Introduction to RoboticsAnalysis, Systems,ApplicationsSaeed B. Niku

Mechanical Engineering DepartmentCalifornia Polytechnic State UniversitySan Luis Obispo

PrenticeHall Prentice Hall

Upper Saddle River, NJ 07458

Contents

1 Fundamentals 1

1.1. Introduction 11.2. What is a Robot? 21.3. Classification of Robots 21.4. What is Robotics? 41.5. History of Robotics 41.6. Advantages and Disadvantages of Robots 51.7. Robot Components 61.8. Robot Degrees of Freedom 81.9. Robot Joints 111.10. Robot Coordinates 111.11. Robot Reference Frames 121.12. Programming Modes 131.13. Robot Characteristics 151.14. Robot Workspace 161.15. Robot Languages 161.16. Robot Applications 201.17. Other Robots and Applications 24

vii

viii Contents

1.18. Social Issues 251.19. Summary 25

References 26Problems 27

2 Robot Kinematics: Position Analysis 2'.

2.1. Introduction 292.2. Robots as Mechanisms 292.3. Matrix Representation 31

2.3.1. Representation of a point in space 312.3.2. Representation of a vector in space 322.3.3. Representation of a frame at the origin of a reference frame 332.3.4. Representation of a frame in a reference frame 342.3.5. Representation of a Rigid Body 35

2.4. Homogeneous Transformation Matrices 38

2.5. Representation of Transformations 382.5.1. Representation of a pure translation 392.5.2. Representation of a pure rotation about an axis 402.5.3. Representation of combined transformations 432.5.4. Transformations relative to the rotating 46

2.6. Inverse of Transformation Matrices 48

2.7. Forward and Inverse Kinematics of Robots 532.7.7. Forward and Inverse Kinematic Equations for Position 542.7.2. Forward and Inverse Kinematic Equations for Orientation 592.7.3. Forward and Inverse Kinematic Equations for Position

and Orientation 67

2.8. Denavit-Hartenberg Representation of Forward KinematicEquations of Robots 67

2.9. The Inverse Kinematic Solution of Robots 762.10. Inverse Kinematic Programming of Robots 802.11. Degeneracy and Dexterity 822.12. The Fundamental Problem with the Denavit-Hartenberg

Representation 832.13. Design Project 1: A three-degree-of-freedom Robot 852.14. Summary 86

References 87Problems 88

Contents ix

3 Differential Motions and Velocities 95

3.1. Introduction 953.2. Differential Relationships 953.3. Jacobian 973.4. Differential Motions of a Frame 99

3.4.1. Differential Translations 1003.4.2. Differential Rotations 1003.4.3. Differential Rotation about a general axis k 1013.4.4. Differential Transformations of a Frame 102

3.5. Interpretation of the Differential Change 1043.6. Differential Changes Between Frames 1043.7. Differential Motions of a Robot and Its Hand Frame 1063.8. Calculation of the Jacobian 1073.9. How to Relate the Jacobian and the Differential Operator 1103.10. Inverse Jacobian 1113.11. Design Project 1153.12. Summary 116

References 116Problems 117

4 Dynamic Analysis and Forces 119

4.1. Introduction 1194.2. Lagrangian Mechanics: A Short Overview 1204.3. Effective Moments of Inertia 1274.4. Dynamic Equations for Multiple-Degree-of-Freedom Robots 128

4.4.1. Kinetic Energy 1284.4.2. Potential Energy 1324.4.3. The Lagrangian 1334.4.4. Robot's Equations of Motion 133

4.5. Static Force Analysis of Robots 1394.6. Transformation of Forces and Moments Between

Coordinate Frames 1414.7. Design Project 1434.8. Summary 143

Contents

References 144Problems 144

5 Trajectory Planning 14.

5.1. Introduction 1475.2. Path vs. Trajectory 1475.3. Joint-Space vs. Cartesian-Space Descriptions 1485.4. Basics of Trajectory Planning 1505.5. Joint-Space Trajectory Planning 153

5.5.1. Third-Order Polynomial Trajectory Planning 1545.5.2. Fifth-Order Polynomial Trajectory Planning 1575.5.3. Linear Segments with Parabolic Blends 1575.5.4. Linear Segments with Parabolic Blends and Via Points 1605.5.5. Higher Order Trajectories 1615.5.6. Other Trajectories 165

5.6. Cartesian-Space Trajectories 1655.7. Continuous Trajectory Recording 1705.8. Design Project 1705.9. Summary 171

References 171Problems 172

6 Actuators 7i

6.1. Introduction 1736.2. Characteristics of Actuating Systems 174

6.2.1. Weight, Power-to-Weight Ratio, Operating Pressure 1746.2.2. Stiffness vs. Compliance 1746.2.3. Use of Reduction Gears 175

6.3. Comparison of Actuating Systems 1786.4. Hydraulic Devices 1786.5. Pneumatic Devices 1846.6. Electric Motors 186

6.6.1. DC Motors 1886.6.2. AC Motors 1896.6.3. Brushless DC motors 1896.6.4. Direct Drive Electric Motors 189

Contents xi

6.6.5. Servomotors 1906.6.6. Stepper Motors 191

6.7. Microprocessor Control of Electric Motors 2076.7.1. Pulse Width Modulation. 2096.7.2. Direction Control of DC Motors with an H-Bridge 210

