Frontier-Based Exploration using Harmonic Transformations

In this work, a novel reactive, frontier-based exploration scheme is presented. The approach is based on harmonic transformations, which provide a homeomorphism of arbitrary workspaces onto a punctured disk, thus enabling provably safe navigation. Additionally, in contrast to previous reactive methods, the proposed scheme enables choosing any unexplored frontier for further exploration, while preserving full exploration guarantees in finite time. The relevant claims are proven mathematically, while the scheme is validated via synthetic simulation environments, as well as via a real-world experiment with a mobile robot, demonstrating the capabilities and applicability of the method. The method is successful in all tested cases, while also outperforming relevant schemes in computational time.