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آشنایی با kinematics و هندسه حرکت

آشنایی با kinematics و هندسه حرکت

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Contents


1 INTRODUCTION 5

1.1 Robotics

1.2 History of Robotics

1.3 Components and Structure of Robots

1.3.1 Symbolic Representation of Robots

1.3.2 Degrees of Freedom and Workspace

1.3.3 Classification of Robots

1.3.4 Common Kinematic Arrangements

1.3.5 Robotic Systems

1.3.6 Accuracy and Repeatability

1.3.7 Wrists and End-Effectors

1.4 Outline of the Text

2 RIGID MOTIONS AND HOMOGENEOUS TRANSFORMATIONS 29

2.1 Representing Positions

2.2 Representing Rotations

2.2.1 Rotation in the plane

2.2.2 Rotations in three dimensions

2.3 Rotational Transform ations

2.3.1 Summary

2.4 Composition of Rotations

2.4.1 Rotation with respect to the current coordinate frame

2.4.2 Rotation with respect to a fixed frame

2.4.3 Summary

2.5 Parameterizations of Rotations

2.5.1 Euler Angles

2.5.2 Roll, Pitch, Yaw Angles

2.5.3 Axis/Angle Representation

2.6 Homogeneous Transformations

3

4 CONTENTS

3 FORWARD KINEMATICS: THE DENAVIT-HARTENBERG CONVENTION

57

3.1 Kinematic Chains

3.2 Denavit Hartenberg Representation

3.2.1 Existence and uniqueness issues

3.2.2 Assigning the coordinate frames

3.2.3 Summary

3.3 Examples

4 INVERSE KINEMATICS 79

4.1 The General Inverse Kinematics Problem

4.2 Kinematic Decoupling

4.3 Inverse Position: A Geometric Approach

4.4 Inverse Orientation

5 VELOCITY KINEMATICS – THE MANIPULATOR JACOBIAN 95

5.1 Angular Velocity: The Fixed Axis Case

5.2 Skew Symmetric Matrices

5.3 Angular Velocity: The General Case

5.4 Addition of Angular Velocities

5.5 Linear Velocity of a Point Attached to a Moving Frame

5.6 Derivation of the Jacobian

5.6.1 Angular Velocity

5.6.2 Linear Velocity

5.7 Examples

5.8 The Analytical Jacobian

5.9 Singularities

5.9.1 Decoupling of Singularities

5.9.2 Wrist Singularities

5.9.3 Arm Singularities

5.10 Inverse Velocity and Acceleration

5.11 Redundant Robots and Manipulability

5.11.1 Redundant Manipulators

5.11.2 The Inverse Velocity Problem for Redundant Manipulators

5.11.3 Singular Value Decomposition (SVD)

5.11.4 Manipulability

6 COMPUTER VISION 127

6.1 The Geometry of Image Formation

6.1.1 The Camera Coordinate Frame

6.1.2 Perspective Projection

6.1.3 The Image Plane and the Sensor Array

6.2 Camera Calibration

CONTENTS 5

6.2.1 Extrinsic Camera Parameters

6.2.2 Intrinsic Camera Parameters

6.2.3 Determining the Camera Parameters

6.3 Segmentation by Thresholding

6.3.1 A Brief Statistics Review

6.3.2 Automatic Threshold Selection

6.4 Connected Components

6.5 Position and Orientation

6.5.1 Moments

6.5.2 The Centroid of an Object

6.5.3 The Orientation of an Object

7 PATH PLANNING AND COLLISION AVOIDANCE 147

7.1 The Configuration Space

7.2 Path Planning Using Configuration Space Potential Fields

7.2.1 The Attractive Field

7.2.2 The Repulsive field

7.2.3 Gradient Descent Planning

7.3 Planning Using Workspace Potential Fields

7.3.1 Defining Workspace Potential Fields

7.3.2 Mapping workspace forces to joint forces and torques

7.3.3 Motion Planning Algorithm

7.4 Using Random Motions to Escape Local Minima

7.5 Probabilistic Roadmap Methods

7.5.1 Sampling the configuration space

7.5.2 Connecting Pairs of Configurations

7.5.3 Enhancement

7.5.4 Path Smoothing

7.6 Historical Perspective

8 TRAJECTORY PLANNING 169

8.1 The Trajectory Planning Problem

8.2 Trajectories for Point to Point Motion

8.2.1 Cubic Polynomial Trajectories

8.2.2 Multiple Cubics

8.2.3 Quintic Polynomial Trajectories

8.2.4 Linear Segments with Parabolic Blends (LSPB)

8.2.5 Minimum Time Trajectories

8.3 Trajectories for Paths Specified by Via Points

8.3.1 4-3-4 trajectories

6 CONTENTS

9 DYNAMICS 187

9.1 The Euler-Lagrange Equations

9.1.1 One Dimensional System

9.1.2 The General Case

9.2 General Expressions for Kinetic and Potential Energy

9.2.1 The Inertia Tensor

9.2.2 Kinetic Energy for an n-Link Robot

9.2.3 Potential Energy for an n-Link Robot

9.3 Equations of Motion

9.4 Some Common Configurations

9.5 Properties of Robot Dynamic Equations

9.5.1 The Skew Symmetry and Passivity Properties

9.5.2 Bounds on the Inertia Matrix

9.5.3 Linearity in the Parameters

9.6 Newton-Euler Formulation

9.7 Planar Elbow Manipulator Revisited

10 INDEPENDENT JOINT CONTROL 225

10.1 Introduction

10.2 Actuator Dynamics

10.3 Set-Point Tracking

10.3.1 PD Compensator

10.3.2 Performance of PD Compensators

10.3.3 PID Compensator

10.3.4 Saturation

10.4 Feedforward Control and Computed Torque

10.5 Drive Train Dynamics

11 MULTIVARIABLE CONTROL 247

11.1 Introduction

11.2 PD Control Revisited

11.3 Inverse Dynamics

11.3.1 Task Space Inverse Dynamics

11.4 Robust and Adaptive Motion Control

11.4.1 Robust Feedback Linearization

11.4.2 Passivity Based Robust Control

11.4.3 Passivity Based Adaptive Control

12 FORCE CONTROL 263

12.1 Introduction

12.2 Constrained Dynamics

12.2.1 Static Force/Torque Relationships

12.2.2 Constraint Surfaces

CONTENTS 7

12.2.3 Natural and Artificial Constraints

12.3 Network Models and Impedance

12.3.1 Impedance Operators

12.3.2 Classification of Impedance Operators

12.3.3 Th´evenin and Norton Equivalents

12.4 Force Control Strategies

12.4.1 Impedance Control

12.4.2 Hybrid Impedance Control

13 FEEDBACK LINEARIZATION 281

13.1 Introduction

13.2 Background: The Frobenius Theorem

13.3 Single-Input Systems

13.4 Feedback Linearization for N-Link Robots

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#2 مهدی 23 دی 1391 ساعت 15:37
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