Vehicle Lateral Control Strategy Integrating Road Curvature Feedforward

doi:10.3969/j.issn.1004-132X.2025.11.036

Abstract

Abstract:

Aiming at the problems of low tracking accuracy of autonomous vehicles in the road with large curvature curves， the influences of road curvature on the lateral control strategy were focused， the lateral control strategy was improved and optimized based on the traditional model predictive control（MPC） algorithm from three aspects of vehicle model modeling， yaw stability and time domain optimization， respectively. The road curvature was integrated into the vehicle model， and an error dynamics model with curvature feedforward was established. And then， a lateral control strategy was designed based on curvature feedforward MPC algorithm. Then， a lateral stability constraint consisting of lateral vehicle speed and steady-state lateral angular velocity was added to the strategy to enhance the lateral stability of the vehicles under high curvature conditions. A MAP map was established based on genetic algorithm to optimize the prediction and control time domains of the strategy， taking into account the relationships among vehicle speed， road curvature and time domain. Simulation analysis was conducted， and the results show that the improved lateral control strategy may effectively improve the path tracking precision and lateral stability of the vehicles. Finally， the effectivenesses of the curvature feedforward MPC strategy were verified through real vehicle road tests.

Key words: curvature feedforward, lateral control strategy, vehicle model modeling, yaw stability, time domain optimization

摘要：

针对自动驾驶汽车在道路大曲率弯道下跟踪精度不高的问题，聚焦于道路曲率对横向控制策略的影响，分别从车辆模型建模、横摆稳定性和时域优化三个角度对基于传统模型预测控制（MPC）算法的横向控制策略进行了改进优化。将道路曲率融入车辆模型，建立了曲率前馈的误差动力学模型，并以此为基础设计了基于曲率前馈MPC算法的横向控制策略。然后在策略中添加了一个由横向车速和稳态横摆角速度组成的横摆稳定性约束来提高车辆在大曲率工况时的横摆稳定性。基于遗传算法建立了车速、道路曲率和时域三者之间的MAP图，以优化策略的预测时域和控制时域。进行了仿真分析，结果表明改进后的横向控制策略能够有效提高车辆的路径跟踪精度和横摆稳定性。最后，实车道路试验验证了曲率前馈MPC策略的有效性。

关键词: 曲率前馈, 横向控制策略, 车辆模型建模, 横摆稳定性, 时域优化

CLC Number:

U463.6

Xinyou LIN, Zhongwei JIN, Yunliang TANG. Vehicle Lateral Control Strategy Integrating Road Curvature Feedforward[J]. China Mechanical Engineering, 2025, 36(11): 2774-2782.

林歆悠, 金忠伟, 唐云亮. 融合道路曲率前馈的车辆横向控制策略[J]. 中国机械工程, 2025, 36(11): 2774-2782.

Figures/Tables 23

Fig.1 Monorail kinematic model

Fig.2 Pacejka tire model

Fig.3 Monorail dynamic model

Fig.4 Design flowchart of fusion curvature feedforward MPC control strategy

Fig.5 Schematic diagram of tracking error considering road curvature

Fig.6 Double line tracking results in different time domains at 60km/h

Fig.7 Fitting diagram of vehicle speed-curvature radius-prediction time domain

Fig.8 Fitting diagram of vehicle speed-curvature radius-control time domain

Tab.1 General parameters of control strategy

参数名称	取值
车辆质量m/kg	1530
车辆前后轴到质心的距离 $l f$ ， $l r$ /m	1.05，1.55
转动惯量 $I z$ /（ $k g ⋅ m 2$ ）	2059.2
采样时间/s	0.05
权重矩阵 Q	$1000010$
权重矩阵 R	［10］
转角增量限制/（°）	0.86
转角限制/（°）	25

Tab.1 General parameters of control strategy

参数名称	取值
车辆质量m/kg	1530
车辆前后轴到质心的距离 $l f$ ， $l r$ /m	1.05，1.55
转动惯量 $I z$ /（ $k g ⋅ m 2$ ）	2059.2
采样时间/s	0.05
权重矩阵 Q	$1000010$
权重矩阵 R	［10］
转角增量限制/（°）	0.86
转角限制/（°）	25

Fig.9 Comparison of path tracking effects at 36 km/h

Fig.10 Comparison of path tracking effects at 54 km/h

Fig.11 Comparison of path tracking effects at 72 km/h

Fig.12 Comparison of path tracking effects at 90 km/h

Fig.13 Comparison of the influence of road curvature on lateral control strategies

