Robotics and Control: Fundamental Algorithms in MATLAB®

Foreword
Foreword to the Second Edition
Preface
Contents
Nomenclature
Chapter
1 Introduction
	1.1
Robots, Jobs and Ethics
	1.2 About the Book
		1.2.1
MATLAB Software and the Toolboxes
		1.2.2
Notation, Conventions and Organization
		1.2.3
Audience and Prerequisites
		1.2.4
Learning with the Book
		1.2.5
Teaching with the Book
		1.2.6
Outline
Part I Foundations
Chapter
2 Representing Position and Orientation
	2.1
Working in Two Dimensions (2D)
		2.1.1
Orientation in 2-Dimensions
		2.1.2
Pose in 2-Dimensions
	2.2
Working in Three Dimensions (3D)
		2.2.1
Orientation in 3-Dimensions
		2.2.2
Pose in 3-Dimensions
	2.3
Advanced Topics
		2.3.1
Normalization
		2.3.2
Understanding the Exponential Mapping
		2.3.3
More About Twists
		2.3.4
Dual Quaternions
		2.3.5
Configuration Space
	2.4
Using the Toolbox
	2.5
Wrapping Up
Chapter 3
Time and Motion
	3.1
Time-Varying Pose
		3.1.1
Derivative of Pose
		3.1.2
Transforming Spatial Velocities
		3.1.3
Incremental Rotation
		3.1.4
Incremental Rigid-Body Motion
	3.2
Accelerating Bodies and Reference Frames
		3.2.1
Dynamics of Moving Bodies
		3.2.2
Transforming Forces and Torques
		3.2.3
Inertial Reference Frame
	3.3
Creating Time-Varying Pose
		3.3.1
Smooth One-Dimensional Trajectories
		3.3.2
Multi-Dimensional Trajectories
		3.3.3
Multi-Segment Trajectories
		3.3.4
Interpolation of Orientation in 3D
		3.3.5
Cartesian Motion in 3D
	3.4
Application: Inertial Navigation
		3.4.1
Gyroscopes
		3.4.2
Accelerometers
		3.4.3
Magnetometers
		3.4.4
Sensor Fusion
	3.5
Wrapping Up
Part II Mobile Robots
Chapter
4 Mobile Robot Vehicles
	4.1
Wheeled Mobile Robots
		4.1.1
Car-Like Mobile Robots
		4.1.2
Differentially-Steered Vehicle
		4.1.3
Omnidirectional Vehicle
	4.2
Flying Robots
	4.3
Advanced Topics
		4.3.1
Nonholonomic and Under-Actuated Systems
	4.4
Wrapping Up
Chapter 5
Navigation
	5.1
Reactive Navigation
		5.1.1
Braitenberg Vehicles
		5.1.2
Simple Automata
	5.2
Map-Based Planning
		5.2.1
Distance Transform
		5.2.2
D*
		5.2.3
Introduction to Roadmap Methods
		5.2.4
Probabilistic Roadmap Method (PRM)
		5.2.5
Lattice Planner
		5.2.6
Rapidly-Exploring Random Tree (RRT)
	5.3
Wrapping Up
Chapter 6
Localization
	6.1
Dead Reckoning
		6.1.1
Modeling the Vehicle
		6.1.2
Estimating Pose
	6.2
Localizing with a Map
	6.3
Creating a Map
	6.4
Localization and Mapping
	6.5
Rao-Blackwellized SLAM
	6.6
Pose Graph SLAM
	6.7
Sequential Monte-Carlo Localization
	6.8
Application: Scanning Laser Rangefinder
	6.9
Wrapping Up
Part III Arm-Type Robots
Chapter
7 Robot Arm Kinematics
	7.1
Forward Kinematics
		7.1.1
2-Dimensional (Planar) Robotic Arms
		7.1.2
3-Dimensional Robotic Arms
	7.2
Inverse Kinematics
		7.2.1
2-Dimensional (Planar) Robotic Arms
		7.2.2
3-Dimensional Robotic Arms
	7.3
Trajectories
		7.3.1
