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RobotManipulatorRedundancyResolution
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WILEY-ASMEPRESSSERIESLIST
RobustAdaptiveControlforFractional-Order Shi November2017
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Robot Manipulator Redundancy Resolution
YunongZhangandLongJin
SunYat-senUniversity
Guangzhou,China
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ThisWorkisaco-publicationbetweenASMEPressandJohnWiley&SonsLtd
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©2018JohnWiley&SonsLtd
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LibraryofCongressCataloging-in-PublicationData
Names:Zhang,Yunong,1973-author.|Jin,Long,1988-author.
Title:Robotmanipulatorredundancyresolution/YunongZhang,LongJin,Sun
YatsenUniversity.
Description:Hoboken,NewJersey:Wiley,[2017]|Includesbibliographical
referencesandindex.|
Identifiers:LCCN2017018502(print)|LCCN2017019566(ebook)|ISBN
9781119381426(pdf)|ISBN9781119381433(epub)|ISBN9781119381235
(cloth)
Subjects:LCSH:Robots–Controlsystems.|Manipulators(Mechanism)|
Redundancy(Engineering)
Classification:LCCTJ211.35(ebook)|LCCTJ211.35.Z442017(print)|DDC
629.8/933–dc23
LCrecordavailableathttps://lccn.loc.gov/2017018502
Coverimage:©kynny/Gettyimages
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
10 9 8 7 6 5 4 3 2 1
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Toourparentsandancestors,asalways
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vii
Contents
ListofFigures xiii
ListofTables xxv
Preface xxvii
Acknowledgments xxxiii
Acronyms xxxv
PartI Pseudoinverse-BasedZDApproach 1
1 RedundancyResolutionviaPseudoinverseandZDModels 3
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1.1 Introduction 3
1.2 ProblemFormulationandZDModels 5
1.2.1 ProblemFormulation 5
1.2.2 Continuous-TimeZDModel 6
1.2.3 Discrete-TimeZDModels 7
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1.2.3.1 Euler-TypeDTZDModelwithJ(t)Known 7
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1.2.3.2 Euler-TypeDTZDModelwithJ(t)Unknown 7
1.2.3.3 Taylor-TypeDTZDModels 8
1.3 ZDApplicationstoDifferent-TypeRobotManipulators 9
1.3.1 ApplicationtoaFive-LinkPlanarRobotManipulator 9
1.3.2 ApplicationtoaThree-LinkPlanarRobotManipulator 12
1.4 ChapterSummary 14
PartII Inverse-FreeSimpleApproach 15
2 G1TypeSchemetoJVLInverseKinematics 17
2.1 Introduction 17
2.2 PreliminariesandRelatedWork 18
2.3 SchemeFormulation 18
2.4 ComputerSimulations 19
2.4.1 Square-PathTrackingTask 19
2.4.2 “Z”-ShapedPathTrackingTask 22
2.5 PhysicalExperiments 25
2.6 ChapterSummary 26
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viii Contents
3 D1G1TypeSchemetoJALInverseKinematics 27
3.1 Introduction 27
3.2 PreliminariesandRelatedWork 28
3.3 SchemeFormulation 28
3.4 ComputerSimulations 29
3.4.1 Rhombus-PathTrackingTask 29
3.4.1.1 Verifications 29
3.4.1.2 Comparisons 30
3.4.2 Triangle-PathTrackingTask 32
3.5 ChapterSummary 36
