Introduction to Robotics Analysis, Systems, Applications

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1 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 BIBLIOTHEK Inventar-Nf.: M y ~ ol > SS Sachgobtete: Prentice Hall Prentice Hall Upper Saddle River, NJ 07458

San Luis Obispo Technische Urw/carsMt Darmstadt FACHBEREfCH IWFOR^ATiK

2 1 Fundamentals Introduction What is a Robot? Classification of Robots What is Robotics? History of Robotics Advantages and Disadvantages of Robots Robot Components Robot Degrees of Freedom Robot Joints Robot Coordinates Robot Reference Frames Programming Modes Robot Characteristics Robot Workspace Robot Languages Robot Applications Other Robots and Applications 24 vii

9. Robot Joints 11 1.10. Robot Coordinates 11 1.11. Robot Reference Frames 12 1.12. Programming Modes 13

3 viii Contents Social Issues Summary 25 References 26 Problems 27 2 Robot Kinematics: Position Analysis Introduction Robots as Mechanisms Matrix Representation Representation of a point in space Representation of a vector in space Representation of a frame at the origin of a reference frame Representation of a frame in a reference frame Representation of a Rigid Body Homogeneous Transformation Matrices Representation of Transformations Representation of a pure translation Representation of a pure rotation about an axis Representation of combined transformations Transformations relative to the rotating Inverse of Transformation Matrices Forward and Inverse Kinematics of Robots Forward and Inverse Kinematic Equations for Position Forward and Inverse Kinematic Equations for Orientation Forward and Inverse Kinematic Equations for Position and Orientation Denavit-Hartenberg Representation of Forward Kinematic Equations of Robots The Inverse Kinematic Solution of Robots Inverse Kinematic Programming of Robots Degeneracy and Dexterity The Fundamental Problem with the Denavit-Hartenberg Representation Design Project 1: A three-degree-of-freedom Robot Summary 86 References 87 Problems 88

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.

4 ix 3 Differential Motions and Velocities Introduction Differential Relationships Jacobian Differential Motions of a Frame Differential Translations Differential Rotations Differential Rotation about a general axis k Differential Transformations of a Frame Interpretation of the Differential Change Differential Changes Between Frames Differential Motions of a Robot and Its Hand Frame Calculation of the Jacobian How to Relate the Jacobian and the Differential Operator Inverse Jacobian Design Project Summary 116 References 116 Problems Dynamic Analysis and Forces Introduction Lagrangian Mechanics: A Short Overview Effective Moments of Inertia Dynamic Equations for Multiple-Degree-of-Freedom Robots Kinetic Energy Potential Energy The Lagrangian Robot's Equations of Motion Static Force Analysis of Robots Transformation of Forces and Moments Between Coordinate Frames Design Project Summary 143

Differential Changes Between Frames 104 3.7. Differential Motions of a Robot and Its Hand Frame 106 3.8. Calculation of the Jacobian 107 3.9.

5 References 144 Problems Trajectory Planning Introduction Path vs. Trajectory Joint-Space vs. Cartesian-Space Descriptions Basics of Trajectory Planning Joint-Space Trajectory Planning Third-Order Polynomial Trajectory Planning Fifth-Order Polynomial Trajectory Planning Linear Segments with Parabolic Blends Linear Segments with Parabolic Blends and Via Points Higher Order Trajectories Other Trajectories Cartesian-Space Trajectories Continuous Trajectory Recording Design Project Summary 171 References 171 Problems Actuators Introduction Characteristics of Actuating Systems Weight, Power-to-Weight Ratio, Operating Pressure Stiffness vs. Compliance Use of Reduction Gears Comparison of Actuating Systems Hydraulic Devices Pneumatic Devices Electric Motors DC Motors AC Motors Brushless DC motors Direct Drive Electric Motors 189

5.5. Higher Order Trajectories 161 5.5.6. Other Trajectories 165 5.6. Cartesian-Space Trajectories 165 5.7. Continuous Trajectory Recording 170 5.8. Design Project 170 5.9.

6 xi Servomotors Stepper Motors Microprocessor Control of Electric Motors Pulse Width Modulation Direction Control of DC Motors with an H-Bridge Magnetostrictive Actuators Shape-Memory Type Metals : Speed Reduction Design Project Design Project Summary 216 References 217 Problems Sensors Introduction Sensor Characteristics Position Sensors Potentiometers Encoders Linear Variable Differential Transformers (LVDT) Resolvers Time-of-Travel Displacement Sensor Velocity Sensors Encoders Tachometers Differentiation of position signal Acceleration Sensors Force and Pressure Sensors Piezoelectric Force Sensing resistor Strain gauges Torque Sensors Microswitches Light and Infrared Sensors Touch and Tactile Sensors 234

Summary 216 References 217 Problems 218 7 Sensors 219 7.1. Introduction 219 7.2. Sensor Characteristics 219 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.

7 xii Contents Proximity Sensors Magnetic Proximity Sensors Optical Proximity Sensors Ultrasonic Proximity Sensors Inductive Proximity Sensors Capacitive Proximity Sensors Eddy Current Proximity Sensors Range-finders Ultrasonic Range Finders Light Based Range Finders Sniff Sensors Vision Systems Voice Recognition Devices Voice Synthesizers Remote Center Compliance (RCC) Device Design Project Summary 246 References Image Processing and Analysis with Vision Systems Introduction Image Processing versus Image Analysis Two- and Three-Dimensional Image Types ' What is an Image Acquisition of Images Vidicon Camera Digital Camera Digital Images Frequency Domain vs. Spatial Domain Fourier Transform of a Signal and its Frequency Content Frequency Content of an Image; Noise, Edges Spatial Domain Operations: Convolution Mask Sampling and Quantization Sampling Theorem Image-Processing Techniques 267

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.

8 xiii Histogram of Images Thresholding Connectivity Noise Reduction Convolution Masks Image Averaging Frequency Domain Median Filters Edge Detection Hough Transform Segmentation Segmentation by Region Growing and Region Splitting Binary Morphology Operations Thickening Operation Dilation Erosion Skeletonization Open Operation Close Operation Fill Operation Gray Morphology Operations Erosion Dilation Image Analysis Object Recognition by Features Basic Features Used for Object Identification Moments Template Matching Discrete Fourier Descriptors Computed Tomography Depth Measurement with Vision Systems Scene Analysis vs. Mapping Range Detection and Depth Analysis Stereo Imaging Scene Analysis with Shading and Sizes Specialized Lighting Image Data Compression Intraframe Spatial Domain Techniques Interframe Coding Real-Time Image Processing 304

22.2. Dilation 285 8.22.3. Erosion 285 8.22.4. Skeletonization 286 8.22.5. Open Operation 287 8.22.6. Close Operation 287 8.22.7. Fill Operation 287 8.23. Gray Morphology Operations 288 8.23.1.

9 xiv Contents Heuristics Applications of Vision Systems Design project Summary 306 References 307 Problems Fuzzy Logic Control Introduction Fuzzy Control: What is needed Crisp Values vs. Fuzzy Values Fuzzy Sets: Degrees of Membership and Truth Fuzzification Fuzzy Inference Rule Base Defuzzification 318 P.7.7. Center-of-Gravity Method Mamdani's Inference Method Simulation of Fuzzy Logic Controller Applications of Fuzzy Logic in Robotics Design Project Summary 328 References 328 Problems 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 336 Problems 338 INDEX 339

7.2. Mamdani's Inference Method 318 9.8. Simulation of Fuzzy Logic Controller 322 9.9. Applications of Fuzzy Logic in Robotics 323 9.10. Design Project 327 9.11.

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