Dynamics and Control of Robotic Systems

Content: Preface xiiiAcknowledgment xvAbout the Companion Website xvii1 Introduction 11.1 Motivation 11.2 Origins of Robotic Systems 51.3 General Structure of Robotic Systems 71.4 Robotic Manipulators 91.4.1 Typical Structure of Robotic Manipulators 91.4.2 Classification of Robotic Manipulators 111.4.2.1 Classification by Motion Characteristics 111.4.2.2 Classification by Degrees of Freedom 121.4.2.3 Classification by Driver Technology and Drive Power 121.4.2.4 Classification by Kinematic Structure 121.4.2.5 Classification by Workspace Geometry 141.4.3 Examples of Robotic Manipulators 141.4.3.1 Cartesian Robotic Manipulator 151.4.3.2 Cylindrical Robotic Manipulator 161.4.3.3 SCARA Robotic Manipulator 161.4.3.4 Spherical Robotic Manipulator 171.4.3.5 PUMA Robotic Manipulator 181.4.4 Spherical Wrist 181.4.5 Articulated Robot 201.5 Mobile Robotics 201.5.1 Humanoid Robots 201.5.2 Autonomous Ground Vehicles 221.5.3 Autonomous Air Vehicles 231.5.4 Autonomous Marine Vehicles 251.6 An Overview of Robotics Dynamics and Control Problems 261.6.1 Forward Kinematics 271.6.2 Inverse Kinematics 281.6.3 Forward Dynamics 281.6.4 Inverse Dynamics and Feedback Control 291.6.5 Dynamics and Control of Robotic Vehicles 301.7 Organization of the Book 311.8 Problems for Chapter 1 332 Fundamentals of Kinematics 352.1 Bases and Coordinate Systems 352.1.1 N-Tuples and M x N Arrays 352.1.2 Vectors, Bases and Frames 392.1.2.1 Vectors 402.1.2.2 Bases and Frames 412.2 Rotation Matrices 492.3 Parameterizations of Rotation Matrices 522.3.1 Single Axis Rotations 522.3.2 Cascades of Rotation Matrices 562.3.2.1 Cascade Rotations about Moving Axes 562.3.2.2 Cascade Rotations about Fixed Axes 572.3.3 Euler Angles 572.3.3.1 The 3-2-1 Yaw-Pitch-Roll Euler Angles 582.3.3.2 The 3-1-3 Precession-Nutation-Spin Euler Angles 622.3.4 Axis Angle Parameterization 652.4 Position, Velocity, and Acceleration 682.5 Angular Velocity and Angular Acceleration 772.5.1 Angular Velocity 772.5.2 Angular Acceleration 832.6 Theorems of Kinematics 842.6.1 Addition of Angular Velocities 842.6.2 Relative Velocity 872.6.3 Relative Acceleration 882.6.4 Common Coordinate Systems 912.6.4.1 Cartesian Coordinates 912.6.4.2 Cylindrical Coordinates 922.6.4.3 Spherical Coordinates 942.7 Problems for Chapter 2, Kinematics 962.7.1 Problems on N-tuples and M x N Arrays 962.7.2 Problems on Vectors, Bases, and Frames 972.7.3 Problems on Rotation Matrices 982.7.4 Problems on Position, Velocity, and Acceleration 1022.7.5 Problems on Angular Velocity 1042.7.6 Problems on the Theorems of Kinematics 1042.7.6.1 Problems on the Addition of Angular Velocities 1042.7.7 Problems on Relative Velocity and Acceleration 1052.7.8 Problems on Common Coordinate Systems 1083 Kinematics of Robotic Systems 1093.1 Homogeneous Transformations and Rigid Motion 1093.2 Ideal Joints 1153.2.1 The Prismatic Joint 1163.2.2 The Revolute Joint 1173.2.3 Other Ideal Joints 1193.3 The Denavit-Hartenberg Convention 1213.3.1 Kinematic Chains and Numbering in the DH Convention 1213.3.2 Definition of Frames in the DH Convention 1233.3.3 Homogeneous Transforms in the DH Convention 1243.3.4 The DH Procedure 1273.3.5 Angular Velocity and Velocity in the DH Convention 1333.4 Recursive O(N) Formulation of Forward Kinematics 1383.4.1 Recursive Calculation of Velocity and Angular Velocity 1403.4.2 Efficiency and Computational Cost 1433.4.3 Recursive Calculation of Acceleration and Angular Acceleration 1473.5 Inverse Kinematics 1603.5.1 Solvability 1603.5.2 Analytical Methods 1633.5.2.1 Algebraic Methods 1633.5.2.2 Geometric Methods 1743.5.3 Optimization Methods 1763.5.4 Inverse Velocity Kinematics 1843.5.4.1 Singularity 1853.6 Problems for Chapter 3, Kinematics of Robotic Systems 1863.6.1 Problems on Homogeneous