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

On the Convergence of an improper Integral Evaluated along the Solution of a Differential Equation

A production system is modeled as a stochastic discrete-event process. The production system produces discrete parts from an infinite supply of raw materials. The production time for a part is exponentially distributed and can be affected by a control variable-the production rate, which can be adjusted only at production initiation epochs for the discrete parts. A short-term cost criterion is introduced to accommodate two primary economic factors: cost due to the control effort and cost based on missing production deadlines. This short-term cost function depends only on quantities in the production of a single part, but with a correction term to achieve better long-term performance. Two cases are considered in detail: one case where the penalty on missing the part production deadline is asymmetric and another case where the penalty is symmetric. In each case, the optimal operating policy is determined by minimizing the short-term cost function. Properties of the resultant optimal control policy are investigated; the closed-loop behavior of the production system under the optimal control policy is discussed for each case. >

Control of a discrete parts production system with random part production times to meet a given schedule

This note considers a linear estimation problem for a stochastic process viewed as the output signal of a linear second-order vector difference equation (VDE) driven by a white-noise input. An innovations approach is applied directly to develop the one-stage prediction estimator and associated error covariances. It is shown that the estimator can be expressed as a second-order recursion that preserves the mathematical structure of the given signal model with innovations feedback loops. It is also shown that the innovations can be computed through a first-order recursion in terms of one-stage prediction estimates and the measurements.

/pdf/signal-estimation-for-second-order-vector-difference-6otkwrsewy.pdf

Signal estimation for second-order vector difference equations

Consider a camera that moves through a stationary environment. The time-varying range to features in the camera's field of view may be estimated recursively using a sequence of images. We study processing these images adaptively; our goal is accurate range estimation and increased range map density in the presence of constrained computational resources. The problem of autonomous nap-of-the-earth rotorcraft flight motivates our work. An onboard camera and inertial measurement unit provide sensing for the construction of local range maps for an obstacle avoidance function. To provide more features yielding accurate range estimates, we assume a high resolution, high data rate camera. The resulting explosion in the image measurement data rate can be handled by selecting which measurements to process, and by making the best use of onboard computation in processing these measurements. Computer vision research provides many ideas on selecting which measurements to process. We study how to process the measurements. Specifically, for a single feature, we explore the idea of adaptively trading spatial resolution and image rate to obtain accurate range estimation while simultaneously satisfying an upper limit on computation rate. Simulations are presented to explore the effectiveness of this idea. Our work is applicable to other vision-based ranging problems.

Adaptive Processing for Vision-Based Ranging

This paper considers a linear estimation problem for a stochastic process viewed as the output signal of a linear second-order vector difference equation (VDE) driven by a white-noise input. An innovations approach is applied directly to develop the one-stage prediction estimator and associated error covariances. It is shown that the estimator can be expressed as a second-order recursion that preserves the mathematical structure of the given signal model with innovations feedback loops. It is also shown that the innovations can be computed through a first-order recursion in terms of one-stage prediction estimates and the measurements. Formulas for the filtered estimate and the associated error covariance matrices are developed in terms of the corresponding error quantities.

N.H. McClamroch

Papers

On the Convergence of an improper Integral Evaluated along the Solution of a Differential Equation

Control of a discrete parts production system with random part production times to meet a given schedule

Signal estimation for second-order vector difference equations

Adaptive Processing for Vision-Based Ranging

Signal estimation for second-order vector difference equations