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 |  موضوع: كتاب A Mathematical Introduction to Robotic Manipulation الثلاثاء 14 مايو 2013, 5:09 pm | |
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A Mathematical Introduction to Robotic Manipulation - Murray
ويتناول الموضوعات الأتية :
Introduction
Brief History
Multifingered Hands and Dextrous Manipulation
Outline of the Book
Manipulation using single robots
Coordinated manipulation using multifingered robot
hands
Nonholonomic behavior in robotic systems
Bibliography
Rigid Body Motion
Rigid Body Transformations
Rotational Motion in R
Properties of rotation matrices
Exponential coordinates for rotation
Other representations
Rigid Motion in R
Homogeneous representation
Exponential coordinates for rigid motion and twists
Screws: a geometric description of twists
Velocity of a Rigid Body
Rotational velocity
Rigid body velocity
Velocity of a screw motion
Coordinate transformations
Wrenches and Reciprocal Screws
Wrenches
Screw coordinates for a wrench
Reciprocal screws
Summary
Bibliography
Exercises
Manipulator Kinematics
Introduction
Forward Kinematics
Problem statement
The product of exponentials formula
Parameterization of manipulators via twists
Manipulator workspace
Inverse Kinematics
A planar example
Paden-Kahan subproblems
Solving inverse kinematics using subproblems
General solutions to inverse kinematics problems
The Manipulator Jacobian
End-effector velocity
End-effector forces
Singularities
Manipulability
Redundant and Parallel Manipulators
Redundant manipulators
Parallel manipulators
Four-bar linkage
Stewart platform
Summary
Bibliography
Exercises
Robot Dynamics and Control
Introduction
Lagrange’s Equations
Basic formulation
Inertial properties of rigid bodies
Example: Dynamics of a two-link planar robot
Newton-Euler equations for a rigid body
Dynamics of Open-Chain Manipulators
The Lagrangian for an open-chain robot
Equations of motion for an open-chain manipulator
Robot dynamics and the product of exponentials formula
Lyapunov Stability Theory
Basic definitions
The direct method of Lyapunov
The indirect method of Lyapunov
Examples
Lasalle’s invariance principle
Position Control and Trajectory Tracking
Problem description
Computed torque
PD control
Workspace control
Control of Constrained Manipulators
Dynamics of constrained systems
Control of constrained manipulators
Example: A planar manipulator moving in a slot
Summary
Bibliography
Exercises
Multifingered Hand Kinematics
Introduction to Grasping
Grasp Statics
Contact models
The grasp map
Force-Closure
Formal definition
Constructive force-closure conditions
Grasp Planning
Bounds on number of required contacts
Constructing force-closure grasps
Grasp Constraints
Finger kinematics
Properties of a multifingered grasp
Example: Two SCARA fingers grasping a box
Rolling Contact Kinematics
Surface models
Contact kinematics
Grasp kinematics with rolling
Summary
Bibliography
Exercises
Hand Dynamics and Control
Lagrange’s Equations with Constraints
Pfaffian constraints
Lagrange multipliers
Lagrange-d’Alembert formulation
The nature of nonholonomic constraints
Robot Hand Dynamics
Derivation and properties
Internal forces
Other robot systems
Redundant and Nonmanipulable Robot Systems
Dynamics of redundant manipulators
Nonmanipulable grasps
Example: Two-fingered SCARA grasp
Kinematics and Statics of Tendon Actuation
Inelastic tendons
Elastic tendons
Analysis and control of tendon-driven fingers
Control of Robot Hands
Extending controllers
Hierarchical control structures
Summary
Bibliography
Exercises
Nonholonomic Behavior in Robotic Systems
Introduction
Controllability and Frobenius’ Theorem
Vector fields and flows
Lie brackets and Frobenius’ theorem
Nonlinear controllability
Examples of Nonholonomic Systems
Structure of Nonholonomic Systems
Classification of nonholonomic distributions
Examples of nonholonomic systems, continued
Philip Hall basis
Summary
Bibliography
Exercises
Nonholonomic Motion Planning
Introduction
Steering Model Control Systems Using Sinusoids
First-order controllable systems: Brockett’s system
Second-order controllable systems
Higher-order systems: chained form systems
General Methods for Steering
Fourier techniques
Conversion to chained form
Optimal steering of nonholonomic systems
Steering with piecewise constant inputs
Dynamic Finger Repositioning
Problem description
Steering using sinusoids
Geometric phase algorithm
Summary
Bibliography
Exercises
Future Prospects
Robots in Hazardous Environments
Medical Applications for Multifingered Hands
Robots on a Small Scale: Microrobotics
A Lie Groups and Robot Kinematics
Lie Groups and Robot Kinematics
Differentiable Manifolds
Manifolds and maps
Tangent spaces and tangent maps
Cotangent spaces and cotangent maps
Vector fields
Differential forms
Lie Groups
Definition and examples
The Lie algebra associated with a Lie group
The exponential map
Canonical coordinates on a Lie group
Actions of Lie groups
The Geometry of the Euclidean Group
Basic properties
Metric properties of SE()
Volume forms on SE()
B A Mathematica Package for Screw Calculus
Bibliography
Index
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