Learning Wheel Motion Uncertainty for Degeneracy-Aware LiDAR-Inertial Odometry on Quadrupedal Wheel-Legged Robots

Reliable odometry for legged robots without cameras or LiDAR remains challenging due to IMU drift and noisy joint velocity sensing. This paper presents a purely proprioceptive state estimator that uses only IMU and motor measurements to estimate body pose and velocity, with a unified formulation applicable to quadruped and wheel-legged robots and extensible to other legged morphologies. The key idea is to treat each reliable contact as a kinematic anchor: joint-torque--based foot wrench estimation selects stance contacts, and the corresponding footfall records provide intermittent world-frame constraints that suppress long-term drift. To prevent elevation drift during extended traversal, we introduce a lightweight height clustering and time-decay correction that snaps newly recorded footfall heights to previously observed support planes. For wheel-legged platforms, the recorded contact is further propagated by effective wheel rolling displacement with shank-motion compensation and a slope-aware rolling direction. To improve foot velocity observations under encoder quantization, we retain an inverse-kinematics cubature Kalman filter as an optional velocity-enhancement module that filters foot-end velocities from joint angles and velocities. The implementation further mitigates yaw drift through multi-contact geometric consistency, which is injected as a soft heading prior rather than as a hard reset of the attitude state. The method is evaluated on four quadruped platforms.

Odometry estimation using light detection and ranging (LiDAR) and an inertial measurement unit (IMU), known as LiDAR-inertial odometry (LIO), often suffers from performance degradation in degenerate environments, such as long corridors or single-wall scenarios with narrow field-of-view LiDAR. To address this limitation, we propose ALIVE-LIO, a degeneracy-aware LiDAR-inertial odometry framework that explicitly enhances state estimation in degenerate directions. The key contribution of ALIVE-LIO is the strategic integration of a deep neural network into a classical error-state Kalman filter (ESKF) to compensate for the loss of LiDAR observability. Specifically, ALIVE-LIO employs a neural network to predict the body-frame velocity and selectively fuses this prediction into the ESKF only when degeneracy is detected, providing effective state updates along degenerate directions. This design enables ALIVE-LIO to utilize the probabilistic structure and consistency of the ESKF while benefiting from learning-based motion estimation. The proposed method was evaluated on publicly available datasets exhibiting degeneracy, as well as on our own collected data. Experimental results demonstrate that ALIVE-LIO substantially reduces pose drift in degenerate environments, yielding the top-ranked result in 22 out of 32 sequences. Our code is available at https://github.com/cocel-postech/alive-lio.

Wheel odometry provides an efficient motion prior for ground robots but is prone to transient violations such as wheel slip or terrain-induced tilt. In filtering-based odometry, these violations frequently trigger divergence when they coincide with constrained geometric observability (e.g., featureless corridors). We address this challenge by proposing ToF-Wheel Odometry (TWO), a tightly-coupled filtering framework that integrates wheel kinematics with geometric constraints from Time-of-Flight (ToF) cameras. The primary contribution of this work is a degeneracy-aware, directional covariance-shaping strategy that replaces heuristic online covariance tuning with geometry-conditioned inflation. The core idea is to infer process noise from geometric corrections with a strict reliability check. We decompose the posterior-to-prior correction into a wheel-explainable subspace and an orthogonal remainder. The process covariance is anisotropically adjusted according to the observability of the ToF update: if the geometry is degenerate in non-kinematic directions, the remainder is suppressed as sensor noise; if the geometry is distinct, it is admitted as a valid kinematic violation. Additionally, we introduce an intra-frame feedback loop that retrospectively repairs the process covariance within the current frame to reduce structural lag during bursty disturbances. Extensive experiments on challenging scenarios demonstrate that TWO improves trajectory accuracy and robustness compared to static and adaptive Gaussian filtering, robustly navigating the trade-off between kinematic reliability and limited sensing capabilities.