Please wait a minute...
Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (8): 1638-1649    DOI: 10.3785/j.issn.1008-973X.2026.08.003
    
Model predictive control parameter optimization in autonomous driving considering both subjective and objective factors
Tiangen CHANG1(),Guofu TIAN1,*(),Yuanyuan TANG2,Mingxue CAO1
1. School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China
2. Engineering Training Center, Shenyang University of Technology, Shenyang 110870, China
Download: HTML     PDF(1783KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

A novel parameter optimization method for model predictive control was proposed to address the problems of insufficient tracking accuracy and poor real-time performance of model predictive controllers in trajectory tracking of autonomous vehicles. An improved non-dominated sorting whale optimization algorithm (NSWOA) based on the improved Sinusoidal mapping and a Lévy flight strategy was proposed to solve the problem of relatively concentrated and out-of-bound optimal solutions obtained by the NSWOA. The parameter optimization problem of model predictive controllers was formulated as a multi-objective optimization problem. The predictive horizon, control horizon, and sampling time were used as optimization variables. The sum of squared lateral trajectory errors and total computation time were used as optimization objectives. The improved NSWOA was employed to solve the multi-objective optimization problem and obtain the Pareto optimal solution set. The optimal controller parameter combination was determined by using the expert scoring method, the continuous ordered weighted averaging operator method, the game theory-based combined weighting method, and the technique for order preference by similarity to an ideal solution. The tracking accuracy of the proposed method was improved by an average of 56.27%, and the computation time was reduced by an average of 21.54%. This method provides a new idea that balances high tracking accuracy and high real-time performance for the tuning strategy of model predictive control parameters.



Key wordsautonomous driving      model predictive control      whale optimization algorithm      continuous ordered weighted averaging operator      game theory-based combined weighting     
Received: 30 June 2025      Published: 16 July 2026
CLC:  TP 393  
Fund:  国家自然科学基金资助项目(52375258).
Corresponding Authors: Guofu TIAN     E-mail: 1473505308@qq.com;tianguofu@126.com
Cite this article:

Tiangen CHANG,Guofu TIAN,Yuanyuan TANG,Mingxue CAO. Model predictive control parameter optimization in autonomous driving considering both subjective and objective factors. Journal of ZheJiang University (Engineering Science), 2026, 60(8): 1638-1649.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.08.003     OR     https://www.zjujournals.com/eng/Y2026/V60/I8/1638


考虑主客观因素的自动驾驶模型预测控制参数优化

针对自动驾驶汽车轨迹跟踪过程中模型预测控制器跟踪精度不足和实时性差的问题,提出考虑主客观因素的模型预测控制参数优化方法. 针对非支配排序鲸鱼优化算法(NSWOA)得到的最优解相对集中和超出边界的问题,提出基于改进Sinusoidal映射和莱维飞行策略的改进NSWOA. 将模型预测控制器的参数优化问题转化为多目标优化问题,以预测时域、控制时域和采样时间作为优化变量,以横向轨迹误差平方和与总计算时间作为优化目标,利用改进NSWOA求解多目标优化问题,获得Pareto最优解集. 采用专家打分法、连续有序加权平均算子法、博弈论组合赋权法和逼近理想解排序法,确定最佳的控制器参数组合. 所提方法的跟踪精度平均提高了56.27%,计算时间平均减少了21.54%,为模型预测控制参数的整定策略提供了兼顾高跟踪精度和高实时性的新思路.


