Topological trajectory classification with filtrations of simplicial complexes and persistent homology

Florian T. Pokorny, Majd Hawasly, Subramanian Ramamoorthy

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)204-223
Number of pages20
JournalInternational Journal of Robotics Research
Volume35
Issue number1-3
Early online date21 Aug 2015
DOIs
Publication statusPublished - 1 Jan 2016

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