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GRASP Lab Seminar 2003-2004
April 2, 11:00 AM, Levine Hall 307, hosted by Vijay Kumar.
Robert Ghrist
University of Illinois
Optimal Coordination on Roadmaps
Abstract: Given a collection of robots sharing a common environment, assume that each possesses an individual roadmap for its C-space and a cost function for attaining a goal. How do you coordinate simultaneous motion in an optimal way? What is meant by "optimal" when each robot has distinct goals and cost functions? We use vector-valued (or "Pareto") optimization for collision-free coordination .
Unfortunately, such optima are by no means unique: in fact, continua of optimal coordinations are possible. We use methods inspired by geometric group theory to identify a natural class of systems which have a finite number of canonical optima. Surprisingly, abstract results about the topology of cubical complexes aids greatly in the computation of these optimal coordinations. Joint work with S. LaValle and J. O'Kane.Biography: Robert Ghrist is an Associate Professor of Mathematics at the University of Illinois, Urbana-Champaign. His Ph.D. is in applied mathematics [Cornell 1995]. Prof. Ghrist has held faculty positions at the University of Texas, Austin and Georgia Tech; and visiting positions at Princeton University, the Institute for Advanced Study, and the Issac Newton Institute at Cambridge. Prof. Ghrist's research focus is on topological methods, with applications to fluid dynamics, robotics, differential equations, and more.
