考虑终端约束的自动驾驶车辆随机管型MPC路径跟踪控制

doi:10.3901/JME.260482

摘要/Abstract

摘要： 可靠的路径跟踪功能是自动驾驶技术落地的关键，然而模型不确定性会不可避免的导致路径跟踪性能下降。管型模型预测控制(Tube-based model predictive control,TMPC)是一种有效的解决方案，但面临基于扰动有界假设的过保守性和难以应对大幅值扰动的局限。为此，提出一种考虑终端约束的预瞄随机TMPC (Preview stochastic TMPC,PSTMPC)方法，以减少其保守性并扩大其适用范围。该方法在不确定扰动有界假设的基础上考虑其概率分布特性，引入概率可达集以收紧名义系统约束。同时，在极限工况下结合无限时域和终端不等式约束，以提升控制器处理大幅值扰动的能力。此外，基于预瞄思想提出一种将模型曲率项视为已知控制序列的策略，以充分利用曲率信息、增强跟踪性能。数值计算结果表明，概率可达集能有效放宽名义系统可行域；仿真结果验证了PSTMPC方法在路径跟踪性能上的显著提升；硬件在环试验结果进一步证明了该方法的有效性。

关键词: 自动驾驶, 路径跟踪控制, 模型不确定性, 模型预测控制, 概率约束

Abstract: Reliable path tracking function is the key to the implementation of autonomous driving technology, but model uncertainty will inevitably cause path tracking performance to degrade. tube-based model predictive control(TMPC) is an effective solution, but it faces the limitations of being overly conservative and having difficulty coping with large-value disturbances due to the bounded disturbance assumption. To this end, a preview stochastic TMPC(PSTMPC) method considering terminal constraints is proposed to reduce its conservatism and expand its scope of application. This method considers the probability distribution characteristics of uncertain disturbances based on the bounded assumption and introduces probabilistic reachable sets to tighten the nominal system constraints. At the same time, infinite time domain and terminal inequality constraints are combined under extreme conditions to improve the controller's ability to handle large disturbances. In addition, basedt on the preview idea, a strategy that regards the model curvature term as a known control sequence is proposed to make full use of the curvature information and enhance the tracking performance. Numerical calculation results show that the probability reachable set can effectively broaden the feasible domain of the nominal system. Simulation results verify that the PSTMPC method significantly improves path tracking performance; hardware-in-the-loop experimental results further prove the effectiveness of the method.

Key words: autonomous vehicle, path tracking control, model uncertainty, model predictive control, chance constraints

中图分类号:

TP242

雍浩楠, 卢少波, 谢文科, 崔天倍, 杨帆. 考虑终端约束的自动驾驶车辆随机管型MPC路径跟踪控制[J]. 机械工程学报, 2026, 62(14): 325-337.

YONG Haonan, LU Shaobo, XIE Wenke, CUI Tianbei, YANG Fan. Stochastic Tube MPC Based Automated Vehicle Path Tacking Control Considering Terminal Constraint[J]. Journal of Mechanical Engineering, 2026, 62(14): 325-337.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.260482

