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

In this paper, we demonstrate that, in fact, two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished in a specific sense. The complete spacecraft dynamics cannot be stabilized to an equilibrium attitude. However, the spacecraft equations are small time locally controllable in a reduced nonlinear sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to an equilibrium attitude using a time-invariant continuous feedback control law, but a discontinuous feedback control strategy is constructed which asymptotically stabilizes an equilibrium attitude of the spacecraft. Consequently, arbitrary reorientation of the spacecraft can be accomplished using this discontinuous feedback control strategy.

Attitude stabilization of a rigid spacecraft using momentum wheel actuators operating in a failure mode

Three dimensional attitude and shape control problems are studied for a class of spacecraft with articulated appendages and reaction wheels. We provide a new unified formulation which includes many of the attitude control problems that have been studied previously. The development is based on a nonlinear, drift-free, control model that characterizes the attitude and shape change dynamics, assuming zero angular momentum of the system. Controllability results are presented for the general case, and specialized results are identified for interesting multibody spacecraft configurations. These results are made explicit by providing computable formulas for the Lie brackets in terms of the spacecraft geometry, inertial properties, and shape. Emphasis is given to the interplay between the shape change dynamics and the attitude change dynamics.

Three dimensional attitude and shape control of spacecraft with articulated appendages and reaction wheels

Formulates a conflict detection problem for two aircraft performing general flight maneuvers. The key ingredient is the development of probabilistic models for flight control errors that arise due to wind, navigational uncertainties, flight control errors and intent. It is assumed that each aircraft is performing a trimmed flight maneuver. Assumptions are made so that the relative position errors are characterized by a Chi-square distribution. The relative position errors of the aircraft are described by an ellipsoid that translates, rotates, and changes shape and size. The conflict detection problem is formulated in terms of suitable separation measures of this ellipsoid and an ellipsoid that defines a protected zone. A separation measure is introduced that provides an upper bound for the conflict probability. A simple and numerically efficient algorithm is given so that quantitative measures of the aircraft separation can be efficiently computed.

A computational approach to conflict detection problems for air traffic control

Feedback controllers that guarantee asymptotic stabilization of either the hanging equilibrium or the inverted equilibrium of the 3D pendulum are presented and experimentally evaluated using the triaxial attitude control testbed (TACT). Asymptotic stabilization results obtained previously are shown to guarantee almost global response properties, but the local response properties near the equilibrium show non-exponential convergence. These feedback controllers are modified to guarantee almost global response properties and improved local response near the equilibrium. Experimental results illustrate the closed loop time responses for various feedback controllers.

/pdf/experimental-results-for-almost-global-asymptotic-and-1msxb0h7if.pdf

Experimental results for almost global asymptotic and locally exponential stabilization of the natural equilibria of a 3D pendulum

The attitude dynamics of an air spindle and platform testbed, controlled by two proof mass actuators fixed to the platform, are studied assuming that the air spindle is not exactly vertical. A tilt angle of the air spindle induces a gravity moment that has a long term effect on the rotational dynamics. A mathematical model is used to study the free dynamics with the proof masses fixed, as a basis for parameter identification and to explain the longer term dynamics that have been observed in experiments. Feedback compensation for these gravity effects is discussed.

N.H. McClamroch

Papers

Attitude stabilization of a rigid spacecraft using momentum wheel actuators operating in a failure mode

Three dimensional attitude and shape control of spacecraft with articulated appendages and reaction wheels

A computational approach to conflict detection problems for air traffic control

Experimental results for almost global asymptotic and locally exponential stabilization of the natural equilibria of a 3D pendulum

Attitude control of a tilted air spindle testbed using proof mass actuators