自动驾驶车辆紧急避撞线性时变模型预测轨迹跟踪控制

doi:10.3969/j.issn.1674-8484.2025.06.013

汽车安全与节能学报 ›› 2025, Vol. 16 ›› Issue (6): 934-944.DOI: 10.3969/j.issn.1674-8484.2025.06.013

自动驾驶车辆紧急避撞线性时变模型预测轨迹跟踪控制

吴杭哲¹(), 焦一洲², 刘洋¹, 钟薇³, 王水河², 郭景华²^,^*(), 赵健⁴

1.中国第一汽车股份有限公司，高端汽车集成与控制全国重点实验室，长春 130013，中国
2.厦门大学机电工程系，厦门 361005，中国
3.清华大学车辆与运载学院，北京 100084，中国
4.吉林大学汽车工程学院，长春 130022，中国

收稿日期:2025-10-18 修回日期:2025-11-10 出版日期:2025-12-31 发布日期:2026-01-12
通讯作者: * 郭景华，副教授。E-mail：guojh@xmu.edu.cn。
作者简介:吴杭哲（1991—），女（汉），吉林，高级工程师。E-mail：wuhangzhe@faw.com.cn。
基金资助:
国家自然科学基金面上项目(52372419)

Predictive trajectory tracking control by a linear time-varying model for emergency collision avoidance of autonomous vehicles

WU Hangzhe¹(), JIAO Yizhou², LIU Yang¹, ZHONG Wei³, WANG Shuihe², GUO Jinghua²^,^*(), ZHAO Jian⁴

1. State Key Laboratory of Advanced Vehicle Integration and Control, China FAW Group Co., LTD. Changchun 130013, China
2. Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China
3. School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China
4. College of Automotive Engineering, Jilin University, Changchun 130022, China

Received:2025-10-18 Revised:2025-11-10 Online:2025-12-31 Published:2026-01-12

摘要/Abstract

摘要： 为提高自动驾驶车辆紧急避撞的稳定性和安全性，提出一种轨迹跟踪方法。以双轨车辆动力学模型为基础，建立了三自由度双轨非线性车辆动力学模型，推导出线性时变轨迹跟踪预测模型。将轨迹跟踪控制算法转化为在线二次规划问题，求解最优控制输入。进行了仿真试验与实车实验。结果表明：当车速为50 km/h，路面附着因数为0.5~1.0时，双移线仿真的横向位移误差小于90 mm，航向角误差小于50 mrad；当车速为60 km/h，路面附着因数为0.38时，换道实验的最大横向误差160 mm，最大航向角跟踪误差34 mrad。从而，本轨迹跟踪控制器的有效性和鲁棒性，能够保证车辆在换道过程中的稳定性和安全性。

关键词: 自动驾驶, 紧急避撞, 线性时变, 模型预测控制, 轨迹跟踪

Abstract:

A trajectory tracking method was proposed to improve the stability and safety of autonomous vehicles during emergency collision avoidance. A three-freedom dual-track nonlinear vehicle dynamics model was established based on the dual-track vehicle dynamics model to build a linear time-varying trajectory tracking prediction model; The trajectory tracking control algorithm were converted into an online quadratic programming problem to solve for the optimal control input. Simulation tests and real-vehicle experiments were conducted. The results show that the lateral displacement error is less than 90 mm and yaw angle error is less than 50 mrad in the double lane change simulations at the vehicle speed of 50 km/h with the road adhesion coefficients range of 0.5~1.0. The maximum lateral error is 160 mm with the maximum yaw angle tracking error of 34 mrad in the lane change experiments at the vehicle speed of 60 km/h with a road adhesion coefficient of 0.38. Therefore, the trajectory tracking controller exhibits effectiveness and robustness, guaranteeing the vehicle’s stability and safety during lane changes.

Key words: autonomous driving, emergency collision avoidance, linear time-varying, model predictive control, trajectory tracking

中图分类号:

吴杭哲, 焦一洲, 刘洋, 钟薇, 王水河, 郭景华, 赵健. 自动驾驶车辆紧急避撞线性时变模型预测轨迹跟踪控制[J]. 汽车安全与节能学报, 2025, 16(6): 934-944.

WU Hangzhe, JIAO Yizhou, LIU Yang, ZHONG Wei, WANG Shuihe, GUO Jinghua, ZHAO Jian. Predictive trajectory tracking control by a linear time-varying model for emergency collision avoidance of autonomous vehicles[J]. Journal of Automotive Safety and Energy, 2025, 16(6): 934-944.

