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Driven by the need to achieve superior control performances for robots with hyper degrees of freedom, the virtual decomposition control approach is thoroughly presented in this book. This approach uses subsystem (such as links and joints of a complex robot) dynamics to conduct control design, while guaranteeing the stability and convergence of the entire complex robot without compromising the rigorousness of the system analysis. The central concept of this approach is the definition of the virtual stability. The stability of the entire complex robot is mathematically equivalent to the virtual stability of every subsystem. This fact allows us to convert a large problem to a few simple problems with mathematical certainty.

This book comprises fourteen chapters. The first five chapters form the foundation of this approach. The remaining nine chapters are relatively independent. Starting from Chapter 6, each chapter deals with a particular type of systems including motor/transmission assemblies, hydraulic robots, coordinated multiple robots, space robots, humanoid robots, adaptive teleoperation, and modular robot manipulators. At the end, the extensions of this approach to distributed-parameter systems and to electrical circuits are given, paving the way for other applications to follow.

This book is intended for practitioners, researchers, and graduate students who have acquired fundamental knowledge on robotics and control systems and have been committed to achieving the best control performances on complex robotics systems and beyond.

Inhaltsverzeichnis

Frontmatter

Virtual Decomposition Control Theory

Frontmatter

Introduction

Abstract
Robots, with different definitions and unfinished scope, have substantially influenced our lives. As is by now well known, the term “robot” was initiated in Karel Capek’s 1921 play Rossum’s Universal Robots (RUR), and the concept quickly found its way into the popular imagination, becoming the subject of various dramas, books, and movies. The term “robotics” and the famous three laws of robotics were first introduced in Isaac Asimov’s science fiction. Real robots could be said to date from a collaboration between inventor George Devol and entrepreneur Joseph Engelberger in 1956 which established Unimation–the first company started robot business which characterizes the birth of robot-centered flexible automation.
Wen-Hong Zhu

Mathematical Preliminaries

Abstract
In this chapter, mathematical tools to be used throughout this book are given.
Starting from notation, this chapter presents spaces and groups first. After that, vectors and coordinate systems are introduced, particularly the body-frame referenced vector expressions are emphasized. Orientations expressed by quaternions are given. Then, linear/angular velocity vectors and force/moment vectors are defined, leading to the rigid body dynamics expressed in a body frame. Two functions to be used in the parameter adaptation are subsequently defined. Furthermore, the concept of the virtual decomposition is presented and the terminology of the virtual power flow is introduced, giving rise to the definition of the virtual stability in conjunction with a simple oriented graph. This chapter ends with a formal definition of algebraic loops.
Wen-Hong Zhu

Virtual Decomposition Control - A Two DOF Example

Abstract
In this chapter, the virtual decomposition control (VDC) approach is being presented with respect to a simple robot having two degrees of freedom (DOFs) in free motion. The purpose of this chapter is to give readers an intuitive impression and a detailed understanding on how this approach works.
Wen-Hong Zhu

Virtual Decomposition Control - General Formulation

Abstract
In this section, the general formulation of the virtual decomposition control (VDC) approach will be presented, aimed at achieving a full-dynamics-based control on robots with hyper degrees of freedom. At the beginning, a complex robot is virtually “broken” into “pieces” (subsystems) and is represented by a simple oriented graph. Then, the subsystem dynamics based control is applied to make each subsystem qualified to be virtually stable, subject to certain geometric and force constraints. The virtual stability of every subsystem results in the stability and convergence of the entire robot, in which the concept of virtual power flow plays a vital role in representing the dynamic interactions among the subsystems.
Wen-Hong Zhu

Virtual Decomposition Control Applications

Frontmatter

Control of Electrically Driven Robots

Abstract
The control of single-arm robot manipulators is one of the mostly studied topics in robotics community. With respect to this very popular type of systems, the application of the virtual decomposition control (VDC) approach will be demonstrated in this chapter. In the first part, the control of single-arm robot manipulators in free motion is to be mainly focused by showing how a robot manipulator is virtually decomposed into several rigid links and joints and how the control design for each link or joint can be conducted independently from the rest of the manipulator, while ensuring the virtual stability of every subsystem necessarily needed to guarantee the stability of the entire robot. Three joint control modes, namely torque control mode, current control mode, and voltage control mode, are to be presented in detail. In the second part of the chapter, the force control issues will be exploited.
Wen-Hong Zhu

Control of Motor/Transmission Assemblies

Abstract
The results in the previous chapters reveal that the dynamics of rigid bodies and the dynamics of joints are needed to conduct the virtual decomposition control (VDC) design. Consider the fact that a joint motor/transmission assembly consists of merely rigid bodies. A natural question is, therefore, raised about the possibility of replacing the joint dynamics by rigid body dynamics.
Wen-Hong Zhu

