"Foundations of Robotics" (MIT Press, 1990)


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Table of Contents


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

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
      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

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
      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
      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
      3.6.3 Identification of Load

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
      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

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
  5.3 Two-Stage Control by Linearization and Servo
      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
      5.5.2 Application to Manipulators
      5.5.3 Consideration of Actuator Dynamics
  5.6 Adaptive Control

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

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
  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

      Appendix 1  Function atan2

      Appendix 2  Pseudo-Inverses

      Appendix 3  Singular-Value Decomposition

      Appendix 4  Lyapunov Stability Theory

      Solutions to Sclectcd Exercises


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