Observability Analysis of Joint Steering and Extrinsic Calibration

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.

In this paper, we present a visual-inertial-wheel odometry (VIWO) framework with online calibration for four-wheel independently steered and driven (4WIS4WID) mobile robots. We derive a 2D odometry model directly from the four driving velocities and steering angles, using both the longitudinal rolling constraints and the lateral no-slip constraints of all wheels. A preintegration model and analytical Jacobians are developed for efficient filtering and calibration. An observability analysis of the linearized VIWO system shows that a drive-only model makes all steering offsets unobservable, whereas the proposed redundant model restores their observability. The analysis also identifies four standard VINS unobservable directions and three additional directions associated with the arbitrary placement of the odometry reference frame. Furthermore, we characterize several degenerate motions, including zero yaw rate, constant steering, and a non-rolling wheel, and derive the corresponding excitation conditions for the thirteen wheel intrinsics that remain after fixing the odometry frame reference. The performance of the proposed system has been demonstrated in both simulation and real-world experiments on a 4WIS4WID mobile robot.

Target-based extrinsic calibration estimates the rigid transform between sensors from a few observations of a known target, and its result is commonly assessed by the root-mean-square error of the fitted residuals. However, this scalar error is computed on the same observations and therefore cannot indicate whether to accept the result, re-extract, recollect or add observations. This paper presents VeriCalib, which formulates extrinsic calibration as a verifiable estimation problem and reports a calibration state. The key insight is a two-level extrinsic compensation mechanism, in which the extrinsic compensates the rigid part of each observation error at the residual level, and rotation and translation compensate each other at the parameter level. Consequently, the fitted residual can reveal neither an inconsistency between the observations and the model nor whether the estimated extrinsic is reliable in every direction. Accordingly, we assess the calibration through a structured covariance that jointly propagates the uncertainty of the camera and LiDAR board features with a known-geometry prior, and estimate its scale as a variance component from the residuals. On this covariance, we decouple rotation and translation to resolve the precision along each direction and guide data collection toward the weakest one. Since this precision presumes consistent observations, we further develop within-view and cross-view checks that examine the internal residual and the rigid discrepancy between observations, respectively, with thresholds that hold their significance level under an unknown noise level. We also extend the minimal detectable bias to the extrinsic to bound the smallest detectable fault along each direction. These criteria form a calibration state that indicates whether to accept the result or how to collect the data...