基于自适应预测时域MPC的轨迹跟踪控制

doi:10.3969/j.issn.1674-8484.2025.05.012

摘要/Abstract

摘要： 针对自动驾驶车辆轨迹跟踪控制中通常未考虑道路曲率和车速信息的问题，为抑制车辆轨迹跟踪过程中的横向偏差并增强控制系统的抗干扰性，提出了一种结合模糊控制策略的时域自适应调整模型预测控制（MPC）轨迹跟踪控制算法。通过建立车辆的运动学模型以及模型预测控制器，设计不同速度工况，将道路曲率和期望车速作为模糊控制输入，利用模糊控制器优化模型预测控制算法的预测时域参数；采用Carsim和Simulink联合仿真，分别在2个不同曲率的轨迹上进行不同速度的轨迹跟踪控制。结果表明：自适应时域模型预测控制器（MPC）在双移线工况下，相比固定时域控制器和线性二次型调节器（LQR），低速（30 km/h）和高速（90 km/h）时横向误差最大降低85.81%和78.86%；在多弯道工况下，低速和高速时横向误差最大降低96.32%和86.4%。该控制策略能显著提升系统跟踪性能，在不同速度工况下能够有效降低轨迹偏差并维持车辆动态稳定性。

关键词: 自动驾驶, 轨迹跟踪, 自适应, 模型预测控制（MPC）

Abstract:

A trajectory tracking control algorithm integrating fuzzy control strategy with time-domain adaptive adjustment model predictive control (MPC) was proposed. to address the issue that road curvature and vehicle speed information are usually not considered in autonomous vehicle trajectory tracking control, and to suppress lateral deviations during vehicle trajectory tracking while enhancing the anti-interference ability of the control system, A vehicle kinematic model and a model predictive controller were established, different speed conditions were designed, road curvature and desired vehicle speed were taken as fuzzy control inputs, and the prediction horizon parameters of the MPC algorithm were optimized via the fuzzy controller. Joint simulations using Carsim and Simulink were carried out to implement trajectory tracking control at different speeds on two trajectories with distinct curvatures. The results show that, in the double lane change scenario, compared with the fixed-horizon controller and linear quadratic regulator (LQR), the adaptive time-domain MPC controller achieves a maximum reduction of 85.81% and 78.86% in lateral errors at low speed (30 km/h) and high speed (90 km/h) respectively; in the multi-curve scenario, it realizes a maximum reduction of 96.32% and 86.4% in lateral errors at low speed and high speed respectively. These findings confirm that the proposed control strategy can significantly improve the system's tracking performance, effectively reduce trajectory deviations and maintain the dynamic stability of the vehicle under different speed conditions.

Key words: autonomous driving, trajectory tracking, adaptive, model predictive control (MPC)

中图分类号:

U471.15

郑讯佳, 曹泽义, 陈星, 刘辉, 高建杰. 基于自适应预测时域MPC的轨迹跟踪控制[J]. 汽车安全与节能学报, 2025, 16(5): 773-783.

ZHENG Xunjia, CAO Zeyi, CHEN Xing, LIU Hui, GAO Jianjie. Trajectory tracking control based on adaptive prediction time-domain MPC[J]. Journal of Automotive Safety and Energy, 2025, 16(5): 773-783.

图/表 14

图1 三自由度车辆动力学模型

图2 控制系统整体结构框架

图3 30 km/h工况下的轨迹跟踪性能与横向误差分析

图4 90 km/h工况下的轨迹跟踪性能与横向误差分析

图5 道路曲率

图6 道路曲率隶属度函数图

图7 车速隶属度函数图

图8 预测时域隶属度函数关系

曲率	车速
曲率	TV	NV	SV	MV	FV	HV
TK	HL	HL	FL	ML	ML	NL
SK	HL	HL	FL	ML	ML	NL
MK	ML	ML	SL	NL	NL	TL
FK	ML	ML	SL	NL	TL	TL
HK	NL	NL	TL	TL	TL	TL

