NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine.
This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine.
The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce Alberts is president of the National Academy of Sciences.
The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. William A. Wulf is interim president of the National Academy of Engineering.
The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine.
The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. William A. Wulf are chairman and interim vice-chairman, respectively, of the National Research Council.
The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the Board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the Board is designed to conduct studies for federal agencies and maintain liaison with the mathematical sciences communities and academia, professional societies, and industry.
The Board on Mathematical Sciences is supported by core funding from the following federal agencies: Air Force Office of Scientific Research, Army Research Office, Department of Energy, National Science Foundation, National Security Agency, and Office of Naval Research. This activity was supported by core funding. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the organizations or agencies that provided support for the Board.
Copyright 1997 by the National Academy of Sciences. All rights reserved.
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Cover: Rolling your finger in a circular motion on a rolling sphere generates rotations. Drawing courtesy of Jerrold E. Marsden, California Institute of Technology.
BOARD ON MATHEMATICAL SCIENCES
AVNER FRIEDMAN,
University of Minnesota,
Chair
LOUIS AUSLANDER,
City University of New York
MARY ELLEN BOCK,
Purdue University
PETER E. CASTRO,
Eastman Kodak Company
FAN R.K. CHUNG,
University of Pennsylvania
R. DUNCAN LUCE,
University of California, Irvine
ROBERT MACPHERSON,
Institute for Advanced Study
SUSAN MONTGOMERY,
University of Southern California
GEORGE NEMHAUSER,
Georgia Institute of Technology
ANIL NERODE,
Cornell University
DIANNE P. O'LEARY,
University of Maryland
INGRAM OLKIN,
Stanford University
RONALD F. PEIERLS,
Brookhaven National Laboratory
DONALD ST. P. RICHARDS,
University of Virginia
WILLIAM P. ZIEMER,
Indiana University
Ex Officio Member
DARYL PREGIBON,
Bell Laboratories
Chair,
Committee on Applied and Theoretical Statistics
Staff
JOHN R. TUCKER, Director
RUTH E. O'BRIEN, Staff Associate
BARBARA W. WRIGHT, Administrative Assistant
COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS
ROBERT J. HERMANN,
United Technologies Corporation,
Co-chair
W. CARL LINEBERGER,
University of Colorado,
Co-chair
PETER M. BANKS,
Environmental Research Institute of Michigan
LAWRENCE D. BROWN,
University of Pennsylvania
RONALD G. DOUGLAS,
Texas A&M University
JOHN E. ESTES,
University of California, Santa Barbara
L. LOUIS HEGEDUS,
Elf Atochem North America Inc.
JOHN E. HOPCROFT,
Cornell University
RHONDA J. HUGHES,
Bryn Mawr College
SHIRLEY A. JACKSON,
U.S. Nuclear Regulatory Commission
KENNETH H. KELLER,
University of Minnesota
KENNETH I. KELLERMANN,
National Radio Astronomy Observatory
MARGARET G. KIVELSON,
University of California, Los Angeles
DANIEL KLEPPNER,
Massachusetts Institute of Technology
JOHN KREICK,
Sanders, a Lockheed Martin Company
MARSHA I. LESTER,
University of Pennsylvania
THOMAS A. PRINCE,
California Institute of Technology
NICHOLAS P. SAMIOS,
Brookhaven National Laboratory
L.E. SCRIVEN,
University of Minnesota
SHMUEL WINOGRAD,
IBM T.J. Watson Research Center
CHARLES A. ZRAKET,
Mitre Corporation (retired)
NORMAN METZGER, Executive Director
Preface
The symposium "Motion, Control, and Geometry" was held on April 12, 1994, at the National Academy of Sciences in Washington, D.C. This symposium focused on control theory as a fundamental aspect of motion generation in many emerging areas. Those areas include microsurgery (for example, involving microrobots or "snakes" capable of locomotion in confined spaces such as an intestinal tract), spacecraft positioning, biological and robotic movement, motor miniaturization, and motion engineering (for instance, via coupled-oscillator pattern generation). Traditional control theory methods have been supplemented by the growing body of techniques associated with dynamical systems and geometric mechanics.
This symposium addressed the exciting interdisciplinary synergy that is developing on the basis of theoretical insight and technological inventiveness. The speakers at the symposium discussed both cutting-edge research and technology developments. The symposium and proceedings will help to inform researchers, practitioners, federal and state program managers, policy experts, and decision makers, as well as the scientific, engineering, and technology communities, of important issues in the mathematical sciences and of the relation of the mathematical sciences to other areas and to national interests. The Board on Mathematical Sciences, which organized the symposium, hopes the information presented here will help foster increased awareness of how research on questions of fundamental interest often can naturally connect to practical benefits for the nation and society.
Contents
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Geometric Foundations of Motion and Control |
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Cycles That Effect Change |
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Geometric Phases, Control Theory, and Robotics |
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Motion Control and Coupled Oscillators |
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