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Topology and Robotics
Edited by: M. Farber, University of Durham, United Kingdom, R. Ghrist, University of Illinois at Urbana-Champaign, IL, M. Burger, ETH, Zurich, Switzerland, and D. Koditschek, University of Pennsylvania, Philadelphia, PA
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Contemporary Mathematics
2007; 192 pp; softcover
Volume: 438
ISBN-10: 0-8218-4246-3
ISBN-13: 978-0-8218-4246-1
List Price: US$61
Member Price: US$48.80
Order Code: CONM/438
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Ever since the literary works of Čapek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science.

Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.

Readership

Graduate students and research mathematicians interested in the application of topological methods of robotics.

Table of Contents

  • R. Ghrist -- Winding numbers for networks with weak angular data
  • E. Rodriguez -- The snake charmer's algorithm
  • B. Tovar, L. Freda, and S. M. LaValle -- Using a robot to learn geometric information from permutations of landmarks
  • J.-Cl. Hausmann -- Geometric descriptions of polygon and chain spaces
  • Y. Gur and N. Sochen -- Diffusion over tensor fields via Lie group pde flows: Lagrangian action approach
  • M. Farber, M. Grant, and S. Yuzvinsky -- Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles
  • M. Farber and M. Grant -- Symmetric motion planning
  • L. Lechuga and A. Murillo -- Topological complexity of formal spaces
  • S. Yuzvinsky -- Topological complexity of generic hyperplane complements
  • A. D. Ames -- Homotopy meaningful hybrid model structures
  • D. Farley -- Presentations for the cohomology rings of tree braid groups
  • Y. Gabriely and E. Rimon -- Competitive disconnection detection in on-line mobile robot navigation
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