表1 模糊规则表

整车质量/ kg	1 416
转动惯量/ (kg·m²)	1 536.7
前轴到质心的距离/ mm	1 015
后轴到质心的距离/ mm	1 895
前轮侧偏刚度/ (N·rad^-1)	-112 600
后轮侧偏刚度/ (N·rad^-1)	-89 500

表2 车辆模型参数

图9 30 km/h工况下轨迹跟踪与动态参数分析

图10 90 km/h工况下轨迹跟踪与动态参数分析

图11 30 km/h工况下轨迹跟踪与动态参数分析

图12 90 km/h工况下轨迹跟踪与动态参数分析

参考文献 18

[1]	石钧仁, 孙冬野, 秦大同, 等. 装载机避障轨迹规划及模型预测轨迹跟踪[J]. 中国公路学报, 2021, 34(5): 224-236. doi: 10.19721/j.cnki.1001-7372.2021.05.021
	SHI Junren, SUN Dongye, QIN Datong, et al. Obstacle avoidance trajectory planning and model predictive trajectory tracking for loaders[J]. China J Highw Transport. 2021, 34(5): 224-236. (in Chinese)
[2]	张平, 陈一凡, 江书真, 等. 高速公路上自动超车过程的轨迹规划与跟踪控制[J]. 汽车安全与节能学报, 2022, 13(3): 463-472.
	ZHANAG Ping, CHEN Yifan, JIANG Shuzhen, et al. Trajectory planning and tracking control for automatic overtaking process on highways[J]. J Autom Safe Energ, 2022, 13(3): 463-472. (in Chinese)
[3]	刘平, 刘自斌, 杨明亮, 等. 考虑道路曲率的多约束高速无人驾驶汽车横向跟踪控制方法[J]. 长安大学学报(自然科学版), 2023, 43(2): 120-134.
	LIU Ping, LIU Zifu, YANG Mongliang, et al. A multi-constraint lateral tracking control method for high-speed autonomous vehicles considering road curvature[J]. J Chang'an Univ (Nat Sci Edit). 2023, 43(2): 120-134. (in Chinese)
[4]	ZHENG Xunjia, LI Huilan, ZHANG Qiang, et al. Intelligent decision-making method for vehicles in emergency conditions based on artificial potential fields and finite state machines[J]. J Intel Connect Vehi. 2024, 7(1): 19-29.
[5]	刘卫东, 张超, 江会华, 等. 基于改进纯跟踪的低速智能汽车轨迹跟踪控制[J]. 科学技术与工程, 2024, 24(25): 10983-10992.
	LIU Weidong, ZHNAG Chao, JIANG Huihua, et al. Trajectory tracking control for low-speed intelligent vehicles based on improved pure pursuit[J]. Sci Tech Engi. 2024, 24(25): 10983-10992. (in Chinese)
[6]	孙晓晋, 杨帆, 马惠雯, 等. 基于模型预测控制的无人矿车轨迹跟踪[J]. 天津城建大学学报, 2024. 30(5): 365-371.
	SUN Xiaojin, YANG Fan, MA Huiwen, et al. Trajectory tracking of unmanned mining vehicles based on model predictive control[J]. J Tianjin Chengjian Univ, 2024, 30(5): 365-371. (in Chinese)
[7]	石振新, 冯剑波, 王衍学. 基于MPC和模糊控制的智能汽车路径追踪研究[J]. 车辆与动力技术. 2022(2): 7-11.
	SHI Zhenxin, FENG Jianbo, WANG Yanxue. Research on path tracking of intelligent vehicles based on MPC and fuzzy control[J]. Vehi Powe Tech, 2022(2), 7-11. (in Chinese)
[8]	Park M, Kang Y. Experimental verification of a drift controller for autonomous vehicle tracking: a circular trajectory using LQR method[J]. Int’l J Contr Autom Syst, 2021, 19: 404-416.
[9]	张志勇, 龙凯, 杜荣华, 等. 自动驾驶汽车高速超车轨迹跟踪协调控制[J]. 汽车工程, 2021, 43(7): 995-1004.
