Table of Contents

1 Introduction 1
1.1 Underactuated Manipulators 1
1.2 CharacteristicAnalysis 3
1.3 ControlMethodDesign 4
1.3.1 EnergyBasedControl. 5
1.3.2 SlidingModeControl 6
1.3.3 Backstepping Control 7
1.3.4 Partial Feedback LinearizationControl 8
1.3.5 Approximate LinearizationControl 8
1.3.6 Model ReductionControl 10
1.4 Intelligent and OptimizationControl 11
1.4.1 Fuzzy Control 11
1.4.2 NeuralNetworkControl. 12
1.4.3 Optimization-BasedControl 13
1.5 OrganizationofThisBook 14
References 16
2 Modeling and Characteristics Analysis of Underactuated Manipulators 23
2.1 Dynamic ModelingofTypical Underactuated Manipulators 23
2.1.1 The Inertia Wheel Pendulum Manipulator 24
2.1.2 Two-Link Underactuated Manipulator 26
2.1.3 Multi-link Underactuated Manipulator 30
2.1.4 FlexibleManipulator 39
2.2 Characteristics Analysis of Underactuated Mechanical System 52
2.2.1 Dynamics Analysis 53
2.2.2 Controllability Analysis 55
2.3 Conclusions 57
References 57
3 Control of Vertical Underactuated Manipulator 61
3.1 ALyapunov-Based Unified ControlStrategy 61
3.1.1 Dynamic Model 62
3.1.2 ControlStrategyfor theSwing-Up Area 63
3.1.3 ControlStrategyfortheAttractiveArea 65
3.1.4 Local and Global Stability Analysis 66
3.1.5 SimulationResults 70
3.2 ARewinding Approach-BasedControlStrategy 74
3.2.1 ModelingandAnalysis 74
3.2.2 MotionPlanning 77
3.2.3 TrajectoryTracking Control 79
3.2.4 SimulationResults 81
3.3 StableControlofThree-Link Underactuated Manipulators 82
3.3.1 Model andDivisionof Motion Space 84
3.3.2 Swing-UpControllerDesign. 86
3.3.3 SingularityAvoidancein Swing-Up Controller 88
3.3.4 Balance Controller Design 93
3.3.5 SimulationResults 94
3.4 StableControlofn-Link Underactuated Manipulators 96
3.4.1 Dynamic Model and Analysis 96
3.4.2 ControllerDesigninStage1 101
3.4.3 ControllerDesigninStage2 104
3.4.4 SimulationResults 109
3.5 Conclusions 111
References 113
4 Control of Planar Underactuated Manipulator with a Passive First Joint 117
4.1 Motion-StateConstraintAnalysis 117
4.1.1 Integrability 119
4.1.2 Motion-StateConstraint on AngularVelocities 119
4.1.3 Motion-StateConstraint on Angles 120
4.2 Motion-StateConstraint-Based ControlofPlanar Acrobot 124
4.2.1 MotionCharacteristicAnalysis 125
4.2.2 MotionOptimization 126
4.2.3 ControllerDesign. 127
4.2.4 SimulationResults 129
4.3 StableControlofPlanar Three-LinkPAAManipulator 130
4.3.1 MotionStrategyofAnglestoTargetValues 131
4.3.2 PSO-BasedTarget Angle Optimization 133
4.3.3 Target Angle-BasedControllers Design 134
4.3.4 SimulationResults 138
4.4 Two-Stage ControlofPlanarn-Link (n > 3) PAn.1 Manipulator 140
4.4.1 Controllers Designof Stage1for Model Reduction 141
4.4.2ControllersDesignofStage2 143
4.4.3 GA-PSO-BasedTarget Angle Optimization 144
4.4.4 SimulationResults 146
4.5 Intelligent Optimization-BasedContinuous ControlMethod 147
4.5.1 ProblemFormulation. 148
4.5.2 Continuous ControllerDesignfor Active Joints 149
4.5.3 OptimizationofDesignParameters andTarget Angles 150
4.5.4 SimulationResults 152
4.6 Nonlinear MPC-BasedRobustControlMethod 155
4.6.1 ProblemFormulation. 155
4.6.2 ControlIdea 156
4.6.3 Nonlinear Model PredictiveControl-BasedMotion Planning 157
4.6.4 FastTerminal SlidingMode Controller Design 159
4.6.5 SimulationResults 165
4.7 OnlineIterative Correction-BasedRobustControl Method 167
4.7.1 Uncertain Model 167
4.7.2 Uncertain PlanarVirtualPAA System 169
4.7.3 Controller Designfor Model Reduction 170
4.7.4 ControlofPlanarVirtualPAA System 174
4.7.5 OnlineIterativeCorrection 175
4.7.6 SimulationResults 176
4.8 Conclusions 179
References 180
5 Control of Planar Underactuated Manipulator with an Active First Joint 183
5.1 FourierTransformation-BasedControl Method forPlanar Pendubot 183
5.1.1 Dynamic Modelof Planar Pendubot 184
5.1.2 Controllers Design with Disturbance Observer 185
5.1.3 SimulationResults 189
5.2 Energy Attenuation Approach-BasedControlMethod forPlanarAPAA Manipulator 192
5.2.1 TargetAnglesCalculation. 193
5.2.2 StableControl. 197
5.2.3 SimulationResults 202
5.3 ChainedForm-Based ControlMethod forPlanar AAPA Manipulator 204
5.3.1 Model Reduction 204
5.3.2 Controllers Design forthe Manipulator with Reduced Order 211
5.3.3 SimulationResults 215
5.4 AGeneralPositionControlMethodforPlanarUnderactuated Manipulator 220
5.4.1 DynamicModelandControlScheme 221
5.4.2 Bi-Directional MotionPlanning 224
5.4.3 TrajectoryTrackingControllers Design 228
5.4.4SimulationResults 230
5.5 Conclusions 234
References 234
6 Control of Flexible Manipulator 237
6.1 StableControlforFlexible-Joint Manipulator 237
6.1.1 EIDBasedControlApproach 238
6.1.2 SimulationResults 244
6.2 TrajectoryTrackingControlforFlexible-JointManipulato