Robotics: Science and Systems X

Multiscale Topological Trajectory Classification with Persistent Homology

Florian T. Pokorny, Majd Hawasly, Subramanian Ramamoorthy


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 sampling-based 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 sampling-based 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.



    AUTHOR    = {Florian T. Pokorny AND Majd Hawasly AND Subramanian Ramamoorthy}, 
    TITLE     = {Multiscale Topological Trajectory Classification with Persistent Homology}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2014}, 
    ADDRESS   = {Berkeley, USA}, 
    MONTH     = {July},
    DOI       = {10.15607/RSS.2014.X.054}