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

The dynamics of a dumbbell shaped spacecraft are modeled as two identical mass particles connected by a linear elastic spring. The equations of motion of the spacecraft in a planar orbit in a central gravitational field are presented. The equations of motion characterize orbit, attitude, and shape (or elastic deformation) degrees of freedom and the coupling between them. Relative equilibria, corresponding to circular planar orbits, are obtained from these equations of motion. Linear equations of motion that describe perturbations from these relative equilibria are presented. New dynamics and control problems are introduced for these linear equations. Controllability results are presented for various actuation assumptions, based on the linear equations.

Dynamics and control of an elastic dumbbell spacecraft in a central gravitational field

We study several flight control problems for the standard planar vertical take off and landing (PVTOL) flight control model, which has been developed as a simplified model for Harrier-like aircraft. In particular, we study the execution of a manoeuvre for which the aircraft is intended to follow a circular path in a vertical plane. We first formulate the problem as a nonlinear tracking control problem. Controllers are developed for two cases: a non-aggressive manoeuvre and an aggressive manoeuvre. We demonstrate the need to develop a controller that includes feedforward terms in order to achieve aggressive maneuvering. We next formulate a related path following or manoeuvre regulation problem. A controller is developed for this case, and it is compared with a controller that solves the related output tracking problem. This comparison demonstrates the practical value of the manoeuvre regulation controller. Our approach throughout is to make use of nonlinear control theory, which is complicated by the non-minimum phase characteristics of the PVTOL model.

A study of flight manoeuvres for the PVTOL aircraft model

A planar system of rigid bodies interconnected by one degree of freedom rotational joints is considered. This multibody system is referred to as a multilink, and the rigid bodies are referred to as links. The angular momentum of the multilink is conserved but is not necessarily zero. We show that if the number of links is at least four, then periodic joint motions can make the absolute orientation of a specified base link track exactly a specified function of time whose time derivative is periodic. This result on the use of periodic joint motions for orientation tracking extends previous work [15], [20], [22] on using periodic joint motions for rest-to-rest reorientation. It has interesting physical consequences. Specifically, in the case of non-zero angular momentum periodic joint motions can maintain the orientation of the base link constant. In the case of zero angular momentum periodic joint motions can change the orientation of the base link at a specified angular rate. We also demonstrate that if the multilink consists of at least three links, then for any value of the angular momentum joint motions can reorient the multilink arbitrarily over anarbitrary time interval. This result extends similar results in [15] for zero angular momentum and in [20] that apply for nonzero angular momentum but not for an arbitrary time interval. In terms of their control-theoretic aspects, the problems treated in the paper can be viewed as controllability problems for a class of nonlinear control system with time-dependent drift.

/pdf/new-results-on-control-of-multibody-systems-which-conserve-3jidceatir.pdf

New results on control of multibody systems which conserve angular momentum

We present a general intrinsic controller for stabilization of an arbitrary configuration of a fully actuated simple mechanical control system, evolving on a Riemannian manifold. We explicitly determine conditions for an error function on the configuration manifold and present a family of controllers. We show that under certain assumptions the controllers achieve stabilization with an almost global domain of attraction. The controllers do not cancel benign nonlinearities and can accommodate control saturation effects. Being intrinsic, we do not assume any coordinates. Finally, we illustrate our technique by explicitly deriving a control law that almost globally asymptotically stabilizes the inverted position of a spherical pendulum. Continuing this work by N. A. Chaturvedi, et al., we explicitly present error functions for many configuration manifolds encountered in engineering examples, and show how to design almost globally stabilizing controllers, under saturation effects. In this paper, we present the structure of such a controller and establish the properties of the resulting closed-loop.

Global stabilization of a fully actuated mechanical system on a Riemannian manifold: controller structure

We study several flight control problems for a conventional aircraft take off and landing (CTOL) flight control model, a simplified nonlinear model for aircraft longitudinal flight dynamics. In particular, we study the execution of a maneuver for which the aircraft is intended to follow a path in a vertical plane corresponding to a specified change in altitude. First we formulate the problem as a nonlinear output tracking control problem. Next we formulate a related path following or maneuver regulation problem. A controller is developed for this case, and it is compared with a controller that solves the related output tracking problem. This comparison demonstrates the practical value of the maneuver regulation controller. Our approach throughout is to make use of nonlinear control theory, which is complicated by the non-minimum phase characteristics of the CTOL model.

N.H. McClamroch

Papers

Dynamics and control of an elastic dumbbell spacecraft in a central gravitational field

A study of flight manoeuvres for the PVTOL aircraft model

New results on control of multibody systems which conserve angular momentum

Global stabilization of a fully actuated mechanical system on a Riemannian manifold: controller structure

Trajectory tracking control and maneuver regulation control for the CTOL aircraft model