhiddenlayerneuronsfortheNNischosenas N = 15,andtheNNweight updationgainsareselectedas G w 1 = G w 2 = 5 I 16 ; G v 1 = 5 I 5 ; where I p 2 R p p denotestheidentitymatrix. Figure3-3showsthepositionoftheneedletip x t ,whichasymptoticallyapproaches thedesiredposition x d = 60 mm .Then,theerrorgoestozeroastimegoestoinnityasshown inFigure3-4.Duringtherststage,between0and20 mm orbetween0and54 ms ,theforce betweentheneedleandthetissueisequaltozerobecausetheneedledoesnottouchthetissue yetasitcanbeseenonFigures3-5and3-6.Then,between20 mm andthemaximallydeformed 28

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Figure3-3.Positionoftheneedletip x t tissueat36 mm ,theneedleforceincreases,astheneedlecontactsthetissue;theneedleforce isthenequaltotheHunt-Crossleyforce.Themaximumforce : 6 N isfollowedbyasudden dropinforceastheneedlepuncturesthetissueandnowonlyneedstoovercomethefrictionand cuttingforces,whicharesmallerthanthetissuestiffnessforce.Thelaststageistheinsertion throughthetissuetoreachthetarget. 29

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Figure3-4.Positiontrackingerror e t Figure3-5.Needleforce f needle asafunctionoftime. 30

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Figure3-6.Needleforce f needle asafunctionoftheneedletipposition x t 31

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CHAPTER4 TELEOPERATEDROBOTFORNEEDLEINSERTIONINTOVISCOELASTICTISSUE Thischapterdescribesthedevelopmentofacontrollertoensurethataneedletipmounted onaslaverobottracksthetrajectorygivenbythesurgeonmanipulatingthemasterrobot.The trajectorymovesfromanon-contactpositionintoviscoelastictissue. 4.1DynamicModel Thedynamicmodelforaone-degree-of-freedomtranslationmasterandaone-degree-offreedomtranslationslaverobotisdescribedby g T 1 + F 1 = g M 1 q 1 q 1 + h 1 q 1 ; T 2 )]TJ/F54 11.9552 Tf 10.95 0 Td [(F 2 = M 2 q 2 q 2 + h 2 q 2 : In4and4, g 2 R denotesapositiveadjustablepowerscalingterm, q i t ; q i t ; q i t 2 R denotetherobotend-effectorposition,velocity,andacceleration,respectively, 8 i = 1 ; 2where i = 1denotesthemastermanipulatorand i = 2denotestheslavemanipulator, M i q i 2 R denotestheinertia, h i q i 2 R denotesconservativeforces, T i t 2 R denotestheforcecontrol input, F 1 t 2 R denotestheuserinputforce,and F 2 t 2 R denotestheforceinputfrom theenvironment,i.e.,theinteractionforcebetweentherobotandthetissueduringtheneedle insertion.Theforce F 2 t isdiscontinuousbecauseofthetransitionbetweenneedle-tissue contactandinsertionthroughthetissue. Assumption4.1. Theposition q i t andthevelocity q i t aremeasurable. Assumption4.2. Theuserforce F 1 t andtheenvironmentforce F 2 t arebounded. Assumption4.3. Thedynamicmodelsofthetworobotsareknown. 32

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4.2ControlDevelopment 4.2.1ControlObjectiveandModelTransformation Therstcontrolobjectiveistoensurethattheslaverobottracksthemasterrobotposition, whichgoesfromafree-spacepositionintoaviscoelastictissue,inthefollowingsense: q 2 t q 1 t ast : Energeticpassivityisimportanttoensuretherobotinteractswiththetissueinastableandsafe manner.Then,theotherobjectiveistoensurethatthesystemremainspassivewithrespecttothe scaleduserandenvironmentalpowerinthesensethat[76] t t 0 g q 1 t F 1 t )]TJ/F23 11.9552 Tf 12.844 0 Td [( q 2 F 2 t d t )]TJ/F54 11.9552 Tf 21.235 0 Td [(c ; where c 2 R isapositiveconstantwhichdependsontheinitialcondition,and g wasintroduced in4.Theequationin4meansthattheenergyproducesbytheslaverobotcannotbe biggerthanthesumoftheenergyfromthemasterrobotandtheinitialenergyinthesystem.An auxiliarycontrolobjectiveisemployedtoensurethepassivityobjectiveandforcereection,in thesensethat[41] q 1 t + q 2 t x d 2 t ast ; where x d t = x d 1 t x d 2 t T 2 R 2 isadesiredboundedtrajectory. Tofacilitatethesubsequentdevelopment,agloballyinvertibletransformationisdenedthat encodesboththecoordinationandthepassivityobjectives,i.e., x Sq + 2 6 4 x d 1 0 3 7 5 ; where x t x 1 t x 2 t T 2 R 2 q t q 1 t q 2 t T 2 R 2 ,and S 2 R 2 2 isdened asfollows: S 2 6 4 1 )]TJ/F23 11.9552 Tf 9.289 0 Td [(1 11 3 7 5 ; S )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 1 2 2 6 4 11 )]TJ/F23 11.9552 Tf 9.289 0 Td [(11 3 7 5 : 33

