2016/06/30 by Alireza Dirafzoon, Dirafzoon, Alireza, Alper Bozkurt +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algebraic Topology (math.AT) #Cell Image Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Morphological variations and asymmetry #Robotics (cs.RO) #Topological and Geometric Data Analysis #cs.RO #math.AT #stat.ML
paper · pdf · doi:10.48550/arxiv.1607.00051
arxiv created 2016/06/30 · openalex publication_date 2016/06/30 · arxiv updated 2016/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this study, we present and analyze a framework for geometric and topological estimation for mapping of unknown environments. We consider agents mimicking motion behaviors of cyborg insects, known as biobots, and exploit coordinate-free local interactions among them to infer geometric and topological information about the environment, under minimal sensing and localization constraints. Local interactions are used to create a graphical representation referred to as the encounter graph. A metric is estimated over the encounter graph of the agents in order to construct a geometric point cloud using manifold learning techniques. Topological data analysis (TDA), in particular persistent homology, is used in order to extract topological features of the space and a classification method is proposed to infer robust features of interest (e.g. existence of obstacles). We examine the asymptotic behavior of the proposed metric in terms of the convergence to the geodesic distances in the underlying manifold of the domain, and provide stability analysis results for the topological persistence. The proposed framework and its convergences and stability analysis are demonstrated through numerical simulations and experiments.