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浙江大学学报(工学版)  2026, Vol. 60 Issue (8): 1638-1649    DOI: 10.3785/j.issn.1008-973X.2026.08.003
能源工程、机械工程     
考虑主客观因素的自动驾驶模型预测控制参数优化
常天根1(),田国富1,*(),唐媛媛2,曹明学1
1. 沈阳工业大学 机械工程学院,辽宁 沈阳 110870
2. 沈阳工业大学 工程实训中心,辽宁 沈阳 110870
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
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摘要:

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    
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 words: autonomous driving    model predictive control    whale optimization algorithm    continuous ordered weighted averaging operator    game theory-based combined weighting
收稿日期: 2025-06-30 出版日期: 2026-07-16
CLC:  TP 393  
基金资助: 国家自然科学基金资助项目(52375258).
通讯作者: 田国富     E-mail: 1473505308@qq.com;tianguofu@126.com
作者简介: 常天根(1996—),男,博士生,从事自动驾驶汽车决策规划控制技术研究. orcid.org/0009-0003-9821-4700. E-mail:1473505308@qq.com
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引用本文:

常天根,田国富,唐媛媛,曹明学. 考虑主客观因素的自动驾驶模型预测控制参数优化[J]. 浙江大学学报(工学版), 2026, 60(8): 1638-1649.

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.

链接本文:

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

图 1  模型预测控制参数优化方法的整体框架
图 2  三自由度车辆动力学模型
图 3  不同输入参数对应的单次计算时间
图 4  改进NSWOA的求解流程图
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
表 1  不同函数下各算法的反转世代距离和世代距离
图 5  不同函数下各算法的解与真实最优解对比
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
表 2  专家对横向轨迹误差平方和与总计算时间的打分
图 6  采用优化方法计算得到的最优解集
图 7  双移线工况下的跟踪轨迹和横向轨迹误差
$ {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
表 3  双移线工况下跟踪精度和计算时间统计
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