# Second edition

A Geometric Introduction to Robotics and Manipulation |

Second Edition |

Richard M. Murray, Zexiang Li and S. Shankar Sastry |

This page contains information on the second edition of *A Mathematical Introduction to Robotic Manipulation*. This book is currently being written and is expected to be available from CRC Press in 2012.

### Table of Contents

New sections (or those containing substantial new material) are marked in blue. Tentative sections for inclusion in the second edition are marked in red.

Chapter 1. Introduction

- Brief History
- Outline of the Book
- Bibliography

Chapter 2. Rigid Body Motion

- Rigid Body Transformations
- Rotational Motion in R^3
- Rigid Motion in R^3
- Velocity of a Rigid Body
- Wrenches and Reciprocal Screws
- Summary
- Exercises

Chapter 3. Manipulator Kinematics

- Introduction
- Forward Kinematics
- Inverse Kinematics
- The Manipulator Jacobian
- Redundant Manipulators
- Bibliography
- Exercises

Chapter 4. Manipulator Dynamics

- Introduction
- Lagrange's Equations
- Dynamics of Open-Chain Manipulators
- Coordinate Invariant Algorithms
- Lagrange's Equations with Constraints
- Bibliography
- Exercises

Chapter 5. Manipulator Control

- Introduction
- Trajectory Generation
- Position Control and Trajectory Tracking
- Control of Constrained Manipulators
- PD Control on Lie Groups*
- Bibliography
- Exercises

Chapter 6. Parallel Manipulators

- Introduction
- Configuration Space and Singularities
- Singularity Classification
- Dynamics and Control
- Bibliography
- Exercises

Chapter 7. Mechanism Synthesis and Design

- Introduction
- Constrained Rigid Motions
- Synthesis of Open-Chain Manipulators
- Synthesis of Parallel Manipulators
- Mechanism Design
- Bibliography
- Exercises

Chapter 8. Multifingered Grasping and Manipulation

- Introduction to Grasping
- Grasp Statics
- Force-Closure
- Grasp Planning
- Grasp constraints
- Kinematics of Contact
- Hand KInematics
- Grasp Force Optimization
- Coordinated Control
- Bibliography
- Exercises

Chapter 9. Nonholonomic Systems and Motion Planning

- Introduction
- Controllability and the Frobenius theorem
- Examples of Nonholonomic Systems
- Nonholonomic Planning Using Differential Flatness
- Locomotion Systems
- Bibliography
- Exercises

Appendix A. Lie Groups and Robot Kinematics

- Differentiable Manifolds
- Lie Groups
- The Geometry of the Euclidean Group

Appendix B. Lyapunov Stability Theory