A Journey from Robot to Digital Human

  Modeling and Optimization in Science and Technologies Edward Y.L. Gu

  A Journey from Robot to Digital Human

  Mathematical Principles and

Applications with MATLAB Programming Modeling and Optimization in Science and Technologies Volume 1 Series Editors Srikanta Patnaik (Editor-in-Chief) SOA University, Orissa, India Ishwar K. Sethi Oakland University, Rochester, USA Xiaolong Li Indiana State University, Terre Haute, USA Editorial Board Li Cheng, Kay Chen Tan, Department of Mechanical Engineering, Department of Electrical and The Hong Kong Polytechnic University, Computer Engineering, Hong Kong National University of Singapore,

  Singapore Jeng-Haur Horng, Department of Power Mechnical Yeon-Mo Yang,

Engineering, Department of Electronic Engineering,

National Formosa University, Kumoh National Institute of Technology, Yulin, Gumi, South Korea Taiwan Liangchi Zhang,

Pedro U. Lima, School of Mechanical and Manufacturing Institute for Systems and Robotics, Engineering, Lisbon, The University of New South Wales, Portugal Australia Mun-Kew Leong, Baojiang Zhong, Institute of Systems Science, School of Computer Science and National University of Singapore Technology, Soochow University, Suzhou, China Muhammad Nur, Faculty of Sciences and Mathematics, Ahmed Zobaa, Diponegoro Unersity, School of Engineering and Design, Semarang, Brunel University, Uxbridge, Indonesia Middlesex, UK For further volumes: About This Series

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  Edward Y.L. Gu A Journey from Robot to Digital Human

Mathematical Principles and Applications with

MATLAB Programming

  Edward Y.L. Gu Dept. of Electrical and Computer Engineering Oakland University

  Rochester, Michigan USA

ISSN 2196-7326

  ISSN 2196-7334 (electronic)

ISBN 978-3-642-39046-3

  ISBN 978-3-642-39047-0 (eBook) DOI 10.1007/978-3-642-39047-0 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013942012 _c Springer-Verlag Berlin Heidelberg 2013

  

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  To my family Sabrina,

Heather and Jacob Preface

  This book is intended to be a robotics textbook with an extension to digital _{T M} human modeling and MATLAB programming for both senior undergrad- uate and graduate engineering students. It can also be a research book for researchers, scientists, and engineers to learn and review the fundamentals of robotic systems as well as the basic methods of digital human modeling and motion generation. In the past decade, I wrote and annually updated two lecture notes: Robotic Kinematics, Dynamics and Control, and Modern Theories of Nonlinear Systems and Control. Those lecture notes were success- fully adopted by myself as the official textbooks for my dual-level robotics course and graduate-level nonlinear control systems course in the School of Engineering and Computer Science, Oakland University. Now, the major sub- jects of those two lecture notes are systematically mixed together and further extended by adding more topics, theories and applications, as well as more _{T M} examples and MATLAB programs to form the first part of the book.

  I had also been invited and worked for the Advance Manufacturing Engi- neering (AME) of Chrysler Corporation as a summer professor intern for the past 12 consecutive summers during the 2000’s. The opportunity of working with the automotive industry brought to me tremendous real-world knowl- edge and experience that was almost impossible to acquire from the class- room. In more than ten years of the internship program and consulting work, I was personally involved in their virtual assembly and product design inno- vation and development, and soon became an expert in major simulation soft- ware tools, from IGRIP robotic models, the early product of Deneb Robotics (now Dassault/Delmia) to the Safework mannequins in CATIA. Because of this unique opportunity, I have already been on my real journey from robot to digital human.

  Therefore, it has been my long-term intention to merge both the robot analysis and digital human modeling into one single book in order to share my enjoyable journey with the readers. On the other hand, it is, indeed, not an easy job to integrate these two rapidly and dynamically growing research VIII Preface

  areas together, even though the latter often borrows the modeling theories and motion generation algorithms from the former.

  Almost every chapter in the book has a section of exercise problems and/or computer projects, which will be beneficial for students to reinforce their understanding of every concept and algorithm. It is the instructor’s discretion to select sections and chapters to be covered in a single-semester robotics course. In addition, I highly recommend that the instructor teach students _{T M} to write a program and draw a robot or a mannequin in MATLAB with realistic motion by following the basic approaches and illustrations from the book.

