Cooperative trajectory control for synchronizing the movement of two connected and autonomous vehicles separated in a mixed traffic flow

When connected and autonomous vehicles (CAVs) are widely used in the future, we can foresee many essential applications, such as platoon formation and autonomous police patrolling, which need two CAVs, initially separated in a mixed traffic flow involving CAVs and human-drive vehicles (HDVs), to quickly approach each other and then keep a stable car-following mode. The entire process should not jeopardize surrounding traffic safety and efficiency. The existing literature has not studied this CAV synchronization control well, and this study seeks to make up this gap partially. To do that, we developed a Model Predictive Control model embedded with a mixed-integer nonlinear program (MINLP-MPC), which integrates micro- and macro-traffic flow models to capture hybrid traffic flow dynamics. Specifically, the MPC will generate control law at each discrete timestamp to manage the microscopic movements of the two subject CAVs while predicting their neighboring vehicles’ movement by well-accepted car-following models and estimating the distant upstream traffic’ response by the macroscopic traffic model such as cell transmission model (CTM). The MINLP-MPC is multi-objective, seeking to sustain both synchronization and traffic efficiencies. To generate such well-balanced optimal control, we noticed that the synchronization experiences two distinct phases, sequentially completing the catch-up and platooning tasks. Accordingly, we transferred MINLP-MPC to a hybrid MPC system consisting of two sequential MPCs, respectively prioritizing the catch-up and platooning control. Then, we developed a weighting strategy to tune the control priorities adaptively. The recursive feasibility of the MPC is mathematically proved. Furthermore, we generalized the MPC and the hybrid MPC system to enable multi-vehicle synchronization. A numerical study built upon the NGSIM dataset demonstrates the efficiency and effectiveness of our approaches under different congestion levels and CAV penetrations.