In this talk I will motivate and introduce techniques for topological reasoning in various motion planning problems in robotics, along with their applications to real-world robotics problems. In particular, I will focus on three broad areas of research involving topological motion planning: First, I will describe techniques for computing homology/homotopy invariants that can be used, in conjunction with graph research algorithms, to find optimal paths in different topological classes, with applications to multi-robot systems and tethered robots. Second, I will illustrate how topological constructions such as simplicial complexes can be effectively used to represent and plan motions for swarms of mobile robots with extremely limited sensing capabilities in GPS-denied, unknown environments for coverage, exploration and transportation tasks. Third, I will show how Morse theory can be used for effective dimensionality-reduction of high-dimensional configuration spaces enabling path planning for articulated robots. Following this I will give a quick overview of a few other emerging applications of topology and few applications of differential geometry in robot motion planning problems.
Subhrajit Bhattacharya is a postdoctoral researcher in the Department of Mathematics of University of Pennsylvania, working with Professor Robert Ghrist and Professor Vijay Kumar. He completed his Ph.D. in Mechanical Engineering and Applied Mechanics under the guidance of Professor Vijay Kumar and Professor Maxim Likhachev in 2012. He received his Bachelor of Technology in Mechanical Engineering from Indian Institute of Technology (IIT), Kharagpur in 2006. Subhrajit’s current research interest is centered around the application of algebraic and differential topology to problems of robot motion planning, coverage, sensor networks and control.