Abstract: Considering the vehicle understeer, an adaptive linear quadratic regulato (LQR) control algorithm with feedforward is proposed to accomplish lane change in lateral and longitudinal control of automatic driving. Firstly, the longitudinal dual proportion integration differentiation (PID) controller is built by making the throttle brake meter. Then, the LQR lateral controller is designed based on the two-degree of freedom dynamic model of the vehicle with path tracking error, and the feedforward feedback method is used to give the vehicle an extra corner to eliminate the steady-state error. Then, by analyzing the parameters of LOR controller and considering the two key evaluation indexes of vehicle, such as stability and ride comfort, a weight parameter calculation method considering path curvature and path tracking error is proposed, so as to ensure the vehicle trajectory tracking error within a certain range. Finally, the adaptive LQR controller is effective by MATLAB/Simulink and CarSim co-simulation. The results suggest that the controller can accurately track the lane change path with a maximum lateral error of 0.027 m and a maximum heading error of 0.041 rad.

Key words: Self-driving vehicle; Lateral and longitudinal control; Adaptive LQR control; Trajectory tracking

摘要： 针对自动驾驶横纵向控制换道问题，并考虑到车辆转向不足，提出了一种带有前馈控 制的自适应线性二次型调节器（LQR）控制算法。首先，通过油门刹车表的制作搭建了纵向 双比例-积分-微分（PID）控制器，然后，基于路径跟踪误差的车辆二自由度动力学模型设计 了 LQR 横向控制器，并使用前馈反馈的方法给予车辆一个额外的转角，消除了稳态误差。再 分析 LQR 控制器参数并考虑车辆稳定性和乘坐舒适性二项关键评价指标，提出了一种考虑路 径曲率和路径跟踪误差的权重参数计算方法，从而保证了车辆轨迹跟踪误差在一定范围内。 最后，通过 MATLAB/Simulink 和 CarSim 联合仿真验证所设计的自适应 LQR 控制器。结果表 明，该控制器可以较精确地跟踪该换道路径，最大横向误差为 0.027 m，最大航向误差为 0.041 rad。

关键词: 自动驾驶车辆；横纵向运动控制；自适应 LQR 控制；轨迹跟踪