Traffic conflict identification method on curved road based on Frenet coordinate system.

Wu, Jingan; Zhu, Shunying; Jiang, Ruoxi; He, Taotao; Chen, Jinquan · 2026 · DOAJ

DOI: 10.1371/journal.pone.0344023

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Summary

This paper addresses the limitations of traditional traffic conflict identification methods, specifically Time to Collision (TTC) and its derivatives, when applied to curved road segments. Existing approaches predominantly rely on the Cartesian coordinate system, which assumes vehicles maintain constant speed and direction. This assumption leads to unclear definitions of vehicle trajectory on curves and results in significant missed or erroneous judgments of conflicts, particularly at junctions between straight and curved sections. To resolve these issues, the authors propose a new method based on the Frenet coordinate system, which simplifies trajectory calculation by aligning coordinates with the road centerline. The methodology involves three main steps. First, a Frenet coordinate system is established using the road centerline as a reference, converting vehicle trajectory coordinates from Cartesian to Frenet space. Second, a vehicle state determination process classifies vehicles as either in a "non-lane-change" or "lane-change" state based on the parallelism of their trajectory to the road centerline over a 0.5-second interval. Third, TTC is calculated within this framework to identify rear-end and lane-change conflicts. The study validates this approach using 4 hours of video data collected via drone from the K283 lane-switch work zone of the Jiqing Highway in China. The data processing pipeline included image calibration, vehicle detection using adjacent frame subtraction, and tracking via a spatio-temporal context-based method. The results demonstrate that the Frenet-based method significantly improves conflict identification accuracy compared to the traditional Cartesian approach. The new method reduced missed judgments of serious rear-end conflicts, particularly at straight-to-curve transition zones, and eliminated wrong judgments of serious lane-change conflicts where traditional methods projected conflict points outside the road. Specifically, the new method identified 125 additional serious rear-end conflicts. Analysis of these added conflicts revealed that the maximum deceleration of 10 involved vehicles exceeded dangerous thresholds (−4 m/s² and −1.5 m/s²), confirming the validity of the newly identified risks. The significance of this research lies in its ability to expand traffic conflict identification from straight roads to full-line road alignments, including complex curved sections. By combining the Frenet coordinate system with vehicle state determination and TTC, the method provides a more reliable and computationally efficient tool for assessing traffic safety on curved roads. This approach offers better generalization across varied scenarios and helps researchers and practitioners more accurately identify and mitigate risks associated with vehicle maneuvers on curves.

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