A Sigmoid-Based Car-Following Model to Improve Acceleration Stability in Traffic Oscillation and Following Failure in Free Flow
Xingyu Chen, Weihua Zhang, Haijian Bai, Rui Jiang, Heng Ding, Liyang Wei
Abstract
This paper presents an improved Intelligent Driving Model (Sigmoid-IDM) to address the issues of excessive acceleration in traffic oscillation and following failure in free flow. The Sigmoid-IDM utilizes a Sigmoid function to enhance the starting-following characteristics, improve the output strategy of the spacing term, and stabilize the steady-state velocity in free flow. Furthermore, the model’s asymmetry is enhanced by introducing cautious following distance, caution driving factor, and segmentation function. The anti-interference ability of the Sigmoid-IDM is demonstrated through local stability and string stability analyses. The model parameters were calibrated using the Hefei dataset and High D data across various traffic scenarios: start-up, stop-go, and free-flow. The Sigmoid-IDM outperforms the IDM by significantly reducing errors and enhancing performance metrics. Specifically, in start-up and stop-go scenarios, the Sigmoid-IDM achieves a 28.57% and 19.04% reduction in Root Mean Square Error (RMSE) for acceleration, respectively. Comfort error during start-up is also lowered by 18.1%. In the free-flow scenario, the RMSE for spacing and velocity decreases by 15.64% and 16.36%, respectively. Furthermore, the Sigmoid-IDM demonstrates a more pronounced asymmetric behavior than the IDM, offering a more accurate representation of human drivers’ following patterns. The model’s efficacy was further validated through circular road simulation and Simulink-Carsim co-simulation, confirming its ability to accurately simulate the transition from synchronized flow to wide moving jams under variable parameters, as well as the traceability of its trajectory planning.