This paper presents a novel approach to range-based cooperative localization for robot swarms in GPS-denied environments, addressing the limitations of current methods in noisy and sparse settings. We propose a robust multi-layered localization framework that combines shadow edge localization techniques with the strategic deployment of UAVs. This approach not only addresses the challenges associated with nonrigid and poorly connected graphs but also enhances the convergence rate of the localization process. We introduce two key concepts: the S1-Edge approach in our distributed protocol to address the rigidity problem of sparse graphs and the concept of a powerful UAV node to increase the sensing and localization capability of the multi-robot system. Our approach leverages the advantages of the 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 shadow edge localization. Extensive simulation experiments confirm the superior performance of our method compared to state-of-the-art techniques, resulting in up to 95\% reduction in localization error, demonstrating substantial improvements in localization accuracy and robustness to sparse graphs. This work provides a decisive advancement in the field of multi-robot localization, offering a powerful tool for high-performance and reliable operations in challenging environments.

翻译：本文提出了一种在GPS拒止环境下机器人集群基于测距的协同定位新方法，解决了现有方法在噪声和稀疏场景下的局限性。我们提出了一种鲁棒的多层定位框架，将阴影边缘定位技术与无人机的策略性部署相结合。该方法不仅解决了与非刚性及弱连通图相关的挑战，还提升了定位过程的收敛速度。我们引入了两个关键概念：分布式协议中的S1-Edge方法以应对稀疏图的刚性问题，以及强效无人机节点概念以增强多机器人系统的感知与定位能力。我们的方法充分利用分布式定位技术的优势，提升了大规模机器人网络的可扩展性与适应性。我们为新的S1-Edge建立了理论条件，确保即使在噪声存在时解仍然存在，从而验证了阴影边缘定位的有效性。大量仿真实验证实，与现有先进技术相比，我们的方法具有优越性能，定位误差降低高达95%，在定位精度和对稀疏图的鲁棒性方面均展现出显著提升。本研究为多机器人定位领域提供了决定性进展，为在挑战性环境中实现高性能可靠操作提供了有力工具。