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2010 | Buch

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Theory of Applied Robotics

Kinematics, Dynamics, and Control (2nd Edition)

verfasst von: Reza N. Jazar

Verlag: Springer US

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

The second edition of this book would not have been possible without the comments and suggestions from my students, especially those at Columbia University. Many of the new topics introduced here are a direct result of student feedback that helped me refine and clarify the material. My intention when writing this book was to develop material that I would have liked to had available as a student. Hopefully, I have succeeded in developing a reference that covers all aspects of robotics with sufficient detail and explanation. The first edition of this book was published in 2007 and soon after its publication it became a very popular reference in the field of robotics. I wish to thank the many students and instructors who have used the book or referenced it. Your questions, comments and suggestions have helped me create the second edition. Preface This book is designed to serve as a text for engineering students. It introduces the fundamental knowledge used in robotics. This knowledge can be utilized to develop computer programs for analyzing the kinematics, dynamics, and control of robotic systems.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

Law Zero: A robot may not injure humanity, or, through inaction, allow humanity to come to harm.

Law One: A robot may not injure a human being, or, through inaction, allow a human being to come to harm, unless this would violate a higher order law.

Law Two: A robot must obey orders given it by human beings, except where such orders would conflict with a higher order law.

Law Three: A robot must protect its own existence as long as such protection does not conflict with a higher order law.

Reza N. Jazar

Kinematics

Frontmatter

2. Rotation Kinematics

Abstract

Consider a rigid body with a fixed point. Rotation about the fixed point is the only possible motion of the body. We represent the rigid body by a body coordinate frame B, that rotates in another coordinate frame G, as is shown in Figure 2.1. We develop a rotation calculus based on transformation matrices to determine the orientation of B in G, and relate the coordinates of a body point P in both frames.

Reza N. Jazar

3. Orientation Kinematics

Abstract

We can decompose any rotation φ of a rigid body with a fixed point O, about a globally fixed axis û into three rotations about three given non coplanar axes. Furthermore, the finial orientation of a rigid body after a finite number of rotations is equivalent to a unique rotation about a unique axis. Determination of the angle and axis is called the orientation kinematics of rigid bodies.

Reza N. Jazar

4. Motion Kinematics

Abstract

A rotation φ about an axis û and a displacement d is the general motion of a rigid body B in a global frame G. The rigid body motion can be defined by a 4 by 4 matrix.

Reza N. Jazar

5. Forward Kinematics

Abstract

Having the joint variables of a robot, we are able to determine the position and orientation of every link of the robot, for a given set of geometrical characteristics of the robot. We attach a coordinate frame to every link and determine its configuration in the neighbor frames using rigid motion method. Such an analysis is called forward kinematics.

Reza N. Jazar

6. Inverse Kinematics

Abstract

What are the joint variables for a given configuration of a robot? This is the inverse kinematic problem. The determination of the joint variables reduces to solving a set of nonlinear coupled algebraic equations. Although there is no standard and generally applicable method to solve the inverse kinematic problem, there are a few analytic and numerical methods to solve the problem. The main difficulty of inverse kinematic is the multiple solutions such as the one that is shown in Figure 6.1 for a planar 2R manipulator.

Reza N. Jazar

7. Angular Velocity

Abstract

Angular velocity of a rotating body B in a global frame G is the instantaneous rotation of the body with respect to G. Angular velocity is a vectorial quantity. Using the analytic description of angular velocity, we introduce the velocity and time derivative of homogenous transformation matrices.

Reza N. Jazar

8. Velocity Kinematics

Abstract

Velocity analysis of a robot is divided into forward and inverse velocity kinematics. Having the time rate of joint variables and determination of the Cartesian velocity of end-effector in the global coordinate frame is the forward velocity kinematics. Determination of the time rate of joint variables based on the velocity of end-effector is the inverse velocity kinematics.

Reza N. Jazar

9. Numerical Methods in Kinematics

Abstract

By increasing the number of links, the analytic calculation in robotics becomes a tedious task and numerical calculations are needed. We review the most frequent needed numerical analysis in robotics.

Reza N. Jazar

Dynamics

Frontmatter

10. Acceleration Kinematics

Abstract

Angular acceleration of a rigid body with respect to a global frame is the time derivative of instantaneous angular velocity of the body. In general, it is a vectorial quantity that is in a different direction than angular velocity. We review and develop the acceleration kinematics of robots.

Reza N. Jazar

11. Motion Dynamics

Abstract

Relation between kinematics and the cause of change of kinematics is called the equation of motion. Derivation of equation of motion and the expression of their solution is called dynamics. We review the elements of equations of motion and methods of their derivation.

Reza N. Jazar

12. Robot Dynamics

Abstract

We find the dynamics equations of motion of robots by two methods: Newton-Euler and Lagrange. The Newton-Euler method is more fundamental and finds the dynamic equations to determine the required actuators’ force and torque to move the robot, as well as the joint forces. Lagrange method provides only the required differential equations that determines the actuators’ force and torque.

Reza N. Jazar

Control

Frontmatter

13. Path Planning

Abstract

Path planning includes three tasks: 1–Defining a geometric curve for the end-effector between two points. 2–Defining a rotational motion between two orientations. 3–Defining a time function for variation of a coordinate between two given values. All of these three definitions are called path planning. Figure 13.1 illustrates a path of the tip point of a 2R manipulator between points P1 and P2 to avoid two obstacles.

Reza N. Jazar

14. ★ Time Optimal Control

Abstract

The main job of an industrial robot is to move an object on a pre-specified path, rest to rest, repeatedly. To increase productivity, the robot should do its job in minimum time. We introduce a numerical method to solve the time optimal control problem of multi degree of freedom robots.

Reza N. Jazar

15. Control Techniques

Abstract

Using inverse kinematics, we can calculate the joint kinematics for a desired geometric path of the end-effector of a robot. Substitution of the joint kinematics in equations of motion provides the actuator commands. Applying the commands will move the end-effector of the robot on the desired path ideally. However, because of perturbations and non-modeled phenomena, the robot will not follow the desired path. The techniques that minimize or remove the difference are called the control techniques.

Reza N. Jazar

Backmatter

Titel: Theory of Applied Robotics
verfasst von: Reza N. Jazar
Verlag: Springer US
Electronic ISBN: 978-1-4419-1750-8
Print ISBN: 978-1-4419-1749-2
DOI: https://doi.org/10.1007/978-1-4419-1750-8

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