Transformations 1863.6.2 Problems on Ideal Joints and Constraints 1883.6.3 Problems on the DH Convention 1883.6.4 Problems on Angular Velocity and Velocity for Kinematic Chains 1903.6.5 Problems on Inverse Kinematics 1954 Newton-Euler Formulations 1974.1 Linear Momentum of Rigid Bodies 1974.2 Angular Momentum of Rigid Bodies 2034.2.1 First Principles 2034.2.2 Angular Momentum and Inertia 2084.2.3 Calculation of the Inertia Matrix 2144.2.3.1 The Inertia Rotation Transformation Law 2144.2.3.2 Principal Axes of Inertia 2184.2.3.3 The Parallel Axis Theorem 2214.2.3.4 Symmetry and Inertia 2244.3 The Newton-Euler Equations 2294.4 Euler\'s Equation for a Rigid Body 2334.5 Equations of Motion for Mechanical Systems 2354.5.1 The General Strategy 2354.5.2 Free Body Diagrams 2364.6 Structure of Governing Equations: Newton-Euler Formulations 2584.6.1 Differential Algebraic Equations (DAEs) 2584.6.2 Ordinary Differential Equations (ODEs) 2604.7 Recursive Newton-Euler Formulations 2624.8 Recursive Derivation of the Equations of Motion 2714.9 Problems for Chapter 4, Newton-Euler Equations 2744.9.1 Problems on Linear Momentum 2744.9.2 Problems on the Center of Mass 2774.9.3 Problems on the Inertia Matrix 2794.9.4 Problems on Angular Momentum 2814.9.5 Problems on the Newton-Euler Equations 2825 Analytical Mechanics 2855.1 Hamilton\'s Principle 2855.1.1 Generalized Coordinates 2855.1.2 Functionals and the Calculus of Variations 2885.1.3 Hamilton\'s Principle for Conservative Systems 2925.1.4 Kinetic Energy for Rigid Bodies 2995.2 Lagrange\'s Equations for Conservative Systems 3035.3 Hamilton\'s Extended Principle 3075.3.1 Virtual Work Formulations 3075.4 Lagrange\'s Equations for Robotic Systems 3225.4.1 Natural Systems 3225.4.2 Lagrange\'s Equations and the Denavit-Hartenberg Convention 3265.5 Constrained Systems 3295.6 Problems for Chapter 5, Analytical Mechanics 3345.6.1 Problems on Hamilton\'s Principle 3345.6.2 Problems on Lagrange\'s Equations 3375.6.3 Problems on Hamilton\'s Extended Principle 3395.6.4 Problems on Constrained Systems 3456 Control of Robotic Systems 3476.1 The Structure of Control Problems 3476.1.1 Setpoint and Tracking Feedback Control Problems 3486.1.2 Open Loop and Closed Loop Control 3496.1.3 Linear and Nonlinear Control 3496.2 Fundamentals of Stability Theory 3506.3 Advanced Techniques of Stability Theory 3576.4 Lyapunov\'s Direct Method 3586.5 The Invariance Principle 3616.6 Dynamic Inversion or Computed Torque Control 3666.7 Approximate Dynamic Inversion and Uncertainty 3766.8 Controllers Based on Passivity 3896.9 Actuator Models 3936.9.1 Electric Motors 3936.9.2 Linear Actuators 4006.10 Backstepping Control and Actuator Dynamics 4046.11 Problems for Chapter 6, control of Robotic Systems 4076.11.1 Problems on Gravity Compensation and PD Setpoint Control 4076.11.2 Problems on Computed Torque Tracking Control 4126.11.3 Problems on Dissipativity Based Tracking Control 4137 Image Based Control of Robotic Systems 4157.1 The Geometry of Camera Measurements 4157.1.1 Perspective Projection and Pinhole Camera Models 4157.1.2 Pixel Coordinates and CCD Cameras 4187.1.3 The Interaction Matrix 4197.2 Image Based Visual Servo Control 4237.2.1 Control Synthesis and Closed Loop Equations 4247.2.2 Calculation of Initial Conditions 4277.3 Task Space Control 4417.4 Task Space and Visual Control 4477.5 Problems for Chapter 7 459A Appendix 465A.1 Fundamentals of Linear Algebra 465A.1.1 Solution of Matrix Equations 467A.1.2 Linear Independence and Rank 468A.1.3 Invertibility and Rank 470A.1.4 Least Squares Approximation 470A.1.5 Rank Conditions and the Interaction Matrix 475A.2 The Algebraic Eigenvalue Problem 475A.2.1 Self-adjoint Matrices 476A.2.2 Jordan Canonical Form 478A.3 Gauss Transformations and LU Factorizations 479References 485Index 489