  I hereby acknowledge my indebtedness to the people who helped me with different aspects of collecting knowledge, experience, data and programming skills towards the book completion. First, I wish to express my grateful appre- ciations to Dr. Leo Oriet who was the former senior manager when I worked for the AME of Chrysler Corporation, and Yu Teng who was/is a manager and leader of the virtual assembly and product design group in the AME of Chrysler. They both not only provided me with a unique opportunity to work on the digital robotic systems and human modeling for their ergonomics and product design verification and validation in the past, but also gave me ev- ery support and encouragement in recent years. I also wish to thank Michael Hicks who is an engineer working for General Dynamics Land Systems, and Ashley Liening who is a graduate student majoring in English at Oakland University for helping me polish my writing.

  Furthermore, the author is under obligation to Fanuc Robotics, Inc., Robotics Research Corporation, and Aldebaran Robotics, Paris, France for their courtesies and permissions to include their photographs into the book.

  Edward Y.L. Gu, Rochester, Michigan guy@oakland.edu April, 2013

  Contents

   2.4.3 Unit Screw and Special Orthogonal Dual Matrix . . .

   4.1 The Denavit-Hartenberg (D-H) Convention . . . . . . . . . . . . . .

   4 Robotic Kinematics and Statics . . . . . . . . . . . . . . . . . . . . . .

   References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   3.5 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   3.4 Tangent Space and Jacobian Transformations . . . . . . . . . . . .

  3.3 Unified Representations between Position and Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  

   3.2 Linear Velocity versus Angular Velocity . . . . . . . . . . . . . . . . .

   3.1 Translation and Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   3 Representations of Rigid Motion . . . . . . . . . . . . . . . . . . . . .

   References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   2.6 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   2.5 Introduction to Exterior Algebra . . . . . . . . . . . . . . . . . . . . . . .

   2.4.2 Dual Vector and Dual Matrix . . . . . . . . . . . . . . . . . . . .

  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   2.4.1 Calculus of the Dual Ring . . . . . . . . . . . . . . . . . . . . . . .

   2.4 The Dual Number, Dual Vector and Their Algebras . . . . . . .

   2.3 The Exponential Mapping and k–φ Procedure . . . . . . . . . . . .

   2.2 Lie Group and Lie Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   2.1 Vectors, Transformations and Spaces . . . . . . . . . . . . . . . . . . . .

   2 Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . .

   References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  1.3 A Journey from Robot Analysis to Digital Human Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  

  1.2 Digital Human Modeling: History, Achievements and New Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  

   1.1 Robotics Evolution: The Past, Today and Tomorrow . . . . . .

  1 Introduction to Robotics and Digital Human Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   X Contents

  4.3 Solutions of Inverse Kinematics . . . . . . . . . . . . . . . . . . . . . . . .

  7.1 Geometrical Interpretation of Robotic Dynamics . . . . . . . . .

  6 Digital Mock-Up and 3D Animation for Robot Arms . . .

  6.1 Basic Surface Drawing and Data Structure in MATLAB ^{T M} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  6.2 Digital Modeling and Assembling for Robot Arms . . . . . . . .

  6.3 Motion Planning and 3D Animation . . . . . . . . . . . . . . . . . . . .

  6.4 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  7 Robotic Dynamics: Modeling and Formulations . . . . . . . .

  7.2 The Newton-Euler Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.5.1 Two Computer Simulation Projects . . . . . . . . . . . . . . .

  7.3 The Lagrangian Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.4 Determination of Inertial Matrix . . . . . . . . . . . . . . . . . . . . . . .

  7.5 Configuration Manifolds and Isometric Embeddings . . . . . . .

  7.5.1 Metric Factorization and Manifold Embedding . . . . .

  7.5.2 Isometric Embedding of C-Manifolds . . . . . . . . . . . . . .

  7.5.3 Combined Isometric Embedding and Structure Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.5.2 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.5 Computer Projects and Exercises of the Chapter . . . . . . . . .

  

  4.7.3 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.4 Jacobian Matrix and Differential Motion . . . . . . . . . . . . . . . .

