Robot Modeling and Control.pdf 评分

P reface TO APPEAR Contents Preface TABLE OF CONTENTS I NTRODUCTION 1.1 Mathematical Modeling of Robots 1.1.1 Syrnbolic Representation o/ Robots 130 .1.2 he Con力 guration Space 1.3 The State space 1. 1.4 The Workspace 1.2 Robots as Mechanical Devices 1.2.1 Classification of Robotic Manipulators 1. 2. 2 Robotic Systems 5577 1.2.3 Accuracy and Repeatability 1.2.4 Wrists and Erd-EJfeclors 1.3 Common Kinematic Arrangements of Manipulators 1.3.1 Articulated manipulatoR(RRR) 10 1.3.2 Spherical Manipulator (RRP)I 11 11.3.3 SCARA Manipulator (RRP) 12 i CONTENTS 1.3.4 Cylindrical Manipulator(RPP) 13 1.3.5 Cartesian, manipulator(PPp) 1.3.6 Parallel manipulator 15 ·4 Outline of the Te t 16 1.5 Chaplet summary 26 2 RIGID MOTIONS AND HOMOGENEOUS TRANSFORMATIONS 29 1 Representing positions 90 2. 2 Representing Rotation.s 92 2.2.1 Rotation in the plane 32 2.2.2 Rotations in three dirrensions 35 2. 3 Rotational Transformations 97 12.3. 1 Similarity Transformations .A Composition of rotations 42 2.1 Rotation with respect to the current frame 9 2. 4.2 Rotation with respect to the fi.zed frame] 2.5 Parameterizations of rotations 46 2.5. 1 Euler Argles 47 12. 5. 2 Roll, Pilch, Yaw Argles 49 2.5.3 A is/ Angle Representation 50 2.6 Rigid tions 5 2.7 Homogeneous Transformations 2.8 Chapter Summary 57 B FORWARD AND INVERSE KINEMATICS 65 3.1 Kinematic chain,s 65 3.2 Forward Kinematics: The Denavit-Hartenberg Convention 9. 2. 1 Eristence and uniqueness issues 69 9. 2.2 Assigning the coordinate frames Examples 3.3 murse kinematics 5 3. 3. 1 The General Inverse kinematics Problem85 3.3.2 Kinenatic Decoupling 87 3.3.3 Inver se Positior A Geometric Approach 89 19.3. 4 Inverse Orienlalior 97 13.3.5 Examples 98 CONTENTS v 3.′C" hapter Summar 100 5 Notes and References 109 Problems 103 4 VELOCITY KINEMATICS- THE MANIPULATOR JACOBIAM113 44.1 Argular Velocily: The Fived A zis Cuse 114 4. 2 Skew Symmetric Matrices 115 4.2.1 Properlies o/ Skew Symmetric Malrices 116 4. 2. 2 The Derwualive o/ a Rolation Malriz 117 3 Angular Velocity: The General Case 118 Addition o/ Angular Velocities 119 4.5 Linear Velocily ofa Poinl Allached to a Moving frame 12 4.6 Derivation of the Jacobian 09 .6.1 velocity 133 4.6 Linear velocity 4.6.3 Combining Che Angular and Linear Jacobians 4. 7 Examples 127 4. 8 The Analytical Jacobian 131 .05m0007es 132 4.9. 1 Decoupling of singularities 133 4.9.2 Wrist Singularities 134 4.9.3 Arm Singularities 134 4. 10 Inverse velocity and acceleration 139 141 4. 12 Chapter Summary 144 Problerns 146 5 PATH AND TRAJECTORY PLANNING] 149 5.1 The Configuration space 150 15. 2 Path Planning Using Confiquration space Potential ields 5.2.1 The Attractive Fiele 154 5.2.2 The Repulsive field 156 5.2.9 Gradient Descent Planning 157 5.3 Planning Using Workspace Potential fields 158 5.3. 1 Defining Workspace Potential Fields 159 CONTENTS 5.3.2 Mapping workspace forces to joint forces and torqu.es ⑤3M0 tion Planning algo7+hm 165 5.4 Using random Motions to Escape Local Minima 166 5.5 Probabilistic Roadmap methods 167 5.5. 1 Sampling the configuration space 1690 5.5.3C ng Pairs of Configurations] 169 5.5.3 Enhancement 10 5. 5. 