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Basedon4,thedynamicmodelgivenin4and4canbeexpressedas M x x )]TJ/F23 11.9552 Tf 15.373 2.379 Td [( M x 2 6 4 x d 1 0 3 7 5 + h x = T t + F t ; where M x S )]TJ/F54 8.9664 Tf 6.967 0 Td [(T 2 6 4 g M 1 0 0 M 2 3 7 5 S )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 2 R 2 2 ; h x S )]TJ/F54 8.9664 Tf 6.967 0 Td [(T 2 6 4 g h 1 h 2 3 7 5 2 R 2 ; T t S )]TJ/F54 8.9664 Tf 6.967 0 Td [(T 2 6 4 g T 1 T 2 3 7 5 2 R 2 ; F t 2 6 4 F 1 F 2 3 7 5 = S )]TJ/F54 8.9664 Tf 6.967 0 Td [(T 2 6 4 g F 1 )]TJ/F54 11.9552 Tf 9.289 0 Td [(F 2 3 7 5 2 R 2 : Property3. Thesubsequentdevelopmentisbasedonthepropertythat M x ,denedin4,is apositivedeniteandsymmetricmatrixinthesensethat m 1 k x k 2 x T M x x m 2 k x k 2 ; where x 2 R 2 ,and m 1 ; m 2 2 R arepositiveconstants. Apositiontrackingerror e 1 t 2 R 2 andalteredtrackingerror e 2 t 2 R 2 aredesignedto quantifythecontrolobjectiveas e 1 x )]TJ/F54 11.9552 Tf 10.95 0 Td [(x d ; e 2 e 1 + a 1 e 1 ; where a 1 2 R isapositiveconstantcontrolgain,and x d t 2 R 2 isintroducedin4.Based onthedenitionof x t in4and e 1 t in4,itisclearthatif k e 1 k 0as t then 34

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q 2 t q 1 t and q 1 t + q 2 t x d 2 t as t .Toensurethatthesystemremainspassive asdenedin4,thedesiredtrajectory x d t isgeneratedbythefollowingexpression M x d + B T x d + K T x d + 1 2 M x d = F ; where B T ; K T 2 R representpositiveconstants, M 2 R 2 2 isintroducedin4,and F 2 R 2 isa subsequentlydesignedforceestimator. 4.2.2Closed-LoopErrorSystem Premultiplyingthesecondtimederivativeofthetrackingerror e 1 t in4bytherobot inertiamatrix M x ,andusingthesystemdynamics4andthedesiredtrajectorydynamics 4,theopen-looproboterrorsystemcanbewrittenas M e 1 = T + F + M 2 6 4 x d 1 0 3 7 5 )]TJ/F23 11.9552 Tf 11.948 2.851 Td [( h )]TJ/F23 11.9552 Tf 14.01 2.379 Td [( F + B T x d + K T x d + 1 2 M x d : Basedontheassumptionofexactmodelknowledgeoftherobotdynamicsandthesubsequent stabilityanalysis,therobotcontrolinput T t isdesignedas T )]TJ/F23 11.9552 Tf 13.712 2.379 Td [( M 2 6 4 x d 1 0 3 7 5 + h )]TJ/F54 11.9552 Tf 10.95 0 Td [(B T x d )]TJ/F54 11.9552 Tf 10.95 0 Td [(K T x d )]TJ/F23 11.9552 Tf 12.145 8.094 Td [(1 2 M x d )]TJ/F23 11.9552 Tf 15.373 2.379 Td [( M a 1 e 1 )]TJ/F52 11.9552 Tf 10.949 0 Td [(b sgn e 2 )]TJ/F23 11.9552 Tf 12.145 8.093 Td [(1 2 e T 2 Me 2 ; where b 2 R isapositiveconstantcontrolgain.Using4,4canbewrittenas M e 1 = F )]TJ/F23 11.9552 Tf 14.01 2.379 Td [( F )]TJ/F23 11.9552 Tf 15.373 2.379 Td [( M a 1 e 1 )]TJ/F52 11.9552 Tf 10.949 0 Td [(b sgn e 2 )]TJ/F23 11.9552 Tf 12.145 8.093 Td [(1 2 e T 2 Me 2 : Using4andthetimederivativeofthelteredtrackingerror e 2 t ,4becomes M e 2 = F )]TJ/F23 11.9552 Tf 14.01 2.379 Td [( F )]TJ/F52 11.9552 Tf 10.95 0 Td [(b sgn e 2 )]TJ/F23 11.9552 Tf 12.145 8.094 Td [(1 2 e T 2 Me 2 : 35