http://www.cjmenet.com.cn/CN/Y2026/V62/I14/325

参考文献

[1] 彭湃，耿可可，王子威，等. 智能汽车环境感知方法综述[J]. 机械工程学报，2023，59(20)：281-303. PENG Pai，GENG Keke，WANG Ziwei，et al. Review on environmental perception methods of autonomous vehicles[J]. Journal of Mechanical Engineering，2023，59(20)：281-303.
[2] Society of Automotive Engineers. SAE-J3016_202104 Taxonomy and definitions for terms related to driving automation systems for on-road motor vehicles[S]. Worrendale：SAE International，2021.
[3] 熊璐，杨兴，卓桂荣，等. 无人驾驶车辆的运动控制发展现状综述[J]. 机械工程学报，2020，56(10)：127-143. XIONG Lu，YANG Xing，ZHUO Guirong，et al. Review on motion control of autonomous vehicles[J]. Journal of Mechanical Engineering，2020，56(10)：127-143.
[4] 梁艺潇，李以农，AMIR K，等. 基于转向与主动横摆力矩协调的四轮驱动智能电动汽车路径跟踪控制[J]. 机械工程学报，2021，57(6)：142-155. LIANG Yixiao，LI Yinong，AMIR K，et al. Path following control for four-wheel drive electric intelligent vehicle based on coordination between steering and direct yaw moment system[J]. Journal of Mechanical Engineering，2021，57(6)：142-155.
[5] NGUYEN A-T，SENTOUH C，ZHANG Hui，et al. Fuzzy static output feedback control for path following of autonomous vehicles with transient performance improvements[J]. IEEE Transactions on Intelligent Transportation Systems，2020，21(7)：3069-3079.
[6] LIU Taiyou，WANG Xiaowei，ZHAO Jing，et al. Robust H-infinity fuzzy output feedback control for path following of FWID-EVs with actuator saturation[J]. International Journal of Fuzzy Systems，2023，25(4)：1674-1688.
[7] CAO Xuanhao，XU Tao，TIAN Yantao，et al. Gain-scheduling LPV synthesis H∞ robust lateral motion control for path following of autonomous vehicle via coordination of steering and braking[J]. Vehicle System Dynamics，2023，61(4)：968-991.
[8] CHEN Jiancheng，SHUAI Zhibin，ZHANG Hui，et al. Path following control of autonomous four-wheel-independent-drive electric vehicles via second-order sliding mode and nonlinear disturbance observer techniques[J]. IEEE Transactions on Industrial Electronics，2021，68(3)：2460-2469.
[9] LIANG Zhongchao，ZHAO Jing，LIU Bo，et al. Velocity-based path following control for autonomous vehicles to avoid exceeding road friction limits using sliding mode method[J]. IEEE Transactions on Intelligent Transportation Systems，2022，23(3)：1947-1958.
[10] HU Chuan，CHEN Yimin，WANG Junmin. Fuzzy observer-based transitional path-tracking control for autonomous vehicles[J]. IEEE Transactions on Intelligent Transportation Systems，2021，22(5)：3078-3088.
[11] WANG Haoyu，ZUO Zhiqiang，WANG Yijing，et al. Composite nonlinear path-following control for unmanned ground vehicles with anti-windup ESO[J]. IEEE Transactions on Systems，Man，and Cybernetics：Systems，2022，52(9)：5865-5876.
[12] CHU Shaoqiang，XIE Zhengchao，WONG P K，et al. Observer-based gain scheduling path following control for autonomous electric vehicles subject to time delay[J]. Vehicle System Dynamics，2022，60(5)：1602-1626.
[13] TAGHAVIFAR H，HU Chuan，QIN Yechen，et al. EKF-neural network observer based type-2 fuzzy control of autonomous vehicles[J]. IEEE Transactions on Intelligent Transportation Systems，2021，22(8)：4788-4800.
[14] ZHOU Xingyu，WANG Zejiang，WANG Junmin. Automated vehicle path following：A non-quadratic-lyapunov-function-based model reference adaptive control approach with e∞-smooth projection modification[J]. IEEE Transactions on Intelligent Transportation Systems，2022，23(11)：21653-21664.
[15] LIANG Zhongchao，WANG Zhongnan，ZHAO Jing，et al. Fixed-time prescribed performance path-following control for autonomous vehicle with complete unknown parameters[J]. IEEE Transactions on Industrial Electronics，2023，70(8)：8426-8436.
[16] MA Yan，CHEN Jian，WANG Junmin，et al. Path-tracking considering yaw stability with passivity-based control for autonomous vehicles[J]. IEEE Transactions on Intelligent Transportation Systems，2022，23(7)：8736-8746.
[17] AREEROB P，PANOMRUTTANARUG B. Iterative learning control for lateral tracking with repeated path in autonomous vehicles for dynamic environments[J]. International Journal of Control，Automation and Systems，2023，21(11)：3712-3723.
[18] WANG Chengyu，WANG Luhan，LU Zhaoming，et al. SRL-TR2：A safe reinforcement learning based trajectory tracker framework[J]. IEEE Transactions on Intelligent Transportation Systems，2023，24(6)：5765-5780.
[19] ARTUñEDO A，MORENO-GONZALEZ M，VILLAGRA J. Lateral control for autonomous vehicles：A comparative evaluation[J]. Annual Reviews in Control，2024，57：100910.