关键词: 自动驾驶,  模型预测控制,  鲸鱼优化算法,  连续有序加权平均算子,  博弈论组合赋权 
Fig.1 Overall framework of parameter optimization method for model predictive control
Fig.2 Three-degree-of-freedom vehicle dynamics model
Fig.3 Single calculation time corresponding to different input parameters
Fig.4 Flowchart of improved NSWOA solution
函数算法IGDGD
ZDT1NSWOA0.117 440.005 89
SNSWOA0.010 160.004 79
SLNSWOA0.010 110.004 54
ZDT2NSWOA0.159 740.003 22
SNSWOA0.010 560.003 20
SLNSWOA0.010 490.003 17
ZDT4NSWOA0.211 460.006 47
SNSWOA0.009 710.004 84
SLNSWOA0.009 560.004 74
ZDT6NSWOA0.007 070.096 67
SNSWOA0.006 570.023 48
SLNSWOA0.005 520.021 54
Tab.1 IGD and GD of each algorithm under different functions
Fig.5 Comparison of solutions and true optimal solution of each algorithm under various functions
序号$ {Z_{{\text{Yet}}}} $$ {Z_{{T_{\mathrm{t}}}}} $序号$ {Z_{{\text{Yet}}}} $$ {Z_{{T_{\mathrm{t}}}}} $
1351134
2541253
3531345
4341453
5531545
6451653
7351754
8541835
9531954
10452035
Tab.2 Expert scores for sum of squared lateral trajectory errors and total computation time
Fig.6 Optimal solution set obtained by optimization methods
Fig.7 Tracking trajectories and lateral trajectory errors under double lane change condition
$ {v_x} $/(m·s?1)方法Yet/mm2Tt/sts/ms?Yet/%?Tt/%
10MPC1 658.965 13.302 15.485 2
FIS-MPC1 313.173 72.640 84.386 820.8420.03
PSO-MPC1 076.707 73.168 35.263 035.104.05
SWSLN-MPC1 145.736 52.816 54.678 630.9414.71
OWSLN-MPC1 136.686 32.803 44.656 931.4815.10
SOWSLN-MPC1 136.924 62.446 94.064 731.4725.90
15MPC2 223.386 03.197 05.310 7
FIS-MPC1 505.635 52.628 44.366 232.2817.79
PSO-MPC847.031 63.473 55.769 961.90?8.65
SWSLN-MPC1 032.351 52.802 54.655 353.5712.34
OWSLN-MPC1 023.662 82.999 04.981 853.966.19
SOWSLN-MPC737.434 72.520 14.186 366.8321.17
17MPC2 656.029 83.059 65.082 4
FIS-MPC1 684.968 12.728 94.533 036.5610.81
PSO-MPC969.590 13.050 15.066 563.490.31
SWSLN-MPC1 203.585 62.785 84.627 654.688.95
OWSLN-MPC1 194.374 92.761 14.586 555.039.76
SOWSLN-MPC782.955 32.522 24.189 770.5217.56
Tab.3 Statistics of tracking accuracy and computation time under double lane change condition
[1]   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
doi: 10.3901/JME.2020.10.127
[2]   梁忠超, 张欢, 赵晶, 等 基于自适应MPC的无人驾驶车辆轨迹跟踪控制[J]. 东北大学学报: 自然科学版, 2020, 41 (6): 835- 840
LIANG Zhongchao, ZHANG Huan, ZHAO Jing, et al Trajectory tracking control of unmanned vehicles based on adaptive MPC[J]. Journal of Northeastern University: Natural Science, 2020, 41 (6): 835- 840
[3]   XIN Z, WANG W, LIANG S Path following and lateral-yaw-roll stability integrated control method for autonomous distributed drive electric buses[J]. International Journal of Automotive Technology, 2023, 24 (4): 1117- 1128
doi: 10.1007/s12239-023-0091-9
[4]   ZHU G, JIE H, HONG W Nonlinear model predictive path tracking control for autonomous vehicles based on orthogonal collocation method[J]. International Journal of Control, Automation and Systems, 2023, 21 (1): 257- 270
doi: 10.1007/s12555-021-0812-7
[5]   王宏伟, 刘晨宇, 李磊, 等 基于高效NMPC算法的无人车轨迹跟踪控制研究[J]. 汽车工程, 2022, 44 (10): 1494- 1502
WANG Hongwei, LIU Chenyu, LI Lei, et al Research on trajectory tracking control of unmanned vehicle based on efficient NMPC algorithm[J]. Automotive Engineering, 2022, 44 (10): 1494- 1502
[6]   DAI Y, WANG D A tube model predictive control method for autonomous lateral vehicle control based on sliding mode control[J]. Sensors, 2023, 23 (8): 3844
doi: 10.3390/s23083844
[7]   贺伊琳, 马建, 杨舒凯, 等 融合预瞄特性的智能电动汽车稳定性模型预测控制研究[J]. 汽车工程, 2023, 45 (5): 719- 734
HE Yilin, MA Jian, YANG Shukai, et al Research on stability model predictive control of intelligent electric vehicle with preview characteristics[J]. Automotive Engineering, 2023, 45 (5): 719- 734
[8]   王志文, 辛鹏, 孙洪涛, 等 基于收缩约束模型预测控制的无人车辆路径跟踪[J]. 控制与决策, 2022, 37 (3): 625- 634