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Basedontheuniversalfunctionapproximationpropertyandresultsfrom[66]forapproximation ofjumpfunctions,thediscontinuousforce F t ,denedin4,canbeapproximatedbya three-layerinput,hidden,andoutputneuralnetworkNNas F = W T 1 s )]TJ/F54 11.9552 Tf 4.878 -9.689 Td [(V T 1 y + W T 2 j )]TJ/F54 11.9552 Tf 4.878 -9.689 Td [(V T 2 y + e y ; wheretheNNinput y t isdenedas y t = 1 x T e T 1 e T 2 T 2 R 7 W 1 ; W 2 2 R N + 1 2 and V 1 ; V 2 2 R 7 N areidealNNweights, N 2 R isthenumberofhiddenlayerneuronsofthe NN, s )]TJ/F54 11.9552 Tf 4.878 -9.69 Td [(V T 1 y = s 2 R N + 1 isasigmoidactivationfunction, j )]TJ/F54 11.9552 Tf 4.878 -9.69 Td [(V T 2 y = j 2 R N + 1 isasigmoid jumpapproximationfunction,and e y 2 R 2 isthefunctionalreconstructionerroroftheNN. Theweights V 2 areknown,givenbythedesigneranddependonthelocationofthejumps.The subsequentstabilityanalysisindicatesthat,providedsomesufcientgainconditionsaresatised, if y 0 isinacompactset,then y t remainsinacompactset 8 t Property4. BoundednessoftheIdealWeightsTheidealweightsareassumedtoexistandto beboundedbyknownpositivevaluessothat k V i k 2 F = tr V T i V i V iB ; k W i k 2 F = tr W T i W i W iB ; where V iB and W iB arepositiveconstantsfor i = 1 ; 2, k k F istheFrobeniusnormofamatrix,and tr isthetraceofamatrix. Theestimatefor F t ,denotedas F t 2 R 2 ,isdenedas F W T 1 s )]TJ/F23 11.9552 Tf 7.597 -7.311 Td [( V T 1 y + W T 2 j )]TJ/F54 11.9552 Tf 4.878 -9.69 Td [(V T 2 y ; where W 1 t ; W 2 t 2 R N + 1 2 and V 1 t 2 R 7 N aretheestimatesoftheidealweightsandare generatedbyintegratingtheadaptiveupdatelaws 36

