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Multiscale Topological Trajectory Classification with Persistent Homology
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.ORCID iD: 0000-0003-1114-6040
University of Edinburgh, School of Informatics, IPAB.
University of Edinburgh, School of Informatics, IPAB.
2014 (English)In: Proceedings of Robotics: Science and Systems, 2014, 2014Conference paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Keyword [en]
Motion Classification, Persistent Homology, Trajectory Classification, Filtration, Motion Planning
National Category
Research subject
Computer Science
URN: urn:nbn:se:kth:diva-159003OAI: diva2:781917
The 2014 Robotics: Science and Systems Conference, July 12 - 16, 2014 Berkeley, USA
EU, FP7, Seventh Framework Programme, 270436EU, FP7, Seventh Framework Programme, 318493

QC 20150205

Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2015-02-05Bibliographically approved

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Pokorny, Florian T.
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