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Analysis and Mathematical Modeling of Car-Following Behavior of Automated Vehicles for Safety Evaluation

Journal Article
ISSN: 2641-9637, e-ISSN: 2641-9645
Published April 02, 2019 by SAE International in United States
Analysis and Mathematical Modeling of Car-Following Behavior of Automated Vehicles for Safety Evaluation
Citation: Rao, S., Seitz, T., Lanka, V., and Forkenbrock, G., "Analysis and Mathematical Modeling of Car-Following Behavior of Automated Vehicles for Safety Evaluation," SAE Int. J. Adv. & Curr. Prac. in Mobility 1(3):876-882, 2019,
Language: English


With the emergence of Driving Automation Systems (SAE levels 1-5), the necessity arises for methods of evaluating these systems. However, these systems are much more challenging to evaluate than traditional safety features (SAE level 0). This is because an understanding of the Driving Automation system’s response in all possible scenarios is desired, but prohibitive to comprehensively test. Hence, this paper attempts to evaluate one such system, by modeling its behavior. The model generated parameters not only allow for objective comparison between vehicles, but also provide a more complete understanding of the system. The model can also be used to extrapolate results by simulating other scenarios without the need for conducting more tests.
In this paper, low speed automated driving (also known as Traffic Jam Assist (TJA)) is studied. This study focused on the longitudinal behavior of automated vehicles while following a lead vehicle (LV) in traffic jam scenarios. The automated vehicle behavior is modeled using three car-following models. The models are then used to predict the behavior of the vehicle in a randomized scenario. This also serves as validation of the models.
In this study, three vehicles were used: a 2017 Mercedes E300, a 2017 Tesla Model S 90D, and a 2017 Volvo S90. The vehicles were tested using a typical traffic scenario, where the subject vehicle (SV) follows an LV (a 2015 Lexus LS460L). Two different velocity profiles were used, one for model fit and another for model validation. The acceleration, velocity, and position of both the SV and LV were recorded. The data for each SV were fit to three car-following models: Gazis-Herman-Rothery (GHR) model, and two novel physics-based car-following models; Stationary Time-To-Collision (STTC) model and Spring-Mass-Damper (SMD) model.
The performance of these models was evaluated by assessing their ability to predict the resulting acceleration of the SV when presented with random LV speed data. The car-following model parameters for the vehicles were then used to objectively compare their relative performance and safety. The model parameters were used to compute metrics like the SV’s response delay, system dynamics, steady-state response, time-to-collision (TTC) characteristics, etc.
The results indicate that the new SMD and STTC models are comparable in performance to the GHR model in predicting the SV accelerations. The SMD model, in addition to being accurate, also gives further insight into the safety of the vehicles. Though the STTC model predicted the SV acceleration accurately, the model coefficients could not be used to reliably gain insights into the vehicle following behavior.