  LiDAR-based place recognition plays a crucial role in Simultaneous
Localization and Mapping (SLAM) and LiDAR localization.
  Despite the emergence of various deep learning-based and hand-crafting-based
methods, rotation-induced place recognition failure remains a critical
challenge.
  Existing studies address this limitation through specific training strategies
or network structures.
  However, the former does not produce satisfactory results, while the latter
focuses mainly on the reduced problem of SO(2) rotation invariance. Methods
targeting SO(3) rotation invariance suffer from limitations in discrimination
capability.
  In this paper, we propose a new method that employs Vector Neurons Network
(VNN) to achieve SO(3) rotation invariance.
  We first extract rotation-equivariant features from neighboring points and
map low-dimensional features to a high-dimensional space through VNN.
  Afterwards, we calculate the Euclidean and Cosine distance in the
rotation-equivariant feature space as rotation-invariant feature descriptors.
  Finally, we aggregate the features using GeM pooling to obtain global
descriptors.
  To address the significant information loss when formulating
rotation-invariant descriptors, we propose computing distances between features
at different layers within the Euclidean space neighborhood.
  This greatly improves the discriminability of the point cloud descriptors
while ensuring computational efficiency.
  Experimental results on public datasets show that our approach significantly
outperforms other baseline methods implementing rotation invariance, while
achieving comparable results with current state-of-the-art place recognition
methods that do not consider rotation issues.