Control of Hydraulic Robots

Abstract
Hydraulic actuation has been widely used in industrial applications, attributed to its characteristic of having a large power to mass ratio. Although this feature dramatically increases the operational capability of a hydraulically driven robot, the inherent nonlinear dynamics associated with hydraulic cylinders substantially challenge the controller design. It is obvious that the specific difficulties existed in the control of hydraulically driven robots arise from the specific dynamics of the hydraulic cylinders.
Wen-Hong Zhu

Control of Coordinated Multiple Robot Manipulators

Abstract
The use of coordinated multiple robot manipulators to hold a common object is motivated by applications where the object to be transported is either too large or too heavy and, therefore, beyond the capacity of a single robot. When multiple robot manipulators holding a common object altogether, the number of the degrees of freedom (DOFs) of motion is often less than the number of total actuators. This over-actuation gives rise to the creation of the internal forces. Therefore, not only the motion but also the internal forces resulting from the over-actuation need to be controlled.
Wen-Hong Zhu

Control of Space Robots

Abstract
Space robot, referring to a robot manipulator or a group of robot manipulators mounted on a platform in a space orbit, possesses unique challenges to control and motion planning due to the nature of its underactuation leading to the existence of the nonholonomic constraints governed by the momentum conservation law. In general, there exist six nonholonomic constraints on each orbital space robot. These six nonholonomic constraints comprise three constraints for the linear motion and the other three constraints for the rotational motion. If thrusters are enabled in all three directions, the number of nonholonomic constraints reduces to three. In the control and motion planning, the three- or six-dimensional nonholonomic constraints that make the kinematics no longer independent of the dynamics need to be properly handled.
Wen-Hong Zhu

Control of Humanoid Robots

Abstract
Since “Asimo” was introduced by Honda in 2000, humanoid robots have drawn increasing attentions of both academics and general public. To make a humanoid robot function as expected, control plays a vital role. Unfortunately, due to the difficulties in implementing a full-dynamics-based real-time control for a humanoid robot with hyper degrees of freedom, most state-of-the-art control approaches use ZMP (zero moment point) technique in which the dynamic interactions among different parts of a robot are treated as disturbances and only the gravity compensation with a rough dynamic force prediction is integrated into the decentralized joint PID controller. The lack of a precise modeling, without doubting, limits the control performances of biped systems and consequently limits the speeds in dynamic walking.
Wen-Hong Zhu

Control of Force-Reflected Bilateral Teleoperation

Abstract
A teleoperated system can extend human’s reach to a remote site which is either hazard or impossible for humans to present. Examples include operations in nuclear facilities, in deep sea or deep space. Teleoperation systems can also enhance a human’s capability to handle both the macro and the micro worlds by scaling up or scaling down operation tasks for easy and accurate operations. Examples include hydraulic excavation and eye/brain surgeries.
Wen-Hong Zhu

Control of Modular Robot Manipulators

Abstract
Today’s robot manipulators are generally called integrated manipulators. Not only their mechanical structure, sensors, and actuators, but also their electronics and computing systems are specifically designed, fabricated, and integrated before being delivered to users. While being operationally effective and precise in well-structured assembly lines, these manipulators, on the other hand, possess weak adaptability, flexibility, and versatility against task variations in unstructured environments. The fact of having a fixed structure limits the capability of these integrated manipulators to perform a variety of tasks that require different robot structures with different degrees of freedom of motion. Besides being unable to have their structures changed on-site applications, the integrated robot manipulators are generally stand-along devices with separate control cabinets. This characteristic makes them difficult to be incorporated into mobile platforms.
Wen-Hong Zhu

Control of Flexible Link Robots

Abstract
Most applications discussed in the previous chapters are based on the rigid link (body) assumption. However, mechanical structures are flexible in nature. Rigidity is only an approximation when the flexibility is ignorable. In robotic applications, lightweight arms are always desirable due to their cost advantages, and long arms are needed for certain applications ranging from the assembly tasks of the International Space Station (ISS) to aircraft cleaning tasks. When either lightweight or long arms are used, the flexibility shows up inevitably regardless of the materials the arm is made of. This fact can be seen from the Euler-Bernoulli equation which implies that the static deformation of a uniform cantilever beam subject to a force at its free end is proportional to the third power of the beam length. By restricting robot control design to rigid models, the operational efficiency can be severely affected due to the extra time needed to damp out vibrations for safe executions of robotic tasks. This situation technically motivates the need of developing appropriate control approaches for flexible link robots.
Wen-Hong Zhu

Applications to Electrical Circuits

Abstract
In the previous chapters, the virtual decomposition control (VDC) approach has been extensively applied to a variety of robotic systems. In this chapter, this novel approach will be applied to electrical systems in terms of the duality between mechanical and electrical systems.
Wen-Hong Zhu

Backmatter

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