  4.5 Dual-Number Transformations . . . . . . . . . . . . . . . . . . . . . . . . .

  4.6 Robotic Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.7 Computer Projects and Exercises of the Chapter . . . . . . . . .

  4.7.1 Stanford Robot Motions . . . . . . . . . . . . . . . . . . . . . . . . .

  4.7.2 The Industrial Robot Model and Its Motions . . . . . .

  5 Redundant Robots and Hybrid-Chain Robotic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.4.3 Modeling and Analysis of 3+3 Hybrid Robot Arms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.1 The Generalized Inverse of a Matrix . . . . . . . . . . . . . . . . . . . .

  5.2 Redundant Robotic Manipulators . . . . . . . . . . . . . . . . . . . . . . .

  5.3 Hybrid-Chain Robotic Systems . . . . . . . . . . . . . . . . . . . . . . . . .

  5.4 Kinematic Modeling for Parallel-Chain Mechanisms . . . . . . .

  5.4.1 Stewart Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.4.2 Jacobian Equation and the Principle of Duality . . . .

  7.5.4 The Minimum Isometric Embedding and Isometrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents

  XI

  7.6 A Compact Dynamic Equation . . . . . . . . . . . . . . . . . . . . . . . . .

  7.7 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8 Control of Robotic Systems . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.1 Path Planning and Trajectory Tracking . . . . . . . . . . . . . . . . .

  8.2 Independent Joint-Servo Control . . . . . . . . . . . . . . . . . . . . . . .

  8.3 Input-Output Mapping and Systems Invertibility . . . . . . . . .

  8.3.1 The Concepts of Input-Output Mapping and Relative Degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.3.2 Systems Invertibility and Applications . . . . . . . . . . . .

  8.4 The Theory of Exact Linearization and Linearizability . . . .

  8.4.1 Involutivity and Complete Integrability . . . . . . . . . . .

  8.4.2 The Input-State Linearization Procedure . . . . . . . . . .

  8.4.3 The Input-Output Linearization Procedure . . . . . . . .

  8.4.4 Dynamic Extension for I/O Channels . . . . . . . . . . . . .

  8.4.5 Linearizable Subsystems and Internal Dynamics . . . .

  8.4.6 Zero Dynamics and Minimum-Phase Systems . . . . . .

  8.5 Dynamic Control of Robotic Systems . . . . . . . . . . . . . . . . . . .

  8.5.1 The Theory of Stability in the Lyapunov Sense . . . . .

  8.5.2 Set-Point Stability and Trajectory-Tracking Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.6 Backstepping Control Design for Multi-Cascaded Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.6.1 Control Design with the Lyapunov Direct Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.6.2 Backstepping Recursions in Control Design . . . . . . . .

  8.7 Adaptive Control of Robotic Systems . . . . . . . . . . . . . . . . . . .

  8.8 Computer Projects and Exercises of the Chapter . . . . . . . . .

  8.8.1 Dynamic Modeling and Control of a 3-Joint Stanford-Like Robot Arm . . . . . . . . . . . . . . . . . . . . . . .

  8.8.2 Modeling and Control of an Under-Actuated Robotic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.8.3 Dynamic Modeling and Control of a Parallel-Chain Planar Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.8.4 Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9 Digital Human Modeling: Kinematics and Statics . . . . . .

  9.1 Local versus Global Kinematic Models and Motion Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.2 Local and Global Jacobian Matrices in a Five-Point Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.3 The Range of Motion (ROM) and the Range of Strength (ROS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII Contents

  9.3.1 Basic Concepts of the Human Structural System . . .

  10.3 Motion Planning and Formatting . . . . . . . . . . . . . . . . . . . . . . .

  11.7 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  11.6 Future Perspectives of Digital Human Modeling . . . . . . . . . .

  11.5.2 An Active Suspension Model and Human-Machine Interactive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  11.5.1 Modeling and Control of Active Vehicle Restraint Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  11.5 Dynamic Interactive Control of Vehicle Active Systems . . . .

  11.4 Modeling and Analysis of Mannequin Dynamics in Response to an IED Explosion . . . . . . . . . . . . . . . . . . . . . . . . .

