基于无模型自适应控制的无人驾驶汽车横向控制方法
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 自动化学报  2017, Vol. 43 Issue (11): 1931-1940 PDF

1. 北京交通大学电子信息工程学院先进控制系统研究所 北京 100044;
2. 清华大学计算机系, 智能技术与系统国家重点实验室, 清华信息科学与技术国家实验室 (筹) 北京 100084

Model-free Adaptive Control Based Lateral Control of Self-driving Car
TIAN Tao-Tao1, HOU Zhong-Sheng1, LIU Shi-Da1, DENG Zhi-Dong2
1. Advanced Control Systems Laboratory, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044;
2. Department of Computer Science, State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084
Manuscript received : September 5, 2016, accepted: January 5, 2017.
Foundation Item: Supported by National Natural Science Foundation of China (61120106009, 61433002, 91420106), Beijing Natural Science Foundation Joint Fund for Science and Technology Rail Transportation (W17E000020)
Corresponding author. HOU Zhong-Sheng Professor at the Advanced Control Systems Laboratory, School of Electronic and Information Engineering, Beijing Jiaotong University. His research interest covers model free adaptive control, data-driven control, learning control, intelligent transportation system, and application of data mining in medical and traffic field. Corresponding author of this paper
Recommended by Associate Editor WEI Qing-Lai
Abstract: In this paper, a control scheme based on model free adaptive control is proposed for the lateral control problem of self-driving car. First, the trajectory tracking problem for self-driving car is converted into the stabilization problem concerning a preview-deviation-yaw. Then, the lateral control system of the self-driving car is converted into a virtual dynamical linearization data model via a novel dynamic linearization technique. After that, a model free adaptive control algorithm, and its corresponding pseudo gradient estimating algorithm and pseudo gradient resetting algorithm are designed, such that the automatic drive of the self-driving car can be realized. The implementation of the proposed method only utilizes the input and output data of the self-driving car, avoiding complex modeling of the self-driving car. Thus, it has good adaptability to complex operation processes of self-driving car and is also applicable to other self-driving cars. Furthermore, the proposed scheme is employed in the experimental platform of self-driving car developed by Tsinghua University. Finally, the effectiveness of the proposed method is verified via the field tests in Fengtai District, Beijing, the field tests in the freeway of Changshu, Jiangsu, and the field applications in "2015 Chinese Intelligent Car Future Challenge Competition".
Key words: Model-free adaptive control (MFAC)     self-driving car     lateral control     preview-deviation-yaw

1 无人驾驶控制问题描述 1.1 无人驾驶汽车平台简介

 图 1 车载传感器分布图 Figure 1 Vehicle sensors distribution

1.2 无人驾驶汽车的控制结构

 图 2 控制系统结构图 Figure 2 Control system structure

2 基于预瞄偏差角跟踪的无人驾驶汽车横向控制方案 2.1 基本概念

 图 3 预瞄点与预瞄距离示意图 Figure 3 Preview point and preview distance profile

 \begin{align} l(v) = \begin{cases} {l_{\min }},&v \le {v_{\min }}{\rm{ }}\\ av + {l_{\min }},&{v_{\min }} < v \le {v_{\max }}\\ {l_{\max }},&v > {v_{\max }} \end{cases} \end{align} (1)

 图 4 横向控制问题示意图 Figure 4 Schematic diagram of lateral control problem

2.2 预瞄偏差角跟踪方案

 $$$\sin \theta = \frac{{LD}}{{len}}$$$ (3)

$\theta\rightarrow0$时, 由于两点距离$len\neq0$, 所以有$LD \rightarrow$ 0.

 图 5 预瞄偏差角跟踪情况与汽车运行情况图 Figure 5 Preview-deviation-yaw tracking condition and self-driving car operation condition

3 预瞄偏差角跟踪系统控制器设计 3.1 问题描述

3.2 MFAC动态线性化

 $$${{\pmb U}_L}(k) = {[u(k), \cdots, u(k-L + 1)]^{\rm T}}$$$ (5)

 $$$|\theta ({k_1} + 1) -\theta ({k_2} + 1)| \le b\|{{\pmb U}_L}({k_1}) -{{\pmb U}_L}({k_2})\|$$$ (6)

$\Delta{\pmb U}_L(k)={\pmb U}_L(k)-{\pmb U}_L(k-1)$, 可以给出如下引理.

