**Contemporary Mathematics**

Volume: 438;
2007;
192 pp;
Softcover

MSC: Primary 55; 58; 68;

Print ISBN: 978-0-8218-4246-1

Product Code: CONM/438

List Price: $65.00

Individual Member Price: $52.00

**Electronic ISBN: 978-0-8218-8117-0
Product Code: CONM/438.E**

List Price: $65.00

Individual Member Price: $52.00

# Topology and Robotics

Share this page *Edited by *
*M. Farber; R. Ghrist; M. Burger; D. Koditschek*

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.

#### Table of Contents

# Table of Contents

## Topology and Robotics

- Contents v6 free
- Preface vii8 free
- Winding numbers for networks with weak angular data 110 free
- The snake charmer's algorithm 1928
- Using a robot to learn geometric information from permutations of landmarks 3342
- Geometric descriptions of polygon and chain spaces 4756
- Diffusion over tensor fields via Lie group PDE flows: Lagrangian action approach 5968
- Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles 7584
- Symmetric Motion Planning 8594
- Topological complexity of formal spaces 105114
- Topological complexity of generic hyperplane complements 115124
- Homotopy Meaningful Hybrid Model Structures 121130
- Presentations for the cohomology rings of tree braid groups 145154
- Competitive Disconnection Detection in On-Line Mobile Robot Navigation 173182

#### Readership

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