Geometric Degeneracy from Bilateral Symmetry Is Associated with Directional Localization Error in Simulated 2D LiDAR Navigation

Bilateral (Z2) symmetry produces perceptual aliasing in 2D LiDAR localization, yet whether it predicts localization failure and its direction is uncharacterized. Linking the bilateral symmetry of a laser scan to the anisotropy of the scan-matching information matrix, we predict that (i) the detected symmetry axis aligns with the axis pair of the degenerate geometry and (ii) localization error grows more along the degenerate direction than in total magnitude. All experiments are simulation-only (Gazebo, TurtleBot4, AMCL on a known map), without real-robot validation, and involve an irregular maze (control), a warehouse, and a symmetric corridor, with ten independent runs each. The symmetry axis locks onto the corridor axis pair (median folded deviation of 1.4∘ to 3.2∘, versus 14.0∘ in the control; 22.5∘ by chance), and does so in two exploratory probes. Without trajectory alignment, degeneracy correlates negatively with the error along the degenerate axis in 10/10 runs of both symmetric environments (sign test p < 0.001), but weakly to moderately (median Spearman ρ = −0.46 and −0.23), below the pre-registered threshold within individual runs; in the corridor, the effect is a contrast between fully degenerate and remaining frames, not a graded trend. The control shows neither. The geometric axis coincides with the major axis of the filter’s position uncertainty (1.1∘ to 2.7∘) but does not predict the error direction better: its value is an interpretable geometric explanation of that direction, computed from the raw scan.