Time to Line Crossing for Lane Departure Avoidance: A Theoretical Study and an Experimental Setting

Mammar, Saïd; Glaser, Sébastien; Netto, Mariana · 2006 · OpenAlex-citations

DOI: 10.1109/tits.2006.874707

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the challenge of accurately computing Time to Line Crossing (TLC), a critical metric for lane departure avoidance systems and driver assistance technologies. While TLC is essential for evaluating driver performance and triggering corrective actions, real-time computation is hindered by the difficulty of observing vehicle state variables and predicting trajectories on curved roads. Existing methods often rely on simplified approximations, such as the ratio of lateral distance to lateral speed, which are invalid when lateral speed varies or when road curvature is significant. The authors aim to develop a robust Distance to Line Crossing (DLC) based computation of TLC that accounts for vehicle dynamics, road curvature, and varying steering conditions. The study employs a theoretical approach combined with experimental validation. The authors derive geometric formulas for DLC and TLC using kinematic and dynamic models of the vehicle. These derivations cover both straight and curved road sections, considering scenarios with zero steering angle and constant non-zero steering angles. To handle the complexity of curved paths, the paper provides approximate solutions suitable for real-time computation. Additionally, a linear dynamic model is utilized to predict future vehicle positions, and an unknown input observer scheme is proposed to estimate unmeasured vehicle states and road curvature. The theoretical methods are evaluated on a digitalized test track and validated through experiments using an equipped prototype vehicle on a 3.5 km test track featuring both straight and curved sections. The results demonstrate that the proposed observer effectively estimates track curvature, enabling accurate TLC computation. The analysis reveals that simple approximations are insufficient for reliable lane departure prediction. Specifically, the findings highlight the necessity of incorporating vehicle dynamics into TLC calculations to serve as a valid indicator for lane departure avoidance. The derived formulas successfully account for the influence of road radius of curvature and vehicle positioning, providing a more comprehensive assessment of the time available before a lane boundary is crossed. The significance of this work lies in its contribution to the development of advanced driver assistance systems. By providing a method to compute TLC that accounts for complex driving scenarios, including curved roads and dynamic vehicle behavior, the paper supports the design of more effective preventive and short-term decision assistance systems. The ability to accurately estimate TLC allows for better timing of warnings and active trajectory corrections, thereby enhancing safety and driver performance evaluation. The study underscores the importance of integrating vehicle dynamics and road geometry in the design of intelligent transportation systems.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• lane positioning