4 Z1G1TypeSchemetoJALInverseKinematics 37
4.1 Introduction 37
4.2 ProblemFormulationandZ1G1TypeScheme 37
4.3 ComputerSimulations 38
4.3.1 DesiredInitialPosition 38
4.3.1.1 Isosceles-TrapezoidPathTracking 40
4.3.1.2 Isosceles-TrianglePathTracking 41
4.3.1.3 SquarePathTracking 42
4.3.2 NondesiredInitialPosition 44
4.4 PhysicalExperiments 45
4.5 ChapterSummary 45
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PartIII QPApproachandUnification 47
5 RedundancyResolutionviaQPApproachandUnification 49
5.1 Introduction 49
5.2 RoboticFormulation 50
5.3 HandlingJointPhysicalLimits 52
5.3.1 Joint-VelocityLevel 52
5.3.2 Joint-AccelerationLevel 52
5.4 AvoidingObstacles 53
5.5 VariousPerformanceIndices 54
5.5.1 ResolvedatJoint-VelocityLevel 55
5.5.1.1 MVNscheme 55
5.5.1.2 RMPscheme 55
5.5.1.3 MKEscheme 55
5.5.2 ResolvedatJoint-AccelerationLevel 55
5.5.2.1 MANscheme 55
5.5.2.2 MTNscheme 56
5.5.2.3 IIWTscheme 56
5.6 UnifiedQPFormulation 56
5.7 OnlineQPSolutions 57
5.7.1 TraditionalQPRoutines 57
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Contents ix
5.7.2 CompactQPMethod 57
5.7.3 DualNeuralNetwork 57
5.7.4 LVI-AidedPrimal-DualNeuralNetwork 57
5.7.5 NumericalAlgorithmsE47and94LVI 59
5.7.5.1 NumericalAlgorithmE47 59
5.7.5.2 NumericalAlgorithm94LVI 59
5.8 ComputerSimulations 61
5.9 ChapterSummary 66
PartIV IllustrativeJVLQPSchemesandPerformances 67
6 VaryingJoint-VelocityLimitsHandledbyQP 69
6.1 Introduction 69
6.2 PreliminariesandProblemFormulation 70
6.2.1 Six-DOFPlanarRobotSystem 70
6.2.2 VaryingJoint-VelocityLimits 73
6.3 94LVIAssistedQPSolution 76
6.4 ComputerSimulationsandPhysicalExperiments 77
6.4.1 Line-SegmentPath-TrackingTask 77
6.4.2 Elliptical-PathTrackingTask 85
6.4.3 SimulationswithFasterTasks 87
(cid:2) 6.4.3.1 Line-Segment-Path-TrackingTask 87 (cid:2)
6.4.3.2 Elliptical-Path-TrackingTask 89
6.5 ChapterSummary 92
7 Feedback-AidedMinimumJointMotion 95
7.1 Introduction 95
7.2 PreliminariesandProblemFormulation 97
7.2.1 MinimumJointMotionPerformanceIndex 97
7.2.2 VaryingJoint-VelocityLimits 100
7.3 ComputerSimulationsandPhysicalExperiments 101
7.3.1 “M”-ShapedPath-TrackingTask 101
7.3.1.1 SimulationComparisonswithDifferent𝜅 101
p
7.3.1.2 SimulationComparisonswithDifferent𝛾 103
7.3.1.3 SimulativeandExperimentalVerificationsofFAMJMScheme 105
7.3.2 “P”-ShapedPathTrackingTask 107
7.3.3 ComparisonswithPseudoinverse-BasedApproach 108
7.3.3.1 ComparisonwithTrackingTaskofLarger“M”-ShapedPath 110
7.3.3.2 ComparisonwithTrackingTaskofLarger“P”-ShapedPath 112
7.4 ChapterSummary 119
8 QPBasedManipulatorStateAdjustment 121
8.1 Introduction 121
8.2 PreliminariesandSchemeFormulation 122
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x Contents
8.3 QPSolutionandControlofRobotManipulator 124
8.4 ComputerSimulationsandComparisons 125
8.4.1 StateAdjustmentwithoutZIVConstraint 125
8.4.2 StateAdjustmentwithZIVConstraint 128
8.5 PhysicalExperiments 132
8.6 ChapterSummary 136
PartV Self-MotionPlanning 137
9 QP-BasedSelf-MotionPlanning 139