图/表 10

参考文献 24

[1]	李克强, 罗禹贡, 郭景华. 先进车辆系统动力学与控制[M]. 武汉: 华中科技大学出版社, 2021: 11-18.
	LI Keqiang, LUO Yugong, GUO Jinghua, Advanced Vehicle Dynamic and Control[M]. Wuhan: Huazhong Univ Sci Tech Pres, 2021: 11-18. (in Chinese)
[2]	郭景华, 李克强, 罗禹贡. 智能车辆运动控制研究综述[J]. 汽车安全与节能学报, 2016, 7(2): 151-159.
	GUO Jinghua, LI Keqiang, LUO Yugong. Review on the research of motion control for intelligent vehicles[J]. J Autom Safe Energy, 2016, 7(2): 151-159. (in Chinese)
[3]	赵治国, 周良杰, 朱强. 无人驾驶车辆路径跟踪控制预瞄距离自适应优化[J]. 机械工程学报. 2018, 54(24): 166-173. doi: 10.3901/JME.2018.24.166
	ZHAO Zhiguo, ZHOU Liangjie, ZHU Qiang. Preview distance adaptive optimization for the path tracking control of unmanned vehicle[J]. J Mech Engi, 2018, 54(24): 166-173. (in Chinese)
[4]	GUO Jinghua, LUO Yugong, LI Keqiang. An adaptive hierarchical trajectory following control approach of autonomous four-wheel independent drive electric vehicles[J]. IEEE Trans Intel Transport Syst, 2017, 19(8): 2482-2492.
[5]	CHEN Yimin, Stout C, Joshi A, et al. Driver-assistance lateral motion control for in-wheel-motor-driven electric ground vehicles subject to small torque variation[J]. IEEE Trans Vehi Tech, 2018, 67(8): 6838-6850.
[6]	GUO Jinghua, LUO Yugong, WANG Jingyao, et al. An adaptive cascade trajectory tracking control for over-actuated autonomous electric vehicles with input saturation[J]. Sci Chin: Tech Sci, 2019, 62(12): 2153-2160.
[7]	Taghavifar H, Rakheja S. Path-tracking of autonomous vehicles using a novel adaptive robust exponential-like-sliding-mode fuzzy type-2 neural network controller[J]. Mech Syst Sign Process, 2019, 130: 41-55. doi: 10.1016/j.ymssp.2019.04.060 URL
[8]	YUE Ming, HOU Xiaoqiang, ZHAO Xudong, et al. Robust tube-based model predictive control for lane change maneuver of tractor-trailer vehicles based on a polynomial trajectory[J]. IEEE Trans Syst, Man, Cybern: Syst, 2018, 50(12): 5180-5188.
[9]	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 Indu Electron, 2021, 68(9): 8698-8707.
[10]	WANG Xin, SUN Weichao. Trajectory tracking of autonomous vehicle: A differential flatness approach with disturbance-observer-based control[J]. IEEE Trans Intel Vehi, 2023, 8(2): 1368-1379.
[11]	CHU Duanfeng, LI Haoren, ZHAO Chengyang, et al. Trajectory tracking of autonomous vehicle based on model predictive control with PID feedback[J]. IEEE Trans Intel Transport Syst, 2023, 24(2): 2239-2250.
[12]	SONG Jiarui, TAO Gang, ZANG Zheng, et al. Isolating trajectory tracking from motion control: A model predictive control and robust control framework for unmanned ground vehicles[J]. IEEE Robot Autom Lett, 2023, 8(2): 1699-1706.
[13]	Sekban H T, Basci A. Designing new model-based adaptive sliding mode controllers for trajectory tracking control of an unmanned ground vehicle[J]. IEEE Access, 2023, 11: 101387-101397. doi: 10.1109/ACCESS.2023.3313942 URL
[14]	Pauca G S, Caruntu C F. Nonlinear model predictive control for vehicle dynamics with optimized velocity profile[C]// Int’l Conf Contr Syst Compu Sci (CSCS), Bucharest, Romania, 2025: 19-24.
[15]	ZHENG Xunjia, CAO Zeyi, CHEN Xing, et al. Research on trajectory tracking control based on adaptive prediction time-domain MPC[C]// Int’l Conf Autom-Intel-Safe (ICAIS), Xi'an, China, 2025: 1-6.
[16]	HAN Sangwon, SONG Yuho, Kim S, et al. A path tracking controller for heavy-duty buses based on robust model predictive control with a novel enhanced kinematic model[J]. IEEE Trans Intel Vehi, 2025, 10(2): 1273-1288.
[17]	GAO Zhenhai, WEN Wenhao, XING Yang, et al. An integrated framework for autonomous driving planning and tracking based on NNMPC considering road surface variations[J]. IEEE Trans Intel Vehi, 2025, 10(2): 848-862.
[18]	Thakur A, Mishra S K, Kumar A, et al. Optimizing lateral motion control of an autonomous ground vehicle using modified particle swarm optimization with model predictive controller[C]// Int’l Conf Comput, Electron-Elect-Eng (IC2E3), 2024: 1-6.
[19]	Diklić V, Novoselnik B. Comparison of linear and nonlinear Model Predictive Control for vehicle path following[C]// MIPRO ICT Electron Conv (MIPRO), 2024: 1794-1799.
[20]	XIE Zhaoxi, WU Yanfeng, GAO Jianping, et al. Emergency obstacle avoidance system of driverless vehicle based on model predictive control[C]// Int’l Conf Advan Mech Syst (ICAMechS), Tokyo, Japan, 2021: 22-27.
[21]	LI Shengqin, ZHAO Qingqing. Research on the emergency obstacle avoidance strategy of intelligent vehicles based on a safety distance model[J]. IEEE Access, 2023, 11: 7124-7134. doi: 10.1109/ACCESS.2023.3238056 URL
[22]	Domina Á, Tihanyi V. LTV-MPC approach for automated vehicle path following at the limit of handling[J]. Sensors, 2022, 22(15): No 5807.
[23]	龚建伟, 姜岩, 徐威. 无人驾驶车辆模型预测控制[M]. 北京: 北京理工大学出版社, 2014: 86-88.
	GONG Jianwei, JIANG Yan, XU Wei. Model Predictive Control for Autonomous Vehicles[M]. Beijing: Beijing Inst Tech Pre, 2014: 86-88. (in Chinese)
[24]	马思群, 王兆强, 韩博, 等. 改进的 LQR 横向路径跟踪控制器[J]. 机械科学与技术, 2024, 43(1): 130-140.
	MA Siqun, WANG Zhaoqiang, HAN Bo, et al. Improved LQR lateral path tracking controller[J]. J Mech Sci Tech, 2024, 43(1): 130-140. (in Chinese)

