INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

http://www.cds.caltech.edu/%7Emurray/books/MLS/pdf/mls94-complete.pdf

A Mathematical Introduction to Robotic Manipulation

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Basic problems in stability and design of switched systems

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.

Perspectives and results on the stability and stabilizability of hybrid systems

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

An attitude control problem for a tethered spacecraft is studied. The tethered spacecraft is viewed as a multibody spacecraft consisting of a base body, a massless tether that connects the base body and an end mass, and tether actuator dynamics. Moments about the pitch and roll axes of the base spacecraft arise by control of the point of attachment of the tether to the base spacecraft. The control objective is to stabilize the attitude of the base spacecraft while keeping the perturbations of the tether small. Analysis shows that linear equations of motion for the tethered spacecraft are not completely controllable. We study two different control design approaches: (I) we decouple the attitude dynamics from the tether dynamics and we design a linear feedback to achieve stabilization of the attitude dynamics, and (2) we decouple the controllable modes from the uncontrollable mode using Kalman decomposition and we design a linear feedback to achieve stabilization of the controllable modes. Simulation results show that, although it is difficult to control the tether, the tether motion can be maintained within an acceptable range while subilizing the attitude dynamics of the base spacecraft.

Attitude control of a tethered spacecraft

In the context of modern control theory, optimum performance of a system is of primary concern. In most applications, however, one must be satisfied with something short of optimum performance as a consequence of the use of a suboptimal controller or plant parameter variations. Using a scalar measure for the deviation of the actual performance, a general approach to the evaluation of suboptimality and sensitivity for control and filtering processes is suggested. Some specific results involving only algebraic conditions are obtained.

Evaluation of suboptimality and sensitivity in control and filtering processes

https://ieeexplore.ieee.org/iel5/9/24095/01098585.pdf

On equivalent systems in optimal control and stability theory

We study control problems for a specific mechanical system consisting of a rigid base body with an unactuated internal degree of freedom. The key assumptions are that the translational and rotational motion of the base body can be completely controlled by external forces and moments, while the internal degree of freedom is unactuated. This specific example is representative of a class of underactuated mechanical control systems that are not linearly controllable. This class of control problems presents major theoretical and practical difficulties, and such models do arise in important terrestrial and spacecraft applications. Our focus in this paper is on the simplest mechanical example in this class; it illustrates important features and difficulties associated with the class of such problems.

Control problems for planar motion of a rigid body with an unactuated internal degree of freedom

The control problem of time-optimal, rest to rest, slewing of a rigid body with flexible appendages through a large angle is considered. A finite dimesional time optimal slewing problem is proposed as a relaxation of an ill-posed infinite dimensional time optimal slewing problem. The optimal control history is shown to have an important time symmetry property. The switching times, final time and costates at mid-maneuver are shown to satisfy a system of nonlinear algebraic equations.

N.H. McClamroch

Papers

Attitude control of a tethered spacecraft

Evaluation of suboptimality and sensitivity in control and filtering processes

On equivalent systems in optimal control and stability theory

Control problems for planar motion of a rigid body with an unactuated internal degree of freedom

Time optimal slewing of a rigid body with flexible appendages