Robot Modeling and Control

Robot Modeling and Control
PREFACE
CONTENTS
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
		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
		1.4.2 Underactuated and Mobile Robots
	Problems
	Notes and References
I THE GEOMETRY OF ROBOTS
	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
		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
		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
	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
		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
	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
			4.6.3 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
	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
II DYNAMICS AND MOTION PLANNING
	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
		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
		6.7 Chapter Summary
		Problems
		Notes and References
	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 Q = R²
			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 Q = Rⁿ
			7.3.2 Potential Fields for Q ≠ Rⁿ
		7.4 Sampling-Based Methods
			7.4.1 Probabilistic Roadmaps (PRM)
			7.4.2 Rapidly-Exploring Random Trees (RRTs)
		7.5 Trajectory Planning
			7.5.1 Trajectories for Point-to-Point Motion
			7.5.2 Trajectories for Paths Specified by Via Points
		7.6 Chapter Summary
		Problems
		Notes and References
III CONTROL OF MANIPULATORS
	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
	9 NONLINEAR AND MULTIVARIABLE CONTROL
		9.1 Introduction
		9.2 PD Control Revisited
		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
	10 FORCE CONTROL
		10.1 Coordinate Frames and Constraints
			10.1.1 Reciprocal Bases
			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
	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
		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
	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
IV CONTROL OF UNDERACTUATED SYSTEMS
	13 UNDERACTUATED ROBOTS
		13.1 Introduction
		13.2 Modeling
		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
		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
			13.6.2 Virtual Holonomic Constraints
		13.7 Passivity-Based Control
			13.7.1 The Simple Pendulum
			13.7.2 The Reaction-Wheel Pendulum
			13.7.3 Swingup and Balance of The Acrobot
		13.8 Chapter Summary
		Problems
		Notes and References
	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
			14.6.1 Conversion to Chained Forms
			14.6.2 Differential Flatness
		14.7 Feedback Control of Driftless Systems
			14.7.1 Stabilizability
			14.7.2 Nonsmooth Control
			14.7.3 Trajectory Tracking
			14.7.4 Feedback Linearization
		14.8 Chapter Summary
		Problems
		Notes and References
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
BIBLIOGRAPHY
INDEX
EULA