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Topological trajectory classification with filtrations of simplicial complexes and persistent homology
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.ORCID iD: 0000-0003-1114-6040
2016 (English)In: The international journal of robotics research, ISSN 0278-3649, E-ISSN 1741-3176, Vol. 35, no 1-3, 204-223 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this work, we present a sampling-based approach to trajectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and 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. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, 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 in real-world experiments using a Baxter robot and motion capture data.

Place, publisher, year, edition, pages
Sage Publications, 2016. Vol. 35, no 1-3, 204-223 p.
Keyword [en]
motion classification, Persistent homology, topological robotics
National Category
Robotics
Identifiers
URN: urn:nbn:se:kth:diva-181447DOI: 10.1177/0278364915586713ISI: 000368032600012ScopusID: 2-s2.0-84953282328OAI: oai:DiVA.org:kth-181447DiVA: diva2:900194
Note

QC 20160203

Available from: 2016-02-03 Created: 2016-02-02 Last updated: 2016-02-24Bibliographically approved

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Pokorny, Florian T.
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