Introduction to Robotics Analysis, Systems, Applications

Introduction to Robotics Analysis, Systems, Applications Saeed B. Niku Mechanical Engineering Department California Polytechnic State University San Luis Obispo

Technische Urw/carsMt Darmstadt FACHBEREfCH IWFOR^ATiK

B I B L I O T H E K Inventar-Nf.:

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Sachgobtete:

Prentice Hall

Prentice Hall Upper Saddle River, NJ 07458

Contents

1

Fundamentals

1

1.1. Introduction 1 1.2. What is a Robot? 2 1.3. Classification of Robots 2 1.4. What is Robotics? 4 1.5. History of Robotics 4 1.6. Advantages and Disadvantages of Robots 5 1.7. Robot Components 6 1.8. Robot Degrees of Freedom 8 1.9. Robot Joints 11 1.10. Robot Coordinates 11 1.11. Robot Reference Frames 12 1.12. Programming Modes 13 1.13. Robot Characteristics 15 1.14. Robot Workspace 16 1.15. Robot Languages 16 1.16. Robot Applications 20 1.17. Other Robots and Applications 24 vii

viii

Contents

1.18. Social Issues 25 1.19. Summary 25 References 26 Problems 27 2

Robot Kinematics: Position Analysis

29

2.1. Introduction 29 2.2. Robots as Mechanisms 29 2.3. Matrix Representation 31 2.3.1. Representation of a point in space 31 2.3.2. Representation of a vector in space 32 2.3.3. Representation of a frame at the origin of a reference frame 33 2.3.4. Representation of a frame in a reference frame 34 2.3.5. Representation of a Rigid Body 35 2.4.

Homogeneous Transformation Matrices

38

2.5.

Representation of Transformations 38 2.5.7. Representation of a pure translation 39 2.5.2. Representation of a pure rotation about an axis 40 2.5.3. Representation of combined transformations 43 2.5.4. Transformations relative to the rotating 46

2.6.

Inverse of Transformation Matrices

2.7.

Forward and Inverse Kinematics of Robots 53 2.7.1. Forward and Inverse Kinematic Equations for Position 54 2.7.2. Forward and Inverse Kinematic Equations for Orientation 59 2.7.3. Forward and Inverse Kinematic Equations for Position and Orientation 67

2.8.

Denavit-Hartenberg Representation of Forward Kinematic Equations of Robots 67

2.9.

The Inverse Kinematic Solution of Robots

48

2.10. Inverse Kinematic Programming of Robots 2.11. Degeneracy and Dexterity

76 80

82

2.12. The Fundamental Problem with the Denavit-Hartenberg Representation 83 2.13. Design Project 1: A three-degree-of-freedom Robot 2.14. Summary References Problems

86 87 88

85

Contents 3

Differential Motions and Velocities

ix 95

3.1.

Introduction

95

3.2.

Differential Relationships

3.3.

Jacobian

3.4.

Differential Motions of a Frame 99 3.4.1. Differential Translations 100 3.4.2. Differential Rotations 100 3.4.3. Differential Rotation about a general axis k 101

95

97

3.4.4. Differential Transformations of a Frame 102 3.5.

Interpretation of the Differential Change

3.6.

Differential Changes Between Frames

3.7.

Differential Motions of a Robot and Its Hand Frame

3.8.

Calculation of the Jacobian

3.9.

How to Relate the Jacobian and the Differential Operator

3.10. Inverse Jacobian 3.11. Design Project 3.12. Summary

4

104 106

107 110

111 115

116

References Problems

104

116 117

Dynamic Analysis and Forces

119

4.1.

Introduction

119

4.2.

Lagrangian Mechanics: A Short Overview

4.3.

Effective Moments of Inertia

4.4.

Dynamic Equations for Multiple-Degree-of-Freedom Robots 4.4.1. Kinetic Energy 128 4.4.2. Potential Energy 132 4.4.3. The Lagrangian 133 4.4.4. Robot's Equations of Motion 133

4.5.

Static Force Analysis of Robots

4.6.

Transformation of Forces and Moments Between Coordinate Frames 141

4.7.

Design Project

4.8.

Summary

143

143

120

127

139

128

Contents

References 144 Problems 144 5

Trajectory Planning

147

5.1. Introduction 147 5.2. Path vs. Trajectory

147

5.3. Joint-Space vs. Cartesian-Space Descriptions 148 5.4. Basics of Trajectory Planning 150 5.5. Joint-Space Trajectory Planning 153 5.5.1. 5.5.2. 5.5.3. 5.5.4. 5.5.5.

Third-Order Polynomial Trajectory Planning 154 Fifth-Order Polynomial Trajectory Planning 157 Linear Segments with Parabolic Blends 157 Linear Segments with Parabolic Blends and Via Points Higher Order Trajectories 161

5.5.6. Other Trajectories

160

165

5.6. Cartesian-Space Trajectories

165

5.7. Continuous Trajectory Recording 170 5.8. Design Project

170

5.9. Summary 171 References

171

Problems 172 6 Actuators

173

6.1. Introduction 173 6.2. Characteristics of Actuating Systems 174 6.2.7. Weight, Power-to-Weight Ratio, Operating Pressure 6.2.2. Stiffness vs. Compliance 174 6.2.3. Use of Reduction Gears 175

6.3. Comparison of Actuating Systems 178 6.4. Hydraulic Devices 178 6.5. Pneumatic Devices 184 6.6. Electric Motors 186 6.6.1. 6.6.2. 6.6.3. 6.6.4.

