Online Joint Calibration of Steering Offset and Planar LiDAR Extrinsics for Wheeled Mobile Robots

Subodh Mishra; Arindam Dhar; Suprotim Majumdar; Naveen Arulselvan

cs.ROAug 27, 2026

Online Joint Calibration of Steering Offset and Planar LiDAR Extrinsics for Wheeled Mobile Robots

Authors: Subodh Mishra, Arindam Dhar, Suprotim Majumdar, Naveen Arulselvan

Organizations: ATI Motors, Bangalore, India

Abstract

Accurate steering sensing and LiDAR-to-vehicle extrinsics are crucial for reliable path tracking in warehouse mobile robots (WMRs); miscalibration often leads to snaking, weaving, and elevated cross-track error (CTE). In practice, steering ``zero'' is commonly set manually (e.g., eyeballing straightness via a PS4 joystick), while LiDAR extrinsics are assumed from CAD and may drift after maintenance. Such static, manual procedures frequently cause miscalibration in safety-critical environments. This paper presents an Extended Kalman Filter (EKF)--based method for online estimation of steering offset and planar LiDAR extrinsics within a bicycle-kinematics model, providing a principled alternative to manual calibration. Experiments on real datasets show that correcting steering offset reduces CTE substantially, validating the effectiveness of the proposed approach.

Figures & tables

Panel of Figure 1 — Fig. 1: Experimental WMR Platforms . (a) An autonomous tugger that hauls trailers/payloads in industrial sites. (b) Experimental platform used for validation and benchmarking of autonomy algorithms. Both platforms use an Ouster 32-channel LiDAR running at 10 Hz. The 3D point cloud is converted to 2D range scan after filtering out moving objects, the floor and the ceiling and then by setting the z of all the remaining points to zero. Encoder-derived longitudinal velocity and steering angle arrive at 100 Hz.

Fig. 2: Motion-Based Calibration Constraint.

Trial	$x_{\text{off}}$ [m]	$y_{\text{off}}$ [m]	$\theta_{\text{off}}$ [°]	$\delta_{\text{off}}$ [°]
Unladen	0.43	0.0046	0.72	0.92
Laden (500 kg)	0.44	0.0055	0.73	0.92

TABLE I: Converged estimates under different load conditions. The known reference for the extrinsics is

[0.434m,\,0.0,\,0.0]

. Comparison of calibration results for (a) unladen and (b) laden (500 kg) conditions. A consistent

\sim 1\,\text{cm}

shift in the

x

-component of the estimated extrinsics is observed, which may be attributed to LiDAR–odometry noise or load-induced mechanical drift between the vehicle body (kinematics frame) and the chassis where the LiDAR is mounted.

Panel of Figure 5 — Fig. 4: Estimator convergence. In both load conditions, the estimator was initialized at CAD-provided values and converges to the steady-state values in Table I . Note that the $\theta$ axis is on the right.

Trial	$x_{\text{off}}$ [m]	$y_{\text{off}}$ [m]	$\theta_{\text{off}}$ [°]	$\delta_{\text{off}}$ [°]
Unladen	0.43	0.0052	0.72	0.91
Laden (500 kg)	0.44	0.0056	0.73	0.91

TABLE II: Converged estimates under circumstances similar to I . The known reference for the extrinsics is

[0.434m,\,0.0,\,0.0]

. The filter was intialized to

0

for all the states under consideration.

Panel of Figure 7 — Fig. 5: Estimator convergence. With zero initialization, the estimator begins at $\mathbf{0}$ and converges to the steady–state values listed in Table II . The initial covariance (faded $3\sigma$ bounds) is intentionally relaxed to allow recovery of the true extrinsic parameters. Note that the $\theta$ axis is on the right.

Dataset	Estimated $\delta_{\text{off}}$ [°]	$x_{\text{off}}$ [m]	$y_{\text{off}}$ [m]	$\theta_{\text{off}}$ [°]
Induced $\delta_{\text{off}}=-9^{\circ}$	$-8.73^{\circ}$	0.4259	-0.0239	0.67
Induced $\delta_{\text{off}}=7.4^{\circ}$	$7.23^{\circ}$	0.4359	-0.0146	0.79
Induced $\delta_{\text{off}}=5^{\circ}$	$4.87^{\circ}$	0.4185	-0.0034	0.88
Induced $\delta_{\text{off}}=5^{\circ}$	$4.87^{\circ}$	0.4212	0.0100	0.81
Induced $\delta_{\text{off}}=5^{\circ}$	$4.92^{\circ}$	0.4235	0.0135	0.66

TABLE III: Detecting physically induced steering offset. The known reference for the extrinsics is

[0.434m,\,0.0,\,0.0]

Run	$\delta_{\text{off}}~[^{\circ}]$	$x_{\text{off}}$ [m]	$y_{\text{off}}$ [m]	$\theta_{\text{off}}~[^{\circ}]$	RMSE-CTE [m]
Run Set 1
Calibration run	-1.25	0.4393	-0.0088	0.71	0.14
$\delta_{\text{off}}=-1.25^{\circ}$ added	-2.53	0.4383	-0.0132	0.68	0.20
$\delta_{\text{off}}=-1.25^{\circ}$ subtracted	-0.07	0.4394	-0.0119	0.69	0.09
Run Set 2
Calibration run	-0.41	0.4356	-0.0158	0.75	0.09

TABLE IV: Effect of Estimated Steering Offset on Cross-Track Error (CTE) Across Three Experimental Run Sets. The known reference for the extrinsics is

[0.434m,\,0.0,\,0.0]

. The topmost row contains labels for the estimated steering offset, the extrinsics, and RMSE-CTE.

Panel of Figure 10 — Fig. 6: Comprehensive evaluation across three experimental conditions: (i) calibration run, (ii) physically added steering offset, (iii) physically removed steering offset. Columns correspond to Runsets 1–3; rows correspond to the three test scenarios.

Panel of Figure 11 — Fig. 7: Comparison of EKF-estimated trajectory with uncompensated and steering-bias-corrected bicycle propagation across (a) manual teleoperation and (b) autonomous navigation trials. In both cases, the compensated model closely follows the EKF estimate, whereas the uncompensated model exhibits significant drift.

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Aug 28, 2026J/K move · Enter open · S save

Observability Analysis of Joint Steering and Extrinsic Calibration

Subodh Mishra

Lidar-Camera Extrinsic Calibration Parameter Identifiability Dynamical Systems

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This technical report studies the local weak observability of a planar bicycle-model vehicle when vehicle pose, planar LiDAR extrinsic calibration, and steering-angle bias are estimated jointly. A Lie-derivative-based nonlinear observability analysis is used to examine stationary, straight-line, constant-curvature, and combined straight-plus-arc motion. The resulting observability matrices and nullspaces describe how pose, LiDAR translation and yaw offsets, and steering bias become coupled under different motion primitives. Stationary motion and individual motion primitives retain unobservable directions, whereas the combination of straight and curved motion removes the identified degeneracies and yields full local weak observability of the seven-state system. The analysis provides a theoretical basis for selecting calibration trajectories that sufficiently excite both steering and sensor-extrinsic parameters.

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