"Foundations of Robotics" (MIT Press, 1990)


by Tsuneo YOSHIKAWA


Table of Contents

Preface

1  0verview of Robotic Mechanisms and Controller
  l.l Mechanisms
  1.2 Controller
      Exercises
      References

2  Kinematics
  2.1 Position and Orientation of Objects
      2.1.1 Object Coordinate Frame
      2.1.2 Rotation Matrix
      2.1.3 Euler Angles
      2.1.4 Roll, Pitch, and Yaw Angles
  2.2 Coordinate Transformation
      2.2.1 Homogeneous Transform
      2.2.2 Product and Inverse of Homogeneous Transform
  2.3 Joint Variables and Position of End Effector
      2.3.1 General Relation
      2.3.2 Link Parameters
      2.3.3 Link Frames
      2.3.4 Solution to Direct Kinematics Problem
  2.4 Inverse Kinematics Problem
  2.5 Jacobian Matrix
      2.5.1 Translational and Rotational Velocity of Objects
      2.5.2 Definition of the Jacobian Matrix
      2.5.3 Link Velocities of a Manipulator
      2.5.4 General Expression of the Jacobian Matrix Jv
      2.5.5 Joint Velocity for Achieving Desired End-Effector
            Velocity
      2.5.6 Singular Configurations
  2.6 Statics and Jacobian Matrices
      2.6.1 Equivalent Forces Represented in Different Frames
      2.6.2 Joint Driving Force Equivalent to Force Applied to
            Tip of Manipulator
      Exercises
      References

3  Dynamics
  3.1 Lagrangian and Newton-Euler Formulations
  3.2 Some Basics of Kinematics
      3.2.1 Newton's Equation and Euler's Equation
      3.2.2 Lagrange's Equation
  3.3 Derivation of Dynamics Equations Based on Lagrangian
      Formulation
      3.3.l Two-Link Manipulator
      3.3.2 n-Link Manipulator
      3.3.3 Parallel-Drive Two-Link Manipulator
  3.4 Derivation of Dynamic Equations Based on Newton-Euler
      Formulation
      3.4.1 Basic Procedure of Newton-Euler Formulation
      3.4.2 Link Accelerations of a Manipulator
      3.4.3 n-Link Manipulator
  3.5 Use of Dynamics Equations and Computational Load
      3.5.1 Real-Time Control---Inverse Dynamics Problem
      3.5.2 Simulation---Direct Dynamics Problem
  3.6 Identification of Manipulator Dynamics
      3.6.1 Identification Problem of Manipulators
      3.6.2 Identiiication Scheme Based on Lagrangian
            Formulation
      3.6.3 Identification of Load
      Exercises
      References

4  Manipulability
  4.1 Manipulability Ellipsoid and Manipulability Measure
  4.2 Best Configurations of Robotic Mechanisms from
      Manipulability Viewpoint
      4.2.1 Two-Link Mechanism
      4.2.2 SCARA-Type Robot Manipulator
      4.2.3 PUMA-Type Robot Manipulator
      4.2.4 0rthogona1-, Cylindrical-, and Polar-Coordinate
            Manipulators
      4.2.5 Four-Joint Robotic Finger
  4.3 Various Indices of Manipulability
  4.4 Dynamic Manipulability
      4.4.I Dynamic-Manipulability Ellipsoid and Dynamic-
            Manipulability Measure
      4.4.2 Two-Link Mechanism
   Exercises
   References

5 Position Control
  5.1 Generatiftg a Desired Trajectory
      5.1.1 Joint-Variable Scheme
      5.1.2 Scheme for Position Variables of End Effector
  5.2 Linear Feedback Control
      5.2.I Effectiveness of Linear Feedback Control
      5.2.2 Stability of Proportional and Differential Feedback
            Control
  5.3 Two-Stage Control by Linearization and Servo
      Compensation
      5.3.I Basic Concept of Two-Stage Control
      5.3.2 Structure of Control System
      5.3.3 Parallel Processing Scheme
  5.4 Design and Evaluation of Servo Compensation
      5.4.1 Linear Servosystem Theory
      5.4.2 Stability Margin and Sensitivity
  5.5 Decoupling Control
      5.5.1 Theory of Decoupling Control For Nonlinear
            Systems 
      5.5.2 Application to Manipulators
      5.5.3 Consideration of Actuator Dynamics
  5.6 Adaptive Control
    Exercises
    References

6  Force Control             ,
  6.I Impedance Control
      6.1.1 Passive-Impedance Method
      6.1.2 Active-Impedance Method---One-Degree-of-
            Freedom Case
      6.I.3 Active-Impedance Method---General Case
  6.2 Hybrid Control
      6.2.1 flybrid Control via Feedback Compensation 
      6.2.2 Dynamic Hybrid Control
  Exercises
  References

7 Control of Redundant Manipulators
  7.1 Redundant Manipulators
  7.2 Task-Decomposition Approach
      7.2.1 Decomposing a Task into Subtasks with Priority Order
      7.2.2 Basic Equations
      7.2.3 Second Subtask Given by Desired Trajectory
      7.2.4 Second Subtask Given by Criterion Function
      7.2.5 Formulation as Instantaneous Optimization
            Problem 
  7.3 Application to Avoiding Obstacles and Singularitie's 
      7.3.1 Avoiding Obstacles 
      7.3.2 Avoiding Singularities 
  7.4 Computational Method far Desired Joint Velocity
  Exercises
  References

  Appendix 1 Function atan2

  Appendix 2 Pseudo-Inverses

  Appendix 3 Singular-Value Decomposition

  Appendix 4 Lyapunov Stability Theory

  Solutions to Sclectcd Exercises

  Index


Click here to go to Yoshikawa Home Page. (Last updated July 31, 2001.)