Solution manual for Introduction to Robotics Mechanics and Control 4th Edition by John Craig ISBN 9780133489835 0133489833

Chapter 1 Introduction

1.1 Background

1.2 The Mechanics and Control of Mechanical Manipulators

Description of Position and Orientation

Forward Kinematics of Manipulators

Inverse Kinematics of Manipulators

Velocities, Static Forces, Singularities

Dynamics

Trajectory Generation

Manipulator Design and Sensors

Linear Position Control

Nonlinear Position Control

Force Control

Programming Robots

Off-Line Programming and Simulation

1.3 Notation

Bibliography

General-Reference Books

General-Reference Journals and Magazines

Exercises

Programming Exercise (Part 1)

Matlab Exercise 1

Chapter 2 Spatial Descriptions and Transformations

2.1 Introduction

2.2 Descriptions: Positions, Orientations, and Frames

Description of a Position

Description of an Orientation

Description of a Frame

2.3 Mappings: Changing Descriptions from Frame to Frame

Mappings Involving Translated Frames

Mappings Involving Rotated Frames

Mappings Involving General Frames

2.4 Operators: Translations, Rotations, and Transformations

Translational Operators

Rotational Operators

Transformation Operators

2.5 Summary of Interpretations

2.6 Transformation Arithmetic

Compound Transformations

Inverting a Transform

2.7 Transform Equations

2.8 More on Representation of Orientation

X–Y–Z Fixed Angles

Z–Y–X Euler Angles

Z–Y–Z Euler Angles

Other Angle-Set Conventions

Equivalent Angle–Axis Representation

Euler Parameters

Taught and Predefined Orientations

2.9 Transformation of Free Vectors

2.10 Computational Considerations

Bibliography

Exercises

Programming Exercise (Part 2)

Matlab Exercise 2A

Matlab Exercise 2B

Chapter 3 Manipulator Kinematics

3.1 Introduction

3.2 Link Description

3.3 Link-Connection Description

Intermediate Links in the Chain

First and Last Links in the Chain

Link Parameters

3.4 Convention for Affixing Frames to Links

Intermediate Links in the Chain

First and Last Links in the Chain

Summary of the Link Parameters in Terms of the Link Frames

Summary of Link-Frame Attachment Procedure

3.5 Manipulator Kinematics

Derivation of Link Transformations

Concatenating Link Transformations

3.6 Actuator Space, Joint Space, and Cartesian Space

3.7 Examples: Kinematics of Two Industrial Robots

The PUMA 560

The Yasukawa Motoman L-3

3.8 Frames with Standard Names

The Base Frame, {B}

The Station Frame, {S}

The Wrist Frame, {W}

The Tool Frame, {T}

The Goal Frame, {G}

3.9 Where is the Tool?

3.10 Computational Considerations

Bibliography

Exercises

Programming Exercise (Part 3)

Matlab Exercise 3

Chapter 4 Inverse Manipulator Kinematics

4.1 Introduction

4.2 Solvability

Existence of Solutions

Multiple Solutions

Method of Solution

4.3 The Notion of Manipulator Subspace When n<6

4.4 Algebraic vs. Geometric

Algebraic Solution

Geometric Solution

4.5 Algebraic Solution by Reduction to Polynomial

4.6 Pieper’s Solution When Three Axes Intersect

4.7 Examples of Inverse Manipulator Kinematics

The Unimation PUMA 560

The Yasukawa Motoman L-3

4.8 The Standard Frames

4.9 Solve-ing a Manipulator

4.10 Repeatability and Accuracy

4.11 Computational Considerations

Bibliography

Exercises

Programming Exercise (Part 4)

Matlab Exercise 4

Chapter 5 Jacobians: Velocities and Static Forces

5.1 Introduction

5.2 Notation for Time-Varying Position and Orientation

Differentiation of Position Vectors

The Angular Velocity Vector

5.3 Linear and Rotational Velocity of Rigid Bodies

Linear Velocity

Rotational Velocity

Simultaneous Linear and Rotational Velocity

5.4 More on Angular Velocity

A Property of the Derivative of an Orthonormal Matrix

Velocity of a Point Due to Rotating Reference Frame

Skew-Symmetric Matrices and the Vector Cross-Product

Gaining Physical Insight Concerning the Angular-Velocity Vector

Other Representations of Angular Velocity

5.5 Motion of the Links of a Robot

5.6 Velocity “Propagation” from Link to Link

5.7 Jacobians

Changing a Jacobian’s Frame of Reference

5.8 Singularities

5.9 Static Forces in Manipulators

5.10 Jacobians in the Force Domain

5.11 Cartesian Transformation of Velocities and Static Forces

Bibliography

Exercises

Programming Exercise (Part 5)

