Characterization of String Stability for Nonlinear Automated Vehicles Theory and Field-data Verify

This study proposes an advanced non-linear car-following model for automated vehicles (AVs) equipped with adaptive cruise control (ACC) function, referred to as the multivariate piecewise linear (MPL) model. The MPL model is a progression from the traditional piecewise linear model, integrating multiple breakpoints to illustrate the non-linearity of AVs across inputs from multivariate dimensions. These breakpoints, determined through analysis of real trajectory data, facilitate the reflection of the true behavioral characteristics of ACC vehicles. Thus, the MPL model not only maintains the interpretability inherent to traditional linear car-following models but also enhances fitness accuracy, ensuring a more precise representation of the AV's movement dynamics. The MPL model was calibrated using data collected from a large-scale field experiment by Tesla Model 3. The calibration and verification outcomes indicate that our model provides a superior fit compared to traditional linear models and enhanced intelligent driver models for ACC vehicles. Of particular note are the final breakpoints in the MPL model, which are < ![if !msEquation] > < ![endif] >, < ![if !msEquation] > < ![endif] >, and < ![if !msEquation] > < ![endif] >. . This marked double increment is intriguing and is likely attributable to the synergy between Tesla's initial controller and powertrain design.

The MPL model is open source and can be customized and implemented into existing microsimulation simulation platforms to meet different application requirements in the future. A use case is conducted on an I-75 highway segment in a microsimulation simulation platform where the proposed MPL model is used to control ACC vehicles’ car-following behavior in mixed traffic This use case drew a set of managerial insights into how different market penetration rates and high/low-volume impact the traffic performance including mobility, stability, and fundamental diagram (density versus volume) to demonstrate the performance of the proposed MPL model.