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

Hairuo Wei; Yunfan Ren; Renda Yang; Qiangsheng Huang; Zhongyu Li

cs.ROOct 19, 2026

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

Authors: Hairuo Wei, Yunfan Ren, Renda Yang, Qiangsheng Huang, Zhongyu Li

Organizations: The Chinese University of Hong Kong, Hong Kong SAR, China. · Tongji University, Shanghai, China. · SEER Robotics.

Abstract

Wheel kinematics can support odometry for quadrupedal wheel-legged robots when LiDAR geometry provides weak motion constraints. However, slip and contact loss make rolling predictions unreliable, and contact state alone cannot determine their reliability across motion directions. We propose a tightly coupled LiDAR-inertial-kinematic odometry framework that retains analytical rolling predictions and learns per-wheel, direction-dependent process covariances from proprioceptive history. The estimator maintains moving wheel-center states, allowing the learned uncertainty to regulate the influence of rolling predictions through forward-kinematic corrections. Degeneracy-aware projection (DAP) complements this mechanism by suppressing LiDAR constraints along geometrically weak directions. The learned covariance network (CovNet) is trained through a differentiable filter using simulated velocity supervision and deployed on the real robot without fine-tuning. On the six room sequences with the highest degeneracy ratios in our indoor dataset, the method reduces mean per-sequence position root mean square error (RMSE) by 66.2% relative to FAST-LIO2 and by 31.0% relative to a fixed-covariance variant. In a severely degenerate corridor run, it achieves an endpoint position error of 0.198 m, compared with 7.531 m for FAST-LIO2. These results demonstrate robust odometry under challenging geometric and wheel-motion conditions. We plan to publicly release our code and multimodal dataset. Project website: https://weihairuo.github.io/wheel-motion-uncertainty/

Figures & tables

Fig. 1: Quadrupedal wheel-legged state estimation using proposed method, which fuses LiDAR, inertial measurement unit (IMU), and encoder measurements together with learned wheel-motion uncertainty. Yellow ellipsoids represent covariance.

Fig. 2: Overview of the proposed system. Given IMU, encoder, and LiDAR measurements, a learned covariance network (CovNet) predicts wheel-motion process covariances from proprioceptive history, while degeneracy-aware projection (DAP) suppresses direct LiDAR information along geometrically weak directions during the LiDAR update. The system then fuses these measurements to estimate the robot state and build a point cloud map.

Fig. 3: Point contact (left) and wheel contact (right). The effective radius

r_{i}

, wheel axis

{}^{I}\mathbf{h}_{i}

, and estimated normal

{}^{I}\mathbf{n}

define the assumed contact geometry. The vector

{}^{I}\bm{\rho}_{i}

points from the wheel center to the assumed contact point.

Fig. 4: Joint six-dimensional analysis of LiDAR degeneracy through $\mathbf{A}_{L}=\mathbf{V}\bm{\Lambda}\mathbf{V}^{\top}$ . Eigenvalue screening separates weak (orange) and retained (green) directions for Jacobian projection in DAP. Here, $\theta$ denotes the local rotation coordinates of the IMU attitude, and $p_{I}$ denotes the IMU position in the global frame; $\delta$ denotes their perturbations. Rotation and translation are drawn separately for clarity; the spectrum is illustrative.

Fig. 5: Experimental setup. (a) Experimental platform: a quadrupedal wheel-legged robot equipped with an Odin1 module (Manifold Tech) and a Jetson Orin NX onboard computer. We use the module’s integrated LiDAR, with a depth resolution of $240\times 180$ pixels and a field of view of $120^{\circ}\times 90^{\circ}$ . (b) Communication among sensors: Raw encoder and IMU measurements are synchronized by the robot’s internal low-level controller into a 100 Hz data stream, while raw LiDAR data are provided at 10 Hz.

Fig. 6: Corridor maps: (a) FAST-LIO2; (b) NCDM; (c) Fixed-Cov.; (d) Ours without DAP; (e) Ours. We use the internally colorized point cloud produced by Odin1 for visualization only. All evaluated methods use the raw point cloud output of the Odin1 LiDAR as input. Only Ours avoids pronounced global drift of the corridor map, yielding the most consistent reconstruction among the compared methods.

Fig. 7: Rolling-model failures: (a1) slip on a smooth plastic sack; (a2) tether dragging; (a3) a kick lifting all wheels; (a4) a kick causing sliding. Corresponding maps use (b1)–(b4) Ours without LiDAR and (c1)–(c4) Ours. LiDAR points in (b) serve only to visualize estimated poses.

Fig. 8: Outdoor mapping on mixed terrain. The large map uses Ours; upper-right panels compare Ours, FAST-LIO2, and NCDM. Photographs show terrain along the route; the lower-right panel compares their top-down trajectories. The route approximately returns to its starting location; because Mocap is unavailable outdoors, the point clouds and top-down trajectories provide a qualitative comparison. Our method produces the most geometrically consistent map, particularly in the underground garage shown in the upper-right close-ups: FAST-LIO2 and NCDM exhibit visibly misaligned, duplicated walls, whereas our method preserves a coherent wall structure.

Setting	Value
Input history length $H$	20
Hidden layer widths	(128, 64)
Activation	ELU
Parallel environments	4,096
Batch size	512
Learning rate	$3\times 10^{-5}$

TABLE I: Training and deployment settings.

Seq.	DR (%)	FAST- LIO2	NCDM	Fixed- Cov.	Without DAP	Ours
Easy ( $\mathrm{DR}=0$ )
00	0.000	0.079	0.082	0.079	0.075	0.075
01	0.000	0.189	0.197	0.187	0.153	0.153
02	0.000	0.167	0.175	0.179	0.167	0.167
03	0.000	0.087	0.093	0.090	0.071	0.071
04	0.000	0.064	0.037	0.040	0.040	0.040

TABLE II: Room ATE RMSE and corridor E2E position error (m).

Method	slip00	slip01	kick00	kick01
Ours without LiDAR	0.844	0.640	1.439	1.014
Ours	0.125	0.220	0.061	0.057

TABLE III: Position RMSE under slip and disturbances (m).

Fig. 9: CPU time per scan: totals and breakdown of Ours. Deskew: IMU propagation/deskewing; Res.: point-to-plane residual construction; DAP: degeneracy-aware projection; Cov.: network inference; FK Upd.: FK reconstruction/wheel update; LiDAR Upd.: remaining iterative update; Others: remaining computation. Diamonds/numbers show means, lines medians, boxes interquartile ranges, and whiskers 5th–95th percentiles.

LiDAR Odometry

LiDAR odometry (light detection and ranging) estimates a robot’s motion by aligning successive laser scans, often with inertial data.

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Feb 19, 2026J/K move · Enter open · S save

Contact-Anchored Proprioceptive Odometry for Legged and Wheel-Legged Robots

Minxing Sun, Yao Mao

Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, China · Institute for Infocomm Research (I2R), Agency for Science, Technology and Research, Singapore. · Shenzhen Astralldynamics Technology.

Legged Robotics Robot State Estimation

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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.

Abstract

LiDAR Odometry

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