This book offers a unique compendium of the authors´ own research on the use of theoretical stability analysis, showing how to take advantage of local stability design and ultimate boundedness for practical robot control. It addresses researchers and postgraduate students dealing with control theory, particularly with nonlinear systems. Thanks to the numerous worked examples, it could also be used as a textbook in postgraduate courses.
Author(s): Marco A. Arteaga, Alejandro Gutiérrez-Giles, Javier Pliego-Jiménez
Series: Lecture Notes in Electrical Engineering, 798
Publisher: Springer
Year: 2021
Language: English
Pages: 388
City: Cham
Preface
Contents
Part I Preliminaries
1 A General Overview of Robot Manipulators
1.1 Brief History of Robot Manipulators
1.2 Industrial Robots
1.3 Common Kinematic Arrangements
1.3.1 Articulated Manipulator
1.3.2 Spherical Manipulator
1.3.3 SCARA Manipulator
1.3.4 Cylindrical Manipulator
1.3.5 Cartesian Manipulator
1.4 Wrists and End-Effectors
1.4.1 Spherical Wrist
1.4.2 Common End-Effectors
1.5 Some Other Important Issues to Take into Account
References
2 Position, Orientation and Velocity of Rigid Robot Manipulators
2.1 Rigid Motions and Homogeneous Transformations
2.1.1 Rotations
2.1.2 Composition of Rotations
2.1.3 Different Parametrizations for Rotation Matrices
2.1.4 Unit Quaternion
2.1.5 Homogeneous Transformations
2.1.6 Skew Symmetric Matrices
2.1.7 Angular Velocity and Acceleration
2.2 Direct Kinematics
2.2.1 Kinematic Chains
2.2.2 The Denavit-Hartenberg Representation
2.3 Inverse Kinematics
2.3.1 Introduction
2.3.2 Kinematic Decoupling
2.3.3 Inverse Position
2.4 Differential Kinematics
2.4.1 Analytic Jacobian
2.4.2 Geometric Jacobian
2.4.3 Singularities
References
3 Dynamics of Rigid Robot Manipulators
3.1 Dynamic Modeling of Rigid Robot Manipulators
3.1.1 Euler-Lagrange Equations of Motion
3.1.2 Kinetic Energy
3.1.3 Potencial Energy
3.2 Equations of Motion of a Robot Manipulator
3.2.1 Generalized Model
3.3 Inclusion of Environmental Forces
3.4 Model Properties
3.4.1 Vectors and Matrices Properties
3.4.2 Norm Related Properties
3.4.3 Whole Model Related Properties
3.4.4 Holonomic Constraints Properties
3.5 Inclusion of DC Motors in the Robot Dynamic Model
References
4 Mathematical Background
4.1 Basic Definitions and Lemmas
4.2 Stability in the Sense of Lyapunov
4.2.1 Definition
4.2.2 Main Stability Theorem
4.2.3 Complementary Results
4.3 Ultimate Boundedness
4.3.1 Definition
4.3.2 An Ultimate Boundedness Theorem
4.4 Sliding Surfaces
References
5 Common Control Approaches for Robot Manipulators
5.1 PD and PD+ Control
5.2 PID Control of Robot Manipulators
5.3 Computed Torque Control
5.4 Exploiting the Passive Structure of Robot Manipulators
5.5 Design in Work Space Coordinates
References
Part II Looking for Semiglobal Stability or Ultimate Boundedness
6 Velocity Observer Design
6.1 The Nicosia and Tomei Observer
6.2 Non Model Based Observer Design
6.3 Non Model Based Observer and Control Design
6.4 Experimental Results
References
7 Adaptive and Robust Control
7.1 The Adaptive Law by Slotine and Li
7.2 Adaptive Scheme with Velocity Observers
7.3 Robust Control
7.4 Control-Observer Robust Scheme
7.5 Generalized Proportional Integral (GPI) Observer
7.6 GPI Observer Without Inertia Matrix
7.7 Experimental Results
7.7.1 Performance Comparison
References
8 Force Control
8.1 Robot Force Control Without Dynamic Model
8.2 Velocity and Force Observers for the Control of Robot Manipulators
8.3 GPI Based Velocity/Force Observer Design for Robot Manipulators
8.4 Experimental Results
References
9 Bilateral Teleoperation
9.1 Fundamental Concepts of Bilateral Manipulators Systems
9.2 Control and Observer Design
9.3 Experimental Results
References
10 Robot Networks
10.1 Basic Characteristic of Robot Networks
10.2 Leaderless Consensus Problem (LCP)
10.3 Experimental Results
10.3.1 Leader-Follower Consensus Problem
References
Part III Different Testbeds and the Adaptation of Industrial Robots for Practical Implementation
11 The Robot CRS 465
11.1 Characteristics of the Robot CRS A465
11.2 Kinematics of the Robot A465
11.3 Dynamics of the Robot A465
12 The Robot CRS 255
12.1 Characteristics of the Robot CRS A255
12.2 Kinematics of the Robot A255
12.3 Dynamics of the Robot A255
13 Adapting the Robots CRS 465 and 255 for Original Control Laws Implementation
13.1 Original System
13.2 Hardware Modification
13.2.1 Signal Routing
13.2.2 Digital Stage for the A465 Manipulator
13.2.3 Digital Stage for the A255 Manipulator
13.2.4 Analog Stage
13.2.5 Power Stage and Electric Protections
13.3 Software Implementation
Reference
14 The Geomagic Touch Haptic Device
14.1 Characteristics of the Geomagic Touch Manipulator
14.1.1 Kinematics of the Full Five DoF Robot
14.1.2 Direct Kinematics of the Full Five DoF Robot
14.1.3 Differential Kinematics of the Full Five DoF Robot
14.1.4 Dynamics of the Full Five DoF Robot
14.2 Simplified Three DoF Geomagic Touch
14.2.1 Kinematics of the Three DoF Robot
14.2.2 Direct Kinematics of the Three DoF Robot
14.2.3 Differential Kinematics of the Three DoF Robot
14.2.4 Dynamics of the Three DoF Robot
14.2.5 Linear Parametrization of the Three DoF Robot
