Screw Theory in Robotics : An Illustrated and Practicable Introduction to Modern Mechanics (Hardcover)

Preface Acknowledgments List of Acronyms and Abbreviations 1. Introduction 1.1 Motivation 1.2 About this Book 1.3 Preview 1.4 Audience 1.5 Further Reading 2. Mathematical Tools 2.1 Rigid Body Motion 2.2 Homogeneous Representation 2.2.1 Exercise: Homogeneous Rotation 2.2.2 Exercise: Homogeneous Rotation plus Translation 2.3 Exponential Representation 2.3.1 Exercise: Exponential Rotation 2.3.2 Exercise: Exponential Rotation plus Translation 2.4 Summary 3. Forward Kinematics 3.1 Problem Statement in Robotics 3.2 Denavit-Hartenberg Convention 3.2.1 Puma robots (e.g., ABB IRB120) 3.3 Product of Exponentials Formulation 3.3.1 General Solution to Forward Kinematics 3.3.2 Puma robots (e.g., ABB IRB120) 3.3.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 3.3.4 Bending backwards robots (e.g., ABB IRB1600) 3.3.5 Gantry robots (e.g., ABB IRB6620LX) 3.3.6 Scara robots (e.g., ABB IRB910SC) 3.3.7 Collaborative robots (e.g., UNIVERSAL UR16e) 3.3.8 Redundant robots (e.g., KUKA IIWA) 3.3.9 Many DoF robots (e.g., RH0 UC3M Humanoid) 3.4 Summary 4. Inverse Kinematics 4.1 Problem Statement in Robotics and Analytical Difficulty 4.2 Numeric vs. Geometric Solutions 4.2.1 Puma robot Inverse Kinematics algorithms 4.3 Canonical subproblems for Inverse Kinematics 4.3.1 Paden-Kahan subproblem One (PK1) ? one rotation 4.3.2 Paden-Kahan subproblem Two (PK2) ? two crossing rotations 4.3.3 Paden-Kahan subproblem Three (PK3) ? rotation to a distance 4.3.4 Pardos-Gotor subproblem One (PG1) ? one translation 4.3.5 Pardos-Gotor subproblem Two (PG2) ? two crossing translations 4.3.6 Pardos-Gotor subproblem Three (PG3) ? translation to a distance 4.3.7 Pardos-Gotor subproblem Four (PG4) ? two parallel rotations 4.3.8 Pardos-Gotor subproblem Five (PG5) ? rotation of a line or plane 4.3.9 Pardos-Gotor subproblem Six (PG6) ? two skewed rotations 4.3.10 Pardos-Gotor subproblem Seven (PG7) ? three rotations to a point 4.3.11 Pardos-Gotor subproblem Eight (PG8) ? three rotations to a pose 4.4 Product of Exponentials Approach 4.4.1 General Solution to Inverse Kinematics 4.4.2 Puma robots (e.g., ABB IRB120) 4.4.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 4.4.4 Bending backwards robots (e.g., ABB IRB1600) 4.4.5 Gantry robots (e.g., ABB IRB6620LX) 4.4.6 Scara robots (e.g., ABB IRB910SC) 4.4.7 Collaborative robots (e.g., UNIVERSAL UR16e) 4.4.8 Redundant robots (e.g., KUKA IIWA) 4.4.9 Many DoF robots (e.g., RH0 UC3M Humanoid) 4.5 Summary 5. Differential Kinematics 5.1 Problem Statement in Robotics 5.2 The Analytic Jacobian 5.2.1 Scara robot (e.g., ABB IRB910SC) 5.2.2 Puma robot (e.g., ABB IRB120) 5.3 The Geometric Jacobian 5.3.1 General solution to Differential Kinematics 5.3.2 Puma robots (e.g., ABB IRB120) 5.3.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 5.3.4 Bending backwards robots (e.g., ABB IRB1600) 5.3.5 Gantry robots (e.g., ABB IRB6620LX) 5.3.6 Scara robots (e.g., ABB IRB910SC) 5.3.7 Collaborative robots (e.g., UNIVERSAL UR16e) 5.3.8 Redundant robots (e.g., KUKA IIWA) 5.4 Summary 6. Inverse Dynamics 6.1 Problem Statement in Robotics 6.2 The Lagrange Characterization 6.2.1 General Non-recursive Solution to Inverse Dynamics 6.2.2 Puma robots (e.g., ABB IRB120) 6.2.