[20] STANO P，MONTANARO U，TAVERNINI D，et al. Model predictive path tracking control for automated road vehicles：A review[J]. Annual Reviews in Control，2023，55：194-236.
[21] GAO Hongbo，KAN Zhen，LI Keqiang. Robust lateral trajectory following control of unmanned vehicle based on model predictive control[J]. IEEE/ASME Transactions on Mechatronics，2022，27(3)：1278-1287.
[22] 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. DU Ronghua，HU Hongfei，GAO Kai，et al. Research on trajectory tracking control of autonomous vehicle based on MPC with variable predictive horizon[J]. Journal of Mechanical Engineering，2022，58(24)：275-288.
[23] 李韶华，杨泽坤，王雪玮. 基于T-S模糊变权重MPC的智能车轨迹跟踪控制[J]. 机械工程学报，2023，59(4)：199-212. LI Shaohua，YANG Zekun，WANG Xuewei. Trajectory tracking control of an intelligent vehicle based on T-S fuzzy variable weight MPC[J]. Journal of Mechanical Engineering，2023，59(4)：199-212.
[24] YANG Kai，TANG Xiaolin，QIN Yechen，et al. Comparative study of trajectory tracking control for automated vehicles via model predictive control and robust H-infinity state feedback control[J]. Chinese Journal of Mechanical Engineering，2021，34(1)：1-14.
[25] RAWLINGS J B，MAYNE D Q，DIEHL M. Model predictive control：Theory，computation，and design[M]. 2^nd ed. Portland，OR，USA：Nob Hill Publishing，2017.
[26] PENG Haonan，WANG Weida，AN Quan，et al. Path tracking and direct yaw moment coordinated control based on robust MPC with the finite time horizon for autonomous independent-drive vehicles[J]. IEEE Transactions on Vehicular Technology，2020，69(6)：6053-6066.
[27] ZHENG Hao，ZHENG Ling，LI Yinong，et al. Varying zonotopic tube RMPC with switching logic for lateral path tracking of autonomous vehicle[J]. Journal of the Franklin Institute，2022，359(7)：2759-2787.
[28] 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.
[29] MAYNE D Q，SERON M M，RAKOVIĆ S V. Robust model predictive control of constrained linear systems with bounded disturbances[J]. Automatica，2005，41(2)：219-224.
[30] WU Xitao，WEI Chao，TIAN Hanqing，et al. Fault-tolerant control for path-following of independently actuated autonomous vehicles using tube-based model predictive control[J]. IEEE Transactions on Intelligent Transportation Systems，2022，23(11)：20282-20297.
[31] HASHIMOTO T. Probabilistic constrained model predictive control for linear discrete-time systems with additive stochastic disturbances[C]//Proceedings of the 52nd IEEE Conference on Decision and Control，December 10-13，2013，Florence，Italy. New York：IEEE，2013：6434-6439.
[32] HEWING L，ZEILINGER M N. Stochastic model predictive control for linear systems using probabilistic reachable sets[C]//Proceedings of the 2018 IEEE Conference on Decision and Control，December 17-19，2018，Miami Beach，FL，USA. New York：IEEE，2018：5182-5188.
[33] RAJAMANI R. Vehicle dynamics and control[M]. Berlin：Springer，2011.
[34] KNAUP J，OKAMOTO K，TSIOTRAS P. Safe high-performance autonomous off-road driving using covariance steering stochastic model predictive control[J]. IEEE Transactions on Control Systems Technology，2023，31(5)：2066-2081.
[35] HEIRUNG T A N，PAULSON J A，O’LEARY J，et al. Stochastic model predictive control — how does it work?[J]. Computers & Chemical Engineering，2018，114：158-170.
[36] ZHOU Xingyu，WANG Zejiang，WANG Junmin. Automated ground vehicle path-following：A robust energy-to-peak control approach[J]. IEEE Transactions on Intelligent Transportation Systems，2022，23(9)：14294-14305.
[37] XU Shaobin，PENG Huei. Design，analysis，and experiments of preview path tracking control for autonomous vehicles[J]. IEEE Transactions on Intelligent Transportation Systems，2020，21(1)：48-58.
[38] CAI Guoshun，XU Liwei，LIU Ying，et al. Robust preview path tracking control of autonomous vehicles under time-varying system delays and saturation[J]. IEEE Transactions on Vehicular Technology，2023，72(7)：8486-8499.
[39] CHEN Guoying，YAO Jun，HU Hongyu，et al. Design and experimental evaluation of an efficient MPC-based lateral motion controller considering path preview for autonomous vehicles[J]. Control Engineering Practice，2022，123：105164.
[40] SUH J，CHAE H，YI K. Stochastic model-predictive control for lane change decision of automated driving vehicles[J]. IEEE Transactions on Vehicular Technology，2018，67(6)：4771-4782.
[41] 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. GONG Jianwei，JIANG Yan，XU Wei. Model predictive control for autonomous vehicles[M]. Beijing：Beijing Institute of Technology Press，2014.