Analytical Anticipative Optimal Drivability Car-Following Model

Replicating a human car-following behavior becomes more important for developing either a human driver model or human-like adaptive cruise control. The human driver model is especially a key element in simulation tools used for the development and evaluation of connected and automated vehicle driving controls. In this paper, we propose an analytical anticipative optimal drivability car-following model that can capture a dynamic car-following behavior while maximizing driving comfort without collisions in a computational-efficient way. We formulate drivability-oriented car-following as an optimal control problem, and then reformulate it to a bi-level optimization problem in order to facilitate analytical treatment. By employing optimal control theory, we can transform the bi-level optimization problem into a nonlinear programming problem and derive its analytical solutions. To validate the proposed model, we post-processed and used Next Generation SIMulation (NGSIM) data. Results show that the proposed parametric model can generate stable car-following behaviors and its vehicle state trajectories are well matched with NGSIM data, thereby significantly improving root-mean-square error of speed and distance gap compared to the existing car-following model.