DC Motors 188 AC Motors 189 Brushless DC motors 189 Direct Drive Electric Motors

189

174

Contents

xi

6.6.5. Servomotors 190 6.6.6. Stepper Motors 191 6.7.

Microprocessor Control of Electric Motors 6.7.7. Pulse Width Modulation. 209

207

6.7.2. Direction Control of DC Motors with an H-Bridge 210 6.8.

Magnetostrictive Actuators

6.9.

Shape-Memory Type Metals

6.10: Speed Reduction

210 211

212

6.11. Design Project 1 215 6.12. Design Project 2 6.13. Summary

216

References Problems 7

215

217 218

Sensors

219

7.1.

Introduction

219

7.2.

Sensor Characteristics

7.3.

Position Sensors 222 7.3.1. Potentiometers 222 7.3.2. Encoders 223 7.3.3. Linear Variable Differential Transformers (LVDT) 226 7.3.4. Resolvers 228 7.3.5. Time-of-Travel Displacement Sensor 229

7.4.

Velocity Sensors 229 7.4.7. Encoders 230 7.4.2. Tachometers 230 7.4.3. Differentiation ofposition signal 230

7.5.

Acceleration Sensors

7.6.

Force and Pressure Sensors

219

230

7.6.7. Piezoelectric 231 7.6.2. Force Sensing resistor 7.6.3. Strain gauges 231

231

231

1.1. Torque Sensors 233 7.8. Microswitches 233 7.9. Light and Infrared Sensors 233 7.10. Touch and Tactile Sensors 234

xii

Contents 7.11. Proximity Sensors 236 7.11.1. Magnetic Proximity Sensors 236 7.11.2. Optical Proximity Sensors 236 7.11.3. Ultrasonic Proximity Sensors 237 7.11.4. Inductive Proximity Sensors 237 7.11.5. Capacitive Proximity Sensors 237 7.11.6. Eddy Current Proximity Sensors 238

7.12. Range-finders 238 7.12.1. Ultrasonic Range Finders

239

7.12.2. Light Based Range Finders

240

7.13. Sniff Sensors 241 7.14. Vision Systems 241 7.15. Voice Recognition Devices 241 7.16. Voice Synthesizers 242 7.17. Remote Center Compliance (RCC) Device 242 7.18. Design Project 245 7.19. Summary 246 References 246 8

Image Processing and Analysis with Vision Systems

8.1. Introduction 248 8.2. Image Processing versus Image Analysis 248 8.3. Two- and Three-Dimensional Image Types 249 8.4. ' What is an Image 249 8.5. Acquisition of Images 250 5.5.7. Vidicon Camera 250 8.5.2. Digital Camera 252 8.6. Digital Images 254 8.7. Frequency Domain vs. Spatial Domain 254 8.8. Fourier Transform of a Signal and its Frequency Content 255 8.9. Frequency Content of an Image; Noise, Edges 257 8.10. Spatial Domain Operations: Convolution Mask 259 8.11. Sampling and Quantization 262 8.12. Sampling Theorem 263 8.13. Image-Processing Techniques 267

248

Contents

8.14. Histogram of Images 267 8.15. Thresholding 268 8.16. Connectivity 269 8.17. Noise Reduction 271 8.17.1 Convolution Masks 272 8.17.2. Image Averaging 273 8.17.3. Frequency Domain 274 8.17.4. Median Filters 274

8.18. Edge Detection 275 8.19. Hough Transform

279

8.20. Segmentation 282 8.21. Segmentation by Region Growing and Region Splitting 282 8.22. Binary Morphology Operations 284 8.22.1. 8.22.2. 8.22.3. 8.22.4. 8.22.5. 8.22.6. 8.22.7.

Thickening Operation 284 Dilation 285 Erosion 285 Skeletonization 286 Open Operation 287 Close Operation 287 Fill Operation 287

8.23. Gray Morphology Operations 288 8.23.1. Erosion 8.23.2. Dilation

288 288

8.24. Image Analysis 288 8.25. Object Recognition by Features 288 8.25.1. 8.25.2. 8.25.3. 8.25.4. 8.25.5.

Basic Features Used for Object Identification Moments 290 Template Matching 297 Discrete Fourier Descriptors 297 Computed Tomography 297

8.26. Depth Measurement with Vision Systems 298 8.26.1. 8.26.2. 8.26.3. 8.26.4.

Scene Analysis vs. Mapping 298 Range Detection and Depth Analysis 299 Stereo Imaging 299 Scene Analysis with Shading and Sizes 300

8.27. Specialized Lighting 301 8.28. Image Data Compression 302 8.28.1. Intraframe Spatial Domain Techniques 8.28.2. Interframe Coding 303

8.29. Real-Time Image Processing 304

302

289

xiii

xiv

Contents 8.30. Heuristics

304

8.31. Applications of Vision Systems 8.32. Design project 8.33. Summary

9

306

306

References Problems

305

307 308

Fuzzy Logic Control 9.1.

Introduction

311

311

9.2. Fuzzy Control: What is needed

313

9.3.

Crisp Values vs. Fuzzy Values

9.4.

Fuzzy Sets: Degrees of Membership and Truth

9.5. Fuzzification

314

315

9.6. Fuzzy Inference Rule Base

316

9.7.

Defuzzification 318 P.7.7. Center-of-Gravity Method 318 9.7.2. Mamdani's Inference Method 318

9.8.

Simulation of Fuzzy Logic Controller

9.9.

Applications of Fuzzy Logic in Robotics

9.10. Design Project 9.11. Summary References Problems

314

322 323

327

328 328 328

APPENDIX A

331

A.I. Matrix Algebra and Notation: A Review

331

A.2. Calculation of an Angle From its Sine, Cosine, or Tangent Problems INDEX

336

338 339