Matlab Exercise 5

Chapter 6 Manipulator Dynamics

6.1 Introduction

6.2 Acceleration of a Rigid Body

Linear Acceleration

Angular Acceleration

6.3 Mass Distribution

6.4 Newton’s Equation, Euler’s Equation

Newton’s Equation

Euler’s Equation

6.5 Iterative Newton Euler Dynamic Formulation

Outward Iterations to Compute Velocities and Accelerations

The Force and Torque Acting on a Link

Inward Iterations to Compute Forces and Torques

The Iterative Newton–Euler Dynamics Algorithm

Inclusion of Gravity Forces in the Dynamics Algorithm

6.6 Iterative vs. Closed Form

6.7 An Example of Closed-Form Dynamic Equations

6.8 The Structure of a Manipulator’s Dynamic Equations

The State-Space Equation

The Configuration-Space Equation

6.9 Lagrangian Formulation of Manipulator Dynamics

6.10 Formulating Manipulator Dynamics in Cartesian Space

The Cartesian State-Space Equation

The Cartesian Configuration Space Torque Equation

6.11 Inclusion of Nonrigid Body Effects

6.12 Dynamic Simulation

6.13 Computational Considerations

A Historical Note Concerning Efficiency

Efficiency of Closed Form vs. that of Iterative Form

Efficient Dynamics for Simulation

Memorization Schemes

Bibliography

Exercises

Programming Exercise (Part 6)

Matlab Exercise 6A

Matlab Exercise 6B

Matlab Exercise 6C

Chapter 7 Trajectory Generation

7.1 Introduction

7.2 General Considerations in Path Description and Generation

7.3 Joint-Space Schemes

Cubic Polynomials

Cubic Polynomials for a Path with via Points

Higher-Order Polynomials

Linear Function with Parabolic Blends

Linear Function with Parabolic Blends for a Path with via Points

7.4 Cartesian-Space Schemes

Cartesian Straight-Line Motion

7.5 Geometric Problems with Cartesian Paths

Problems of Type 1: Intermediate Points Unreachable

Problems of Type 2: High Joint Rates Near Singularity

Problems of Type 3: Start and Goal Reachable in Different Solutions

7.6 Path Generation at Run Time

Generation of Joint-Space Paths

Generation of Cartesian-Space Paths

7.7 Description of Paths with a Robot Programming Language

7.8 Planning Paths When Using the Dynamic Model

7.9 Collision-Free Path Planning

Bibliography

Exercises

Programming Exercise (Part 7)

Matlab Exercise 7

Chapter 8 Manipulator-Mechanism Design

8.1 Introduction

8.2 Basing the Design on Task Requirements

Number of Degrees of Freedom

Workspace

Load Capacity

Speed

Repeatability and Accuracy

8.3 Kinematic Configuration

Cartesian

Articulated

SCARA

Spherical

Cylindrical

Wrists

8.4 Quantitative Measures of Workspace Attributes

Efficiency of Design in Terms of Generating Workspace

Designing Well-Conditioned Workspaces

8.5 Redundant and Closed-Chain Structures

Micromanipulators and Other Redundancies

Closed-Loop Structures

8.6 Actuation Schemes

Actuator Location

Reduction and Transmission Systems

8.7 Stiffness and Deflections

Flexible Elements in Parallel and in Series

Shafts

Gears

Belts

Links

Actuators

8.8 Position Sensing

8.9 More on Optical Encoders

8.10 Force Sensing

Force-Sensor Design Issues

Bibliography

Exercises

Programming Exercise (Part 8)

Matlab Exercise 8

Chapter 9 Linear Control of Manipulators

9.1 Introduction

9.2 Feedback and Closed-Loop Control

9.3 Second-Order Linear Systems

Real and Unequal Roots

Complex Roots

Real and Equal Roots

9.4 Control of Second-Order Systems

9.5 Control-Law Partitioning

9.6 Trajectory-Following Control

9.7 Disturbance Rejection

Steady-State Error

Addition of an Integral Term

9.8 Continuous vs. Discrete Time Control

9.9 Modeling and Control of a Single Joint

Motor-Armature Inductance

Effective Inertia

Unmodeled Flexibility

Estimating Resonant Frequency

Control of a Single Joint

9.10 Architecture of an Industrial-Robot Controller

Bibliography

Exercises

Programming Exercise (Part 9)

