LiDAR-based global localization is a fundamental problem for mobile robots. It consists of two stages, place recognition and pose estimation, which yields the current orientation and translation, using only the current scan as query and a database of map scans. Inspired by the definition of a recognized place, we consider that a good global localization solution should keep the pose estimation accuracy with a lower place density. Following this idea, we propose a novel framework towards sparse place-based global localization, which utilizes a unified and learning-free representation, Radon sinogram (RING), for all sub-tasks. Based on the theoretical derivation, a translation invariant descriptor and an orientation invariant metric are proposed for place recognition, achieving certifiable robustness against arbitrary orientation and large translation between query and map scan. In addition, we also utilize the property of RING to propose a global convergent solver for both orientation and translation estimation, arriving at global localization. Evaluation of the proposed RING based framework validates the feasibility and demonstrates a superior performance even under a lower place density.

Global localization plays a critical role in many robot applications. LiDAR-based global localization draws the community's focus with its robustness against illumination and seasonal changes. To further improve the localization under large viewpoint differences, we propose RING++ which has roto-translation invariant representation for place recognition, and global convergence for both rotation and translation estimation. With the theoretical guarantee, RING++ is able to address the large viewpoint difference using a lightweight map with sparse scans. In addition, we derive sufficient conditions of feature extractors for the representation preserving the roto-translation invariance, making RING++ a framework applicable to generic multi-channel features. To the best of our knowledge, this is the first learning-free framework to address all subtasks of global localization in the sparse scan map. Validations on real-world datasets show that our approach demonstrates better performance than state-of-the-art learning-free methods, and competitive performance with learning-based methods. Finally, we integrate RING++ into a multi-robot/session SLAM system, performing its effectiveness in collaborative applications.