Modeling Trajectories and Trajectory Variation of Turning Vehicles at Signalized Intersections

Dias, Charitha; Iryo-Asano, Miho; Abdullah, Muhammad; Oguchi, Takashi; Alhajyaseen, Wael · 2020 · DOAJ

DOI: 10.1109/ACCESS.2020.3002020

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Summary

This study addresses the lack of a reliable framework for modeling the trajectories of turning vehicles at signalized intersections, a gap that hinders the accuracy of microscopic traffic simulations, driving simulators, and autonomous vehicle motion planning. Existing models often simplify turning maneuvers or require extensive empirical calibration for specific geometries, failing to capture the physical integrity of speed and acceleration profiles influenced by intersection design. The authors propose a novel modeling approach based on the minimum-jerk principle, originally derived from neuroscience to describe smooth human arm movements, to estimate free-flow trajectories that reflect intersection geometry. The methodology combines the minimum-jerk principle with empirical regression models from Wolfermann et al. to estimate the minimum speed and its location along the turn. The model uses boundary conditions—location, velocity, and acceleration at entry and exit points—along with intersection geometric parameters such as corner radius, intersection angle, and lateral exit distance. To solve the resulting fifth-order polynomial equations for trajectory paths, the study utilizes an intermediate point (minimum speed location) to determine movement time. The model was validated using empirical trajectory data extracted via video image processing from four signalized intersections in Nagoya, Japan, covering various geometric configurations under free-flow conditions. Validation results demonstrate that the model accurately reproduces empirical trajectories. Statistical tests confirmed no significant difference between the average estimated and actual paths for right and left turns across the tested intersections. Maximum deviations between estimated and empirical paths ranged from 0.37 m to 1.06 m, with larger deviations observed at intersections with smaller corner radii. The estimated speed and acceleration profiles closely matched empirical data, confirming the model’s ability to capture kinematic properties realistically. Sensitivity analysis revealed that while curve radius did not significantly affect average speed profiles, it did influence acceleration patterns and trajectory variation; larger radii resulted in greater lateral deviation variance due to increased movement time variability. Additionally, the model successfully captured how intersection angles affect path distributions. The significance of this work lies in providing a generalized, physics-based framework for simulating turning vehicle trajectories that accounts for geometric variations without requiring site-specific calibration for every new intersection. By integrating behavioral insights from the minimum-jerk principle with geometric constraints, the model offers a robust tool for improving the reliability of safety assessments, virtual reality applications, and autonomous vehicle navigation systems. This approach enables more realistic representation of driver behavior and vehicle dynamics in complex intersection environments.

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• Theoretical Contribution: computational model