Large-Scale LiDAR-Based Loop Closing via Combination of Equivariance and Invariance on SE(3)

Loop closing is a core module of simultaneous localization and mapping (SLAM) in robotics. It can be achieved through different sensors, of which LiDAR is dominant in large-scale scenes. The LiDAR-based loop closing involves two subtasks: loop closure detection and point cloud registration. Loop closure detection is challenged by large viewpoint changes such as reverse loops, and point cloud registration in Euclidean space is affected by noise and sparsity of point clouds. To solve these problems, we propose to jointly leverage SE(3)-equivariant and -invariant features. Specifically, we first extract equivariant features and map them into invariant features. Then, invariant features are aggregated into global descriptors for loop closure detection. After that, equivariant and invariant features are both applied to point cloud registration. Our strategy has two main advantages. First, our equivariance-to-invariance mapping decouples geometry and pose information in the point cloud. Accordingly, invariant features exhibit high robustness to viewpoint changes by purely encoding the geometry information. Second, equivariant features in latent space, which encode the pose information, are more robust to noise than the points in Euclidean space for pose estimation. Extensive experiments show that our method outperforms state-of-the-art approaches in both accuracy and robustness.