  11.3 Digital Human Dynamic Motion in Car Crash Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  11.1 Dynamic Models, Algorithms and Implementation . . . . . . . . 11.2 δ-Force Excitation and Gait Dynamics . . . . . . . . . . . . . . . . . .

  11 Digital Human Modeling: Dynamics and Interactive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.6 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.5 Generation of Digital Human Realistic Motions . . . . . . . . . .

  10.4 Analysis of Basic Human Motions: Walking, Running and Jumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.2 Hand Models and Digital Sensing . . . . . . . . . . . . . . . . . . . . . . .

  9.3.2 An Overview of the Human Movement System . . . . .

  10.1 Create a Mannequin in MATLAB ^{T M} . . . . . . . . . . . . . . . . . . .

  10 Digital Human Modeling: 3D Mock-Up and Motion Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.6 Exercises of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.5.3 On the Minimum Effort Objective . . . . . . . . . . . . . . . .

  9.5.2 The Criterion of Even Joint Torque Distribution . . .

  9.5.1 The Joint Comfort Criterion . . . . . . . . . . . . . . . . . . . . .

  9.5 Posture Optimization Criteria . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.4.2 Joint Torque Distribution due to Gravity . . . . . . . . . .

  9.4.1 Joint Torque Distribution and the Law of Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.4 Digital Human Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.3.4 The Joint Range of Strength (ROS) . . . . . . . . . . . . . .

  9.3.3 The Range of Motion (ROM) and Joint Comfort Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  List of Figures 1.1 Married with a child . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.3 A curved path before and after the spline and pchip interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.12 A 3-joint RRR robot hanging a simple pendulum . . . . . . . . .

  4.11 The Stanford-type robot is driving a screw into a workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.10 An industrial robot model with coordinate frames assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.9 The motion of link n superimposed by the motion of link i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  

   4.8 The third and fourth I-K solutions for the Stanford arm . . .

   4.7 The first and second I-K solutions for the Stanford arm . . .

   4.6 Two robot arms with their z-axes . . . . . . . . . . . . . . . . . . . . . .

   4.5 Multi-configuration for a two-link arm . . . . . . . . . . . . . . . . . .

   4.4 Example of the position and orientation path planning . . . .

  

  

   4.2 A 6-joint Stanford-type robot arm . . . . . . . . . . . . . . . . . . . . . .

   4.1 Definition of the Denavit-Hartenberg (D-H) Convention . . .

   3.3 Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   3.2 Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   3.1 The webcam position and orientation . . . . . . . . . . . . . . . . . . .

   2.2 Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

   2.1 Two parallel vectors have a common length . . . . . . . . . . . . . .

   1.4 Important definitions in robotics . . . . . . . . . . . . . . . . . . . . . . .

   1.3 Robotics research and evolutions . . . . . . . . . . . . . . . . . . . . . . .

  1.2 A Fanuc M-900iB/700 industrial robot in drilling operation. Photo courtesy of Fanuc Robotics, Inc. . . . . . . . .

  4.13 A robot arm is exerted by a force f and a moment m at point C on the body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIV List of Figures

  4.14 A block diagram of robotic hybrid position/force control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.7 Simulation results - only the rank (minimum-Norm) solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.19 A 6-axis 6-6 parallel-chain hexapod system . . . . . . . . . . . . . .

  5.18 A Nao-H25 humanoid robotic system. Photo courtesy of Aldebaran Robotics, Paris, France. . . . . . . . . . . . . . . . . . . . . .

  5.17 A two-robot coordinated system . . . . . . . . . . . . . . . . . . . . . . . .

  5.16 Kinematic model of the two-arm 17-joint hybrid-chain robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Photo courtesy of Robotics Research Corporation, Cincinnati, OH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.15 A 7-axis dexterous manipulator RRC K-1207 and a dual-arm 17-axis dexterous manipulator RRC K-2017.

  5.14 Stewart platform - a typical 6-axis parallel-chain system . . .

  5.13 A hybrid-chain planar robot . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.12 The Stanford-type robot arm is sitting on a wheel mobile cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.11 A top view of the 7-joint redundant robot with a post and a virtual point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.10 The 7-joint robot is avoiding a collision by a potential function optimization . . . . . . . . . . . . . . . . . . . . . . .

