ROBOT MODELING AND CONTROL 2EDITION

**A New Edition Featuring Case Studies and Examples of the Fundamentals of Robot Kinematics, Dynamics, and Control** In the 2nd Edition of __Robot Modeling and Control__, students will cover the theoretical fundamentals and the latest technological advances in robot kinematics. With so much advancement in technology, from robotics to motion planning, society can implement more powerful and dynamic algorithms than ever before. This in-depth reference guide educates readers in four distinct parts; the first two serve as a guide to the fundamentals of robotics and motion control, while the last two dive more in-depth into control theory and nonlinear system analysis. With the new edition, readers gain access to new case studies and thoroughly researched information covering topics such as: &; Motion-planning, collision avoidance, trajectory optimization, and control of robots &; Popular topics within the robotics industry and how they apply to various technologies &; An expanded set of examples, simulations, problems, and case studies &; Open-ended suggestions for students to apply the knowledge to real-life situations A four-part reference essential for both undergraduate and graduate students, __Robot Modeling and Control__ serves as a foundation for a solid education in robotics and motion planning. 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

A New Edition Featuring Case Studies and Examples of the Fundamentals of Robot Kinematics, Dynamics, and Control

In the 2nd Edition of Robot Modeling and Control, students will cover the theoretical fundamentals and the latest technological advances in robot kinematics. With so much advancement in technology, from robotics to motion planning, society can implement more powerful and dynamic algorithms than ever before. This in-depth reference guide educates readers in four distinct parts; the first two serve as a guide to the fundamentals of robotics and motion control, while the last two dive more in-depth into control theory and nonlinear system analysis.

With the new edition, readers gain access to new case studies and thoroughly researched information covering topics such as:

● Motion-planning, collision avoidance, trajectory optimization, and control of robots

● Popular topics within the robotics industry and how they apply to various technologies

● An expanded set of examples, simulations, problems, and case studies

● Open-ended suggestions for students to apply the knowledge to real-life situations

A four-part reference essential for both undergraduate and graduate students, Robot Modeling and Control serves as a foundation for a solid education in robotics and motion planning.

"A New Edition Featuring Case Studies and Examples of the Fundamentals of Robot Kinematics, Dynamics, and Control. In the 2nd Edition of Robot Modeling and Control, students will cover the theoretical fundamentals and the latest technological advances in robot kinematics. With so much advancement in technology, from robotics to motion planning, society can implement more powerful and dynamic algorithms than ever before. This in-depth reference guide educates readers in four distinct parts; the first two serve as a guide to the fundamentals of robotics and motion control, while the last two dive more in-depth into control theory and nonlinear system analysis. With the new edition, readers gain access to new case studies and thoroughly researched information covering topics such as: Motion-planning, collision avoidance, trajectory optimization, and control of robots. Popular topics within the robotics industry and how they apply to various technologies. An expanded set of examples, simulations, problems, and case studies. Open-ended suggestions for students to apply the knowledge to real-life situations. A four-part reference essential for both undergraduate and graduate students, Robot Modeling and Control serves as a foundation for a solid education in robotics and motion planning"-- Provided by publisher