Analysis of Local Weak Observability in Planar Bicycle-Model Vehicles
This report explores the observability of vehicle pose and sensor calibration in robotics.
This technical report investigates the local weak observability of a planar bicycle-model vehicle by jointly estimating vehicle pose, planar LiDAR extrinsic calibration, and steering-angle bias.
Methodology
A Lie-derivative-based nonlinear observability analysis is employed to assess various motion types, including stationary, straight-line, constant-curvature, and combined straight-plus-arc motion.
Findings
The observability matrices and nullspaces reveal the coupling of pose, LiDAR translation, yaw offsets, and steering bias across different motion primitives. While stationary motion and individual primitives maintain unobservable directions, the combination of straight and curved motion achieves full local weak observability of the seven-state system.
Implications
This analysis lays the groundwork for selecting effective calibration trajectories that adequately excite both steering and sensor-extrinsic parameters.