Robotic Assisted Suturing in Minimally Invasive Surgery
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ROBOTIC ASSISTED SUTURING IN MINIMALLY INVASIVE SURGERY By Hyosig Kang A Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Mechanical Engineering Approved by the Examining Committee: Dr. John T. Wen, Thesis Adviser Dr. Stephen J. Derby, Co-Thesis Adviser Dr. Daniel Walczyk, Member Dr. Harry E. Stephanou, Member Rensselaer Polytechnic Institute Troy, New York May 2002 (For Graduation August 2002) ROBOTIC ASSISTED SUTURING IN MINIMALLY INVASIVE SURGERY By Hyosig Kang An Abstract of a Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Mechanical Engineering The original of the complete thesis is on file in the Rensselaer Polytechnic Institute Library Examining Committee: Dr. John T. Wen, Thesis Adviser Dr. Stephen J. Derby, Co-Thesis Adviser Dr. Daniel Walczyk, Member Dr. Harry E. Stephanou, Member Rensselaer Polytechnic Institute Troy, New York May 2002 (For Graduation August 2002) c Copyright 2002 by Hyosig Kang All Rights Reserved ii CONTENTS LISTOFTABLES................................. vii LISTOFFIGURES................................viii ACKNOWLEDGMENT..............................xiv ABSTRACT....................................xvi 1.INTRODUCTION............................... 1 1.1BackgroundandMotivation....................... 1 1.2ProblemStatement............................ 2 1.3Contributions............................... 3 1.4Outline................................... 4 2.LITERATUREREVIEW........................... 5 2.1RoboticDevicesinSurgicalApplications................ 5 2.2 Augmentation of Human Capability in Surgical Tasks . 7 2.3 Motion and Force Control of Rigid Robot Systems . 8 2.3.1 RobotMotionControl...................... 8 2.3.2 RobotForceControl....................... 9 3.MODELINGANDIDENTIFICATION.................... 11 3.1EndoBotDesign.............................. 11 3.1.1 ManipulatorDesignRequirements................ 11 3.1.2 CurrentPrototype........................ 12 3.2KinematicModelingoftheEndoBot.................. 15 3.2.1 ForwardKinematics....................... 15 3.2.2 InverseKinematics........................ 17 3.2.3 JacobianFormulation....................... 18 3.2.3.1 GeometricJacobian.................. 18 3.2.3.2 AnalyticalJacobian.................. 19 3.2.4 SingularityAnalysis....................... 19 3.3DynamicsoftheEndoBot........................ 20 3.3.1 LagrangianFormulation..................... 20 3.3.2 PropertiesofDynamicModel.................. 21 iii 3.3.3 DynamicModeloftheEndoBot................. 22 3.4FrictionModelingandCompensation.................. 24 3.5IdentificationofDynamicParameters.................. 26 3.5.1 Input Signal Design . 28 3.5.2 Dynamic Models for Parameter Identification . 34 3.5.2.1 UseofDifferentialModel............... 35 3.5.2.2 UseofEnergyModel.................. 36 3.5.3 Experimental Identification of Dynamic Parameters . 38 3.5.3.1 Identification of the Friction Coefficients in Energy Model.......................... 39 3.5.3.2 ExperimentalResults................. 41 3.5.4 Validation of Parameter Identification . 43 4. SUTURING IN MINIMALLY INVASIVE SURGERY . 45 4.1SuturingTaskAnalysis.......................... 45 4.2SutureLengthTracking......................... 48 4.3MotionControlintheStitchingTask.................. 49 4.3.1 DynamicmodelingofStitching................. 49 4.3.1.1 Kinematics of the Suture Motion . 50 4.3.1.2 Static Model of the Suture Tension . 50 4.3.2 ProblemFormulation....................... 51 4.3.3 RegionoftheFeasibleMotion.................. 51 4.3.4 ProblemSimplification...................... 52 4.3.5 ProblemTransformation..................... 52 4.4KnotTying................................ 53 4.4.1 LigationAlgorithm1....................... 54 4.4.2 LigationAlgorithm2....................... 57 4.4.3 LigationAlgorithm3....................... 61 4.5PlacingtheKnot............................. 62 4.5.1 ProblemFormulation....................... 62 4.5.2 Sliding Condition of Knot Placement . 63 4.5.3 Trajectories of Suture Ends for Placing a Knot . 68 4.6ControllerRequirementandArchitecture................ 70 4.6.1 HybridDynamicSystem..................... 70 4.6.1.1 HybridState...................... 70 iv 4.6.1.2 HybridAutomaton................... 71 4.6.2 HumanSharingSupervisoryController............. 72 4.6.3 PlanningofSuturingTask.................... 73 4.6.4 DevelopmentEnvironment....................75 5.MOTIONCONTROL............................. 79 5.1GravityCompensationinManualMode................. 79 5.2MotionControlinAutonomousMode.................. 79 5.2.1 Energy Based Output Feedback Control . 80 5.2.2 Experimental Evaluation of Joint Space Control . 