Research on Lateral Control of Intelligent Vehicles Based on Physics-Learning Hybrid Dynamics Modeling

doi:10.3969/j.issn.1004-132X.2026.08.009

Abstract

Abstract:

To address the insufficient accuracy of traditional dynamic models for intelligent vehicle lateral control under complex operating conditions， this paper proposes a physics-based learning hybrid dynamic modeling method combined with learning-based MPC to enhance lateral control precision and robustness. A single-track model is first adopted as the foundational physical model and augmented with a gated recurrent unit （GRU） network to compensate for unmodeled dynamics， thereby constructing a hybrid model that integrates physical interpretability with data-driven adaptability. The hybrid model is then embedded as the predictive model within an MPC framework， in which an optimization objective function incorporating trajectory tracking errors and control input constraints is designed to compute optimal front -wheel steering angle commands in real time. CarSim/Simulink co-simulation results under double-lane- change and serpentine maneuvers demonstrate that the proposed method reduces both the root-mean-square lateral tracking error and the front-wheel steering angle amplitude compared with benchmark methods， while effectively suppressing unmodeled dynamics inherent in the single-track model. The proposed approach achieves precise control output under complex conditions， improving both lateral control accuracy and stability， and thus demonstrates superior lateral control performance for intelligent vehicles.

Key words: intelligent vehicle, hybrid model, model predictive control （MPC）, lateral control

摘要：

针对智能车辆横向控制中传统动力学模型在复杂工况下精度不足的问题，提出了一种物理-学习混合动力学建模方法，并结合学习型模型预测控制方法以提高横向控制的精度与鲁棒性。首先以单轨模型为基础物理模型，引入门控循环单元（GRU）补偿未建模动态，构建混合物理学习模型，兼具物理可解释性与数据驱动自适应性；然后将混合模型作为预测模型嵌入模型预测控制（MPC）框架，设计考虑轨迹跟踪误差与控制量约束的优化目标函数，实时求解最优前轮转向角指令。CarSim/Simulink联合仿真结果表明，在双移线与蛇形工况下，相较于对比方法，所提方法有效降低了横向跟踪误差均方根，同时减小了前轮转角幅值，有效抑制了单轨模型中的部分未建模动态的影响。所提方法实现了车辆在复杂工况下控制量的精确输出，同步提升了智能车辆的横向控制精度和稳定性，具有良好的横向控制效果。

关键词: 智能车辆, 混合模型, 模型预测控制, 横向控制

CLC Number:

U461.1

SHI Peicheng, SUN Yuchen, CHAKIR Chadia, SUN Yu. Research on Lateral Control of Intelligent Vehicles Based on Physics-Learning Hybrid Dynamics Modeling[J]. China Mechanical Engineering, 2026, 37(8): 1900-1908.

时培成, 孙雨辰, CHAKIR Chadia, 孙羽. 基于物理-学习混合动力学建模的智能车辆横向控制研究[J]. 中国机械工程, 2026, 37(8): 1900-1908.

Figures/Tables 15

Fig.1 Architecture of hybrid physics-data-driven modeling

Fig.2 Single-track vehicle model

Fig.3 GRU-based data-driven model

Tab.1 Intelligent vehicle driving scenario design

场景类型	道路特征	车速范围/（km·h $- 1$ ）	附着系数 $μ$
城市道路	密集路口，启停工况	30～50	0.85/0.5/0.3
高速公路	长直道	90～120	0.85/0.5
公路	连续缓弯	50～70	0.85/0.5/0.3
赛道	S形急弯	70～90	0.85

Tab.1 Intelligent vehicle driving scenario design

场景类型	道路特征	车速范围/（km·h $- 1$ ）	附着系数 $μ$
城市道路	密集路口，启停工况	30～50	0.85/0.5/0.3
高速公路	长直道	90～120	0.85/0.5
公路	连续缓弯	50～70	0.85/0.5/0.3
赛道	S形急弯	70～90	0.85

Fig.4 Simulation data collection system

Tab.2 Comparison of test results between hybrid model and single-track model

变量	模型	平均绝对误差	均方根误差
$v y$	混合模型	0.0352	0.0437
$v y$	单轨模型	0.0673	0.0812
$ω$	混合模型	0.0239	0.0383
$ω$	单轨模型	0.0385	0.0576

Tab.2 Comparison of test results between hybrid model and single-track model

变量	模型	平均绝对误差	均方根误差
$v y$	混合模型	0.0352	0.0437
$v y$	单轨模型	0.0673	0.0812
$ω$	混合模型	0.0239	0.0383
$ω$	单轨模型	0.0385	0.0576

Tab.3 Vehicle parameters for simulation

整车质量m/kg	1270
轴距l/m	2.91
质心到前轴距离a/m	1.015
质心到后轴距离b/m	1.895
转动惯量 $I z$ /（ $k g ∙ m 2$ ）	1536
前轴侧偏刚度 $C f$ /（ $N ∙ r a d - 1$ ）	61 120
后轴侧偏刚度 $C r$ /（ $N ∙ r a d - 1$ ）	51 160

Tab.3 Vehicle parameters for simulation

整车质量m/kg	1270
轴距l/m	2.91
质心到前轴距离a/m	1.015
质心到后轴距离b/m	1.895
转动惯量 $I z$ /（ $k g ∙ m 2$ ）	1536
前轴侧偏刚度 $C f$ /（ $N ∙ r a d - 1$ ）	61 120
后轴侧偏刚度 $C r$ /（ $N ∙ r a d - 1$ ）	51 160

Fig.5 Trajectory tracking performance comparison under double lane change scenario

Fig.6 Lateral tracking error under double lane change scenario

Fig.7 Front wheel steering angle control input under double lane change scenario

Fig.8 Vehicle dynamic state responses under double lane change scenario

Fig.9 Trajectory tracking performance comparison under slalom scenario

Fig.10 Lateral tracking error under slalom scenario

Fig.11 Front wheel steering angle control input under slalom scenario

Fig.12 Vehicle dynamic state responses under slalom scenario

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