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Part IV Control of Underactuated Systems
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Part IV Control of Underactuated Systems
by Mark W. Spong, Seth Hutchinson, M. Vidyasagar
Robot Modeling and Control, 2nd Edition
Cover
Preface:
Chapter 1 Introduction
1.1 Mathematical Modeling of Robots
1.2 Robots as Mechanical Devices
1.3 Common Kinematic Arrangements
1.4 Outline of the Text
Problems
Notes and References
Notes
Part I The Geometry of Robots
Chapter 2 Rigid Motions
2.1 Representing Positions
2.2 Representing Rotations
2.3 Rotational Transformations
2.4 Composition of Rotations
2.5 Parameterizations of Rotations
2.6 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
3.3 Examples
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
4.3 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
4.7 The Tool Velocity
4.8 The Analytical Jacobian
4.9 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
5.4 Inverse Orientation
5.5 Numerical Inverse Kinematics
5.6 Chapter Summary
Problems
Notes and References
Part II Dynamics and Motion Planning
Chapter 6 Dynamics
6.1 The Euler–Lagrange Equations
6.2 Kinetic and Potential Energy
6.3 Equations of Motion
6.4 Some Common Configurations
6.5 Properties of Robot Dynamic Equations
6.6 Newton–Euler Formulation
6.7 Chapter Summary
Problems
Notes and References
Chapter 7 Path and Trajectory Planning
7.1 The Configuration Space
7.2 Path Planning for
7.3 Artificial Potential Fields
7.4 Sampling-Based Methods
7.5 Trajectory Planning
7.6 Chapter Summary
Problems
Notes and References
Notes
Part III Control of Manipulators
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
8.7 Drive-Train Dynamics
8.8 State Space Design
8.9 Chapter Summary
Problems
Notes and References
Notes
Chapter 9 Nonlinear and Multivariable Control
9.1 Introduction
9.2 PD Control Revisited
9.3 Inverse Dynamics
9.4 Passivity-Based Control
9.5 Torque Optimization
9.6 Chapter Summary
Problems
Notes and References
Notes
Chapter 10 Force Control
10.1 Coordinate Frames and Constraints
10.2 Network Models and Impedance
10.3 Task Space Dynamics and Control
10.4 Chapter Summary
Problems
Notes and References
Notes
Chapter 11 Vision-Based Control
11.1 Design Considerations
11.2 Computer Vision for Vision-Based Control
11.3 Camera Motion and the Interaction Matrix
11.4 The Interaction Matrix for Point Features
11.5 Image-Based Control Laws
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
12.2 Feedback Linearization
12.3 Single-Input Systems
12.4 Multi-Input Systems
12.5 Chapter Summary
Problems
Notes and References
Notes
Part IV Control of Underactuated Systems
Chapter 13 Underactuated Robots
13.1 Introduction
13.2 Modeling
13.3 Examples of Underactuated Robots
13.4 Equilibria and Linear Controllability
13.5 Partial Feedback Linearization
13.6 Output Feedback Linearization
13.7 Passivity-Based Control
13.8 Chapter Summary
Problems
Notes and References
Note
Chapter 14 Mobile Robots
14.1 Nonholonomic Constraints
14.2 Involutivity and Holonomy
14.3 Examples of Nonholonomic Systems
14.4 Dynamic Extension
14.5 Controllability of Driftless Systems
14.6 Motion Planning
14.7 Feedback Control of Driftless Systems
14.8 Chapter Summary
Problems
Notes and References
Note
Appendix A Trigonometry
A.1 The Two-Argument Arctangent Function
A.2 Useful Trigonometric Formulas
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
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
End User License Agreement
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Chapter 12 Feedback Linearization
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Chapter 13 Underactuated Robots
Part IV
Control of Underactuated Systems
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