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Online Joint Calibration of Steering Offset and Planar LiDAR Extrinsics for Wheeled Mobile Robots
Subodh Mishra, Arindam Dhar, Suprotim Majumdar, Naveen Arulselvan
TL;DR
Miscalibrated steering sensing and drifting LiDAR-to-vehicle extrinsics complicate reliable WMR path tracking, while manual or CAD-based calibration remains vulnerable to error. The paper introduces an EKF that jointly estimates steering offset and planar LiDAR extrinsics within a bicycle model, and reports that steering compensation reduces CTE in real-robot experiments.
Problem
Manual steering-zero alignment and fixed CAD-based LiDAR extrinsics can leave WMR sensor-fusion parameters miscalibrated, affecting motion estimation and path tracking.
Method
An EKF augments a bicycle-kinematics state with steering bias and planar LiDAR extrinsics, estimating them online by fusing vehicle kinematics with LiDAR odometry.
Results
CTE-RMSE rose from 0.071 m to 0.174 m when miscalibration was exaggerated, while compensation lowered it to 0.059 m in Run Set 3.
Takeaways & Limitations
The results support online joint calibration as a method for detecting steering miscalibration, estimating LiDAR extrinsics, and improving closed-loop path tracking.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
The paper addresses manual steering-zero calibration and fixed LiDAR extrinsics by jointly estimating both online with an EKF during natural WMR motion. Experiments show that the approach detects steering miscalibration, estimates extrinsics, and improves path tracking.
- Motivation: Manual steering-zero alignment and CAD-fixed LiDAR extrinsics can introduce systematic drift, trajectory distortion, and elevated CTE in safety-critical WMR operation.LiDAR mounting flex, vibration, and re-assembly can alter the true extrinsics over time.
- Approach: The proposed EKF jointly estimates steering-angle offset and full planar LiDAR extrinsics within a bicycle-model vehicle during natural motion.The augmented state includes xoff, yoff, θoff, and additive steering bias δoff, fused with LiDAR odometry.
- Findings: The approach correctly detects steering miscalibration, converges to reliable extrinsics, and improves CTE during closed-loop control.These outcomes support evaluating calibration through its effect on the complete calibration-to-control pipeline.
- Evaluation: The authors evaluate convergence, cross-platform generalization, and steering-offset effects on CTE using two WMRs over several days of operation and re-assembly.The study uses LiDAR, wheel-encoder velocity, and steering-angle measurements from the experimental platforms.
- Positioning: Unlike prior approaches, the method requires no external aids or pre-scripted trajectory, while still requiring sufficient motion excitation because of inherent unobservabilities.The paper positions this as online joint calibration for bicycle-model WMRs rather than differential-drive platforms or controlled calibration paths.
III. BICYCLE KINEMATIC MODEL
The paper models the WMR with planar bicycle kinematics and treats steering bias as a slowly varying offset in the measured steering angle. Retaining the full bicycle relationship preserves the coupling between steering miscalibration and trajectory curvature.
- State and inputs: The WMR state contains global pose (xk, yk, θk), with position at the rear-axle center and heading θk, while velocity and steering are encoder-derived inputs.Longitudinal velocity vk comes from wheel encoders, and steering input δmeas,k comes from the steering encoder.
- Steering bias: Mechanical misalignment, wear, or encoder inconsistencies are modeled as a slowly varying steering bias, with δoff,k estimated as an unknown constant or slow-varying offset.The true steering angle is represented as measured steering angle minus the offset.
- Motion model: Under small-slip bicycle kinematics, the vehicle pose evolves using wheelbase L; zero-order-hold discretization over Δtk produces the discrete-time update.The discrete model uses the measured inputs held constant over the sampling interval.
- Observability: Retaining the full bicycle model keeps steering offset coupled to predicted curvature and preserves its observability, unlike a unicycle simplification using yaw rate as control input.The paper identifies the v tan(δ)/L relation as the coupling that the simplification obscures.
B. State Augmentation
The augmented state includes planar LiDAR-to-vehicle extrinsics and steering bias, whose evolution is modeled as a random walk.
- The state vector is augmented with planar LiDAR-to-vehicle extrinsic parameters and steering bias.
- These calibration quantities evolve according to a random-walk model.
- Small process-noise terms allow gradual adaptation to mechanical drift or reassembly-induced changes.
C. Process Model Jacobian
The process and measurement formulation combines a linearized bicycle-model propagation with LiDAR-odometry measurements linked through a motion-based calibration constraint.
- The EKF propagation linearizes the motion model about the current state estimate to obtain state and input Jacobians.
- LiDAR odometry supplies measurements for updating the state variables.
- The motion-based calibration constraint relates motions of two rigidly attached coordinate frames through their extrinsic calibration.
