Multiscale Topological Trajectory Classification with Persistent Homology
Florian T. Pokorny, Majd Hawasly, Subramanian Ramamoorthy · 2014
Topological approaches to studying equivalence classes of trajectories in a configuration space have recently received attention in robotics since they allow a robot to reason about trajectories at a high level of abstraction.While recent work has approached the problem of topological motion planning under the assumption that the configuration space and obstacles within it are explicitly described in a noise-free manner, we focus on trajectory classification and present a samplingbased approach which can handle noise, which is applicable to general configuration spaces and which relies only on the availability of collision free samples.Unlike previous samplingbased approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes.Our approach thereby extracts additional homological information which is essential for a topological trajectory classification.By computing a basis for the first persistent homology groups, we obtain a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension.We furthermore show how an augmented filtration of simplicial complexes based on a cost function can be defined to incorporate additional constraints.We present an evaluation of our approach in 2, 3, 4 and 6 dimensional configuration spaces in simulation and using a Baxter robot.