Control Design and Analysis for Underactuated Robotic Systems [recurso electrónico] $c

The last two decades have witnessed considerable progress in the study of underactuated robotic systems (URSs). __C____ontrol__ __Design and Analysis__ __for__ __U____nderactuated__ __R____obotic__ __S____yste____ms__ presents a unified treatment of control design and analysis for a class of URSs, which include systems with multiple-degree-of-freedom and/or with underactuation degree two. It presents novel notions, features, design techniques and strictly global motion analysis results for these systems. These new materials are shown to be vital in studying the control design and stability analysis of URSs. __Control Design and Analysis for Underactuated Robotic Systems__ includes the modelling, control design and analysis presented in a systematic way particularly for the following examples: l directly and remotely driven Acrobots l Pendubot l rotational pendulum l counter-weighted Acrobot 2-link underactuated robot with flexible elbow joint l variable-length pendulum l 3-link gymnastic robot with passive first joint l n-link planar robot with passive first joint l n-link planar robot with passive single joint double, or two parallel pendulums on a cart l 3-link planar robots with underactuation degree two 2-link free flying robot The theoretical developments are validated by experimental results for the remotely driven Acrobot and the rotational pendulum. __C____ontrol__ __Design and Analysis__ __for__ __U____nderactuated__ __R____obotic__ __S____yste____ms__ is intended for advanced undergraduate and graduate students and researchers in the area of control systems, mechanical and robotics systems, nonlinear systems and oscillation. This text will not only enable the reader to gain a better understanding of the power and fundamental limitations of linear and nonlinear control theory for the control design and analysis for these URSs, but also inspire the reader to address the challenges of more complex URSs. Control Design and Analysis for Underactuated Robotic Systems 3 Preface 6 Contents 8 Acronyms, Notations, and Symbols 13 Chapter 1: Introduction 16 1.1 Nonholonomic Systems via Underactuated Systems 16 1.2 Models 18 1.2.1 First- and Second-Order Nonholonomic Constraints 18 1.2.2 Kinematic and Dynamics Models 20 1.3 Control Design and Analysis Problems 22 1.4 Objective and Contents of This Book 23 1.4.1 Underactuated Robotic Systems 23 1.4.2 Contents and Features 24 Chapter 2: Fundamental Background 34 2.1 Lyapunov Stability Theory 34 2.1.1 Basic Knowledge 34 2.1.2 Direct Method of Lyapunov 35 2.1.3 LaSalle's Invariance Principle 37 2.1.4 Indirect Method of Lyapunov 38 2.1.5 Theorems for Manifolds and Homoclinic Orbits 41 2.2 n-Link Planar Robot 43 2.2.1 Motion Equations 43 2.2.2 Properties of Robot 48 2.3 Three 2-Link Planar Robots 50 2.3.1 Motion Equations 50 2.3.2 Equilibrium Configurations 53 2.3.3 Linearization and Linear Controllability 54 2.4 Control for Underactuated Robotic Systems 56 2.4.1 Partial Feedback Linearization 56 2.4.2 Energy-Based Control Approach 57 2.5 Useful Inequalities 59 Chapter 3: Directly Driven Acrobot 62 3.1 Introduction 62 3.2 Problem Formulation 63 3.3 Swing-up Controller 63 3.4 Global Motion Analysis 66 3.4.1 Convergence of Energy 67 3.4.2 Closed-Loop Equilibrium Points 71 3.5 Discussion 79 3.6 Locally Stabilizing Control 80 3.7 Simulation Results 81 3.8 Conclusion 84 Chapter 4: Remotely Driven Acrobot 86 4.1 Introduction 86 4.2 Swing-up Controller 87 4.3 Global Motion Analysis 89 4.4 Experimental Setup 94 4.5 Simulation and Experimental Results 96 4.6 Conclusion 107 Chapter 5: Pendubot 109 5.1 Introduction 109 5.2 Swing-up Controller 110 5.3 Global