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