Geometric Learning and Topological Inference With Biobotic Networks

Abstract

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 coordinatefree 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.

Book Review: Elementary applied topology; Persistence theory: From quiver representations to data analysis

“…It turns out that there is a Klein bottle parameterizing one of the most fundamental portions of this space [3] and that this geometric model can be used for image compression [23] and classification tasks [25]. In bio-robotics, swarms of insects (Madagascar hissing cockroaches) equipped with wireless neuro-stimulation backpacks, can be used to infer topological maps of physical environments for search and rescue [14]. In mechanical robotics, tools from bundle theory and configuration spaces lead to impossibility theorems, as well as complexity measures, for the existence of solutions to continuous motion planning problems [19].…”

A framework for mapping with biobotic insect networks: From local to global maps

“…Quantitative analysis of metric convergence to the geodesic dissimilarities and their dependence on the number of moving agents and landmarks have been demonstrated through several experiments therein. Furthermore, the robustness of local map estimation with respect to the scaling and number of features has been investigated with random generation of obstacles in fixed size environment in [69].…”

Topological Data Analysis Approaches to Uncovering the Timing of Ring Structure Onset in Filamentous Networks

“… 2018 ; Stolz et al 2018 ), and mapping of unknown spatial environments using biobotic insects (Dirafzoon et al. 2016 ). While the applications for TDA multiply, there is an associated need for statistical methods that can rigorously compare the behaviors of systems when they are subjected to different environments or controls (Wasserman 2018 ).…”

“…In particular, methods from persistent homology are useful in understanding topological invariants such as clusters or loops in data represented as point clouds. Applications of these topological methods in the biological sciences are varied and include quantitative understanding of aggregations such as insect swarms (Topaz et al 2015;Ulmer et al 2019), extracting the topology of functional brain networks from fMRI data (Saggar et al 2018;Stolz et al 2018), and mapping of unknown spatial environments using biobotic insects (Dirafzoon et al 2016). While the applications for TDA multiply, there is an associated need for statistical methods that can rigorously compare the behaviors of systems when they are subjected to different environments or controls (Wasserman 2018).…”