Michael Farber

Motion planning in configuration spaces

I will discuss robot motion planning algorithms and the related topological problems. I will introduce a homotopy invariant of a topological space X which reflects navigational complexity of mechanical systems having X as their configuration space. I will illustrate the general theory by examples of systems of many objects moving in space or along a graph without collisions. This will also include a discussion of cohomology algebras of configuration spaces of graphs and other interesting examples.