Finding Topology in a Factory: Configuration Spaces

Abstract

It is perhaps not universally acknowledged that an outstanding place to find interesting topological objects is within the walls of an automated warehouse or factory. The examples of topological spaces that we construct in this exposition arose simultaneously from two seemingly disparate fields: the first author, in his thesis [1], discovered these spaces after working with H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow on problems about random walks on graphs [2]. The second author discovered these same spaces while collaborating with D. Koditschek in the Artificial Intelligence Lab at the University of Michigan; see [7] and [8]. Sections 1 and 2 give some motivations arising from robotics, as well as a little background on configuration spaces. For the remainder of the paper we focus on a fascinating class of topological spaces related to motion-planning on graphs. 1. Robotics and topological motion planning Consider an automated factory equipped with a cadre of Automated Guided