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robot dynamics and control(机器人动力学与控制).pdf
INTRODUCTION
Robotics
History of Robotics
Components and Structure of Robots
Symbolic Representation of Robots
Degrees of Freedom and Workspace
Classification of Robots
Common Kinematic Arrangements
Robotic Systems
Accuracy and Repeatability
Wrists and End-Effectors
Outline of the Text
RIGID MOTIONS AND HOMOGENEOUS TRANSFORMATIONS
Representing Positions
Representing Rotations
Rotation in the plane
Rotations in three dimensions
Rotational Transformations
Summary
Composition of Rotations
Rotation with respect to the current coordinate frame
Rotation with respect to a fixed frame
Summary
Parameterizations of Rotations
Euler Angles
Roll, Pitch, Yaw Angles
Axis/Angle Representation
Homogeneous Transformations
FORWARD KINEMATICS: THE DENAVIT-HARTENBERG CONVENTION
Kinematic Chains
Denavit Hartenberg Representation
Existence and uniqueness issues
Assigning the coordinate frames
Summary
Examples
INVERSE KINEMATICS
The General Inverse Kinematics Problem
Kinematic Decoupling
Inverse Position: A Geometric Approach
Inverse Orientation
VELOCITY KINEMATICS -- THE MANIPULATOR JACOBIAN
Angular Velocity: The Fixed Axis Case
Skew Symmetric Matrices
Angular Velocity: The General Case
Addition of Angular Velocities
Linear Velocity of a Point Attached to a Moving Frame
Derivation of the Jacobian
Angular Velocity
Linear Velocity
Examples
The Analytical Jacobian
Singularities
Decoupling of Singularities
Wrist Singularities
Arm Singularities
Inverse Velocity and Acceleration
Redundant Robots and Manipulability
Redundant Manipulators
The Inverse Velocity Problem for Redundant Manipulators
Singular Value Decomposition (SVD)
Manipulability
COMPUTER VISION
The Geometry of Image Formation
The Camera Coordinate Frame
Perspective Projection
The Image Plane and the Sensor Array
Camera Calibration
Extrinsic Camera Parameters
Intrinsic Camera Parameters
Determining the Camera Parameters
Segmentation by Thresholding
A Brief Statistics Review
Automatic Threshold Selection
Connected Components
Position and Orientation
Moments
The Centroid of an Object
The Orientation of an Object
PATH PLANNING AND COLLISION AVOIDANCE
The Configuration Space
Path Planning Using Configuration Space Potential Fields
The Attractive Field
The Repulsive field
Gradient Descent Planning
Planning Using Workspace Potential Fields
Defining Workspace Potential Fields
Mapping workspace forces to joint forces and torques
Motion Planning Algorithm
Using Random Motions to Escape Local Minima
Probabilistic Roadmap Methods
Sampling the configuration space
Connecting Pairs of Configurations
Enhancement
Path Smoothing
Historical Perspective
TRAJECTORY PLANNING
The Trajectory Planning Problem
Trajectories for Point to Point Motion
Cubic Polynomial Trajectories
Multiple Cubics
Quintic Polynomial Trajectories
Linear Segments with Parabolic Blends (LSPB)
Minimum Time Trajectories
Trajectories for Paths Specified by Via Points
4-3-4 trajectories
DYNAMICS
The Euler-Lagrange Equations
One Dimensional System
The General Case
General Expressions for Kinetic and Potential Energy
The Inertia Tensor
Kinetic Energy for an n-Link Robot
Potential Energy for an n-Link Robot
Equations of Motion
Some Common Configurations
Properties of Robot Dynamic Equations
The Skew Symmetry and Passivity Properties
Bounds on the Inertia Matrix
Linearity in the Parameters
Newton-Euler Formulation
Planar Elbow Manipulator Revisited
INDEPENDENT JOINT CONTROL
Introduction
Actuator Dynamics
Set-Point Tracking
PD Compensator
Performance of PD Compensators
PID Compensator
Saturation
Feedforward Control and Computed Torque
Drive Train Dynamics
MULTIVARIABLE CONTROL
Introduction
PD Control Revisited
Inverse Dynamics
Task Space Inverse Dynamics
Robust and Adaptive Motion Control
Robust Feedback Linearization
Passivity Based Robust Control
Passivity Based Adaptive Control
FORCE CONTROL
Introduction
Constrained Dynamics
Static Force/Torque Relationships
Constraint Surfaces
Natural and Artificial Constraints
Network Models and Impedance
Impedance Operators
Classification of Impedance Operators
Thévenin and Norton Equivalents
Force Control Strategies