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W 1 proj )]TJ/F55 11.9552 Tf 5.476 -9.69 Td [(G w 1 s e T 2 )]TJ/F55 11.9552 Tf 10.949 0 Td [(G w 1 s 0 V T 1 ye T 2 ; V 1 proj )]TJ/F55 11.9552 Tf 5.476 -9.69 Td [(G v 1 ye T 2 W T 1 s 0 ; W 2 proj )]TJ/F55 11.9552 Tf 5.476 -9.689 Td [(G w 2 j e T 2 ; where G w 1 ; G w 2 2 R N + 1 N + 1 and G v 1 2 R 7 7 areconstant,positivedenite,diagonal, gainmatrices; s 0 2 R N + 1 N denotesthepartialderivativeof s = s )]TJ/F23 11.9552 Tf 7.597 -7.311 Td [( V T 1 y withrespectto itsargument,and proj denotesasmoothprojectionoperator[67,68].Basedonthefact that W 1 t and W 2 t areboundedbytheprojectionoperator,and s and j arebounded activationfunctions,then F t canbeupperboundedas F k ; where k 2 R isaknownpositiveconstant.Using4,4,and4,theexpressionin 4canberewrittenas M e 2 = W T 1 s + W T 2 j + e y )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W T 1 s )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W T 2 j )]TJ/F52 11.9552 Tf 10.949 0 Td [(b sgn e 2 )]TJ/F23 11.9552 Tf 12.145 8.093 Td [(1 2 e T 2 Me 2 : Theestimateerrorsoftheidealweights W 1 t 2 R N + 1 2 V 1 t 2 R 7 N ,and W 2 2 R N + 1 2 are denedas W 1 = W 1 )]TJ/F23 11.9552 Tf 14.374 2.379 Td [( W 1 ; V 1 = V 1 )]TJ/F23 11.9552 Tf 13.071 2.379 Td [( V 1 ; W 2 = W 2 )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W 2 : UsingtheTaylorseriesexpansion[66],theestimateerroroftheactivation s 2 R N + 1 ,denedas s = s )]TJ/F23 11.9552 Tf 13.507 0.52 Td [( s ,canbewrittenas s = s 0 V 1 T y + O V 1 T y 2 : Using4andtheexpressionin4,theclosed-looperrorsystemcanbewrittenas 37

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M e 2 = W T 1 s + W T 1 s 0 V T 1 y )]TJ/F23 11.9552 Tf 14.375 2.379 Td [( W T 1 s 0 V T 1 y + W 2 T j + D )]TJ/F52 11.9552 Tf 10.95 0 Td [(b sgn e 2 )]TJ/F23 11.9552 Tf 12.145 8.094 Td [(1 2 e T 2 Me 2 )]TJ/F54 11.9552 Tf 10.95 0 Td [(ke 2 )]TJ/F54 11.9552 Tf 10.95 0 Td [(e 1 ; aftersomealgebraicmanipulations.Thestatevector z 2 R 4 isdenedas z e 1 ; e 2 e 1 t e 2 t T In4, k 2 R isapositiveconstant,and D z 2 R 2 isdenedas D W T 1 s 0 V T 1 y + W T 1 O V 1 T y 2 + e y + ke 2 + e 1 : Using4,4,and[69],anupperboundfor D z canbedeterminedas k D k z + r k z k k z k ; where r 2 R isapositive,globallyinvertible,nondecreasingfunction,and z 2 R isaknown positiveconstant. 4.3StabilityAnalysis Theorem4.1. Thecontrollergivenin4ensuressemi-globalasymptotictrackinginthe sensethat q 2 t q 1 t ast ; providedcontrolgainsareselectedsufcientlylargeseethesubsequentstabilityanalysis. Proof. Let D R 5 beadomaincontaining v t = 0,where v t 2 R 5 isdenedas v t z T t p Q t T ; andtheauxiliaryfunction Q t 2 R isdenedas Q t 1 2 tr )]TJ/F23 11.9552 Tf 7.598 -7.311 Td [( V T 1 G )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 v 1 V 1 + 1 2 tr )]TJ/F23 11.9552 Tf 8.901 -7.311 Td [( W T 1 G )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 w 1 W 1 + 1 2 tr )]TJ/F23 11.9552 Tf 8.901 -7.311 Td [( W T 2 G )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 w 2 W 2 : 38

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Since G 1 v G w 1 ,and G w 2 areconstant,symmetric,andpositivedenitematrices,itisstraightforwardthat Q t 0. Let V v ; t : D [ 0 ; R beaLypschitzcontinuous,regular,positivedenitefunction denedas V 1 2 e T 2 Me 2 + 1 2 e T 1 e 1 + Q ; whichsatisesthefollowinginequalities: U 1 v V v ; t U 2 v ; wherethecontinuouspositivedenitefunctions U 1 v ; U 2 v 2 R aredenedas U 1 v h 1 k v k 2 ; U 2 v h 2 k v k 2 ; where h 1 ; h 2 2 R areknownpositiveconstants. Thedifferentialequationsoftheclosedloopdynamicsgivenin4arecontinuousexcept insets f v j x = x t g and f v j e 2 = 0 g .UsingFilippov'sdifferentialinclusion[70],theexistenceof solutionscanbeestablishedfor v = f v ,where f v 2 R 5 denotestheright-handsideofthe closed-looperrorsignals.UnderFilippov'sframework,ageneralizedLyapunovstabilitytheory canbeusedtoestablishstrongstabilityoftheclosed-looperrorsystem.Thegeneralizedtime derivativeof4existsalmosteverywherea.e.,and V v 2 a : e : V v where V = x 2 V K e 2 e 1 1 2 Q )]TJ/F23 6.9738 Tf 8.163 3.533 Td [(1 2 Q T ; where V isthegeneralizedgradientof V v [71], K [ ] isdenedin[72]and[73]as K [ f ] d > 0 m = 0 cof B x ; d )]TJ/F55 11.9552 Tf 10.949 0 Td [( ; where m = 0 denotestheintersectionofallsets ofLebesguemeasurezero, co denotesconvex closure,and B x ; d = u 2 R 3 jk u )]TJ/F54 11.9552 Tf 10.949 0 Td [(v k < d .Since V v isaLipschitzcontinuousregular 39

