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 lower-level 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 ~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.

互联和自动驾驶汽车 (CAV) 的轨迹规划有可能提高交通系统中的运营效率和车辆燃油经济性。尽管在该研究领域进行了大量研究，但大多数只考虑纵向维度的轨迹规划或假设完全 CAV 环境。本研究提出了一种在混合交通环境下在孤立的信号交叉口处分散规划 CAV 轨迹的方法，该混合交通环境由连接和人力驱动的车辆 (CHV) 和 CAV 组成。基于离散时间制定了双层优化模型，以优化给定信号时序和周围车辆轨迹信息的单个 CAV 的纵向和横向轨迹。上层模型优化横向换道策略。下层模型根据上层模型的换道策略优化纵向加速度曲线。目标函数中考虑了车辆延误、燃料消耗和换道成本的最小化。车道变换策略树 (LCST) 和并行蒙特卡洛树搜索 (PMCTS) 算法旨在解决双层优化模型。CAV 轨迹是根据它们到停止杆的距离一一规划的。滚动地平线方案用于在时变交通条件下动态实现所提出的模型。与没有 CAV 轨迹规划的基准案例相比，数值研究验证了所提出的轨迹规划模型的优势。可显着降低CAV平均油耗和换道次数，尤其是在高流量需求的情况下。CAV 的延迟平均减少了约 2 秒，这受到固定信号时序计划的限制。CAV的轨迹规划也减少了CHV和混合交通的延误和燃料消耗，特别是在CAV的高渗透率下。敏感性分析表明，200 m的控制区长度足以保证所提出模型的令人满意的性能。