Research on Trajectory Tracking Control of Autonomous Vehicle Based on MPC with Variable Predictive Horizon
-
摘要: 为了保证自动驾驶汽车轨迹跟踪的精度及行驶过程中的稳定性,提出一种基于车辆横向稳定状态在线识别和模糊算法的变预测时域模型预测控制(MPC)方法。针对车辆稳定状态的在线识别,采用k-means聚类算法对车辆行驶状态参数进行聚类分析,得到聚类质心,通过在线对比当前车辆状态量与不同聚类质心之间的欧氏距离获取车辆的实时安全等级。同时计算出当前车辆的轨迹跟踪横向偏移量,以这二者为输入,通过模糊控制算法在线计算出预测时域的变化量并输出给MPC控制器实现预测时域的自适应调整,最后求解出自动驾驶车辆跟踪轨迹的最优的控制序列,以达到在保持车辆稳定的前提下实现高精度轨迹跟踪控制的目的。CarSim/Simulink联合仿真结果表明,改进后的变预测时域MPC算法在提高自动驾驶汽车轨迹跟踪精度及横向稳定性方面的表现优于传统MPC控制器。Abstract: In order to ensure the trajectory tracking accuracy and driving stability of autonomous vehicles, a model predictive control with variable predictive horizon method was proposed based on on-line identification of vehicle lateral stability state and fuzzy algorithm. Aiming at the online recognition of vehicle stable state, k-means clustering algorithm was used to cluster the parameters of vehicle driving state and obtain the cluster centroid. The real-time safety level of vehicle was obtained by comparing the Euclidean distance between the current vehicle state quantity and different cluster centroids online. At the same time, the lateral offset of the current vehicle track tracking is calculated. With the two as inputs, the variation of prediction time domain is calculated online by fuzzy algorithm and output to MPC controller to realize adaptive adjustment of prediction time domain. Finally, the optimal control sequence of the track tracking of the autonomous vehicle is solved to achieve the goal of high precision trajectory tracking control under the premise of maintaining vehicle stability. The results of CarSim/Simulink co-simulation show that the improved MPC algorithm is superior to the traditional MPC controller in improving the trajectory tracking accuracy and lateral stability of autonomous vehicles.
-
Key words:
- automatic drive /
- trajectory tracking /
- k-means algorithm /
- fuzzy algorithm /
- model predictive control
-
表 1 车辆具体参数
参数 数值 簧上质量ms/kg 1 723 绕x轴转动量Ix/(kg·m2) 1 243.1 绕y轴转动量Iy/(kg·m2) 4 331.6 绕z轴转动惯量Iz/(kg·m2) 4 175 质心高度h/mm 460 前轮距质心距离lf/mm 1 232 后轮距质心距离lr/mm
轮距d/mm1 468
310表 2 聚类质心及对应危险等级
危险等级 $ {v_y}/({\text{km/h}}) $ $ {A_y}/({{\rm{m/}}}{{{\rm{s}}}^{\bf{2}}}) $ $ \dot \varphi /(\deg /{{\rm{s}}}) $ $ Roll/(°) $ $ A{V_x}/[(°)/{{\rm{s}}}] $ $ \beta /(°) $ $ \dot \beta /[(°)/{{\rm{s}}}] $ R1 R2 1 0.053 4 0.023 7 0.568 1 0.146 3 0.481 3 0.033 4 0.084 4 0.065 3 0.064 9 2 0.696 4 0.185 0 3.660 9 1.588 7 3.857 8 0.428 9 1.728 6 0.063 4 0.060 4 3 1.059 0 0.378 8 9.286 5 2.358 6 2.257 2 0.663 7 0.696 0 0.067 9 0.051 0 4 1.139 6 0.369 5 11.864 3 1.571 0 2.999 7 0.677 0 4.188 4 0.043 5 0.062 4 5 2.422 8 0.675 9 18.767 9 4.013 9 12.047 0 1.538 2 2.029 0 0.041 6 0.117 2 表 3 量化因子
变量 L ey ΔNP 基本论域 [1, 5] [0, 2] [−10, 10] 模糊论域 [−4, 4] [−4, 4] [−10, 10] 量化因子 2 4 1 表 4 模糊规则表
ΔNP 危险等级L NB NS ZO PM PB 横向偏差ey NB ZO ZO PS PB PB NM NS ZO ZO PM PB NS NS NS NS PM PB ZO NM NS NS PS PB PS NM NM NM PS PB PM NB NB NM NS PB PB PB PB PB PB PB 表 5 仿真结果及对比
仿真工况 Vx=54 km/h
μ=0.9Vx=30 km/h
μ=0.4Vx=80 km/h
μ=0.9评价系数 WY Wφ WY Wφ WY Wφ NP=20 0.075 5 0.014 8 0.318 8 0.038 1 0.493 1 0.034 6 变预测时域MPC 0.058 1 0.013 3 0.290 4 0.037 3 0.406 8 0.030 7 提升比例(%) 23.0 10.1 8.91 2.1 17.9 11.3 表 6 变预测时域MPC算法求解时间及方差
仿真工况 Vx=54 km/h
μ=0.9Vx=30 km/h