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function, V = V T K e 2 e 1 1 2 Q )]TJ/F23 6.9738 Tf 8.163 3.532 Td [(1 2 Q T ; Me 2 e 1 2 Q 1 2 T K e 2 e 1 1 2 Q )]TJ/F23 6.9738 Tf 8.162 3.533 Td [(1 2 Q T : Using4,4,and4,theexpressionin4becomes V e T 2 D )]TJ/F52 11.9552 Tf 10.949 0 Td [(b k e 2 k )]TJ/F54 11.9552 Tf 10.95 0 Td [(ke T 2 e 2 )]TJ/F52 11.9552 Tf 10.95 0 Td [(a 1 e T 1 e 1 : Using4,theexpressionin4canbeupperboundedas V a : e : r k z k k e 2 kk z k )]TJ/F56 11.9552 Tf 10.949 0 Td [( b )]TJ/F52 11.9552 Tf 10.95 0 Td [(z k e 2 k )]TJ/F54 11.9552 Tf 10.95 0 Td [(k k e 2 k 2 )]TJ/F52 11.9552 Tf 10.95 0 Td [(a 1 k e 1 k 2 : Letthecontrolgain k in4bedenedas k k 1 + k 2 ; where k 1 ; k 2 2 R areknownpositiveconstants.Using4andthegaincondition b > z ; theexpressionin4canbeupperboundedas V a : e : )]TJ/F66 11.9552 Tf 24.567 13.277 Td [( k 1 k e 2 k 2 )]TJ/F52 11.9552 Tf 10.949 0 Td [(r k z k k e 2 kk z k )]TJ/F54 11.9552 Tf 10.95 0 Td [(k 2 k e 2 k 2 )]TJ/F52 11.9552 Tf 10.95 0 Td [(a 1 k e 1 k 2 : Completingthesquaresontheterminparenthesesin4yields V a : e : r k z k 2 4 k 1 k z k 2 )]TJ/F54 11.9552 Tf 10.949 0 Td [(k 2 k e 2 k 2 )]TJ/F52 11.9552 Tf 10.95 0 Td [(a 1 k e 1 k 2 : Theexpressionin4canbefurtherupperboundedas 40

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V a : e : )]TJ/F52 11.9552 Tf 23.239 0 Td [(l k z k 2 + r k z k 2 4 k 1 k z k 2 ; where l = min f k 2 ; a 1 g isaknownpositiveconstant.Finally,giventhegaincondition l > r k z k 2 4 k 1 ; theexpressionin4becomes V a : e : )]TJ/F54 11.9552 Tf 22.641 0 Td [(U v ; where U v = m k z k 2 ,forsomepositiveconstant m 2 R isacontinuouspositivesemi-denite functioninthedomain D n v 2 R 5 j k v k r )]TJ/F23 8.9664 Tf 6.966 0 Td [(1 2 p l k 1 o : Theexpressionsin4and4canbeusedtoshowthat V v ; t 2 L ;hence, e 1 t ; e 2 t and Q t 2 L in D .Giventhat e 1 t ; e 2 t 2 L in D ,itcanbeproventhat e 1 t 2 L in D from4.Since e 1 t ; e 2 t 2 L in D ,theassumptionthat x d t ; x d t existandare boundedcanbeusedtoconcludethat x t ; x t 2 L in D and q t ; q t 2 L in D using 4.Similarly,itcanbeshownthat e 2 t 2 L in D .Since e 1 t ; e 2 t 2 L in D ,the denitionsfor U v and z t canbeusedtoprovethat U v isuniformlycontinuousin D Let S D denoteasetdenedasfollows: S v t D U 2 v t < h 1 r )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 2 p l k 1 2 : [74]cannowbeinvokedtostatethat k z t k 2 0 ast 8 v 0 2 S : Basedonthedenitionof v t in4,4canbeusedtoshowthat k e 1 t k 0 ast 8 v 0 2 S : 41