9.1 Introduction 139
9.2 PreliminariesandQPFormulation 140
9.2.1 Self-MotionCriterion 140
9.2.2 QPFormulation 141
9.3 LVIAPDNNAssistedQPSolution 141
9.4 PUMA560BasedComputerSimulations 142
9.4.1 FromInitialConfigurationAtoDesiredConfigurationB 144
9.4.2 FromInitialConfigurationAtoDesiredConfigurationC 146
9.4.3 FromInitialConfigurationEtoDesiredConfigurationF 147
9.5 PA10BasedComputerSimulations 152
9.6 ChapterSummary 158
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10 PseudoinverseMethodandSingularitiesDiscussed 161
10.1 Introduction 161
10.2 PreliminariesandSchemeFormulation 162
10.2.1 ModifiedPerformanceIndexforSMP 163
10.2.2 QP-BasedSMPSchemeFormulation 163
10.3 LVIAPDNNAssistedQPSolutionwithDiscussion 164
10.4 ComputerSimulations 167
10.4.1 Three-LinkRedundantPlanarManipulator 168
10.4.1.1 Verifications 168
10.4.1.2 Comparisons 171
10.4.2 PUMA560RobotManipulator 172
10.4.3 PA10RobotManipulator 176
10.5 ChapterSummary 180
Appendix 181
EquivalenceAnalysisinLimitSituation 181
11 Self-MotionPlanningwithZIVConstraint 183
11.1 Introduction 183
11.2 PreliminariesandSchemeFormulation 184
11.2.1 HandlingJointPhysicalLimits 184
11.2.2 QPReformulation 187
11.2.3 DesignofZIVConstraint 187
11.3 E47AssistedQPSolution 188
11.4 ComputerSimulationsandPhysicalExperiments 189
11.5 ChapterSummary 197
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Contents xi
PartVI ManipulabilityMaximization 199
12 Manipulability-MaximizingSMPScheme 201
12.1 Introduction 201
12.2 SchemeFormulation 202
12.2.1 DerivationofManipulabilityIndex 202
12.2.2 HandlingPhysicalLimits 203
12.2.3 QPFormulation 203
12.3 ComputerSimulationsandPhysicalExperiments 204
12.3.1 ComputerSimulations 204
12.3.2 PhysicalExperiments 205
12.4 ChapterSummary 209
13 Time-VaryingCoefficientAidedMMScheme 211
13.1 Introduction 211
13.2 Manipulability-MaximizationwithTime-VaryingCoefficient 212
13.2.1 NonzeroInitial/FinalJoint-VelocityProblem 212
13.2.2 SchemeFormulation 213
13.2.3 94LVIAssistedQPSolution 215
13.3 ComputerSimulationsandPhysicalExperiments 216
13.3.1 ComputerSimulations 216
13.3.2 PhysicalExperiments 224
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PartVII EncoderFeedbackandJoystickControl 227
14 QPBasedEncoderFeedbackControl 229
14.1 Introduction 229
14.2 PreliminariesandSchemeFormulation 231
14.2.1 JointDescription 231
14.2.2 OMPFCScheme 231
14.3 ComputerSimulations 234
14.3.1 Petal-ShapedPath-TrackingTask 234
14.3.2 ComparativeSimulations 238
14.3.2.1 Petal-ShapedPathTrackingUsingAnotherGroupofJoint-Angle
Limits 238
14.3.2.2 Petal-ShapedPathTrackingviatheMethod4(M4)Algorithm 238
14.3.3 Hexagonal-Path-TrackingTask 239
14.4 PhysicalExperiments 240
14.5 ChapterSummary 248
15 QPBasedJoystickControl 251
15.1 Introduction 251
15.2 PreliminariesandHardwareSystem 251
15.2.1 Velocity-SpecifiedInverseKinematicsProblem 252
15.2.2 Joystick-ControlledManipulatorHardwareSystem 252
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