Joint-Space Motion
		7.3.2
Cartesian Motion
		7.3.3
Kinematics in Simulink
		7.3.4
Motion through a Singularity
		7.3.5
Configuration Change
	7.4
Advanced Topics
		7.4.1
Joint Angle Offsets
		7.4.2
Determining Denavit-Hartenberg Parameters
		7.4.3
Modified Denavit-Hartenberg Parameters
	7.5
Applications
		7.5.1
Writing on a Surface [examples/drawing.m]
		7.5.2
A Simple Walking Robot [examples/walking.m]
	7.6
Wrapping Up
Chapter
8 Manipulator Velocity
	8.1
Manipulator Jacobian
		8.1.1
Jacobian in the World Coordinate Frame
		8.1.2
Jacobian in the End-Effector Coordinate Frame
		8.1.3
Analytical Jacobian
	8.2
Jacobian Condition and Manipulability
		8.2.1
Jacobian Singularities
		8.2.2
Manipulability
	8.3
Resolved-Rate Motion Control
		8.3.1
Jacobian Singularity
	8.4
Under- and Over-Actuated Manipulators
		8.4.1
Jacobian for Under-Actuated Robot
		8.4.2
Jacobian for Over-Actuated Robot
	8.5
Force Relationships
		8.5.1
Transforming Wrenches to Joint Space
		8.5.2
Force Ellipsoids
	8.6
Inverse Kinematics: a General Numerical Approach
		8.6.1
Numerical Inverse Kinematics
	8.7
Advanced Topics
		8.7.1
Computing the Manipulator Jacobian Using Twists
	8.8
Wrapping Up
Chapter
9 Dynamics and Control
	9.1
Independent Joint Control
		9.1.1
Actuators
		9.1.2
Friction
		9.1.3
Effect of the Link Mass
		9.1.4
Gearbox
		9.1.5
Modeling the Robot Joint
		9.1.6
Velocity Control Loop
		9.1.7
Position Control Loop
		9.1.8
Independent Joint Control Summary
	9.2
Rigid-Body Equations of Motion
		9.2.1
Gravity Term
		9.2.2
Inertia Matrix
		9.2.3
Coriolis Matrix
		9.2.4
Friction
		9.2.5
Effect of Payload
		9.2.6
Base Force
		9.2.7
Dynamic Manipulability
	9.3
Forward Dynamics
	9.4
Rigid-Body Dynamics Compensation
		9.4.1
Feedforward Control
		9.4.2
Computed Torque Control
		9.4.3
Operational Space Control
	9.5
Applications
		9.5.1
Series-Elastic Actuator (SEA)
	9.6
Wrapping Up
Appendices
	Appendix
A Installing the Toolbox
	Appendix B
Linear Algebra Refresher
		B.1
Vectors
		B.2
Matrices
			B.2.1
Square Matrices
			B.2.2
Nonsquare and Singular Matrices
	Appendix C
Geometry
		C.1
Euclidean Geometry
			C.1.1
Points
			C.1.2
Lines
			C.1.3
Planes
			C.1.4
Ellipses and Ellipsoids
		C.2
Homogeneous Coordinates
			C.2.1
Two Dimensions
			C.2.2
Three Dimensions
	Appendix D
Lie Groups and Algebras
	Appendix E
Linearization, Jacobians and Hessians
	Appendix F
Solving Systems of Equations
		F.1
Linear Problems
			F.1.1
Nonhomogeneous Systems
			F.1.2
Homogeneous Systems
		F.2
Nonlinear Problems
			F.2.1
Finding Roots
			F.2.2
Nonlinear Minimization
			F.2.3
Nonlinear Least Squares Minimization
			F.2.4
Sparse Nonlinear Least Squares
	Appendix G
Gaussian Random Variables
	Appendix H
Kalman Filter
		H.1
Linear Systems – Kalman Filter
		H.2
Nonlinear Systems – Extended Kalman Filter
	Appendix I
Graphs
Bibliography
Index