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Using4and4,thecontroldevelopmentensuresthat q 2 t q 1 t ast 8 v 0 2 S : Theorem4.2. Thecontrollergivenin4ensuresthattheteleoperatedsystemispassivewith respecttothescaleduserandenvironmentalpower. Proof. See[53]. 4.4SimulationResults Inthissection,simulationresultsaregivenfortwodifferentuserinputforcestodemonstrate theperformanceofthecontrollergivenin4.Themasterandslavesystemdynamicsare simulatedusingthefollowingmodel m q 1 + b q 1 = T 1 )]TJ/F54 11.9552 Tf 10.949 0 Td [(F 1 ; m q 2 + b q 2 = T 2 )]TJ/F54 11.9552 Tf 12.743 0 Td [(f needle q 2 ; q 2 ; where T 1 t and T 2 t areintroducedin4and4, m = 0 : 152 kg b = 1 : 426 N s m )]TJ/F23 8.9664 Tf 6.967 0 Td [(1 whichcorrespondtotheneedleinsertionrobotdescribedin[75].Theneedleinsertionforce f needle q 2 ; q 2 issimulatedusingthedesigndescribedinChapter2,wheretheneedleinsertion forceisthesumofastiffnessforce,africtionforce,andacuttingforce.AsinChapter3,the differentpositionsandparametervaluesarechosentoagreewithadirectinsertionintotheliver. Theinitialpositionsare q 1 = 0 mm and q 2 = )]TJ/F23 11.9552 Tf 9.289 0 Td [(20 mm for t = 0.Thetissuepositionisxedto 200 mm fromtheorigin.Thepositionofthemaximallydeformedtissuesurfacebeforepuncture is216 mm ,whichmeansthattheneedleprogresses16mmwhileincontactwiththeliverbefore thepunctureoccurs.Theparametersforthedesiredtrajectoryintroducedin4arechosenas B T = 15 ; K T = 2 : 42

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ThenumberofhiddenlayerneuronsfortheNNischosenas N = 15,andtheNNweight updationgainsareselectedas G w 1 = G w 2 = 30 I 16 ; G v 1 = 30 I 5 ; where I p 2 R p p denotestheidentitymatrix.Fortherstsimulation,theuserinputforce F 1 t ,whichcorrespondstotheforceprovidedbythesurgeononthemasterrobot,isgivenbya sinusoidalforceas F 1 = 15sin 1 : 1 t : Thissimulationdoesnothaveapracticalmeaningbecauseitwouldmeanthatthesurgeon insertstheneedleintoapatient,removesitandinsertsitagain.However,thisusertrajectorywas simulatedtodemonstratetheperformanceofthecontrollerundersomearbitrarymotion.Figure 4-1showsthemasterposition q 1 t andtheslaveposition q 2 t .AsshowninFigure4-2,the errorbetweenthesetwopositiongoestozeroastimegoestoinnity.Thepassivityobjective, introducedin4,ismetwhenthetrajectoryof q 1 t + q 2 t followsthedesiredtrajectory x d 2 whichcanbeseeninFigure4-3and4-4. Forthesecondsimulation,theuserforce F 1 t issimulatedas F 1 = 8 : Figures4-5and4-6showthepositiontrackingbetweenthemasterrobotposition q 1 t andthe slaverobotposition q 2 t .ThepassivityobjectivecanbeseeninFigures4-7and4-8.InFigure 4-9and4-10,theneedleforce f needle isgivenasafunctionoftimeandpositionoftheneedletip, respectively.Itcanbeseenthatduringtherststagetheforcebetweentheneedleandthetissue isequaltozerobecausetheneedledoesnottouchthetissueyet.Then,theneedleforceincreases toreachamaximumforcewhichisfollowedbyasuddendropinforceastheneedlepunctures thetissueandnowonlyneedstoovercomethefrictionandcuttingforces. 43

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Figure4-1.Trajectoryformasterandslaverobotsfor F 1 = 15sin 1 : 1 t Figure4-2.Positionerrorbetweenmasterandslaverobotfor F 1 = 15sin 1 : 1 t 44