  5.9 The 7-joint robot arm is hitting a post when drawing a circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.8 Simulation results - both the rank and null solutions . . . . . .

  5.6 A three-joint RRR planar redundant robot arm . . . . . . . . . .

  4.15 A Stanford robot is sitting at the Home position and ready to move and draw on a board . . . . . . . . . . . . . . . . . . . . .

  5.5 A 7-joint redundant robot arm . . . . . . . . . . . . . . . . . . . . . . . . .

  5.4 A 7-joint redundant robot arm . . . . . . . . . . . . . . . . . . . . . . . . .

  5.3 A 7-joint redundant robot arm . . . . . . . . . . . . . . . . . . . . . . . . .

  5.2 A 7-joint redundant robot arm . . . . . . . . . . . . . . . . . . . . . . . . .

  5.1 Geometrical decomposition of the general solution . . . . . . . .

  4.23 A beam-sliding 3-joint robot . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.22 A 3-joint RPR robot arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.21 A 2-joint prismatic-revolute planar arm . . . . . . . . . . . . . . . . .

  4.20 Robot 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.19 Robot 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.18 Robot 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.17 The industrial robot model at the Starting and Ending positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  4.16 The Stanford robot is drawing a sine wave on the board . . .

  5.20 Kinematic model of a 3-3 Stewart platform . . . . . . . . . . . . . . List of Figures

  XV

  6.10 A Stewart platform and coordinate frames assignment . . . .

  6.5 Create a full torus surface in MATLAB ^{T M} . . . . . . . . . . . . . .

  6.6 Create a half torus surface in MATLAB ^{T M} . . . . . . . . . . . . . .

  6.7 Making a local deformation for a cylindrical surface in MATLAB ^{T M}

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  6.8 Sending an object from the base to a desired destination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  6.9 D-H modeling of the 7-joint redundant robot . . . . . . . . . . . . .

  6.11 The Stewart platform in motion . . . . . . . . . . . . . . . . . . . . . . . .

  6.3 A diamond and an ellipsoid drawing in MATLAB ^{T M} . . . . .

  6.12 A two-arm robot at its Home position . . . . . . . . . . . . . . . . . . .

  6.13 A two-arm robot is picking up a disc from the floor . . . . . . .

  6.14 A two-arm robot is hanging the disc on the wall . . . . . . . . . .

  6.15 A 3+3 hybrid robot with equilateral triangle configuration at its Home position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  6.16 The 3+3 hybrid robot with equilateral triangle configuration starts drawing a sine wave . . . . . . . . . . . . . . . . .

  6.17 The 3+3 hybrid robot with equilateral triangle configuration ends the drawing . . . . . . . . . . . . . . . . . . . . . . . . .

  6.18 A 3+3 hybrid robot with rectangle configuration at its Home position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  6.4 Create a rectangular surface in MATLAB ^{T M} . . . . . . . . . . . .

  6.2 Data structure of a sphere drawing in MATLAB ^{T M} . . . . . . .

  5.21 Solution to the forward kinematics of the Stewart platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.26 Solve the I-K problem for a 3+3 hybrid robot . . . . . . . . . . . .

  5.22 The definitions of p ⁱ

  6

  ’s on the top mobile disc. They are also applicable to p ⁱ ’s on the base disc of the 6-6 Stewart platform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.23 Two types of the 3-parallel mechanism . . . . . . . . . . . . . . . . . .

  5.24 Kinematic analysis of a 3-leg UPS platform . . . . . . . . . . . . . .

  5.25 Top revolute-joint configurations . . . . . . . . . . . . . . . . . . . . . . .

  5.27 Delta URR vs. UPR 3-leg parallel system . . . . . . . . . . . . . . . .

  6.1 Data structure of a cylinder drawing in MATLAB ^{T M} . . . . .

  5.28 A three-joint RPR planar robot arm . . . . . . . . . . . . . . . . . . . .

  5.29 A 3+3 hybrid robot in rectangle configuration . . . . . . . . . . .

  5.30 A 4-joint beam-hanging PRRP robot . . . . . . . . . . . . . . . . . . .

  5.31 An RRP 3-joint planar robot to touch a bowl . . . . . . . . . . . .

  5.32 An RPR 3-joint planar robot . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.33 A planar mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  5.34 Three parallel-chain systems . . . . . . . . . . . . . . . . . . . . . . . . . . .