Motion Analysis 113 5.4 Simulation Results 118 5.5 Conclusion 121 Chapter 6: Rotational Pendulum 122 6.1 Introduction 122 6.2 Preliminary Knowledge 123 6.3 Swing-up Controller 124 6.4 Global Motion Analysis 127 6.5 Simulation Results for Rotational Pendulum 1 130 6.6 Experimental Verification for Rotational Pendulum 2 131 6.6.1 Experimental Setup 133 6.6.2 Swing-up and Stabilizing Control 134 6.7 Conclusion 138 Chapter 7: Counter-Weighted Acrobot 139 7.1 Introduction 139 7.2 Preliminary Knowledge and Problem Formulation 140 7.2.1 Motion Equation 140 7.2.2 Problem Formulation 141 7.3 Linear Controllability 141 7.4 Energy-Based Controller 142 7.5 Motion Analysis 143 7.6 Simulation Results 145 7.7 Conclusion 148 Chapter 8: Variable Length Pendulum 150 8.1 Introduction 150 8.2 Preliminary Knowledge and Problem Formulation 151 8.2.1 Motion Equation 151 8.2.2 Problem Formulation 152 8.3 Controller Designs 152 8.3.1 Using Total Mechanical Energy Shaping 153 8.3.2 Using Partial Energy Shaping 154 8.4 Motion Analysis 155 8.4.1 Convergence of Energy 155 8.4.2 Closed-Loop Equilibrium Points 157 8.5 Simulation Results 160 8.6 Conclusion 162 Chapter 9: 2-Link Underactuated Robot with Flexible Elbow Joint 165 9.1 Introduction 165 9.2 Preliminary Knowledge 166 9.3 Properties of Robot Under Gravity 167 9.3.1 Linear Controllability 168 9.3.2 Active Link Under Constant Torque 169 9.4 PD Control for Robot with Big Spring Constant 171 9.5 Swing-up Controller for Robot with Small Spring Constant 174 9.5.1 Controller Design 175 9.5.2 Motion Analysis 177 9.6 Simulation Results 180 9.6.1 Case of Big Spring Constant 181 9.6.2 Case of Small Spring Constant 182 9.7 Conclusion 184 Chapter 10: 3-Link Planar Robot with Passive First Joint 185 10.1 Introduction 185 10.2 Preliminary Knowledge and Problem Formulation 186 10.2.1 Motion Equation 186 10.2.2 Problem Formulation 188 10.3 Virtual Composite Link and Coordinate Transformation 189 10.4 Swing-up Controller Using Virtual Composite Link 190 10.5 Global Motion Analysis 193 10.5.1 Convergence of Energy 193 10.5.2 Closed-Loop Equilibrium Points 196 10.6 Discussion 200 10.7 Simulation Results 201 10.8 Conclusion 203 Chapter 11: n-Link Planar Robot with Passive First Joint 205 11.1 Introduction 205 11.2 Problem Formulation 206 11.3 Virtual Composite Links and Coordinate Transformation 207 11.3.1 Virtual Composite Links 207 11.3.2 Coordinate Transformation on Angles of Active Joints 208 11.4 Swing-up Controller Using Virtual Composite Links 212 11.5 Global Motion Analysis 215 11.5.1 Convergence of Energy 215 11.5.2 Closed-Loop Equilibrium Points 216 11.6 Discussion 220 11.7 Simulation Results 223 11.7.1 Model of 4-Link Planar Robot 223 11.7.2 Time Responses of 4-Link Planar Robot 225 11.8 Conclusion 226 Chapter 12: n-Link Planar Robot with Single Passive Joint 228 12.1 Introduction 228 12.2 Problem Formulation 229 12.3 Series of Virtual Composite Links and Coordinate Transformation 231 12.4 Swing-up Controller Using Virtual Composite Links 234 12.5 Global Motion Analysis 236 12.5.1 Convergence of Energy 236 12.5.2 Closed-Loop Equilibrium Points 238 12.6 Discussion 243 12.7 Simulation Results for 4-Link Planar Robots 244 12.7.1 Robot with First Passive Joint 245 12.7.2 Robot with Second Passive Joint 246 12.7.3 Robot with Last Passive Joint 247 12.8 Conclusion 248 Chapter 13: Two Parallel Pendulums on Cart 251 13.1 Introduction 251 13.2 Preliminary Knowledge 252 13.2.1 Motion Equation 252 13.2.2 Swing-up Controller 253 13.3 Convergence of Energy of Each Pendulum 254 13.4 Stability Analysis of Invariant Sets 258 13.5 Simulation Results 263 13.6 Conclusion 263 Chapter 14: Double Pendulum on Cart 265 14.1 Introduction 265 14.2 Preliminary Knowledge and Problem