Matlab Exercise 9

Chapter 10 Nonlinear Control of Manipulators

10.1 Introduction

10.2 Nonlinear and Time-Varying Systems

10.3 Multi-Input, Multi-Output Control Systems

10.4 The Control Problem for Manipulators

10.5 Practical Considerations

Time Required to Compute the Model

Feedforward Nonlinear Control

Dual-Rate Computed-Torque Implementation

Lack of Knowledge of Parameters

10.6 Current Industrial-Robot Control Systems

Individual-Joint PID Control

Addition of Gravity Compensation

Various Approximations of Decoupling Control

10.7 Lyapunov Stability Analysis

10.8 Cartesian-Based Control Systems

Comparison with Joint-Based Schemes

Intuitive Schemes of Cartesian Control

Cartesian Decoupling Scheme

10.9 Adaptive Control

Bibliography

Exercises

Programming Exercise (Part 10)

Chapter 11 Force Control of Manipulators

11.1 Introduction

11.2 Application of Industrial Robots to Assembly Tasks

11.3 A Framework for Control in Partially Constrained Tasks

11.4 The Hybrid Position/Force Control Problem

11.5 Force Control of a Mass Spring System

11.6 The Hybrid Position/Force Control Scheme

A Cartesian Manipulator Aligned with {C}

A General Manipulator

Adding Variable Stiffness

11.7 Current Industrial-Robot Control Schemes

Passive Compliance

Compliance through Softening Position Gains

Force Sensing

Bibliography

Exercises

Programming Exercise (Part 11)

Chapter 12 Robot Programming Languages and Systems

12.1 Introduction

12.2 The Three Levels of Robot Programming

Teach by Showing

Explicit Robot Programming Languages

Task-Level Programming Languages

12.3 A Sample Application

12.4 Requirements of a Robot Programming Language

World Modeling

Motion Specification

Flow of Execution

Programming Environment

Sensor Integration

12.5 Problems Peculiar to Robot Programming Languages

Internal World Model versus External Reality

Context Sensitivity

Error Recovery

Bibliography

Exercises

Programming Exercise (Part 12)

Chapter 13 Off-Line Programming Systems

13.1 Introduction

13.2 Central Issues in OLP Systems

User Interface

3-D Modeling

Kinematic Emulation

Path-Planning Emulation

Dynamic Emulation

Multiprocess Simulation

Simulation of Sensors

Language Translation to Target System

Workcell Calibration

13.3 The ‘Pilot’ Simulator

Physical Modeling and Interactive Systems

Geometric Algorithms for Part Tumbling

Stable-State Probabilities

Adjusting Probabilities as a Function of Drop Height

Simulation of Bounce

Simulation of Stacking and Tangling

Geometric Algorithms for Part Grasping

Computing Which Part to Grasp

Computation of Default Grasp Location

Computation of Alignment of the Part During Grasp

Geometric Algorithms for Part Pushing

Geometric Algorithms for Tray Conveyors

Connecting Tray Conveyors and Sources and Sinks

Pushing of Trays

Geometric Algorithms for Sensors

Proximity Sensors

2-D Vision Systems

Inspector Sensors

Conclusion

13.4 Automating Subtasks in OLP Systems

Automatic Robot Placement

Collision Avoidance and Path Optimization

Automatic Planning of Coordinated Motion

Force-Control Simulation

Automatic Scheduling

Automatic Assessment of Errors and Tolerances

Bibliography

Exercises

Programming Exercise (Part 13)

Appendix A Trigonometric Identities

Appendix B The 24 Angle-Set Conventions

Appendix C Some Inverse-Kinematic Formulas

Solutions to Selected Exercises

Chapter 2 Spatial Descriptions and Transformations Exercises

Chapter 3 Manipulator Kinematics Exercises

Chapter 5 Jacobians: Velocities and Static Forces Exercises

Chapter 6 Manipulator Dynamics Exercises

Chapter 7 Trajectory Generation Exercises

Chapter 10 Nonlinear Control of Manipulators Exercises

Chapter 11 Force Control of Manipulators Exercises

Index