WANG Zhiwen, XIN Peng, SUN Hongtao, et al Unmanned vehicle path tracking based on contraction constraint model predictive control[J]. Control and Decision, 2022, 37 (3): 625- 634
[9]   李兵兵, 庄伟超, 刘昊吉, 等 基于自学习型MPC的网联电动汽车生态驾驶控制策略研究[J]. 机械工程学报, 2024, 60 (10): 453- 462
LI Bingbing, ZHUANG Weichao, LIU Haoji, et al Research on eco-driving control strategy of connected electric vehicle based on learning-MPC[J]. Journal of Mechanical Engineering, 2024, 60 (10): 453- 462
[10]   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
doi: 10.3901/JME.2023.04.199
[11]   TIAN T, LI G, LI N, et al Research on trajectory tracking control of driverless electric formula racing car based on game theory[J]. World Electric Vehicle Journal, 2023, 14 (4): 84
doi: 10.3390/wevj14040084
[12]   何洋, 李刚 基于速度障碍模型的智能汽车轨迹规划控制方法研究[J]. 兵工学报, 2025, 46 (4): 397- 410
HE Yang, LI Gang Research on trajectory planning control method of intelligent vehicle based on velocity obstacle model[J]. Acta Armamentarii, 2025, 46 (4): 397- 410
[13]   WANG H, WANG Q, CHEN W, et al Path tracking based on model predictive control with variable predictive horizon[J]. Transactions of the Institute of Measurement and Control, 2021, 43 (12): 2676- 2688
doi: 10.1177/01423312211003809
[14]   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
doi: 10.3901/JME.2022.24.275
[15]   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 optimized dynamics model[J]. China Mechanical Engineering, 2024, 35 (6): 1000- 1009
[16]   谢宪毅, 王禹涵, 金立生, 等 基于改变控制时域时间步长的智能车轨迹跟踪控制[J]. 吉林大学学报: 工学版, 2024, 54 (3): 620- 630
XIE Xianyi, WANG Yuhan, JIN Lisheng, et al Intelligent vehicle trajectory tracking control based on adjusting step size of control horizon[J]. Journal of Jilin University: Engineering and Technology Edition, 2024, 54 (3): 620- 630
[17]   邵柏岩, 叶伯生, 金雄程, 等 基于增量支配MPC的高速高精轨迹跟踪控制[J]. 华中科技大学学报: 自然科学版, 2025, 53 (5): 1- 8
SHAO Baiyan, YE Bosheng, JIN Xiongcheng, et al High-speed and high-precision trajectory tracking control based on incremental domination MPC[J]. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2025, 53 (5): 1- 8
[18]   袁志群, 陈衍强, 常宇轩, 等 考虑侧风稳定性的汽车轨迹跟踪自适应时域模型预测控制[J]. 汽车工程, 2024, 46 (10): 1829- 1841
YUAN Zhiqun, CHEN Yanqiang, CHANG Yuxuan, et al Model predictive control with adaptive horizon for vehicle trajectory tracking considering crosswind stability[J]. Automotive Engineering, 2024, 46 (10): 1829- 1841
[19]   龚建伟, 刘凯, 齐建永. 无人驾驶车辆模型预测控制: 第2版[M]. 北京: 北京理工大学出版社, 2020: 27–28.
[20]   李一铭, 王跟成 基于坠落机制的混沌麻雀算法AGV路径规划[J]. 制造技术与机床, 2023, (1): 102- 108
LI Yiming, WANG Gencheng Based on falling mechanism chaotic sparrow algorithm of AGV path planning[J]. Manufacturing Technology & Machine Tool, 2023, (1): 102- 108
[21]   LI J, AN Q, LEI H, et al Survey of lévy flight-based metaheuristics for optimization[J]. Mathematics, 2022, 10 (15): 2785
doi: 10.3390/math10152785
[22]   郑婷婷, 毛禧雯, 杨昔阳, 等 基于最小方差C-OWA的评价模型及其应用[J]. 泉州师范学院学报, 2022, 40 (5): 51- 56
ZHENG Tingting, MAO Xiwen, YANG Xiyang, et al The evaluation model based on minimum variance C-OWA and its application[J]. Journal of Quanzhou Normal University, 2022, 40 (5): 51- 56
[23]   王会东, 何世繁, 潘晓宏, 等 基于博弈论权重集化模型的多属性群决策VIKOR方法[J]. 统计与决策, 2019, 35 (15): 39- 43
WANG Huidong, HE Shifan, PAN Xiaohong, et al A new VIKOR method for multi-attribute group decision-making based on game theory weight integration model[J]. Statistics and Decision, 2019, 35 (15): 39- 43
[24]   HU Y, WU L, SHI C, et al Research on optimal decision-making of cloud manufacturing service provider based on grey correlation analysis and TOPSIS[J]. International Journal of Production Research, 2020, 58 (3): 748- 757
doi: 10.1080/00207543.2019.1600760
[25]   曹林, 卢厚清, 冯玉芳 基于博弈论的评估指标权重分配模型[J]. 军事运筹与系统工程, 2019, 33 (1): 11- 14
CAO Lin, LU Houqing, FENG Yufang Evaluating indicators’ weight allocation model based on game theory[J]. Military Operations Research and Systems Engineering, 2019, 33 (1): 11- 14