  6.19 The 3+3 hybrid robot in rectangle configuration is reaching a wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVI List of Figures

  7.1 Two 6-revolute-joint industrial robots: Fanuc R-2000iB (left) and Fanuc M-900iA (right). Photo courtesy of Fanuc Robotics, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.3 A DC-motor electrical and mechanical model . . . . . . . . . . . .

  7.15 The third and forth of four I-K solutions for a Stanford arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.16 An inverted pendulum system . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.17 The minimum embeddable C-manifold of the inverted pendulum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.18 An RRR-type planar robot and its multi-configuration . . . .

  8.1 A joint path example without and with cubic spline function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.2 Joint position and velocity profiles for the second spline function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.4 A block diagram of the DC-motor model . . . . . . . . . . . . . . . .

  7.13 A planar RR-type arm and its C-manifold as a flatted torus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.5 A block diagram of DC-motor position-feedback control . . .

  8.6 A block diagram for an input-state linearized system . . . . . .

  8.7 A block diagram for an input-output linearized trajectory-tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.8 A block diagram for a partially input-output linearized system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.9 The block diagram of a single feedback loop . . . . . . . . . . . . .

  8.10 Model a ball-board control system using the robotic D-H convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.11 The ball is at an initial position to start tracking a sine wave on the board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.14 The first and second of four I-K solutions for a Stanford arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  . . . .

  7.2 RR-type and RP-type 2-link robots . . . . . . . . . . . . . . . . . . . . .

  7.10 The cylindrical and spherical local coordinate systems . . . . .

  7.3 C-manifolds for RR-type and RP-type 2-link robots . . . . . . .

  7.4 A rigid body and its reference frame changes . . . . . . . . . . . . .

  7.5 Getting-busier directions for kinematics and dynamics . . . .

  7.6 Force/torque analysis of link i . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.7 Velocity analysis of a three-joint planar robot arm . . . . . . . .

  7.8 An inertial matrix W is formed by stacking every W j together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  7.9 Axes assignment of the three-joint planar robot . . . . . . . . . .

  7.11 Different mapping cases from S

  2

  1

  to Euclidean spaces . . . . . .

  7.12 A 2D torus T

  2

  situated in Euclidean spaces R

  3

  and R

  8.12 The ball is catching up the track at early time . . . . . . . . . . . List of Figures

  XVII

  9.2 The real human vertebral column and its modeling . . . . . . .

  9.15 Analysis of mannequin force balance in sitting posture . . . .

  9.14 A complete joint torque distribution in standing posture . . .

  9.13 Two arms and torso joint torque distribution in standing posture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.12 Analysis of mannequin force balance in standing posture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.11 A closed boundary for the shoulder ROM and ROS in a chart of joint torque vs. joint angle . . . . . . . . . . . . . . . . . . . . .

  9.10 The angles of human posture in sagittal plane for a joint strength prediction . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.9 Two-joint muscles on the arm and leg . . . . . . . . . . . . . . . . . . .

  9.8 Hip flexion and abduction with joint combination effects to the trunk flexion and lateral flexion . . . . . . . . . . . . . . . . . .

  9.7 Shoulder abduction and its clavicle joint combination effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.6 A block diagram of the five-point model . . . . . . . . . . . . . . . . .

  9.5 The left arm of a digital mannequin is manually maneuvered by a local I-K algorithm with at least two distinct configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.4 Coordinate frame assignment on a digital mannequin . . . . .

  9.3 A block diagram of digital human joint distribution . . . . . . .

  9.1 Major joints and types over an entire human body . . . . . . . .

  8.13 The ball is now on the track by controlling the board orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.25 A block diagram of the DC-motor in driving a robotic link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.24 A 3-piston parallel-chain planar robot . . . . . . . . . . . . . . . . . . .

