Оглавление
Mark W. Spong. Robot Modeling and Control
Robot Modeling and Control
CONTENTS
List of Tables
List of Illustrations
Guide
Pages
Preface
CHAPTER 1 INTRODUCTION
1.1 Mathematical Modeling of Robots
1.1.1 Symbolic Representation of Robot Manipulators
1.1.2 The Configuration Space
1.1.3 The State Space
1.1.4 The Workspace
1.2 Robots as Mechanical Devices
1.2.1 Classification of Robotic Manipulators
Power Source
Method of Control
Application Area
Geometry
1.2.2 Robotic Systems
1.2.3 Accuracy and Repeatability
1.2.4 Wrists and End Effectors
1.3 Common Kinematic Arrangements
1.3.1 Articulated Manipulator (RRR)
1.3.2 Spherical Manipulator (RRP)
1.3.3 SCARA Manipulator (RRP)
1.3.4 Cylindrical Manipulator (RPP)
1.3.5 Cartesian Manipulator (PPP)
1.3.6 Parallel Manipulator
1.4 Outline of the Text
1.4.1 Manipulator Arms
Chapter 2: Rigid Motions
Chapter 3: Forward Kinematics
Chapter 4: Velocity Kinematics
Chapter 5: Inverse Kinematics
Chapter 6: Dynamics
Chapter 7: Path Planning and Trajectory Generation
Chapter 8: Independent Joint Control
Chapter 9: Nonlinear and Multivariable Control
Chapter 10: Force Control
Chapter 11: Vision-Based Control
Chapter 12: Feedback Linearization
1.4.2 Underactuated and Mobile Robots. Chapter 13: Underactuated Systems
Chapter 14: Mobile Robots
Problems
Notes and References
Note
CHAPTER 2 RIGID MOTIONS
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
Similarity Transformations
2.4 Composition of Rotations
2.4.1 Rotation with Respect to the Current Frame
2.4.2 Rotation with Respect to the Fixed Frame
2.4.3 Rules for Composition of Rotations
2.5 Parameterizations of Rotations
2.5.1 Euler Angles
2.5.2 Roll, Pitch, Yaw Angles
2.5.3 Axis-Angle Representation
2.5.4 Exponential Coordinates
Rodrigues’ Formula
2.6 Rigid Motions
2.6.1 Homogeneous Transformations
2.6.2 Exponential Coordinates for General Rigid Motions
2.7 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 3 FORWARD KINEMATICS
3.1 Kinematic Chains
3.2 The Denavit–Hartenberg Convention
3.2.1 Existence and Uniqueness
3.2.2 Assigning the Coordinate Frames
Summary of the DH Procedure
3.3 Examples
3.3.1 Planar Elbow Manipulator
3.3.2 Three-Link Cylindrical Robot
3.3.3 The Spherical Wrist
3.3.4 Cylindrical Manipulator with Spherical Wrist
3.3.5 Stanford Manipulator
3.3.6 SCARA Manipulator
3.4 Chapter Summary
Problems
Notes and References
CHAPTER 4 VELOCITY KINEMATICS
4.1 Angular Velocity: The Fixed Axis Case
4.2 Skew-Symmetric Matrices
4.2.1 Properties of Skew-Symmetric Matrices
4.2.2 The Derivative of a Rotation Matrix
4.3 Angular Velocity: The General Case
4.4 Addition of Angular Velocities
4.5 Linear Velocity of a Point Attached to a Moving Frame
4.6 Derivation of the Jacobian
4.6.1 Angular Velocity
4.6.2 Linear Velocity
Case 1: Prismatic Joints
Case 2: Revolute Joints
4.6.5 Combining the Linear and Angular Velocity Jacobians
4.7 The Tool Velocity
4.8 The Analytical Jacobian
4.9 Singularities
4.9.1 Decoupling of Singularities
4.9.2 Wrist Singularities
4.9.3 Arm Singularities
4.10 Static Force/Torque Relationships
4.11 Inverse Velocity and Acceleration
4.12 Manipulability
4.13 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 5 INVERSE KINEMATICS
5.1 The General Inverse Kinematics Problem
5.2 Kinematic Decoupling
5.3 Inverse Position: A Geometric Approach
5.3.1 Spherical Configuration
5.3.2 Articulated Configuration
5.4 Inverse Orientation
5.5 Numerical Inverse Kinematics
5.6 Chapter Summary
Problems
Notes and References
CHAPTER 6 DYNAMICS
