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.

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