Alper Bozkurt

Alireza Dirafzoon, Alper Bozkurt, Edgar Lobaton

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.

Alireza Dirafzoon, Alper Bozkurt, Edgar Lobaton

In this paper, we present an approach for dynamic exploration and mapping of unknown environments using a swarm of biobotic sensing agents, with a stochastic natural motion model and a leading agent (e.g., an unmanned aerial vehicle). The proposed robust mapping technique constructs a topological map of the environment using only encounter information from the swarm. A sliding window strategy is adopted in conjunction with a topological mapping strategy based on local interactions among the swarm in a coordinate-free fashion to obtain local maps of the environment. These maps are then merged into a global topological map which can be visualized using a graphical representation that integrates geometric as well as topological feature of the environment. Localized robust topological features are extracted using tools from topological data analysis. Simulation results have been presented to illustrate and verify the correctness of our dynamic mapping algorithm.