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

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. EGGED-WHEEL robots combine the speed advantage of wheeled robots with the terrain adaptability advantage of legged robots. Thus, they are well-suited for traversing complex and uneven environments such as bumpy roads, staircases, etc. However, the uneven surface in these environments will cause impulsive velocity variations during the robot's maneuver.