Data-Driven Topological Motion Planning With Persistent Cohomology

In this work, we present an approach to topological motion planning which is fully data-driven in nature and which relies solely on the knowledge of samples in the free configuration space. For this purpose, we discuss the use of persistent cohomology with coefficients in a finite field to compute a basis which allows us to efficiently solve the path planning problem. The proposed approach can he used both in the case where a part of a configuration space is well approximated by samples and, more generally, with arbitrary filtrations arising from real-world data sets. Furthermore, our approach can generate motions in a subset of the configuration space specified by the sub- or superlevel set of a filtration function such as a cost function or probability distribution. Our experiments show that our approach is highly scalable in low dimensions and we present results on simulated PR2 arm motions as well as GPS trace and motion capture data.