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Motion, control, and geometry : proceedings of a symposium / Board on Mathematical Sciences, Commission on Physical Sciences, Mathematics, and Applications, National Research Council.
- Format:
- Book
- Series:
- Compass series (Washington, D.C.)
- The compass series
- Language:
- English
- Subjects (All):
- Automatic control--Congresses.
- Automatic control.
- Control theory--Congresses.
- Control theory.
- Motion--Congresses.
- Motion.
- Geometry--Congresses.
- Geometry.
- Physical Description:
- 1 online resource (80 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Washington, D.C. : National Academy Press, 1997.
- Language Note:
- English
- Summary:
- Some of the modem developments described in Motion, Control, and Geometry include the geometric control of robot motion and craft orientation, how high-power precision micromotors are engineered for less invasive surgery and self-focusing lens applications, what a mobile robot on a surface has in common with one moving in three dimensions, and how the motion-control problem is simplified by a coupled oscillator's geometric grouping of degrees of freedom and motion time scales. The four papers in these proceedings provide a view through the scientific portal of today's motion-control geometric research into tomorrow's technology. The mathematics needed to carry out this research is that of modem differential geometry, and the questions raised in the field of motion-control geometry go directly to the research frontier. Geometry is a mathematical area too often neglected nowadays in a student's education. This publication will help adjust the control initially imposed about 2,300 years ago on one kind of "motion"-that of students entering Plato's Academy, where the following caveat was inscribed above the doorway: "Let no one ignorant of geometry enter here." Readers of these chapters will gain an appreciation of modem geometry and how it continues to play a crucial role in the context of motion control in cutting-edge science and technology.
- Contents:
- MOTION, CONTROL, AND GEOMETRY
- Copyright
- Preface
- Contents
- Introduction
- 1 Geometric Foundations of Motion and Control
- INTRODUCTION
- CONNECTIONS AND BUNDLES
- CONSTRAINTS: ANGULAR MOMENTUM AND ROLLING
- STABILIZATION AND OPTIMAL CONTROL
- THE SNAKEBOARD
- ACKNOWLEDGMENTS
- REFERENCES
- 2 Cycles That Effect Change
- ORDER SOMETIMES MATTERS
- SIMPLE MACHINES AND THE AREA RULE
- VIBRATIONAL, ROTARY, AND LINEAR MOTION
- ELECTRICAL CIRCUITS WITH SWITCHES
- THREE THINGS FROM TWO THINGS
- CONCLUSIONS
- BIBLIOGRAPHY
- 3 Geometric Phases, Control Theory, and Robotics
- LOCOMOTION IN MOBILE ROBOTS
- GRASPING AND MANIPULATION
- APPLICATIONS
- Exploration of Mars
- Medical Robotics: Minimally Invasive Surgery
- CONCLUSIONS AND DISCUSSION
- 4 Motion Control and Coupled Oscillators
- FROM SHAPE CHANGE TO GLOBAL MOVEMENT
- SCRIPTS AND OSCILLATORS
- UNIFYING GEOMETRY
- SOME INTERESTING MACHINES
- Appendixes
- Appendix A Speakers
- Appendix B Symposium Participants.
- Notes:
- Symposium held on April 12, 1994, at the National Academy of Sciences in Washington, D.C.--Pref.
- Includes bibliographical references.
- ISBN:
- 0-309-17475-9
- 1-280-19147-3
- 9786610191475
- 0-309-59061-2
- 0-585-16858-X
- OCLC:
- 44964172
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