DCL-Sparse: Distributed Relative Localization in Sparse Graphs

Abstract

This paper presents a novel approach to range-based distributed cooperative localization (DCL) for robot swarms in GPS-denied environments, relying solely on inter-robot range measurements, specifically addressing the limitations of current methods in noisy and sparse settings where the geometric non-rigidity of the sensing graph creates flipping (suboptimal) effects in the localization outcomes. We propose a robust multilayered localization framework (DCL-Sparse) that utilizes distributed 1-hop shadow edges (S1-Edge) to address the non-rigidity problem and improve localization convergence in sparse and noisy sensing graphs. Our approach leverages the advantages of distributed localization methods, enhancing scalability and adaptability in large robot networks. We establish theoretical conditions for the new S1-Edge that ensure solutions exist even in the presence of noise, thereby validating the effectiveness of the new shadow edge localization. Extensive simulation and real-world experiments confirm the superior performance of our method compared to state-of-the-art techniques, resulting in a reduction of up to 93% in the localization error in DCL. These experiments demonstrate substantial improvements in localization accuracy and robustness to sparse graphs. DCL-Sparse increases the localizability of large multi-robot and sensor networks, offering a powerful tool for high-performance and reliable operations in challenging large-scale environments.