张维刚　张朋　韦昊　熊觉振

摘   要：在低附着路面情况下，针对现有以线性时变模型预测控制（LTVMPC）为基础的无人驾驶汽车路径跟踪精确性和稳定性问题，提出一种改进的控制算法. 以汽车动力学理论为基础，将四轮轮胎侧偏角和滑移率精确地表示为车辆状态量的非线性函数，在预测时域内对车辆状态方程线性化处理而求解雅可比矩阵时，为降低系统维度，将轮速作为非状态量，建立改进的三自由度车辆模型，在二次规划性能指标中加入横摆角速度跟踪误差项以提高路径跟踪性能，考虑质心侧偏角对跟踪精度和车辆稳定性的影响，修正参考横摆角，建立改进的LTVMPC. 在Carsim-Simulink联合仿真平台进行低附着系数路面情况下的双移线跟踪仿真，结果表明改进后的控制算法在保证实时性的前提下，提高了路径跟踪的精确性和车辆行驶的稳定性.

关键词：无人驾驶汽车;路径跟踪;线性时变模型预测控制;二次规划

中图分类号：U467.1                                 文献标志码：A

An Improved Path Tracking Control Algorithm

for Autonomous Vehicle Based on LTVMPC

ZHANG Weigang ZHANG Peng WEI Hao XIONG Juezhen

（State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body，Hunan University，Changsha 410082，China）

Abstract：Under the case of low adhesion road，an improved control algorithm is proposed to solve the problem of the lack of accuracy and stability in the path tracking of autonomous vehicles based on Linear Time-Varying Model Predictive Control （LTVMPC）. Based on vehicle dynamics，the slip angles and ratios of four tires are accurately expressed as the nonlinear function of vehicle state parameters. The Jacobian matrix is obtained by taking wheel speed as constant when linearizing the vehicle state equation in prediction horizon so as to reduce the dimension of the system，which aims to establish the improved 3-DOF vehicle model. The yaw rate tracking error is added into the performance index of quadratic programming to improve the path tracking performance and the influence of the slip angle of vehicle on the tracking accuracy and vehicle stability is considered to modify the reference yaw angle，which improves the overall performance of LTVMPC. The double lane change tracking simulation under the condition of low adhesion coefficient is performed on Carsim-Simulink co-simulation platform，and the results show that the improved control algorithm can increase the accuracy of path tracking and stability of vehicle while ensuring real-time performance.

Key words：autonomous vehicle;path tracking;Linear Time-Varying Model Predictive Control（LTVMPC）;quadratic programming

路径跟踪是无人驾驶汽车自主行驶过程中的基本任务和关键环节，其主要目标是使车辆自动沿着规划路径安全稳定地行驶[1]. 当车辆行驶在低附着路面上时，由于此时车辆极易处于失稳状态，路径跟踪精确性和车辆行驶稳定性就面临着很大的挑战.

为了增强路径跟踪控制效果，相关研究人员提出了许多算法. 模型预测控制（MPC）由于能够有效处理系统约束、方便建立多输入多输出控制系统且具备前……