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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.<\/jats:p>","DOI":"10.1177\/0278364915586713","type":"journal-article","created":{"date-parts":[[2015,8,21]],"date-time":"2015-08-21T21:50:24Z","timestamp":1440193824000},"page":"204-223","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":40,"title":["Topological trajectory classification with filtrations of simplicial complexes and persistent homology"],"prefix":"10.1177","volume":"35","author":[{"given":"Florian T.","family":"Pokorny","sequence":"first","affiliation":[{"name":"Centre for Autonomous Systems, CAS\/CVAP, KTH Royal Institute of Technology, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Majd","family":"Hawasly","sequence":"additional","affiliation":[{"name":"IPAB, School of Informatics, University of Edinburgh, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subramanian","family":"Ramamoorthy","sequence":"additional","affiliation":[{"name":"IPAB, School of Informatics, University of Edinburgh, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,8,21]]},"reference":[{"key":"bibr1-0278364915586713","first-page":"1106","volume-title":"Proceedings of the eighteenth annual ACM\u2013SIAM symposium on Discrete algorithms","author":"Amenta N","year":"2007"},{"key":"bibr2-0278364915586713","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-013-9334-3"},{"key":"bibr3-0278364915586713","doi-asserted-by":"publisher","DOI":"10.1145\/235815.235821"},{"key":"bibr4-0278364915586713","doi-asserted-by":"publisher","DOI":"10.1145\/2582112.2582167"},{"key":"bibr5-0278364915586713","doi-asserted-by":"crossref","unstructured":"Bauer U, Kerber M, Reininghaus J (2013) PHAT (Persistent Homology Algorithm Toolbox). 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