LiDAR-inertial odometry (LIO) has been widely used in robotics due to its high accuracy. However, its performance degrades in degenerate environments, such as long corridors and high-altitude flights, where LiDAR measurements are imbalanced or sparse, leading to ill-posed state estimation. In this letter, we present LODESTAR, a novel LIO method that addresses these degeneracies through two key modules: degeneracy-aware adaptive Schmidt-Kalman filter (DA-ASKF) and degeneracy-aware data exploitation (DA-DE). DA-ASKF employs a sliding window to utilize past states and measurements as additional constraints. Specifically, it introduces degeneracy-aware sliding modes that adaptively classify states as active or fixed based on their degeneracy level. Using Schmidt-Kalman update, it partially optimizes active states while preserving fixed states. These fixed states influence the update of active states via their covariances, serving as reference anchors--akin to a lodestar. Additionally, DA-DE prunes less-informative measurements from active states and selectively exploits measurements from fixed states, based on their localizability contribution and the condition number of the Jacobian matrix. Consequently, DA-ASKF enables degeneracy-aware constrained optimization and mitigates measurement sparsity, while DA-DE addresses measurement imbalance. Experimental results show that LODESTAR outperforms existing LiDAR-based odometry methods and degeneracy-aware modules in terms of accuracy and robustness under various degenerate conditions.

The Iterative Closest Point (ICP) algorithm is a crucial component of LiDAR-based SLAM algorithms. However, its performance can be negatively affected in unstructured environments that lack features and geometric structures, leading to low accuracy and poor robustness in localization and mapping. It is known that degeneracy caused by the lack of geometric constraints can lead to errors in 6-DOF pose estimation along ill-conditioned directions. Therefore, there is a need for a broader and more fine-grained degeneracy detection and handling method. This paper proposes a new point cloud registration framework, LP-ICP, that combines point-to-line and point-to-plane distance metrics in the ICP algorithm, with localizability detection and handling. LP-ICP consists of a localizability detection module and an optimization module. The localizability detection module performs localizability analysis by utilizing the correspondences between edge points (with low local smoothness) to lines and planar points (with high local smoothness) to planes between the scan and the map. The localizability contribution of individual correspondence constraints can be applied to a broader range. The optimization module adds additional soft and hard constraints to the optimization equations based on the localizability category. This allows the pose to be constrained along ill-conditioned directions, with updates either tending towards the constraint value or leaving the initial estimate unchanged. This improves accuracy and reduces fluctuations. The proposed method is extensively evaluated through experiments on both simulation and real-world datasets, demonstrating higher or comparable accuracy than the state-of-the-art methods. The dataset and code of this paper will also be open-sourced at https://github.com/xuqingyuan2000/LP-ICP.