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Figure4-3.Desiredtrajectory x d 2 andpositionof q 1 + q 2 for F 1 = 15sin 1 : 1 t Figure4-4.Errorbetweenthedesiredtrajectory x d 2 and q 1 + q 2 for F 1 = 15sin 1 : 1 t 45

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Figure4-5.Trajectoryformasterandslaverobotsfor F 1 = 8. Figure4-6.Positionerrorbetweenmasterandslaverobotfor F 1 = 8. 46

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Figure4-7.Desiredtrajectory x d 2 andpositionof q 1 + q 2 for F 1 = 8. Figure4-8.Errorbetweenthedesiredtrajectory x d 2 and q 1 + q 2 for F 1 = 8. 47

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Figure4-9.Needleforce f needle asafunctionoftimefor F 1 = 8. Figure4-10.Needleforce f needle asafunctionoftheneedletippositionfor F 1 = 8. 48

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CHAPTER5 CONCLUSION 5.1SummaryofResults InChapter2,adiscussiononsofttissuedeformationisprovided.Theneedleinsertionforce modelingforviscoelastictissueispresentedasthesumofaHunt-Crossleystiffnessforce,a frictionforce,andaconstantcuttingforce. InChapter3,aone-degree-of-freedomtranslationrobotcontrollerisdesignedtoasymptoticallytrackadesiredtrajectorygoingfromanon-contactpositionintoaviscoelastictissue. Theneedleforceisdesignedconsideringthattheviscoelastictissuemodelisthesumofa stiffnessforce,africtionforce,andacuttingforce.Aslidingmodecontrollercombinedwitha multi-layerNNisusedtoensureasymptotictracking.ALyapunov-basedstabilityanalysisis providedtoprovethesemi-globalasymptotictracking.Theefcacyoftheproposedcontrolleris demonstratedthroughsimulations. InChapter4,acontrollerisdesignedtopermitaneedleinsertionslaverobottoasymptoticallytrackthepositionofthemasterrobotgoingfromanon-contactpositionintoatissue.A globallyinvertibletransformationisdenedtoshowstabilityandpassivity.ALyapunov-based stabilityanalysisisprovidedtoprovethesemi-globalasymptotictracking.Simulationresults demonstratethatthepositiontrackingandthepassivityobjectivearemet. Medicalroboticsresearchhasbecomeanimportanttooltoassistthedevelopmentof advancedmedicineandhighprecisionsurgery.Differentmethodshavebeenstudiedtoinserta needleconsideringtheconstraintsimposedbythephysiologicalpropertiesofapatient,butalso togivehapticfeedback,toreducehumanerrorsduetofatigueorhandtremor,andtodevelop medicalsimulatorstotrainmedicalstudentsandsurgeonsforsurgicalprocedures.Robotic needleinsertioncanleadtosaferandmoreaccurateneedleinsertions. 5.2RecommendationsforFutureWork Inthisstudy,undesiredbendingoftheneedleduringinsertionisnottakeintoconsideration. Abeveltipandtissuedeformationscancausetheneedletobendduringinsertionwhenusinga 49

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exibleneedle.Inclinicalpractices,adeviationoftheneedlefromthedesiredpathoftenreduces theeffectivenessoftheprocedures.Experimentally,sensorsorimagingdevicescanbeusedto acquiredataandthencontroltheneedlepositionusingrotationandtranslation. ToimprovethecontrollerdevelopedinChapter3and4,anaccuratedesignfortheposition oftheviscoelastictissuecouldbeused.Thedynamicsofthetissuedependsonforcesfrom surroundingtissueandorgans,andphysiologicalmovementsasheartbeatingorbreathing.In thesechapters,itisonlysupposedthatthepositionofthetissuedependsontimebutaspecic dynamicsisnotused.Adetailedstudyofphysiologicalmovementscouldgiveinformationabout thetissuemovementandthenitcouldbeappliedforthecontrollerdevelopmenttogetamore accurateresult.Thegoalistobeinperfectconformitywiththephysiologicalmovementsbutan easierapproachcouldbetoemployamass-springdynamic. InChapter4,nospecialcareisgivenfortimedelay.Timedelayaffectstheperformance ofdynamicsystem.Somemechanismsandcontrolstrategiescanbeappliedtothesesystemsto compensateforthem.Foramedicalapplication,thereisnorealneedtocompensatefortime delayinpracticeifmasterandslaverobotsareclosetoeachotherandaredirectlyconnected. Foralongdistancesurgeryitisfundamentaltodevelopacontrollerwhichguaranteesstability independentofthedelay. 50

