Topological trajectory classification with filtrations of simplicial complexes and persistent homology. (January 2016)

• Record Type: Journal Article
• Authors: Pokorny, Florian T.; Hawasly, Majd; Ramamoorthy, Subramanian
• Is Part Of: International journal of robotics research. Volume 35:Number 1/2/3(2016:Jan.)
• Page Start: 204
• Page End: 223
• Publication Date: 2016-01
• Subjects: Persistent homology -- motion classification -- topological robotics; Robots -- Periodicals; Robots, Industrial -- Periodicals; 629.89205
• DOI: 10.1177/0278364915586713
• Languages: English
• ISSNs: 0278-3649

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.