Fig.14 Performance comparison of different control strategies at 72 km/h

Fig.15 Performance comparison of different control strategies at 90 km/h

Fig.16 Influence of lateral stability constraints on tire sideslip angle

Fig.17 Comparison of lateral angular velocity at different vehicle speeds

Fig.18 Time domain adaptive tracking effect at 30 km/h

Fig.19 Time domain adaptive tracking effect at 60 km/h

Fig.20 Prototype of real vehicle verification experiment

Fig.21 SLAM mapping and path planning curves

Fig.22 Tracking effect diagram before and after strategy optimization

References 19

[1]	张智能，李以农，余颖弘等. 复杂动态环境下智能汽车局部路径规划与跟踪算法研究［J］. 中国公路学报， 2022，35（9）： 372-386.
	ZHANG Zhineng， LI Yinong， YU Yinghong， et al. Research on Local Path Planning and Tracking Algorithms for Intelligent Vehicles in Complex Dynamic Environments［J］. China Journal of Highway and Transport， 2022， 35（9）： 372-386.
[2]	ABADJO M R， SIERRA-GARCÍA J E， SANTOS M. Evolutive Tuning Optimization of a PID Controller for Autonomous Path-following Robot［C］∥16th International Conference on Soft Computing Models in Industrial and Environmental Applications （SOCO 2021）. Cham： Springer， 2022： 451-460.
[3]	TAGHAVIFAR H， HU C， QIN Y， et al. EKF-Neural Network Observer Based Type-2 Fuzzy Control of Autonomous Vehicles［J］. IEEE Transactions on Intelligent Transportation Systems， 2020， 22（8）： 4788-4800.
[4]	何洋，李刚，余孝楠.基于变论域的高速行驶智能汽车模糊模型预测控制方法研究［J］.中国机械工程，2025，36（3）：604-613.
	HE Yang， LI Gang， YU Xiaonan. Research on Fuzzy Model Predictive Control Method for High-speed Intelligent Vehicles Based on Variable Domain Theory［J］. China Mechanical Engineering， 2025， 36（3）： 604-613.
[5]	XU Yong， ZHENG Guangwu， PAN Yajun. Off-policy Learning-based Following Control of Cooperative Autonomous Vehicles under Distributed Attacks ［J］. IEEE Transactions on Intelligent Transportation Systems， 2023， 24（5）： 5120-5130.
[6]	SHI Tianyu， WANG Pin， CHENG Xuxin， et al. Driving Decision and Control for Automated Lane Change Behavior Based on Deep Reinforcement Learning［C］∥2019 IEEE Intelligent Transportation Systems Conference. Auckland， 2019：2895-2900.
[7]	LIU Lu， WANG Dan， PENG Zhouhua， et al. Distributed Path Following of Multiple Under-actuated Autonomous Surface Vehicles Based on Data-driven Neural Predictors via Integral Concurrent Learning ［J］. IEEE Transactions on Neural Networks and Learning Systems， 2021， 32（12）： 5334-5344.
[8]	林歆悠，叶卓明，周斌豪.基于DQN强化学习的自动驾驶转向控制策略［J］.机械工程学报，2023，59（16）：315-324.
	LIN Xinyou， YE Zhuoming， ZHOU Binhao. Automatic Driving Steering Control Strategy Based on DQN Reinforcement Learning ［J］. Journal of Mechanical Engineering， 2023， 59（16）： 315-324.
[9]	KONG J， PFEIFFER M， SCHILDACH G， et al. Kinematic and Dynamic Vehicle Models for Autonomous Driving Control Design［C］∥2015 IEEE Intelligent Vehicles Symposiun. Seoul，2015：1094-1099.
[10]	LIU Qianjie， SONG Shuang， HU Huosheng， et al. Extended Model Predictive Control Scheme for Smooth Path Following of Autonomous Vehicles ［J］. Frontiers of Mechanical Engineering， 2022， 17（1）：4.
[11]	SHI Man， HE Hongwen， LI Jianwei， et al. Path Planning and Following Control of Autonomous Bus under Time-varying Parameters against Parametric Uncertainties and External Disturbances［J］. IEEE Transactions on Vehicular Technology， 2022， 71（7）： 7057-7070.
[12]	YANG Zeyu， HUANG Jin， YANG Diange， et al. Design and Optimization of Robust Path Tracking Control for Autonomous Vehicles with Fuzzy Uncertainty［J］. IEEE Transactions on Fuzzy Systems， 2022， 30（6）： 1788-1800.
[13]	关龙新，顾祖飞，张超，等. 考虑系统复杂扰动的智能车模型预测路径跟踪控制［J］. 汽车工程， 2022，44（12）： 1844-1855.
	GUAN Longxin， GU Zufei， ZHANG Chao， et al. Intelligent Vehicle Model Predictive Path Tracking Control Considering Complex System Disturbances ［J］. Automotive Engineering， 2022， 44（12）： 1844-1855.
[14]	DAOUD M A， MEHREZ M W， RAYSIDE D， et al. Simultaneous Feasible Local Planning and Path-following Control for Autonomous Driving［J］. IEEE Transactions on Intelligent Transportation Systems， 2022， 23（9）： 16358-16370.
[15]	WANG Weida， ZHANG Yuhang， YANG Chao， et al. Adaptive Model Predictive Control-based Path Following Control for Four-wheel Independent Drive Automated Vehicles［J］. IEEE Transactions on Intelligent Transportation Systems， 2022， 23（9）： 14399-14412.
[16]	MILANI S， KHAYYAM H， MARZBANI H， et al. Smart Autodriver Algorithm for Real-time Autonomous Vehicle Trajectory Control［J］. IEEE Transactions on Intelligent Transportation Systems， 2022， 23（3）： 1984-1995.
[17]	BRUGGEMANN S， POSSIERI C. On the Use of Difference of Log-Sum-Exp Neural Networks to Solve Data-driven Model Predictive Control Tracking Problems［J］. IEEE Control Systems Letters， 2021， 5（4）： 1267-1272.
[18]	何智成，王煜凡，韦宝侣，等.基于优化动力学模型的路径跟踪控制研究［J］.中国机械工程，2024，35（6）：1000-1009.
	HE Zhicheng， WANG Yufan， WEI Baolv， et al. Research on Path Tracking Control Based on Optimization Dynamics Model［J］. China Mechanical Engineering，2024， 35（6）： 1000-1009.
[19]	刘兴初，张建武，刘奋. 四轮转向非线性侧向动力学模型［J］. 上海交通大学学报，2005，39（9）：1465-1469.
	LIU Xingchu， ZHANG Jianwu， LIU Fen. Nonlinear Lateral Dynamics Model for Four-wheel Steering ［J］.Journal of Shanghai Jiao Tong University， 2005， 39（9）：1465-1469.