6.1 The Euler–Lagrange Equations
6.1.1 Motivation
6.1.2 Holonomic Constraints and Virtual Work
6.1.3 D’Alembert’s Principle
6.2 Kinetic and Potential Energy
6.2.1 The Inertia Tensor
6.2.2 Kinetic Energy for an n-Link Robot
6.2.3 Potential Energy for an n-Link Robot
6.3 Equations of Motion
6.4 Some Common Configurations
Two-Link Cartesian Manipulator
Planar Elbow Manipulator
Planar Elbow Manipulator with Remotely Driven Link
Five-Bar Linkage
6.5 Properties of Robot Dynamic Equations
6.5.1 Skew Symmetry and Passivity
6.5.2 Bounds on the Inertia Matrix
6.5.3 Linearity in the Parameters
6.6 Newton–Euler Formulation
6.6.1 Planar Elbow Manipulator Revisited
Forward Recursion Link 1
Forward Recursion: Link 2
Backward Recursion: Link 2
Backward Recursion: Link 1
6.7 Chapter Summary
Problems
Notes and References
CHAPTER 7 PATH AND TRAJECTORY PLANNING
7.1 The Configuration Space
7.1.1 Representing the Configuration Space
7.1.2 Configuration Space Obstacles
7.1.3 Paths in the Configuration Space
7.2 Path Planning for
7.2.1 The Visibility Graph
7.2.2 The Generalized Voronoi Diagram
7.2.3 Trapezoidal Decompositions
7.3 Artificial Potential Fields
7.3.1 Artificial Potential Fields for
The Attractive Field
The Repulsive Field
Gradient Descent Planning
Escaping Local Minima
7.3.2 Potential Fields for
The Attractive Field
The Repulsive Field
Mapping Workspace Forces to Joint Torques
Application to Mobile Robots
Gradient Descent Planning
7.4 Sampling-Based Methods
7.4.1 Probabilistic Roadmaps (PRM)
Sampling the Configuration Space
Connecting Pairs of Configurations
Enhancement
Path Smoothing
7.4.2 Rapidly-Exploring Random Trees (RRTs)
7.5 Trajectory Planning
7.5.1 Trajectories for Point-to-Point Motion
Cubic Polynomial Trajectories
Quintic Polynomial Trajectories
Linear Segments with Parabolic Blends (LSPB)
Minimum-Time Trajectories
7.5.2 Trajectories for Paths Specified by Via Points
7.6 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 8 INDEPENDENT JOINT CONTROL. 8.1 Introduction
8.2 Actuator Dynamics
8.3 Load Dynamics
8.4 Independent Joint Model
8.5 PID Control
8.6 Feedforward Control
8.6.1 Trajectory Tracking
8.6.2 The Method of Computed Torque
8.7 Drive-Train Dynamics
8.8 State Space Design
8.8.1 State Feedback Control
8.8.2 Observers
8.9 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 9 NONLINEAR AND MULTIVARIABLE CONTROL. 9.1 Introduction
9.2 PD Control Revisited
The Effect of Joint Flexibility
9.3 Inverse Dynamics
9.3.1 Joint Space Inverse Dynamics
9.3.2 Task Space Inverse Dynamics
9.3.3 Robust Inverse Dynamics
9.3.4 Adaptive Inverse Dynamics
9.4 Passivity-Based Control
9.4.1 Passivity-Based Robust Control
9.4.2 Passivity-Based Adaptive Control
9.5 Torque Optimization
9.6 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 10 FORCE CONTROL
10.1 Coordinate Frames and Constraints
10.1.1 Reciprocal Bases
Metrics on SO(3) and SE(3)
10.1.2 Natural and Artificial Constraints
10.2 Network Models and Impedance
10.2.1 Impedance Operators
10.2.2 Classification of Impedance Operators
10.2.3 Thévenin and Norton Equivalents
10.3 Task Space Dynamics and Control
10.3.1 Impedance Control
10.3.2 Hybrid Impedance Control
10.4 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 11 VISION-BASED CONTROL
11.1 Design Considerations
11.1.1 Camera Configuration
11.1.2 Image-Based vs. Position-Based Approaches
11.2 Computer Vision for Vision-Based Control
11.2.1 The Geometry of Image Formation
11.2.2 Image Features
Gradient-Based Features
Feature Detection and Tracking
