Probabilistic Degeneracy Detection for Point-to-Plane Error Minimization

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.