  8.23 A 2-joint robot arm sitting on a rolling log . . . . . . . . . . . . . .

  8.22 A 3-joint Stanford-like robot arm . . . . . . . . . . . . . . . . . . . . . . .

  embeddable C-manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  3 as the minimum

  8.21 The simulation results with M

  8.20 An RRP type three-joint robot arm . . . . . . . . . . . . . . . . . . . . .

  8.19 A block diagram of adaptive control design . . . . . . . . . . . . . .

  8.18 A flowchart of backstepping control design for a k-cascaded dynamic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.17 A flowchart of the backstepping control design approach . . .

  8.16 An energy-like function V (x) and a V -lifted trajectory . . . .

  8.15 The ball is successfully reaching the end of the sine wave on the board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  8.14 The ball is well controlled to continue tracking the sine wave on the board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.16 Analysis of mannequin force balance in kneeling posture . . . XVIII List of Figures

  9.17 The joint torque distribution over two arms and torso in sitting posture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.30 A joint torque distribution in placing a load with and without optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.9 A block diagram for the right hand modeling and reversing the order for the left hand . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.8 A skeletal digital mannequin in dancing . . . . . . . . . . . . . . . . .

  10.7 Three different views of the finally assembled digital human model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.6 A digital human thigh/leg model . . . . . . . . . . . . . . . . . . . . . . .

  10.5 A digital human upper arm/forearm model . . . . . . . . . . . . . .

  10.4 A digital human torso model . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.3 A digital human abdomen/hip model . . . . . . . . . . . . . . . . . . .

  10.2 A face picture for texture-mapping onto the surface of a digital human head model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.1 A digital human head model . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.31 A complete joint torque distribution with and without optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.29 The mannequin postures in placing a load on the overhead shelf without and with optimization . . . . . . . . . . . . . . . . . . . .

  9.18 A complete joint torque distribution in sitting posture . . . .

  9.28 A complete joint torque distribution with and without optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.27 A joint torque distribution due to weight-lift without and with optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.26 Mannequin postures in picking up a load without and with optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.25 A 47-joint torque distribution due to gravity after balancing the reaction forces . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.24 A 47-joint torque distribution due to gravity in standing posture before the balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.23 A 47-joint torque distribution due to gravity in neutral standing posture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.22 A mannequin is in neutral standing posture and ready to pick an object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.21 A digital human skeleton model with segment numbering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  9.20 A complete joint torque distribution in kneeling posture . . .

  9.19 The joint torque distribution over two arms and torso in kneeling posture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.10 The joint/link coordinate frame assignment for hand modeling based on the D-H convention . . . . . . . . . . . . . . . . . . List of Figures

  XIX

  10.28 A digital human in jumping . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.38 A digital human in springboard diving . . . . . . . . . . . . . . . . . .

  10.37 A digital human in springboard diving . . . . . . . . . . . . . . . . . .

  10.36 A digital human in springboard diving . . . . . . . . . . . . . . . . . .

  10.35 A digital human is jumping down from the stair . . . . . . . . . .

  10.34 A digital human is climbing up a stair and then jumping down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.33 A digital human is climbing up a stair . . . . . . . . . . . . . . . . . .

  10.32 A digital human in ball-throwing . . . . . . . . . . . . . . . . . . . . . . .

  10.31 A digital human in ball-throwing . . . . . . . . . . . . . . . . . . . . . . .

  10.30 A digital human in running and ball-throwing . . . . . . . . . . . .

  10.29 A relation diagram between the human centered frame and the world base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.23 A digital human in running . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.24 z-trajectories in a jumping case for the feet and hands by a motion capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.25 x-trajectories in a jumping case for the two feet by a motion capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.26 x-trajectories in a jumping case for the two hands by a motion capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.27 x and z-trajectories in a jumping case for the H-triangle by a motion capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.11 The right hand digital model with a ball-grasping gesture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.22 A digital human in walking . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.20 A walking z-coordinates profile for both the feet and hands created by a numerical algorithm . . . . . . . . . . . . . . . . . 10.21 z-trajectories in a running case for the feet and hands created by a numerical model . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.19 A walking x-coordinates profile for the hands created by a numerical algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  10.18 A walking x-coordinates profile for the feet created by a numerical algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .