工程科学学报，第41卷，第7期：947-954,2019年7月 Chinese Journal of Engineering,Vol.41,No.7:947-954,July 2019 D0L:10.13374/j.issn2095-9389.2019.07.014:htp:/journals.usth.edu.cm 基于非线性模型预测控制的自动泊车路径跟踪 顾 青)，白国星)，孟宇12)四，刘立)，罗维东)，甘鑫) 1)北京科技大学机械工程学院，北京1000832)北京科技大学人工智能研究院，北京100083 区通信作者，E-mail:myu@usth.cd.cm 摘要与行驶速度较高的其他无人驾驶工况相比，自动泊车时参考路径的曲率较大，因此车辆转向轮转角速度的限制等系 统约束条件会严重影响自动泊车路径跟踪控制器的性能.为了解决这一问题，提出了基于非线性模型预测控制的自动泊车路 径跟踪控制器，并在MATLAB/Simulink和PreScan联合仿真环境中将该控制器与基于线性时变模型预测控制的控制器进行了 对比.仿真结果表明非线性模型预测控制器可以实现多约束条件下的自动泊车，泊车完成后车辆航向与车位中线的夹角为 0.0189ad,车辆后桥中点与车位中线的距离为0.1045m,仅为车身宽度的5.56%.相比线性时变模型预测控制器，非线性模 型预测控制器具有泊车精度更高、安全裕度更大、泊车耗时更少等优势.在实时性方面，该控制器也能够满足自动泊车的需求. 关键词车辆：自动泊车；路径跟踪；运动控制：非线性模型预测控制 分类号U471.1 Path tracking of automatic parking based on nonlinear model predictive control GU Qing",BAI Guo-xing,MENG Yu',LIU Li,LUO Wei-dong,GAN Xin') 1)School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)Institute of Artificial Intelligence,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:myu@ustb.edu.cn ABSTRACT In megacities,the number of vehicles has rapidly grown.Automatic parking,a special type of unmanned driving,has become an important technology to ease parking difficulties.Path tracking is also a core part of automatic parking.However,during au- tomatic parking,the curvature of the reference path is very large.This poses a challenge in automatic parking and is different from that in high-speed unmanned driving.When the curvature of the reference path is large,the constraints of the system severely restrain the path tracking performance.These constraints include the limit of the steering wheel angle speed.Applying model predictive control is a good way to handle multiple constraints.Recently,a path tracking controller for automatic parking based on linear time-varying model predictive control has been reported.However,for automatic parking,the accuracy of the linearized prediction model is still insuffi- cient.To solve this problem,a path tracking controller based on nonlinear model predictive control was proposed in this paper.This controller was compared with the controller based on linear time-varying model predictive control.The simulation environment is a com- bination of MATLAB/Simulink and PreScan.The simulation results show that the proposed controller could complete automatic parking with multiple constraints.After the parking was completed,the angle between the vehicle heading and the center line of the parking space was 0.0189 rad.The distance between the midpoint of the rear axle of the vehicle and the center line of the parking space was 0.1045 m.This distance was only 5.56%of the width of the vehicle body.Compared with the controller based on linear time-varying model predictive control,the proposed controller for automatic parking exhibited a higher parking precision,larger safety margin,and less parking time.In terms of real-time performance,the proposed controller could also meet the requirements for automatic parking. KEY WORDS vehicle;automatic parking;path tracking;motion control;nonlinear model predictive control 收稿日期：2018-11-13 基金项目：国家重点研发计划资助项目(No.2018YFC0604403,No.2016YFC0802905):国家高技术研究发展计划资助项目(No. 2011AA060408):中央高校基本科研业务费专项资金资助项目(No.FRF-TP-17-010A2)工程科学学报,第 41 卷,第 7 期:947鄄鄄954,2019 年 7 月 Chinese Journal of Engineering, Vol. 41, No. 7: 947鄄鄄954, July 2019 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2019. 07. 014; http: / / journals. ustb. edu. cn 基于非线性模型预测控制的自动泊车路径跟踪 顾 青1) , 白国星1) , 孟 宇1,2) 苣 , 刘 立1) , 罗维东1) , 甘 鑫1) 1) 北京科技大学机械工程学院, 北京 100083 2) 北京科技大学人工智能研究院,北京 100083 苣通信作者, E鄄mail: myu@ ustb. edu. cn 摘 要 与行驶速度较高的其他无人驾驶工况相比,自动泊车时参考路径的曲率较大,因此车辆转向轮转角速度的限制等系 统约束条件会严重影响自动泊车路径跟踪控制器的性能. 为了解决这一问题,提出了基于非线性模型预测控制的自动泊车路 径跟踪控制器,并在 MATLAB/ Simulink 和 PreScan 联合仿真环境中将该控制器与基于线性时变模型预测控制的控制器进行了 对比. 仿真结果表明非线性模型预测控制器可以实现多约束条件下的自动泊车,泊车完成后车辆航向与车位中线的夹角为 0郾 0189 rad,车辆后桥中点与车位中线的距离为 0郾 1045 m,仅为车身宽度的 5郾 56% . 相比线性时变模型预测控制器,非线性模 型预测控制器具有泊车精度更高、安全裕度更大、泊车耗时更少等优势. 在实时性方面,该控制器也能够满足自动泊车的需求. 关键词 车辆; 自动泊车; 路径跟踪; 运动控制; 非线性模型预测控制 分类号 U471郾 1 收稿日期: 2018鄄鄄11鄄鄄13 基金 项 目: 国 家 重 点 研 发 计 划 资 助 项 目 ( No. 2018YFC0604403, No. 2016YFC0802905 ); 国 家 高 技 术 研 究 发 展 计 划 资 助 项 目 ( No. 2011AA060408);中央高校基本科研业务费专项资金资助项目(No. FRF鄄鄄TP鄄鄄17鄄鄄010A2) Path tracking of automatic parking based on nonlinear model predictive control GU Qing 1) , BAI Guo鄄xing 1) , MENG Yu 1,2) 苣 , LIU Li 1) , LUO Wei鄄dong 1) , GAN Xin 1) 1) School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China 苣Corresponding author, E鄄mail: myu@ ustb. edu. cn ABSTRACT In megacities, the number of vehicles has rapidly grown. Automatic parking, a special type of unmanned driving, has become an important technology to ease parking difficulties. Path tracking is also a core part of automatic parking. However, during au鄄 tomatic parking, the curvature of the reference path is very large. This poses a challenge in automatic parking and is different from that in high鄄speed unmanned driving. When the curvature of the reference path is large, the constraints of the system severely restrain the path tracking performance. These constraints include the limit of the steering wheel angle speed. Applying model predictive control is a good way to handle multiple constraints. Recently, a path tracking controller for automatic parking based on linear time鄄varying model predictive control has been reported. However, for automatic parking, the accuracy of the linearized prediction model is still insuffi鄄 cient. To solve this problem, a path tracking controller based on nonlinear model predictive control was proposed in this paper. This controller was compared with the controller based on linear time鄄varying model predictive control. The simulation environment is a com鄄 bination of MATLAB/ Simulink and PreScan. The simulation results show that the proposed controller could complete automatic parking with multiple constraints. After the parking was completed, the angle between the vehicle heading and the center line of the parking space was 0郾 0189 rad. The distance between the midpoint of the rear axle of the vehicle and the center line of the parking space was 0郾 1045 m. This distance was only 5郾 56% of the width of the vehicle body. Compared with the controller based on linear time鄄varying model predictive control, the proposed controller for automatic parking exhibited a higher parking precision, larger safety margin, and less parking time. In terms of real鄄time performance, the proposed controller could also meet the requirements for automatic parking. KEY WORDS vehicle; automatic parking; path tracking; motion control; nonlinear model predictive control