6.8. Magnetostrictive Actuators 210

6.9. Shape-Memory Type Metals 211

6.10: Speed Reduction 212

6.11. Design Project 1 2156.12. Design Project 2 2156.13. Summary 216

References 217

Problems 218

7 Sensors 219

7.1. Introduction 219

7.2. Sensor Characteristics 219

7.3. Position Sensors 2227.3.1. Potentiometers 2227.3.2. Encoders 2237.3.3. Linear Variable Differential Transformers (LVDT) 2267.3.4. Resolvers 2287.3.5. Time-of-Travel Displacement Sensor 229

1.4. Velocity Sensors 2297.4.1. Encoders 2307.4.2. Tachometers 2307.4.3. Differentiation of position signal 230

7.5. Acceleration Sensors 230

7.6. Force and Pressure Sensors 2317.6.1. Piezoelectric 2317.6.2. Force Sensing resistor 2317.6.3. Strain gauges 231

1.1. Torque Sensors 2337.8. Microswitches 2337.9. Light and Infrared Sensors 2337.10. Touch and Tactile Sensors 234

xii Contents

7.11. Proximity Sensors 2367.11.1. Magnetic Proximity Sensors 2367.11.2. Optical Proximity Sensors 2367.11.3. Ultrasonic Proximity Sensors 2377.11.4. Inductive Proximity Sensors 2377.11.5. Capacitive Proximity Sensors 2377.11.6. Eddy Current Proximity Sensors 238

7.12. Range-finders 2387.12.1. Ultrasonic Range Finders 2397.12.2. Light Based Range Finders 240

7.13. Sniff Sensors 2417.14. Vision Systems 2417.15. Voice Recognition Devices 2417.16. Voice Synthesizers 2427.17. Remote Center Compliance (RCC) Device 2427.18. Design Project 2457.19. Summary 246

References 2468 Image Processing and Analysis with Vision Systems

8.1. Introduction 2488.2. Image Processing versus Image Analysis 2488.3. Two- and Three-Dimensional Image Types 2498.4. What is an Image 2498.5. Acquisition of Images 250

8.5.1. Vidicon Camera 2508.5.2. Digital Camera 252

8.6. Digital Images 2548.7. Frequency Domain vs. Spatial Domain 2548.8. Fourier Transform of a Signal and its Frequency Content 2558.9. Frequency Content of an Image; Noise, Edges 2578.10. Spatial Domain Operations: Convolution Mask 2598.11. Sampling and Quantization 2628.12. Sampling Theorem 2638.13. Image-Processing Techniques 267

Contents xiii

8.14. Histogram of Images 267

8.15. Thresholding 268

8.16. Connectivity 269

8.17. Noise Reduction 2718.17.1 Convolution Masks 2728.17.2. Image Averaging 2738.17.3. Frequency Domain 2748.17.4. 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 2848.22.1. Thickening Operation 2848.22.2. Dilation 2858.22.3. Erosion 2858.22.4. Skeletonization 2868.22.5. Open Operation 2878.22.6. Close Operation 2878.22.7. Fill Operation 287

8.23. Gray Morphology Operations 2888.23.1. Erosion 2888.23.2. Dilation 288

8.24. Image Analysis 288

8.25. Object Recognition by Features 2888.25.1. Basic Features Used for Object Identification 2898.25.2. Moments 2908.25.3. Template Matching 2978.25.4. Discrete Fourier Descriptors 2978.25.5. Computed Tomography 297

8.26. Depth Measurement with Vision Systems 2988.26.1. Scene Analysis vs. Mapping 2988.26.2. Range Detection and Depth Analysis 2998.26.3. Stereo Imaging 2998.26.4. Scene Analysis with Shading and Sizes 300

8.27. Specialized Lighting 301

8.28. Image Data Compression 3028.28.1. Intraframe Spatial Domain Techniques 3028.28.2. Interframe Coding 303

8.29. Real-Time Image Processing 304

xiv Contents

8.30. Heuristics 3048.31. Applications of Vision Systems 3058.32. Design project 3068.33. Summary 306

References 307Problems 308

9 Fuzzy Logic Control 31'

9.1. Introduction 3119.2. Fuzzy Control: What is needed 3139.3. Crisp Values vs. Fuzzy Values 3149.4. Fuzzy Sets: Degrees of Membership and Truth 3149.5. Fuzzification 3159.6. Fuzzy Inference Rule Base 3169.7. Denazification 318

9.7.1. Center-of-Gravity Method 3189.7.2. Mamdani's Inference Method 318

9.8. Simulation of Fuzzy Logic Controller 3229.9. Applications of Fuzzy Logic in Robotics 3239.10. Design Project 3279.11. Summary 328

References 328Problems 328

APPENDIX A 3.

A.I. Matrix Algebra and Notation: A Review 331A.2. Calculation of an Angle From its Sine, Cosine, or Tangent 336

Problems 338

INDEX 3