Topology and Robotics
About this Title
M. Farber, R. Ghrist, M. Burger and D. Koditschek, Editors
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.
Graduate students and research mathematicians interested in the application of topological methods of robotics.
Table of Contents
- Robert Ghrist – Winding numbers for networks with weak angular data [MR 2359025]
- Eugenio Rodriguez – The snake charmer’s algorithm [MR 2359026]
- Benjamín Tovar, Luigi Freda and Steven M. LaValle – Using a robot to learn geometric information from permutations of landmarks [MR 2359027]
- Jean-Claude Hausmann – Geometric descriptions of polygon and chain spaces [MR 2359028]
- Yaniv Gur and Nir Sochen – Diffusion over tensor fields via Lie group PDE flows: Lagrangian action approach [MR 2359029]
- Michael Farber, Mark Grant and Sergey Yuzvinsky – Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles [MR 2359030]
- Michael Farber and Mark Grant – Symmetric motion planning [MR 2359031]
- Luis Lechuga and Aniceto Murillo – Topological complexity of formal spaces [MR 2359032]
- Sergey Yuzvinsky – Topological complexity of generic hyperplane complements [MR 2359033]
- Aaron D. Ames – Homotopy meaningful hybrid model structures [MR 2359034]
- Daniel Farley – Presentations for the cohomology rings of tree braid groups [MR 2359035]
- Yoav Gabriely and Elon Rimon – Competitive disconnection detection in on-line mobile robot navigation [MR 2359036]