11.3 Camera Motion and the Interaction Matrix
11.4 The Interaction Matrix for Point Features
11.4.1 Velocity Relative to a Moving Frame
11.4.2 Constructing the Interaction Matrix
11.4.3 Properties of the Interaction Matrix for Points
11.4.4 The Interaction Matrix for Multiple Points
11.5 Image-Based Control Laws
11.5.1 Computing Camera Motion
11.5.2 Proportional Control Schemes
11.5.3 Performance of Image-Based Control Systems
11.6 End Effector and Camera Motions
11.7 Partitioned Approaches
11.8 Motion Perceptibility
11.9 Summary
Problems
Notes and References
Notes
CHAPTER 12 FEEDBACK LINEARIZATION
12.1 Background
12.1.1 Manifolds, Vector Fields, and Distributions
12.1.2 The Frobenius Theorem
12.2 Feedback Linearization
12.3 Single-Input Systems
12.4 Multi-Input Systems
12.5 Chapter Summary
Problems
Notes and References
Notes
CHAPTER 13 UNDERACTUATED ROBOTS. 13.1 Introduction
13.2 Modeling
Upper-Actuated and Lower-Actuated Models
Second-Order Constraints
13.3 Examples of Underactuated Robots
13.3.1 The Cart-Pole System
13.3.2 The Acrobot
13.3.3 The Pendubot
13.3.4 The Reaction-Wheel Pendulum
13.4 Equilibria and Linear Controllability
13.4.1 Linear Controllability
Computation of the Linearization
A Necessary Condition for Linear Controllability
13.5 Partial Feedback Linearization
13.5.1 Collocated Partial Feedback Linearization
13.5.2 Noncollocated Partial Feedback Linearization
13.6 Output Feedback Linearization
13.6.1 Computation of the Zero Dynamics
Feedback Linearization of the Reaction-Wheel Pendulum
13.6.2 Virtual Holonomic Constraints
13.7 Passivity-Based Control
13.7.1 The Simple Pendulum
Saturation
13.7.2 The Reaction-Wheel Pendulum
13.7.3 Swingup and Balance of The Acrobot
13.8 Chapter Summary
Problems
Notes and References
Note
CHAPTER 14 MOBILE ROBOTS
14.1 Nonholonomic Constraints
14.2 Involutivity and Holonomy
Filtrations
14.3 Examples of Nonholonomic Systems
14.4 Dynamic Extension
14.5 Controllability of Driftless Systems
14.6 Motion Planning
14.6.1 Conversion to Chained Forms
Steering Using Sinusoids
Chained Form for Higher Dimensional Systems
14.6.2 Differential Flatness
14.7 Feedback Control of Driftless Systems
14.7.1 Stabilizability
14.7.2 Nonsmooth Control
Sliding-Mode Control
Dynamic Extension
14.7.3 Trajectory Tracking. Lyapunov Design
14.7.4 Feedback Linearization
Dynamic Feedback Linearization
14.8 Chapter Summary
Problems
Notes and References
Note
Appendix A TRIGONOMETRY. A.1 The Two-Argument Arctangent Function
A.2 Useful Trigonometric Formulas
Sum-Difference Identities
Double-Angle Identities
Half-Angle Identities
Law of Cosines
Appendix B LINEAR ALGEBRA
B.1 Vectors
B.2 Inner Product Spaces
B.3 Matrices
B.4 Eigenvalues and Eigenvectors
B.5 Differentiation of Vectors
B.6 The Matrix Exponential
B.7 Lie Groups and Lie Algebras
B.8 Matrix Pseudoinverse
B.9 Schur Complement
B.10 Singular Value Decomposition (SVD)
Appendix C LYAPUNOV STABILITY
C.1 Continuity and Differentiability
Gradient, Hessian, and Jacobian
C.2 Vector Fields and Equilibria
C.3 Lyapunov Functions
C.4 Stability Criteria
C.5 Global and Exponential Stability
C.6 Stability of Linear Systems
C.7 LaSalle’s Theorem
C.8 Barbalat’s Lemma
Appendix D OPTIMIZATION
D.1 Unconstrained Optimization
D.2 Constrained Optimization
Appendix E CAMERA CALIBRATION
E.1 The Image Plane and the Sensor Array
E.2 Extrinsic Camera Parameters
E.3 Intrinsic Camera Parameters
E.4 Determining the Camera Parameters
Note
Bibliography
Index
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