A Mathematical Introduction to Robotic Manipulation 1st Edition by Richard Murray 9781351469784 1351469789

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• ISBN 10: 1351469789 

• ISBN 13: 9781351469784

• Author: Richard Murray

A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation presents a mathematical formulation of the kinematics, dynamics, and control of robot manipulators. It uses an elegant set of mathematical tools that emphasizes the geometry of robot motion and allows a large class of robotic manipulation problems to be analyzed within a unified framework. The foundation of the book is a derivation of robot kinematics using the product of the exponentials formula. The authors explore the kinematics of open-chain manipulators and multifingered robot hands, present an analysis of the dynamics and control of robot systems, discuss the specification and control of internal forces and internal motions, and address the implications of the nonholonomic nature of rolling contact are addressed, as well. The wealth of information, numerous examples, and exercises make A Mathematical Introduction to Robotic Manipulation valuable as both a reference for robotics researchers and a text for students in advanced robotics courses. 

A Mathematical Introduction to Robotic Manipulation 1st Table of contents:

Chapter 1 Introduction
1 Brief History
2 Multifingered Hands and Dextrous Manipulation
3 Outline of the Book
3.1 Manipulation using single robots
3.2 Coordinated manipulation using multifingered robot hands
3.3 Nonholonomic behavior in robotic systems
4 Bibliography
Chapter 2 Rigid Body Motion
1 Rigid Body Transformations
2 Rotational Motion in ℝ3
2.1 Properties of rotation matrices
2.2 Exponential coordinates for rotation
2.3 Other representations
3 Rigid Motion in ℝ3
3.1 Homogeneous representation
3.2 Exponential coordinates for rigid motion and twists
3.3 Screws: a geometric description of twists
4 Velocity of a Rigid Body
4.1 Rotational velocity
4.2 Rigid body velocity
4.3 Velocity of a screw motion
4.4 Coordinate transformations
5 Wrenches and Reciprocal Screws
5.1 Wrenches
5.2 Screw coordinates for a wrench
5.3 Reciprocal screws
6 Summary
7 Bibliography
8 Exercises
Chapter 3 Manipulator Kinematics
1 Introduction
2 Forward Kinematics
2.1 Problem statement
2.2 The product of exponentials formula
2.3 Parameterization of manipulators via twists
2.4 Manipulator workspace
3 Inverse Kinematics
3.1 A planar example
3.2 Paden-Kahan subproblems
3.3 Solving inverse kinematics using subproblems
3.4 General solutions to inverse kinematics problems
4 The Manipulator Jacobian
4.1 End-effector velocity
4.2 End-effector forces
4.3 Singularities
4.4 Manipulability
5 Redundant and Parallel Manipulators
5.1 Redundant manipulators
5.2 Parallel manipulators
5.3 Four-bar linkage
5.4 Stewart platform
6 Summary
7 Bibliography
8 Exercises
Chapter 4 Robot Dynamics and Control
1 Introduction
2 Lagrange’s Equations
2.1 Basic formulation
2.2 Inertial properties of rigid bodies
2.3 Example: Dynamics of a two-link planar robot
2.4 Newton-Euler equations for a rigid body
3 Dynamics of Open-Chain Manipulators
3.1 The Lagrangian for an open-chain robot
3.2 Equations of motion for an open-chain manipulator
3.3 Robot dynamics and the product of exponentials formula
4 Lyapunov Stability Theory
4.1 Basic definitions
4.2 The direct method of Lyapunov
4.3 The indirect method of Lyapunov
4.4 Examples
4.5 Lasalle’s invariance principle
5 Position Control and Trajectory Tracking
5.1 Problem description
5.2 Computed torque
5.3 PD control
5.4 Workspace control
6 Control of Constrained Manipulators
6.1 Dynamics of constrained systems
6.2 Control of constrained manipulators
6.3 Example: A planar manipulator moving in a slot
7 Summary
8 Bibliography
9 Exercises
Chapter 5 Multifingered Hand Kinematics
1 Introduction to Grasping
2 Grasp Statics
2.1 Contact models
2.2 The grasp map
3 Force-Closure
3.1 Formal definition
3.2 Constructive force-closure conditions
4 Grasp Planning
4.1 Bounds on number of required contacts
4.2 Constructing force-closure grasps
5 Grasp Constraints
5.1 Finger kinematics
5.2 Properties of a multifingered grasp
5.3 Example: Two SCARA fingers grasping a box
6 Rolling Contact Kinematics
6.1 Surface models
6.2 Contact kinematics
6.3 Grasp kinematics with rolling
7 Summary
8 Bibliography
9 Exercises
Chapter 6 Hand Dynamics and Control
1 Lagrange’s Equations with Constraints
1.1 Pfaffian constraints
1.2 Lagrange multipliers
1.3 Lagrange-d’Alembert formulation
1.4 The nature of nonholonomic constraints
2 Robot Hand Dynamics
2.1 Derivation and properties
2.2 Internal forces
2.3 Other robot systems
3 Redundant and Nonmanipulable Robot Systems
3.1 Dynamics of redundant manipulators
3.2 Nonmanipulable grasps
3.3 Example: Two-fingered SCARA grasp
4 Kinematics and Statics of Tendon Actuation
4.1 Inelastic tendons
4.2 Elastic tendons
4.3 Analysis and control of tendon-driven fingers
5 Control of Robot Hands
5.1 Extending controllers
5.2 Hierarchical control structures
6 Summary
7 Bibliography
8 Exercises
Chapter 7 Nonholonomic Behavior in Robotic Systems
1 Introduction
2 Controllability and Frobenius’ Theorem
2.1 Vector fields and flows
2.2 Lie brackets and Frobenius’ theorem
2.3 Nonlinear Controllability
3 Examples of Nonholonomic Systems
4 Structure of Nonholonomic Systems
4.1 Classification of nonholonomic distributions
4.2 Examples of nonholonomic systems, continued
4.3 Philip Hall basis
5 Summary
6 Bibliography
7 Exercises
Chapter 8 Nonholonomic Motion Planning
1 Introduction
2 Steering Model Control Systems Using Sinusoids
2.1 First-order controllable systems: Brockett’s system
2.2 Second-order controllable systems
2.3 Higher-order systems: chained form systems
3 General Methods for Steering
3.1 Fourier techniques
3.2 Conversion to chained form
3.3 Optimal steering of nonholonomic systems
3.4 Steering with piecewise constant inputs
4 Dynamic Finger Repositioning
4.1 Problem description
4.2 Steering using sinusoids
4.3 Geometric phase algorithm
5 Summary
6 Bibliography
7 Exercises
Chapter 9 Future Prospects
1 Robots in Hazardous Environments
2 Medical Applications for Multifingered Hands
3 Robots on a Small Scale: Microrobotics
Appendix A Lie Groups and Robot Kinematics
1 Differentiate Manifolds
1.1 Manifolds and maps
1.2 Tangent spaces and tangent maps
1.3 Cotangent spaces and cotangent maps
1.4 Vector fields
1.5 Differential forms
2 Lie Groups
2.1 Definition and examples
2.2 The Lie algebra associated with a Lie group
2.3 The exponential map
2.4 Canonical coordinates on a Lie group
2.5 Actions of Lie groups
3 The Geometry of the Euclidean Group
3.1 Basic properties
3.2 Metric properties of SE(3)
3.3 Volume forms on SE(3)
Appendix B A Mathematica Package for Screw Calculus
Bibliography
Index

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