Abstract: Traditional trajectory planning methods have problems such as high computational complexity and easy to fall into local optimal solution, while model predictive control (MPC) is widely used in trajectory planning because it can consider system constraints and has high precision and robustness. This paper proposes an MPC controller based on closed-loop proportional-integralderivative (PID) for electric vehicle trajectory planning. A seven-degree-of-freedom vehicle dynamics model is constructed, it has three degrees of freedom: longitudinal, transverse and lateral. In order to study the steering characteristics, this paper constructs a two-degree-of-freedom vehicle model,integrates the longitudinal control error model and the lateral control error model to form a MPC controller based on PID, and carries out simulation and comparison test based on CarSim/Simulink. The research results indicate that the proposed trajectory planning method in this paper can achieve lane-changing with effective speed control and minimal error. The MPC controller based on closedloop PID demonstrates good accuracy and lateral stability on low-adhesion surfaces

Key words: PID; MPC; trajectory planning; CarSim/Simulink; longitudinal control; lateral control

摘要： 传统轨迹规划方法存在计算复杂度高、易陷入局部最优解等问题，而模型预测控制 （MPC）因能考虑系统约束、具有高精度和鲁棒性而被广泛应用于轨迹规划。文章针对电动 汽车轨迹规划，提出一种基于闭环比例-积分-微分（PID）的 MPC 控制器，并构建了七自由 度车辆动力学模型，包括纵向、横向、横摆三个自由度。为了研究转向特性，文章构建了二 自由度车辆模型，通过将纵向控制误差模型和横向控制误差模型集成，构成基于 PID 的 MPC 控制器，并基于 CarSim/Simulink 进行仿真对比测试。研究结果表明，文章所提出的轨迹规划 方法能实现换道，且速度控制效果好、误差小；基于闭环 PID 的 MPC 控制器在低附着路面下 具有良好的精度和横向行驶稳定性。

关键词: PID；MPC；轨迹规划；CarSim/Simulink；纵向控制；横向控制