整车质量，m	1.890 t
簧上质量，m_s	1.723 t
质心高度，H	0.60 m
侧倾高度，h	0.54 m
轮距，W	1.625 m
前轴到质心距离，L_f，a	1.421 m
后轴到质心距离，L_r，b	1.479 m
悬架侧倾刚度，K_φ	25 kNm·rad^-1
悬架侧倾阻尼，C_φ	2.0 kNm·s·rad^-1
前轮轮胎侧偏刚度，K_α_f	66.9 kN·rad^-1
后轮轮胎侧偏刚度，K_α_r	62.7 kN·rad^-1
x轴转动惯量，I_x	1.243 t·m²
z轴转动惯量，I_z	4.175 t·m²

整车质量，m	1.890 t
簧上质量，m_s	1.723 t
质心高度，H	0.60 m
侧倾高度，h	0.54 m
轮距，W	1.625 m
前轴到质心距离，L_f，a	1.421 m
后轴到质心距离，L_r，b	1.479 m
悬架侧倾刚度，K_φ	25 kNm·rad^-1
悬架侧倾阻尼，C_φ	2.0 kNm·s·rad^-1
前轮轮胎侧偏刚度，K_α_f	66.9 kN·rad^-1
后轮轮胎侧偏刚度，K_α_r	62.7 kN·rad^-1
x轴转动惯量，I_x	1.243 t·m²
z轴转动惯量，I_z	4.175 t·m²

预测时域，N_P	10
控制时域，N_C	4
采样时间，T	5 ms
权重矩阵，Q	$\left[\begin{array}{cc} 500 & 0 \\ 0 & 50000 \end{array}\right]$
权重矩阵，R	6 000

预测时域，N_P	10
控制时域，N_C	4
采样时间，T	5 ms
权重矩阵，Q	$\left[\begin{array}{cc} 500 & 0 \\ 0 & 50000 \end{array}\right]$
权重矩阵，R	6 000

控制器	μ	Y_RMSE mm	φ_RMSE mrad	Y_{Error_max} mm	φ_{Error_max} mrad
A	1.00	23	18	73	46
	0.75	26	18	81	45
	0.50	25	17	88	47
B	1.00	60	21	169	53
	0.75	156	29	199	46
	0.50	174	30	296	65

自动驾驶车辆紧急避撞线性时变模型预测轨迹跟踪控制

Predictive trajectory tracking control by a linear time-varying model for emergency collision avoidance of autonomous vehicles

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