	ZHANG Zhiyong, LONG Kai, DU Ronghua, et al. Coordinated control for trajectory tracking of autonomous vehicles during high-speed overtaking[J]. Autom Engineering, 2021, 43(7): 995-1004. (in Chinese)
[10]	CHENG Shuo, LI Liang, CHEN Xiang, et al. Model-predictive-control-based path tracking controller of autonomous vehicle considering parametric uncertainties and velocity-varying[J]. IEEE Trans Ind Elect, 2021, 68(9): 8698-8707. doi: 10.1109/TIE.2020.3009585 URL
[11]	ZHANG Kunwu, SUN Qi, SHI Yang. Trajectory tracking control of autonomous ground vehicles using adaptive learning MPC[J]. IEEE Trans Neur Netw Lear Syst, 2021, 32(12): 5554-5564.
[12]	刘溯奇, 王刚, 安伟彪, 等. 基于变预测时域的电动汽车轨迹跟踪控制[J]. 科学技术与工程, 2021, 21(17): 7348-7354.
	LIU Shuoqi, WANG Gang, AN Weibiao, et al. Trajectory tracking control of electric vehicles based on variable prediction horizon[J]. Sci Tech Engi, 2021, 21(17): 7348-7354. (in Chinese)
[13]	李致远, 李晓蕊. 基于自适应LQR的智能汽车横纵向控制[J]. 汽车实用技术. 2023, 48(2): 101-107. doi: 10.16638/j.cnki.1671-7988.2023.02.019
	LI Zhiyuan, LI Xiaoxin. Integrated lateral and longitudinal control of intelligent vehicles based on adaptive LQR[J]. Autom Appl Tech, 2023, 48(2): 101-107. (in Chinese)
[14]	陈梓宁, 童亮, 李晓东, 等. 自适应时域模型预测控制的轨迹跟踪控制[J]. 重庆理工大学学报(自然科学), 2024, 38(5): 78-85.
	CHEN Zining, TONG Liang, LI Xiaodong, et al. Trajectory tracking control based on adaptive time-domain model predictive control[J]. J Chongqing Univ Tech(Nat Sci), 2024, 38(5): 78-85. (in Chinese)
[15]	范贤波, 彭育辉, 钟聪. 基于自适应MPC的自动驾驶汽车轨迹跟踪控制[J]. 福州大学学报(自然科学版), 2021, 49(4): 500-507.
	FAN Xianbo, PENG Yuhui, ZHONG Cong. Trajectory tracking control of autonomous vehicles based on adaptive MPC[J]. J Fuzhou Univ (Nat Sci), 2021, 49(4): 500-507. (in Chinese)
[16]	杜荣华, 胡鸿飞, 高凯, 等. 基于变预测时域MPC的自动驾驶汽车轨迹跟踪控制研究[J]. 机械工程学报, 2022, 58(24): 275-288. doi: 10.3901/JME.2022.24.275
	DU Ronghua, HU Hongfei, GAO Kai, et al. Research on trajectory tracking control of autonomous vehicles based on variable prediction horizon MPC[J]. J Mech Engi, 2022, 58(24): 275-288. (in Chinese)
[17]	章杰, 林华, 高建杰, 等. 考虑变论域模糊转角补偿和网络时滞的智能车辆轨迹跟踪控制[J]. 重庆交通大学学报(自然科学版), 2024, 43(11): 103-113.
	ZHANG Jie, LIN Hua, GAO Jianjie, et al. Trajectory tracking control of intelligent vehicles considering variable universe fuzzy steering compensation and network time delay[J]. J Chongqing Jiaotong Univ (Nat Sc), 2024, 43(11): 103-113. (in Chinese)
[18]	朱方博. 典型工况下的智能车横向跟踪控制及模式切换研究[D]. 镇江: 江苏大学, 2019.
	ZHU Fangbo. Research on lateral tracking control and mode switching of intelligent vehicles under typical operating conditions[D]. Zhenjiang: Jiangsu University, 2019. (in Chinese)