[26]   张志达, 郑玲, 张紫微, 等 基于自适应模型预测的智能汽车横向轨迹跟踪控制[J]. 中国公路学报, 2022, 35 (7): 305- 316
ZHANG Zhida, ZHENG Ling, ZHANG Ziwei, et al Lateral trajectory tracking control of intelligent vehicles based on adaptive model prediction[J]. China Journal of Highway and Transport, 2022, 35 (7): 305- 316
[27]   王玮琛, 李军求, 孙逢春, 等 基于Tube MPC的多轴重型车辆全轮转向路径跟踪策略[J]. 汽车工程, 2022, 44 (11): 1665- 1675
WANG Weichen, LI Junqiu, SUN Fengchun, et al Path tracking strategy for all-wheel steering of multi-axle heavy-duty vehicles based on tube MPC[J]. Automotive Engineering, 2022, 44 (11): 1665- 1675
[1] Mengbin DUAN,Guoxing BAI,Yu MENG,Qing GU,Zhen WANG,Elxat ELHAM,Shaochong LIU. Path planning and tracking control for differential-drive robots based on A* and multi-reference point MPC[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(8): 1627-1637.
[2] Xinmiao YU,Nan XIA,Jiahong JIANG,Ziying HAO,Yunsheng BA. Low-light target detection based on multi-scale feature similarity matching[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(7): 1464-1474.
[3] Zhengrong CHEN,Ruochen WANG,Renkai DING,Feng WEI. Mode-switching strategy for electro-hydraulic composite braking system of electric vehicle[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(6): 1307-1316.
[4] Yanxia SHEN,Shuo WEI,Wei ZHANG. Voltage model predictive control of DAB converter considering current stress optimization[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(6): 1329-1338.
[5] Guoxing BAI,Fei LIU,Yu MENG,Qing GU,Zhiwei SONG,Shaochong LIU. Path tracking of car-like robots based on linear MPC with multiple reference points[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(4): 679-689.
[6] Wenqiang CHEN,Linyue FENG,Dongdan WANG,Yulei GU,Xuan ZHAO. Vehicle trajectory prediction model integrating dynamic risk map and multivariate attention mechanism[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(3): 455-467.
[7] Juntao LV,Jueyu QI,Haochen YU,Lei MA,Huimin MA,Tianyu HU. Current status and future prospect of integrated simulation platform for autonomous driving[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(3): 513-526.
[8] Zili LI,Bing ZHOU,Yangyi LIU,Tian CHAI,Nianfei GAN,Qingjia CUI. Human-machine collaborative planning and shared control considering driving intention[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(9): 1954-1963.
[9] Qi WEI,Jianfeng TAO,Hao SUN,Yulei ZHANG,Chengliang LIU. Nonlinear model predictive trajectory tracking for valve-controlled cylinder with counterbalance valve[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(8): 1565-1573.
[10] Wenqiang CHEN,Dongdan WANG,Wenying ZHU,Yongjie WANG,Tao WANG. Vehicle multimodal trajectory prediction model based on spatio-temporal graph attention network[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(3): 443-450.
[11] Dengfeng LIU,Wenjing GUO,Shihai CHEN. Content-guided attention-based lane detection network[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(3): 451-459.
[12] Zhaolong DONG,He HUANG,Zhanyi LI,Lan YANG,Huifeng WANG. Snowy scene integration construction method in autonomous driving sample library[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(10): 2078-2085.
[13] Yun MENG,Penghui MIAO,Maode YAN,Lei ZUO. Optimal energy consumption control method for mixed vehicle platoon considering passenger comfort[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(10): 2086-2095.
[14] Haipeng QIN,Rui QIN,Xiaofen SHI,Xiaoming ZHU. Motion control of quadruped robot based on model prediction[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(8): 1565-1576.
[15] Junhui ZHANG,Xiaoman GUO,Jingxian WANG,Zongjie FU,Yuxi LIU. Shared lane-keeping control based on non-cooperative game theory[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(5): 1001-1008.