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REFERENCES [1]J.Rosen,B.Hannaford,M.P.MacFarlane,andM.N.Sinanan,Forcecontrolledand teleoperatedendoscopicgrasperforminimallyinvasivesurgery-experimentalperformance evaluation, IEEETrans.Biomed.Eng. ,vol.46,pp.1212,1999. [2]O.Piccin,B.L.,B.Bayle,M.deMathelin,andA.Gangi,Aforcefeedbackteleoperated needleinsertiondeviceforpercutaneousprocedures, Int.J.Robot.Res. ,vol.28,no.9,pp. 1154,2009. [3]M.Shoham,M.Burman,E.Zehavi,L.Joskowicz,E.Batkilin,andY.Kunicher,Bonemountedminiaturerobotforsurgicalprocedures:Conceptandclinicalapplications, IEEE Trans.Robot.Autom. ,vol.19,no.5,pp.893,2003. [4]R.H.Taylor,J.Funda,B.Eldridge,S.Gomory,K.Gruben,D.LaRose,M.Talamini, L.Kavoussi,andJ.Anderson,Ateleroboticassistantforlaparoscopicsurgery, IEEEEng. Med.Biol. ,vol.14,no.3,pp.279,1995. [5]A.El-Hakim,R.A.Leung,andA.Tewari,Roboticprostatectomy:apooledanalysisof publishedliterature. ExpertRev.AnticancerTher. ,vol.6,no.1,pp.11,Jan2006. [6]J.Bauer,B.Lee,D.Stoianovici,J.Bishoff,G.Janetschek,P.Bunyaratavej,W.Kamolpronwijit,S.Ratchanon,S.O'Kelley,J.Cadeddu,S.Micali,F.Micali,M.K.Li,P.Goh, D.Png,andL.Kavoussi,Remotetelesurgicalmentoring:feasibilityandefcacy,in SystemSciences,2000.Proceedingsofthe33rdAnnualHawaiiInternationalConference on ,jan.2000,p.9pp. [7]G.Fichtinger,E.C.Burdette,A.Tanacs,R.Patriciu,D.Mazilu,L.L.Whitcomb,and D.Stoianovici,Roboticallyassistedprostatebrachytherapywithtransrectalultrasound guidance-phantomexperiments, Brachytherapy ,p.2006. [8]A.ZivanovicandB.Davies,Aroboticsystemforbloodsampling, IEEET.Inf.Technol. B. ,vol.4,pp.8,2000. [9]S.Dimaio,N.Archip,N.Hata,I.-F.Talos,S.Wareld,A.Majumdar,N.McDannold, K.Hynynen,P.Morrison,W.Wells,D.Kacher,R.Ellis,A.Golby,P.Black,F.Jolesz,and R.Kikinis,Image-guidedneurosurgeryatbrighamandwomen'shospital, IEEEEng. Med.Biol. ,vol.25,pp.67,2006. [10]H.Kataoka,T.Washio,M.Audette,andK.Mizuhara,Amodelforrelationsbetween needledeection,force,andthicknessonneedlepenetration,in Proceedingsofthe 4thInternationalConferenceonMedicalImageComputingandComputer-Assisted Intervention ,2001. [11]S.P.DiMaioandS.E.Salcudean,Needleinsertionmodelingandsimulation, IEEETrans. Robot.Autom. ,vol.19,no.5,pp.864,Oct.2003. 51

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BIOGRAPHICALSKETCH ClineLaplassottewasborninWissembourg,Francein1989.In2009,sheenteredat TlcomPhysiqueStrasbourg,France.Theyearafter,shepursuedherstudywiththeMaster ImagerieRobotiqueetIngnieriepourleVivantImaging,RoboticsandEngineeringfor SurgeryattheUniversityofStrasbourg.Herinterestslieintheeldofnonlinearcontrol, biomedicalengineeringandrobotics. ThankstotheAtlantisprogram,ClinepursuedadualMasterofSciencedegreebetween theUniversityofStrasbourgandtheNonlinearControlsandRoboticsgroupintheDepartmentof MechanicalandAerospaceEngineeringattheUniversityofFlorida,underthesupervisionofDr. WarrenE.Dixon.Duringherlaboratorytime,shehadtheopportunitytoworkonroboticneedle insertion. 57