A Sigmoid-Based Car-Following Model to Improve Acceleration Stability in Traffic Oscillation and Following Failure in Free Flow

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.