Geometric Learning and Topological Inference With Biobotic Networks

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. A metric estimation procedure is presented over a graphical representation referred to as the encounter graph in order to construct a geometric point cloud using manifold learning techniques. Topological data analysis (TDA) along with the proposed classification method is used to infer robust topological features of the space (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 with Hexbugs.