Trajectory planning for connected and automated vehicles at isolated signalized intersections under mixed traffic environment

Trajectory planning for connected and automated vehicles (CAVs) has the potential to improve operational efficiency and vehicle fuel economy in traffic systems. Despite abundant studies in this research area, most of them only consider trajectory planning in the longitudinal dimension or assume the fully CAV environment. This study proposes an approach to the decentralized planning of CAV trajectories at an isolated signalized intersection under the mixed traffic environment, which consists of connected and human-driven vehicles (CHVs) and CAVs. A bi-level optimization model is formulated based on discrete time to optimize both the longitudinal and lateral trajectories of a single CAV given signal timings and the trajectory information of surrounding vehicles. The upper-level model optimizes lateral lane-changing strategies. The lowerlevel model optimizes longitudinal acceleration profiles based on the lane-changing strategies from the upper-level model. Minimization of vehicle delay, fuel consumption, and lane-changing costs are considered in the objective functions. A Lane-Changing Strategy Tree (LCST) and a Parallel Monte-Carlo Tree Search (PMCTS) algorithm are designed to solve the bi-level optimization model. CAV trajectories are planned one by one according to their distance to the stop bar. A rolling horizon scheme is applied for the dynamic implementation of the proposed model with time-varying traffic conditions. Numerical studies validate the advantages of the proposed trajectory planning model compared with the benchmark cases without CAV trajectory planning. The average fuel consumption and lane-changing numbers of CAVs can be reduced noticeably, especially with high traffic demand. The delay of CAVs is reduced by similar to 2 s on average, which is limited due to the fixed signal timing plans. The trajectory planning of CAVs also reduces the delay and the fuel consumption of CHVs and the mixed traffic, especially with high penetration rates of CAVs. The sensitivity analysis shows that the control zone length of 200 m is sufficient to ensure the satisfactory performance of the proposed model.