μ=0.4Vx=80 km/h
μ=0.9平均求解时间/ms 2.799 2 2.554 4 2.604 9 方差/ms 0.044 7 0.046 8 0.050 3 -
[1] PADEN B, ČÁP M, YONG S, et al. A survey of motion planning and control techniques for self-driving urban vehicles[J]. IEEE Transactions on Intelligent Vehicles, 2016, 1(1): 33-55. doi: 10.1109/TIV.2016.2578706 [2] WANG Huiran, WANG Qidong, CHEN Wuwei, 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 [3] ELBANHAWI M, SIMIC M, JAZAR R. Receding horizon lateral vehicle control for pure pursuit path tracking[J]. Journal of Vibration and Control, 2018, 24(3): 619-642. doi: 10.1177/1077546316646906 [4] MARINO R, SCALZI S, NETTO M. Nested PID steering control for lane keeping in autonomous vehicles[J]. Control Engineering Practice, 2011, 19(12): 1459-1467. doi: 10.1016/j.conengprac.2011.08.005 [5] KIM S, CHANG H W, KIM C. Path tracking motion control using fuzzy inference for a parking-assist system[J]. Transactions of the Korean Society of Automotive Engineers, 2009, 17(2): 1-9. [6] 王艺, 蔡英凤, 陈龙, 等. 基于模型预测控制的智能网联汽车路径跟踪控制器设计[J]. 机械工程学报, 2019, 55(8): 136-144, 153. doi: 10.3901/JME.2019.08.136WANG Yi, CAI Yingfeng, CHEN Long, et al. Design of intelligent and connected vehicle path tracking controller based on model predictive control[J]. Journal of Mechanical Engineering, 2019, 55(8): 136-144, 153. doi: 10.3901/JME.2019.08.136 [7] ZHANG Wenbin, BAI Wenhao, WANG Jinyan, et al. Research on path tracking of intelligent vehicle based on optimal deviation control[J]. Integrated Ferroelectrics, 2018, 191(1): 80-91. doi: 10.1080/10584587.2018.1457370 [8] WURTS J, STEIN J, ERSAL T. Collision imminent steering at high speed using nonlinear model predictive control[J]. IEEE Transactions on Vehicular Technology, 2020, 69(8): 8278-8289. doi: 10.1109/TVT.2020.2999612 [9] XI Yugeng, LI Deweili, LIN Shu. Model predictive control-status and challenges[J]. Acta Automatica Sinica, 2013, 39(3): 222-236. doi: 10.1016/S1874-1029(13)60024-5 [10] GUO Hongyan, LIU Feng, YU Ru, et al. Regional path moving horizon tracking controller design for autonomous ground vehicles[J]. Science China Information Sciences, 2017, 60(1): 1-7. [11] JI Jie, KHAJEPOUR A, MELEK W, et al. Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints[J]. IEEE Transactions on Vehicular Technology, 2016, 66(2): 952-964. [12] GUO Hongyan, CAO Dongpu, CHEN Hong, et al. Model predictive path following control for autonomous cars considering a measurable disturbance: Implementation, testing, and verification[J]. Mechanical Systems and Signal Processing, 2019, 118: 41-60. doi: 10.1016/j.ymssp.2018.08.028 [13] 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. doi: 10.1109/TVT.2020.2981619 [14] ZHANG Bing, ZONG Changfu, CHEN Guoying, et al. An adaptive-prediction-horizon model prediction control for path tracking in a four-wheel independent control electric vehicle[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2019, 233(12): 3246-3262. doi: 10.1177/0954407018821527 [15] EGGIMANN M, CRISALLE O, LONGCHAMP R. A linear-programming predictive controller with variable horizon[C]//1992 American Control Conference. IEEE, 1992: 1568-1575. [16] 范贤波, 彭育辉, 钟聪. 基于自适应MPC的自动驾驶汽车轨迹跟踪控制[J]. 