4 Path Smoothing 170 5.6 trajectory planning 171 5.6.1 Trajectories for Point to Point motion 17 5.6.2 Trajectories for Paths Specified by Via Points 5.7 Historical Perspective 184 Problems 186 67Y MIO 187 6.1 The enler- Lagrange equations 188 6.1.1 One Dimensional System 188 16.1.2 The General Casel 190 6.2 General E. tpressiors for Kinetic and Potential 6.2.1 The inertia Tensor 197 6.2.2 Kinetic Energy for an n-Link Robot 199 6.2.3 Potential Energy for an n-Link Robot g00 6.3 Equations of Motion 200 6. Some Common Configurations 902 6.5 Properties of Robot Dynamic equations 911 6.5.1 The Skew Symmetry and Passivity Properti 6.5.2 Bo1nds on the inertia Matri. 913 6.5.3 Linearity in the Parameters 6.6 Newton euler formulation 215 0.7 Planar Elbow M anp lalor Revisited 922 Problens g25 7 INDEPENDENVT JOINT CONTROL 929 7. 1 Introduction g29 7. Actuator Dynamics 231 CONTENTS vii 7.3 Set- Point Tracking 937 9.38 4.3.2 Performance of PD Compensators 239 23 9 PID Compensator g40 942 7+ Feedforward Control and computed Torque 244 7.5 Drive Train Dynamics 98 7.6 State Space Design 251 .6 1 State Feedback Compensator. 254 7.6.2 Observers g56 Problen 959 8 MULTIVARIABLE CONTROL 963 8.1 Introduction 963 PD Control revisited 264 8.3 Inverse Dynamics g66 8.3.1 Task space Inverse Dymamics 969 8. Robust and Adaptive Motion control 971 1 Robust Feedback linearization 971 8. 4.2 Passivity Based Robust Contro 975 8.4.9 Passivity Based Adaptive control 77 001em5 g79 9 FORCE CONTROL 981 9. 1 Introduction 981 9.2 Coordinate Frames and constraints 282 9.2.1 Nalural and Artificial Constraints 284 9.3 Network Models and Impedance 985 9.3.1 Impedance Operators 9S8 9.3.2 CLassification of Impedance Operators 288 Norton equivalents 289 ask space dynamics and control g90 9.4.1 Static Force Torque Relationships g90 9.4.2 Task Space Dynamics 991 9.4.3 Impedance Control 999 9. 4.4 Hybrid Impedance Control 29.3 Problerns 997 10 GEOMETRIC NONLINEAR CONTROL 299 iii CONTENTS 10.1 Introduction 999 10.2 Background 300 10.2.1 The frobenius Theorem 304 10.3 Feedback Linearization 306 [10.4 Single-Inpul Syslems 308 10.5 Feedback Linearization for n-Link Robots 915 10.6 Nonholonomic Systems 318 10.6. 1 / nvolutionty and Holonomy 919 10.6.2 Driftless Control systems 20 10.6.3 Ecainples of Nonholonomic Systerns 320 110. 7 Chow's T heoreT and Conlrollabilily of Dri lles stems Problems 928 I1 COMPUTER VISION 931 11.1 The Geometry of Image Formation 339 11.1.1 The Camera Coordinate frame 332 21. 1. 2 Perspective Projection 333 1. The Image Plane and the Sensor: Array 354 11.2 Camera Calibration 93 11.2.1 Extrinsic Camera parameters 935 11.2.2 Intrinsic Camera parameters 335 11.2.3 Determining the Camera Parameters :36 11. 3 Segmentation by Thresholding 338 11.3.1 A Brie/ statistics Review 339 11.3.2 Automatic Threshold Selection 941 11.4 Connected Components 346 11. 5 Position and Orientation 348 11.5.1 Moments 349 21.5. 2 The Centroid of an Object] 349 11.5. The Orienlalion o/ an Objecl 350 Proble 95 12 VISION-BASED CONTROL 355 12. 1 Approaches to uision, ba.scd-control 6 12. 1. 1 Where to put the camera 356 12.1.2 How to use the image data 357 12.2 Camera Molion and inleraction Matris 957 12.2. 1 Interaction matri.C us. Image Jacobian 958

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2020-02-16

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