- Vehicle kinematics estimate one frame’s motion, while LiDAR odometry estimates the LiDAR motion.
C. Measurement Model
The measurement model uses relative LiDAR odometry and the motion-based calibration constraint to predict a planar LiDAR transform from the augmented state.
- Relative LiDAR odometry is used as the measurement for the EKF measurement model.
- The measurement is written as a function of the state, zk = h(sk).
- Expanding the model yields a planar relative transform defined using position and heading differences.The differences are Δxk = xk − x0, Δyk = yk − y0, and Δθk = θk − θ0.
- The model and its Jacobian are used in the EKF update to minimize innovation between observed and predicted relative LiDAR poses.
V. EKF FORMULATION
The full formulation casts online calibration as an EKF over vehicle pose, planar LiDAR extrinsics, and steering bias, maintaining a Gaussian belief over the augmented state.
- The full EKF pipeline combines the process and measurement models for online calibration.
- The augmented state contains vehicle pose, planar LiDAR extrinsics, and steering bias.
- The EKF maintains a Gaussian belief represented by the state estimate and covariance, (ŝk, Pk).
A. Nonlinear Process Model
Small random-walk noise is injected into the calibration parameters so they can gradually adapt during online estimation.
- Small random-walk noise is injected into xoff, yoff, θoff, and δoff to allow gradual calibration-parameter adaptation.
B. State Prediction
The EKF predicts state and covariance from the current estimate and process model, then corrects them when LiDAR-odometry poses arrive.
- State Prediction: State prediction uses the current estimate, input, process Jacobians, and process covariance.
- Measurement Correction: LiDAR-odometry availability triggers an EKF correction using a measurement model that predicts the relative LiDAR pose from the current state.
- Measurement Correction: The correction computes the measurement Jacobian, innovation covariance, innovation, and Kalman gain before producing corrected estimates.
- Measurement Correction: Measurement noise covariance is obtained from LiDAR-odometry statistics.
VI. EXPERIMENTAL EVALUATION
Experiments evaluated estimator convergence across load and initialization conditions, including autonomous figure-eight trajectories and zero-state initialization.
- Evaluation Design: The study evaluates convergence under different load and initial conditions among five validation tasks on two WMRs.
- Estimator Convergence: Across no-load and 500 kg-load figure-eight trials, the EKF converges to stable estimates of xoff, yoff, θoff, and δoff.
- Estimator Convergence: Under load conditions, the known extrinsic reference is [0.434m, 0.0, 0.0], with a consistent ∼1 cm estimated x-component shift.
- Zero Initialization: Both CAD-provided and zero initialization strategies yield closely matching estimates.
- Zero Initialization: With zero initialization, the filter converges to steady-state values using intentionally relaxed initial covariance bounds.
B. Cross-Platform Generalization
Cross-platform and induced-offset experiments show stable extrinsic estimation and improved path tracking when steering-offset compensation is applied.
- Cross-Platform Generalization: On a smaller same-family robot, estimated extrinsics converged to [0.2597 m, 0.0101 m, −1.29°] against [0.26 m, 0.0 m, 0.0°], with steering bias −1.11°.
- Physically Induced Steering Offset: Physically induced positive and negative steering offsets were reliably detected, while steering bias and LiDAR extrinsics remained stable.
- Physically Induced Steering Offset: 0.27° was the worst-case steering-offset recovery error, and three independent 5° trials had a standard deviation of 0.03°.
- Impact on Cross-Track Error: In Run Set 3, CTE-RMSE increased from 0.071 m to 0.174 m when miscalibration was exaggerated, then decreased to 0.059 m with compensation.
- Evaluation Boundary: CTE-RMSE summarizes system-level error affected by controller tuning, wheel slip, floor conditions, and transient disturbances.
- Impact on Cross-Track Error: Compensation produced concentrated absolute-CTE distributions with few large-error outliers, unlike the broader, right-shifted distributions under exaggerated offset.
E. Impact of Steering Offset on Odometry
Across manual teleoperation and autonomous navigation, steering-bias compensation keeps bicycle-model propagation aligned with the EKF estimate, while uncompensated propagation drifts substantially.
- In both manual teleoperation and autonomous navigation, the bias-compensated bicycle model remains tightly aligned with the EKF estimate.
- The uncompensated bicycle model diverges rapidly from the true motion across both experiment types.
- The compensated bicycle propagation can provide a standalone local state estimate where LiDAR-odometry updates are unavailable or unreliable.The paper specifically identifies narrow corridors and low-structure regions as settings where LiDAR odometry often fails.
- The method jointly estimates planar LiDAR extrinsics and steering-angle offset using an EKF measurement model based on LiDAR-odometry pose.