Past lectures

Abstract

Topological robotics is a newly created mathematical discipline which studies topological problems inspired by robotics applications. Smooth manifolds appear in robotics as configuration spaces of various mechanisms. Practical problems of design and control for real mechanisms lead to exciting new purely topological problems about smooth manifolds. The course will cover several topics of topological robotics; among them:

1. Topological Approach to the Robot Motion Planning Problem

2. Moduli Spaces of Linkages (after W. Thurston, J.-Cl. Hausmann, A.A. Klyachko)

Universality Theorems for Linkages (after M. Kapovich - J. Millson)

3. Knot Theory for the Robot Arm (after R. Connelly, E. Demaine, G. Rote)

4. Configuration Spaces of Graphs (after R. Ghrist, M. Davis, T. Januszkiewicz)

5. Collision Free Motion Planning Algorithms