Impedance Control
Hybrid Impedance Control
FEEDBACK LINEARIZATION
Introduction
Background: The Frobenius Theorem
Single-Input Systems
Feedback Linearization for N-Link Robots
Robot Dynamics and Control
Second Edition
Mark W. Spong, Seth Hutchinson, and M. Vidyasagar
January 28, 2004
2
Contents
1 INTRODUCTION
1.1 Robotics
1.2 History of Robotics
1.3 Components and Structure of Robots
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
Symbolic Representation of Robots . . . . . . . . . . . . . . . . . . .
1.3.1
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
2.3.1
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 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . .
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
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CONTENTS
3 FORWARD KINEMATICS: THE DENAVIT-HARTENBERG CONVEN-
TION
3.1 Kinematic Chains
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Denavit Hartenberg Representation . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Existence and uniqueness issues
3.2.2 Assigning the coordinate frames
3.2.3
3.3 Examples
4 INVERSE KINEMATICS
4.1 The General Inverse Kinematics Problem . . . . . . . . . . . . . . . . . . .
4.2 Kinematic Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4
Inverse Position: A Geometric Approach
Inverse Orientation
5 VELOCITY KINEMATICS – THE MANIPULATOR JACOBIAN
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
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
5.11.1 Redundant Manipulators
. . . . .
5.11.2 The Inverse Velocity Problem for Redundant Manipulators
5.11.3 Singular Value Decomposition (SVD)
. . . . . . . . . . . . . . . . .
5.11.4 Manipulability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Inverse Velocity and Acceleration
5.11 Redundant Robots and Manipulability
6 COMPUTER VISION
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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CONTENTS
Intrinsic Camera Parameters
6.2.1 Extrinsic Camera Parameters . . . . . . . . . . . . . . . . . . . . . .
6.2.2
. . . . . . . . . . . . . . . . . . . . . .
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
7.3 Planning Using Workspace Potential Fields
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 . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
7.3.1 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
. . . . . . . . . . . . . . . . . . . . . . . .
Sampling the configuration space . . . . . . . . . . . . . . . . . . . .
7.5.1
7.5.2 Connecting Pairs of Configurations . . . . . . . . . . . . . . . . . . .
7.5.3 Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.4 Path Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Historical Perspective
8 TRAJECTORY PLANNING
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
. . . . . . . . . . . . . . . .
4-3-4 trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Trajectories for Paths Specified by Via Points
8.3.1
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9 DYNAMICS
CONTENTS
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
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
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2 PD Control Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3 Inverse Dynamics
11.3.1 Task Space Inverse Dynamics . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
11.4.1 Robust Feedback Linearization . . . . . . . . . . . . . . . . . . . . .
11.4.2 Passivity Based Robust Control . . . . . . . . . . . . . . . . . . . . .
11.4.3 Passivity Based Adaptive Control
. . . . . . . . . . . . . . . . . . .
11.4 Robust and Adaptive Motion Control
12 FORCE CONTROL
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2 Constrained Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2.1 Static Force/Torque Relationships
12.2.2 Constraint Surfaces
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CONTENTS
12.3 Network Models and Impedance
12.2.3 Natural and Artificial Constraints
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
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
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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