A Deterministic Polygon-Based Approach for Real-Time Mobile Robot Localization with Sparse LiDAR Data

This study proposes the Geometric Similarity Registration (GSR) algorithm as a deterministic, computationally efficient framework for real‑time mobile robot localization in sparse, noisy, and incomplete LiDAR data scenarios. The primary objective is to achieve sub‑centimeter translational and sub‑degree rotational accuracy while operating within the strict processing and power constraints of embedded platforms. The novelty lies in formulating localization as a polygonal shape‑based similarity optimization, integrating ISS‑enhanced corner detection, Virtual Straw feature extraction, and ca‑point matching, thereby eliminating dense point correspondences and probabilistic sampling. Experimental figures show rapid alignment of Real Spatial Description (RSD) and Virtual Spatial Description (VSD) contours across displacement–rotation cases up to 300 cm and 45°, with error convergence in 4–5 iterations. Quantitatively, GSR achieved a maximum absolute positional error of 0.12 cm , mean absolute error of 0.07 cm , and maximum orientation error of 0.08°, outperforming the closest baseline by over 50% in accuracy while reducing average execution time from 25.7 ms to 18.3 ms. Robustness tables reveal a success rate of 96.7% under 20% LiDAR point dropout and 88.4% even at 40% dropout, alongside 95.2% success under ±0.5° angular noise. These combined visual and numerical results confirm GSR’s ability to deliver consistent, high‑precision localization for resource‑constrained, safety‑critical robotic applications.