Configuration Spaces, Braids, and Robotics

Braids are intimately related to configuration spaces of points. These configuration spaces give a useful model of autonomous agents (or robots) in an environment. Problems of relevance to autonomous engineering systems (e.g., motion planning, coordination, cooperation, assembly) are directly related to topological and geometric properties of configuration spaces, including their braid groups. These notes detail this correspondence, and explore several novel examples of configuration spaces relevant to applications in robotics. No familiarity with robotics is assumed. These notes shadow a two-hour set of tutorial talks given at the National University of Singapore, June 2007, for the IMS Program on Braids.