82 5.2.3 Nonlinear Decoupled State Feedback Controller . 86 5.2.3.1 Global Linearization of the Nonlinear Robotic System 86 5.2.3.2 Optimal State Feedback Control . 87 5.2.3.3 VelocityEstimation.................. 91 5.2.3.4 Linear Quadratic Gaussian (LQG) Control . 94 6.SHAREDCONTROL.............................100 6.1ConstraintsDescription..........................100 6.2ControlObjective.............................101 6.3TaskSpaceControlDesign........................102 6.3.1 Stability . 102 6.3.2 ControllerDescription......................104 6.3.3 Example..............................104 6.3.4 Experimental Evaluation of Task Space Shared Controller . 105 6.4JointSpaceSharedControlDesign...................109 6.4.1 ControllerDescription......................112 6.4.2 Examples.............................113 6.4.3 Experimental Evaluation of Joint Space Shared Controller . 114 7.TENSIONCONTROL.............................121 7.1SecuringaKnot..............................121 7.1.1 Principle of Direction of Securing a Square Knot . 121 7.2TensionMeasurement...........................123 7.2.1 BasicIdea.............................123 7.2.2 Tension Estimation with a Base Force/Torque Sensor . 125 7.3ForceandPositionControl........................127 v 7.3.1 ProblemFormulation.......................127 7.3.2 Hybrid Force/Position Regulating Control . 128 7.3.3 ExplicitForceControl......................131 7.4 Stability Analysis . 132 7.4.1 Proportional plus Integral Control with Active Damping . 132 7.4.2 Stability of Time Delayed System . 136 7.5ExperimentalStudy............................139 7.5.1 ExperimentationEnvironment..................139 7.5.2 Experimental Evaluation of Tension Controller . 141 8.CONCLUSIONS................................147 8.1Summary.................................147 8.2FutureWork................................148 LITERATURECITED..............................150 APPENDICES A. INVERSE KINEMATICS USING SUBPROBLEMS . 158 B. LAGRANGIAN FOR A ROBOT MANIPULATOR . 159 B.1KineticEnergyofaRobotManipulator.................159 B.2 Potential Energy of a Robot Manipulator . 160 C.LEASTSQUAREMETHOD.........................161 D. PERSISTENT EXCITATION AND OBSERVABILITY GRAMIAN . 163 E.DIFFEOMORPHISM..............................165 vi LIST OF TABLES 3.1 Parametersoftheelectricalsystem..................... 39 3.2 Coefficientsofcrosscorrelation....................... 40 3.3 Frictionparametersofeachlink....................... 41 3.4 Estimates of the dynamic parameters of the EndoBots. 42 5.1 Summary of friction compensation performance. 84 5.2 Circletrackingerror............................. 85 6.1 Parametersforconstrainedline.......................106 6.2 Desired and measured stiffness for shared control. 109 6.3 Effective constraint stiffness for linear trajectory . 117 6.4 Effective constraint stiffness for circular trajectory . 118 7.1 Suturediameter-strengthrelationship....................140 7.2 Suturepulloutvalues.............................141 7.3 Comparison of force controller with active damping. 142 7.4 Effectoftheproportionalgain........................142 7.5 Performance of force controller with a modified force reference trajectory.143 vii LIST OF FIGURES 3.1 Fulcrumeffectinlaparoscopicsurgery.................... 11 3.2 MechanicaloverviewoftheEndoBot.................... 13 3.3 Closeuponsemicirculararches........................ 13 3.4 Translationalstage.............................. 14 3.5 PictureofapairoftheEndoBots...................... 14 3.6 Grasperandsuturingtools.......................... 14 3.7 KinematicdiagramoftheEndoBot..................... 15 3.8 SimplifieddynamicmodeloftheEndoBot................. 22 3.9 Model-basedfrictioncompensation..................... 24 3.10Classicalfrictionmodels........................... 25 3.11Parametricsystemidentification....................... 26 3.12GenerationofPRBS............................. 31 3.13 Schroeder-phased signal design. 32 3.14 Comparison of input signals in time domain. 33 3.15 Comparison of power spectra of input signals. 34 3.16Comparisonoftwoidentificationmethods................. 35 3.17Blockdiagramofvelocitycontrolloop................... 40 3.18Trajectoriesofthefirstjoint......................... 41 3.19 Estimates of the dynamic parameters of the first joint. 42 3.20 Comparison on measured and simulated output trajectories . 43 4.1 Knottyingtechniques............................ 45 4.2 Grasper with a needle in conventional suturing. 47 4.3 Shuttleneedledevice............................. 48 4.4 Componentsofasuture........................... 49 viii 4.5 Autonomous simple knot tying algorithm 1. 56 4.6 Flexiblehookforcatchingthesuture.................... 57 4.7 Autonomous simple