Mechanical and Civil Engineering Seminar

In this talk I will motivate and introduce techniques for topological reasoning in various optimal 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 homotopy 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.