采用状态扩展MPC与转角补偿的无人车路径跟踪控制

寇发荣; 郑文博; 张新乾; 杨慧杰; 贺嘉杰

doi:10.13433/j.cnki.1003-8728.20220088

采用状态扩展MPC与转角补偿的无人车路径跟踪控制

doi: 10.13433/j.cnki.1003-8728.20220088

西安科技大学机械工程学院，西安　710054

基金项目: 国家自然科学基金项目（51775426）、陕西省重点研发计划项目（2020GY-128）、陕西省科技计划项目（2019JQ-795）及陕西省教育厅科学研究计划项目（19JK0532）

详细信息

作者简介:
寇发荣（1973−），教授，博士生导师，研究方向为智能车辆控制，koufarong@xust.edu.cn

中图分类号: U461.99
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- 文章访问数: 111
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- 被引次数: 0
出版历程
- 收稿日期: 2021-04-26
- 刊出日期: 2023-09-30

Path Tracking Control of Unmanned Vehicle Using State Extended Model Predictive Control and Angle Compensation

College of Mechanical Engineering, Xi'an University of Science and Technology, Xi'an 710054, China

摘要

摘要: 采用传统模型预测控制（MPC）的无人车难以同时保证路径跟踪精度和实时性，针对此问题，本文设计了一种采用状态扩展MPC与转角补偿的路径跟踪控制器。建立了车辆三自由度动力学模型，设计了基于状态扩展的双反馈MPC控制器，并根据车速调整控制器参数；建立了车辆-道路跟踪模型，根据车辆横向和航向偏差设计了转角补偿模糊控制器；利用MATLAB/Simulink和Carsim软件对所设计的路径跟踪控制器进行联合仿真分析。结果表明：相比采用传统MPC控制器的车辆，在中、低车速下，状态扩展MPC控制器的控制增量求解时间平均值降低14%以上，路径跟踪控制器跟踪道路的横向和航向偏差最大值分别降低23%和17%以上，具有较好的路径跟踪性能。
- 路径跟踪 /
- 状态扩展 /
- 模型预测控制 /
- 双反馈 /
- 模糊控制
Abstract: It is difficult for an unmanned vehicle to use the traditional model predictive control (MPC) algorithm to ensure path tracking accuracy and real-time performance at the same time. To solve this problem, the paper designs a path tracking controller using the state-extension MPC and angle compensation. A 3-degree-of-freedom vehicle dynamic model is established, a dual-feedback MPC controller based on state extension is designed and the controller's parameters are adjusted according to the unmanned vehicle's speed. The vehicle-road tracking model is established, and the fuzzy controller for angle compensation is designed according to the unmanned vehicle's lateral and heading deviation. The MATLAB/Simulink and Carsim software are used to conduct the joint simulation of the designed path tracking controller. The results show that compared with the traditional MPC controller of an unmanned vehicle, at its medium and low speed, the average time for solving the control increment of the state extension MPC controller is reduced by more than 14% and that the maximum lateral and heading deviation of the path tracking controller is reduced by more than 23% and 17% respectively, thus having a better path tracking performance.
- path tracking /
- state extension /
- model predictive control /
- dual-feedback /
- fuzzy control

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图 1 单轨三自由度车辆模型

Figure 1. The single-track three-degree-of-freedom vehicle model

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图 2 路径跟踪控制器框图

Figure 2. Path tracking controller block diagram

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图 3 状态扩展MPC控制器框图

Figure 3. State-expanding MPC controller block diagram

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图 4 车辆-路径关系模型

Figure 4. The vehicle-path relationship model

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图 5 模糊控制曲面

Figure 5. Fuzzy control surface

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图 6 不同车速下的控制器计算时间

Figure 6. Controller computation time at different vehicle speeds

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图 7 36 km/h路径跟踪精度对比

Figure 7. Path tracking accuracy comparison at 36 km/h

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图 8 54 km/h路径跟踪精度对比

Figure 8. Path tracking accuracy comparison at 54 km/h

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图 9 72 km/h路径跟踪精度对比

Figure 9. Path tracking accuracy comparison at 72 km/h

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表 1 模糊控制规则表

Table 1. Fuzzy control rule table

y_e	$ {\varphi _{{e}}} $
y_e	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PB	PB	PM	PS	PS
NM	PB	PB	PM	PM	PS	ZO	NS
NS	PB	PM	PM	PS	ZO	NM	NM
ZO	PM	PS	PS	ZO	NS	NM	NM
PS	PM	PS	ZO	NS	NM	NM	NB
PM	PS	ZO	NM	NM	NM	NB	NB
PB	NS	NM	NB	NB	NM	NB	NB

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表 2 整车参数

Table 2. Vehicle parameters

参数	数值
整车质量m/kg	1783
横摆转动惯量I_z/（kg·m²）	4175
前轮侧偏刚度C_f/（N·rad⁻¹）	66900
后轮侧偏刚度C_r/（N·rad⁻¹）	62700
质心距前轴距离a/m	1.232
质心距前轴距离b/m	1.468
路面附着系数µ	1
前轮纵向滑移率s_f	0.2
后轮纵向滑移率s_r	0.2

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表 3 状态扩展MPC控制器参数A

Table 3. State-expanding MPC controller parameters A

参数	数值
离散时间步长T/s	0.05
预测时域N_p	10
控制时域N_c	5
输出量误差权重系数矩阵$\bar {\boldsymbol{Q}} $	diag（[200,100]）
控制增量权重系数R	5 × 10⁴

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表 4 状态扩展MPC控制器参数B

Table 4. State-expanding MPC controller parameters B

参数	数值
离散时间步长T/s	0.05
预测时域N_p	12
控制时域N_c	6
输出量误差权重系数矩阵$\bar {\boldsymbol{Q}} $	diag（[200,100]）
控制增量权重系数R	1 × 10⁴

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表 5 双移线工况控制器控制增量求解时间对比

Table 5. Comparison of control increment solution time for the double-shift-line working condition

车速/（ km·h⁻¹）	指标	传统MPC/ms	状态扩展MPC/ms	改善程度/%
36	平均时间	13.56	10.56	22.1
36	最大时间	32.52	19.15	41.1
54	平均时间	14.88	12.66	14.9
54	最大时间	28.46	20.56	27.7
72	平均时间	17.21	12.20	29.1
72	最大时间	37.33	20.14	46.0

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表 6 双移线工况横向偏差对比

Table 6. Comparison of lateral deviation for the double-shift-line working condition

车速/ （km·h⁻¹）	指标	控制器 1/m	控制器 2/m	改善程度/%
36	平均偏差	0.086	0.062	27.9
36	最大偏差	0.509	0.388	23.8
54	平均偏差	0.084	0.072	14.3
54	最大偏差	0.658	0.469	28.7
72	平均偏差	0.125	0.107	14.4
72	最大偏差	0.740	0.517	30.1

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表 7 双移线工况横摆角偏差对比

Table 7. Comparison of yaw angle deviation for the double-shift-line working condition

车速/ （km·h⁻¹）	指标	控制器1/rad	控制器2/rad	改善程度/%
36	平均偏差	0.013	0.010	23.1
36	最大偏差	0.078	0.058	25.6
54	平均偏差	0.015	0.011	26.7
54	最大偏差	0.084	0.069	17.9
72	平均偏差	0.018	0.013	27.8
72	最大偏差	0.090	0.073	18.9

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