Terrain-Awared LiDAR-Inertial Odometry for Legged-Wheel Robots Based on Radial Basis Function Approximation

TL;DR

This work tackles pose drift in LiDAR–inertial odometry for legged-wheel robots navigating unstructured terrains by introducing a terrain-aware framework that models the terrain with adaptively centered Radial Basis Functions (RBFs). The RBF surface provides a smooth, differentiable terrain representation whose weights are updated recursively via ridge regression, yielding a gradient that can be incorporated as soft manifold constraints in the LIO optimization. The approach combines adaptive center selection, Kalman-filter–style weight updates, and GPU-accelerated computation to maintain real-time performance, significantly reducing vertical ($z$-axis) drift in challenging scenes. Empirical results on diverse outdoor datasets show improved localization accuracy over Fast-LIO2 and ROLO-SLAM, especially in scenarios with continuous height changes or sparse features, and a publicly released dataset supports future research in legged-wheel SLAM.

Abstract

An accurate odometry is essential for legged-wheel robots operating in unstructured terrains such as bumpy roads and staircases. Existing methods often suffer from pose drift due to their ignorance of terrain geometry. We propose a terrain-awared LiDAR-Inertial odometry (LIO) framework that approximates the terrain using Radial Basis Functions (RBF) whose centers are adaptively selected and weights are recursively updated. The resulting smooth terrain manifold enables ``soft constraints" that regularize the odometry optimization and mitigates the $z$-axis pose drift under abrupt elevation changes during robot's maneuver. To ensure the LIO's real-time performance, we further evaluate the RBF-related terms and calculate the inverse of the sparse kernel matrix with GPU parallelization. Experiments on unstructured terrains demonstrate that our method achieves higher localization accuracy than the state-of-the-art baselines, especially in the scenarios that have continuous height changes or sparse features when abrupt height changes occur.

Figures (9)

• Figure 1: Robot platform used in our experiments. The system mounts two LiDARs; however, only the top, inverted Mid360 LiDAR (blue) is used in all experiments (the lower LiDAR is not used). The platform is also equipped with a GPS+RTK module (red) and joint sensors (green) for kinematic state estimation. (a) side view, (b) front view.
• Figure 2: Illustration of wheel–manifold contact. Point A (red) denotes the actual contact point, while Point B (blue) denotes the approximated contact point. This approximation simplifies computation.
• Figure 3: Dataset environments: (a) Staircase, (b) Artificial Hill, (c) Rose Garden, (d) Botanical Garden. These datasets include diverse terrain elevations, and each environment contains different stair structures to verify the $z$-axis localization performance of different method.
• Figure 4: 3D trajectories of different methods on the rose garden dataset. While RBF-LIO and its IMU-free variant remain close to the GPS reference, Fast-LIO2 and ROLO-SLAM exhibit noticeable deviations, especially around the staircase section.
• Figure 5: Visualization of the Rose Garden map: (a) RBF mapping result (side view), (b) Fast-LIO2 mapping result (side view). The staircase is highlighted by the red boxes, where Fast-LIO2 exhibits $z$-axis pose drift with layered artifacts, while RBF-LIO preserves the map consistency.