Formulation 266 14.2.1 Motion Equation 266 14.2.2 Problem Formulation 267 14.3 Energy-Based Controller 268 14.4 Global Motion Analysis 270 14.4.1 Convergence of Energy 270 14.4.2 Closed-Loop Equilibrium Points 277 14.5 Simulation Results 280 14.6 Conclusion 284 Chapter 15: 3-Link Planar Robot with Two Passive Joints 285 15.1 Introduction 285 15.2 Preliminary Knowledge and Problem Formulation 286 15.2.1 Preliminary Knowledge 286 15.2.2 Problem Formulation 288 15.3 Energy-Based Controller 289 15.4 Global Motion Analysis 290 15.4.1 Property of Active Link Under Constant Torque 291 15.4.2 Convergence of Energy and Stability of Equilibrium Points 295 15.5 Simulation Results 300 15.6 Conclusion 301 Chapter 16: 2-Link Flying Robot 303 16.1 Introduction 303 16.2 Models of Flying Robot 304 16.3 Problem Formulation 307 16.4 Global Asymptotic Stabilization 308 16.5 Control Designs via Backstepping Approach 309 16.5.1 Virtual Control Input 310 16.5.2 Velocity- and Acceleration-Based Controllers 312 16.6 Discussion 315 16.7 Simulation Results 316 16.8 Conclusion 316 References 318 Index 324 The last two decades have witnessed considerable progress in the study of underactuated robotic systems (URSs). C ontrol Design and Analysis for U nderactuated R obotic S yste ms presents a unified treatment of control design and analysis for a class of URSs, which include systems with multiple-degree-of-freedom and/or with underactuation degree two. It presents novel notions, features, design techniques and strictly global motion analysis results for these systems. These new materials are shown to be vital in studying the control design and stability analysis of URSs. Control Design and Analysis for Underactuated Robotic Systems includes the modelling, control design and analysis presented in a systematic way particularly for the following examples: l directly and remotely driven Acrobots l Pendubot l rotational pendulum l counter-weighted Acrobot 2-link underactuated robot with flexible elbow joint l variable-length pendulum l 3-link gymnastic robot with passive first joint l n-link planar robot with passive first joint l n-link planar robot with passive single joint double, or two parallel pendulums on a cart l 3-link planar robots with underactuation degree two 2-link free flying robot The theoretical developments are validated by experimental results for the remotely driven Acrobot and the rotational pendulum. C ontrol Design and Analysis for U nderactuated R obotic S yste ms is intended for advanced undergraduate and graduate students and researchers in the area of control systems, mechanical and robotics systems, nonlinear systems and oscillation. This text will not only enable the reader to gain a better understanding of the power and fundamental limitations of linear and nonlinear control theory for the control design and analysis for these URSs, but also inspire the reader to address the challenges of more complex URSs. Front Matter....Pages I-XVII Introduction....Pages 1-18 Fundamental Background....Pages 19-46 Directly Driven Acrobot....Pages 47-70 Remotely Driven Acrobot....Pages 71-93 Pendubot....Pages 95-107 Rotational Pendulum....Pages 109-125 Counter-Weighted Acrobot....Pages 127-137 Variable Length Pendulum....Pages 139-153 2-Link Underactuated Robot with Flexible Elbow Joint....Pages 155-174 3-Link Planar Robot with Passive First Joint....Pages 175-194 n -Link Planar Robot with Passive First Joint....Pages 195-217 n -Link Planar Robot with Single Passive Joint....Pages 219-241 Two Parallel Pendulums on Cart....Pages 243-256 Double Pendulum on Cart....Pages 257-276 3-Link Planar Robot with Two Passive Joints....Pages 277-294 2-Link Flying Robot....Pages 295-309 Back Matter....Pages 311-319