 $$$\Delta \theta(k+1)={\pmb \phi}_{p, L}^{\rm T}(k)\Delta {{\pmb U}_L}(k)$$$ (7)

 $$$\theta (k + 1) = \theta (k) + {\pmb \phi}_{p, L}^{\rm T}(k)\Delta {{\pmb U}_L}(k)$$$ (8)
3.3 控制器设计

 \begin{align} J(u(k)) = &\ {\left| {{\theta ^*}(k + 1) -\theta (k + 1)} \right|^2} +\nonumber\\ &\ \lambda {\left| {u(k) -u(k -1)} \right|^2} \end{align} (9)

 \begin{align} u(k) = &\ u(k -1) + \nonumber\\[1mm] &\ \frac{{{\rho _1}{\phi _1}(k)({\theta ^*}(k + 1) -\theta (k))}}{{\lambda + |{\phi _1}(k){|^2}}} -\nonumber\\[1mm] &\ \frac{{{\phi _1}(k)\sum\limits_{i = 2}^L {{\rho _i}{\phi _i}(k)\Delta u(k -i + 1)} }}{{\lambda + |{\phi _1}(k){|^2}}} \end{align} (10)

 \begin{align} J({{\pmb \phi} _{p, L}}(k)) = &\ |\theta (k) -\theta (k -1) -\nonumber\\ &\ {\pmb \phi} _{p, L}^{\rm T}(k)\Delta {{\pmb U}_L}(k -1){|^2} +\nonumber\\ &\ \mu \|{{\pmb \phi} _{p, L}}(k) -{\hat {\pmb \phi} _{p, L}}(k -1)\|{^2} \end{align} (11)

 \begin{align} {\hat {\pmb \phi} _{p, L}}(k) = &\ {\hat {\pmb \phi} _{p, L}}(k -1) +\notag\\[1mm] &\ \frac{{\eta \Delta {{\pmb U}_L}(k -1)(\theta (k) -\theta (k -1))}}{{\mu + \|\Delta {{\pmb U}_L}(k -1)|{|^2}}} -\notag\\[1mm] &\ \frac{{\eta \Delta {{\pmb U}_L}(k -1)({{\hat {\pmb \phi} }^{\rm T}}_{p, L}(k -1)\Delta {{\pmb U}_L}(k -1))}}{{\mu + \|\Delta {{\pmb U}_L}(k -1)|{|^2}}} \end{align} (12)

 $$${\hat {\pmb\phi} _{p, L}}(k) = {\hat {\pmb\phi} _{p, L}}(1)$$$ (13)

4 实验分析

 图 6 低速实验场地图 Figure 6 Low speed experimental site

 图 7 高速公路实验场地图 Figure 7 Highway experimental site
4.1 设备连接关系及调试软件框架

 图 8 设备连接关系及调试软件框架图 Figure 8 Equipment connection and debugging software framework

1) 计算出的方向盘的转角;

2) 计算出的油门和刹车的开度(两者互斥, 用同一变量表示, 该变量为正表示油门输入, 为负则表示刹车输入).

4.2 横向控制实验分析

 \begin{align} du(k) = &\ {K_p}(e(k) -e(k -1)) + {K_i}e(k) +\notag\\ &\ {K_d}(e(k) -2e(k -1) + e(k))\notag\\ u(k) = &\ u(k -1) + du(k) \end{align} (14)

 $$${\rm RMSE}(\cdot) = \sqrt {\frac{1}{N}\sum\limits_{n = 1}^N {|{l_n}{|^2}} }$$$ (15)

 图 9 两种控制方法的跟踪效果对比图 Figure 9 Tracking effect comparison between two control methods
 图 10 预瞄偏差角跟踪效果对比图 Figure 10 Preview-deviation-yaw tracking effect comparison
 图 11 跟踪误差绝对值对比图 Figure 11 Absolute value of tracking error comparison

 图 12 高速跟踪轨迹图 Figure 12 Highway trajectory tracking

 图 13 高速公路轨迹跟踪性能 Figure 13 Performance of highway trajectory tracking

$AB$段的跟踪误差的均方根为0.0738, 最大跟踪误差绝对值为0.1824 m; 预瞄偏差角的均方根为0.0025, 最大绝对值为0.0068 rad.文献[7]所设计的控制器在纵向车速为19 m/s (68.4 km/h)时的跟踪误差均方根为0.0751.文献[6]中实验路段上车速由80 km/h变为60 km/h, 又变回80 km/h, 整个路段的最大误差约为0.5 m.

 图 14 2015年“中国智能车未来挑战赛”部分项目 Figure 14 Several competition items at "2015 Chinese Intelligent Car Future Challenge"
5 结论

1) 避免复杂的无人驾驶汽车机理建模.无人驾驶汽车模型难以建立, 基于预瞄的控制策略也很难进行精确的数学描述, 本文设计的基于MFAC的预瞄偏差角跟踪控制方案不使用汽车的数学模型, 避免了汽车建模带来的困难.