  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.