福州大学学报(自然科学版), 2021, 49(4): 500-507. https://www.cnki.com.cn/Article/CJFDTOTAL-FZDZ202104010.htmFAN Xianbo, PENG Yuhui, ZHONG Cong. Trajectory tracking control of autonomous vehicles based on adaptive MPC[J]. Journal of Fuzhou University(Natural Science Edition), 2021, 49(4): 500-507. https://www.cnki.com.cn/Article/CJFDTOTAL-FZDZ202104010.htm [17] 荆林国, 荆仲毅, 张韶晶, 等. 考虑随机影响因素的电网饱和负荷概率预测方法[J]. 电气工程学报, 2021, 16(3): 99-105. https://www.cnki.com.cn/Article/CJFDTOTAL-DQZH202103014.htmJING Linguo, JING Zhongyi, ZHANG Shaojing, et al. Power grid saturation load probability prediction method considering random influencing factors[J]. Journal of Electrical Engineering, 2021, 16(3): 99-105. https://www.cnki.com.cn/Article/CJFDTOTAL-DQZH202103014.htm [18] 谢林, 李红伟, 袁岳, 等. 基于K-Means聚类和改进多分类相关向量机的台区线损计算方法[J]. 电气工程学报, 2021, 16(1): 62-69. https://www.cnki.com.cn/Article/CJFDTOTAL-DQZH202101009.htmXIE Lin, LI Hongwei, YUAN Yue, et al. Calculation of line loss in transformer district based on K-means clustering algorithm and improved MRVM[J]. Journal of Electrical Engineering, 2021, 16(1): 62-69. https://www.cnki.com.cn/Article/CJFDTOTAL-DQZH202101009.htm [19] 刘凯, 龚建伟, 陈舒平, 等. 高速无人驾驶车辆最优运动规划与控制的动力学建模分析[J]. 机械工程学报, 2018, 54(14): 141-151. doi: 10.3901/JME.2018.14.141LIU Kai, GONG Jianwei, CHENG Shuping, et al. Dynamic modeling analysis of optimal motion planning and control for high-speed self-driving vehicles[J]. Journal of Mechanical Engineering, 2018, 54(14): 141-151. doi: 10.3901/JME.2018.14.141 [20] 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. [21] 刘宏飞, 徐强, 许洪国, 等. 基于k均值聚类分析的车辆横向稳定性判定方法[J]. 湖南大学学报(自然科学版), 2018, 45(8): 48-53. https://www.cnki.com.cn/Article/CJFDTOTAL-HNDX201808007.htmLIU Hongfei, XU Qiang, XU Hongguo, et al. Judgment method of vehicle lateral stability based on k means clustering analysis[J]. Journal of Hunan University(Natural Sciences), 2018, 45(8): 48-53. https://www.cnki.com.cn/Article/CJFDTOTAL-HNDX201808007.htm [22] 韩家炜, MICHELINE K. 数据挖掘: 概念与技术[M]. 北京: 机械工业出版社, 2012.HAN Jiawei, MICHELINE K. Data mining concepts and techniques[M]. Beijing: China Machine Press, 2012. [23] 陈慧, 高博麟, 徐帆. 车辆质心侧偏角估计综述[J]. 机械工程学报, 2013, 49(24): 76-94. http://www.cjmenet.com.cn/CN/Y2013/V49/I24/76CHEN Hui, GAO Bolin, XU Fan. Review on vehicle sideslip angle estimation[J]. Journal of Mechanical Engineering, 2013, 49(24): 76-94 http://www.cjmenet.com.cn/CN/Y2013/V49/I24/76 [24] 夏秋, 陈特, 陈龙, 等. 基于冗余信息融合的车辆质心侧偏角估计方法[J]. 汽车工程, 2022, 44(2): 280-289. https://www.cnki.com.cn/Article/CJFDTOTAL-QCGC202202016.htmXIA Qiu, CHEN Te, CHEN Long, et al. Vehicle sideslip angle estimation method based on redundant information fusion [J]. Automotive Engineering, 2022, 44(2): 280-289. https://www.cnki.com.cn/Article/CJFDTOTAL-QCGC202202016.htm [25] 王银, 张灏琦, 孙前来, 等. 基于自适应MPC算法的轨迹跟踪控制研究[J]. 计算机工程与应用, 2021, 57(14): 251-258. https://www.cnki.com.cn/Article/CJFDTOTAL-JSGG202114032.htmWANG Yin, ZHANG Haoqi, SUN Qianlai, et al. Research on trajectory tracking control based on adaptive MPC algorithm[J]. Computer Engineering and Applications, 2021, 57(14): 251-258. https://www.cnki.com.cn/Article/CJFDTOTAL-JSGG202114032.htm [26] 马浩通. 基于模糊控制的Y形管内高压成形加载路径优化研究[D]. 长春: 吉林大学, 2020.MA Haotong. Research on the optimization of loading path in Y-shape tube hydroforming based on fuzzy control[D]. Changchun: Jilin University, 2020.