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

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.

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...

Target-based LiDAR-camera extrinsic calibration is a prerequisite for multi-sensor fusion in robotics. However, in the widely adopted four-hole pipeline, \rt{calibration accuracy is limited by hole-center extraction in the LiDAR side, where sparse angular coverage and mixed-pixel returns displace the estimated centers}. This paper presents P$^2$Calib, which exploits pattern priors, geometric constraints specified by the CAD model of the target board, to improve calibration accuracy. First, we incorporate the known hole radius as a fitting constraint to prevent center estimates from degrading under sparse angular coverage. Building on the improved hole estimates, we further enforce the rigid rectangular layout of the four holes as a global consistency constraint to correct residual errors across holes. Both priors are integrated into an \rt{interactive tool that runs the pipeline from target detection to the final extrinsic}. Experiments on simulated and real datasets show that P$^2$Calib reduces the joint registration residual by 90% and 82% and the held-out reprojection error by 96% and 77% over the baseline. \rt{We will release the code and data\codelink{} to facilitate future research.