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 6.2 4 Bending backwards robots (e.g., ABB IRB1600) 6.2.5 Gantry robots (e.g., ABB IRB6620LX) 6.2.6 Scara robots (e.g., ABB IRB910SC) 6.2.7 Collaborative robots (e.g., UNIVERSAL UR16e) 6.2.8 Redundant robots (e.g., KUKA IIWA) 6.3 Robot Dynamics Control 6.4 Spatial Vector Algebra 6.5 The Newton-Euler Equations 6.5.1 General Recursive Solution to Inverse Dynamics RNEA with POE 6.5.2 Puma robots (e.g., ABB IRB120) 6.5.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 6.5 4 Bending backwards robots (e.g., ABB IRB1600) 6.5.5 Gantry robots (e.g., ABB IRB6620LX) 6.5.6 Scara robots (e.g., ABB IRB910SC) 6.5.7 Collaborative robots (e.g., UNIVERSAL UR16e) 6.5.8 Redundant robots (e.g., KUKA IIWA) 6.6 Summary 7. Trajectory Generation 7.1 Concepts and Definitions 7.2 Trajectory Planning 7.2.1 General Solution to Trajectory Generation 7.2.2 Puma robots (e.g., ABB IRB120) 7.2.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 7.2 4 Bending backwards robots (e.g., ABB IRB1600) 7.2.5 Gantry robots (e.g., ABB IRB6620LX) 7.2.6 Scara robots (e.g., ABB IRB910SC) 7.2.7 Collaborative robots (e.g., UNIVERSAL UR16e) 7.2.8 Redundant robots (e.g., KUKA IIWA) 7.3 Summary 8. Robotics Simulation 8.1 Robotics Simulation 8.2 Screw Theory Toolbox for Robotics (ST24R) 8.3 Forward Kinematics Simulations 8.3.1 General Solution to Forward Kinematics Simulation 8.3.2 Puma robots (e.g., ABB IRB120) 8.3.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 8.3 4 Bending backwards robots (e.g., ABB IRB1600) 8.3.5 Gantry robots (e.g., ABB IRB6620LX) 8.3.6 Scara robots (e.g., ABB IRB910SC) 8.3.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.3.8 Redundant robots (e.g., KUKA IIWA) 8.4 Inverse Kinematics Simulations 8.4.1 General Solution to Inverse Kinematics Simulation 8.4.2 Puma robots (e.g., ABB IRB120) 8.4.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 8.4 4 Bending backwards robots (e.g., ABB IRB1600) 8.4.5 Gantry robots (e.g., ABB IRB6620LX) 8.4.6 Scara robots (e.g., ABB IRB910SC) 8.4.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.4.8 Redundant robots (e.g., KUKA IIWA) 8.5 Differential Kinematics Simulations 8.5.1 General Solution to Differential Kinematics Simulation 8.3.2 Puma robots (e.g., ABB IRB120) 8.5.3 Puma robots(e.g., ABB IRB120) "Tool-Up" 8.5.4 Bending backwards robots (e.g., ABB IRB1600) 8.5.5 Gantry robots (e.g., ABB IRB6620LX) 8.5.6 Scara robots (e.g., ABB IRB910SC) 8.5.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.5.8 Redundant robots (e.g., KUKA IIWA) 8.6 Inverse Dynamics Simulations 8.6.1 General Solution to Inverse Dynamics Simulation 8.6.2 Puma robots (e.g., ABB IRB120) 8.6.3 Puma robots (e.g., ABB IRB120) "Tool-Up" 8.6 4 Bending backwards robots (e.g., ABB IRB1600) 8.6.5 Gantry robots (e.g., ABB IRB6620LX) 8.6.6 Scara robots (e.g., ABB IRB910SC) 8.6.7 Collaborative robots (e.g., UNIVERSAL UR16e) 8.6.8 Redundant robots (e.g., KUKA IIWA) 8.7 Summary 9. Conclusions 9.1 Summary 9.1.1 Introduction 9.1.2 Mathematical Tools 9.1.3 Forward Kinematics 9.1.4 Inverse Kinematics 9.1.5 Differential Kinematics 9.1.6 Inverse Dynamics 9.1.7 Trajectory Generation 9.1.8 Robotics Simulation 9.2 Future Prospects Bibliography & References Epilogue