Local Stability and Ultimate Boundedness in the Control of Robot Manipulators

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