Probabilistic Degeneracy Detection for Point-to-Plane Error Minimization

TL;DR

This paper addresses degeneracies in LiDAR-based SLAM caused by uninformative geometry by introducing a probabilistic model of Hessian noise to quantify the likelihood that a direction is informative. It integrates this degeneracy information into a real-time degeneracy-aware point-to-plane ICP, attenuating updates in degenerate directions and leveraging a practical covariance estimation for normals. The approach generalizes across datasets by tying parameters to LiDAR noise characteristics and outperforms state-of-the-art degeneracy methods in four real-world experiments. The work provides a principled, implementable framework for robust LiDAR registration with publicly available code, enabling broader adoption in SLAM and mapping pipelines.

Abstract

Degeneracies arising from uninformative geometry are known to deteriorate LiDAR-based localization and mapping. This work introduces a new probabilistic method to detect and mitigate the effect of degeneracies in point-to-plane error minimization. The noise on the Hessian of the point-to-plane optimization problem is characterized by the noise on points and surface normals used in its construction. We exploit this characterization to quantify the probability of a direction being degenerate. The degeneracy-detection procedure is used in a new real-time degeneracy-aware iterative closest point algorithm for LiDAR registration, in which we smoothly attenuate updates in degenerate directions. The method's parameters are selected based on the noise characteristics provided in the LiDAR's datasheet. We validate the approach in four real-world experiments, demonstrating that it outperforms state-of-the-art methods at detecting and mitigating the adverse effects of degeneracies. For the benefit of the community, we release the code for the method at: github.com/ntnu-arl/drpm.

Figures (5)

• Figure 1: The comparison of our proposed approach (middle column) to the state-of-the-art method from zhang2016degeneracy (left column). Our method avoids drift by successfully detecting and accounting for degeneracies. Top row: From the Seemühle underground mine using the legged ANYmal platform (top right). Bottom row: From a cylindrical tank using a flying platform (bottom right).
• Figure 2: Partial maps of all methods from experiment 1 (Rümlang). The field-of-view of the Velodyne VLP-16 LiDAR is reduced to $180^\circ$ to study degeneracies. zhang2016degeneracyhinduja2019degeneracylee2024switch exhibit degeneracy-induced drift, materializing as erroneously repeated structures in the close-ups.
• Figure 3: Partial maps of all methods from experiment 2 (Seemühle), using the using the full $360^\circ$ field-of-view of the Velodyne VLP-16 LiDAR. The repeated walls in the maps of zhang2016degeneracylee2024switch stem from degeneracy-induced drift.
• Figure 4: Partial maps of all methods from experiment 2 (RelyOn). The field-of-view of the Ouster OS0-64 LiDAR is reduced to $180^\circ$ to study degeneracies. zhang2016degeneracyhinduja2019degeneracylee2024switch exhibit degeneracy-induced drift, materializing as repeated structures in the marked areas.
• Figure 5: Partial maps of all methods from experiment 4 (Fyllingsdalen Bicycle Tunnel), using the full $360^\circ$ field-of-view of the Ouster OS0-128 LiDAR. zhang2016degeneracy (second row) and lee2024switch (fourth row) drift in longitudinal and lateral translation, respectively. Ours and hinduja2019degeneracy (third row) yield comparable results, correctly estimating the tunnel section length to $\sim 500$ m.