摘 要

无人驾驶汽车的研究对于减少交通事故与拥堵、保护环境、节约资源、提高汽车的主动安全性有着重要意义。轨迹跟踪控制作为无人驾驶车辆系统架构中的一项关键环节，包括纵向控制和横向控制，其要求车辆在保证操作稳定性的前提下，能够精确地跟踪期望轨迹，同时保持良好的动力性和舒适性。

Apollo D-kit是百度发布的全球首款集Apollo开源软件与线控底盘、传感器硬件于一体的自动驾驶开发套件，旨在帮助开发者快速进行实车测试，加速研发进程。本文基于模型预测控制方法设计横向控制器，控制Apollo小车跟踪双移线轨迹，并从跟踪精度和稳定性角度来验证控制算法的有效性。具体研究内容为：

首先深入了解模型预测控制的三项基本原理：预测模型、滚动优化和反馈矫正，设计了应用模型预测控制器进行轨迹跟踪的技术方案，在Carsim中设置好Apollo D-kit的车辆参数和双移线仿真工况。在若干理想化假设的前提下建立基于前轮转角较小和线性轮胎假设的车辆三自由度非线性动力学模型，并采用近似的方法将其线性化。

其次从预测模型、目标函数和约束条件三方面设计模型预测控制器。基于上述线性动力学模型设计预测模型，从而通过车辆当前的状态和控制时域内的控制增量便可以预测未来一段时间的状态量和输出量。选用合适的目标函数，并结合车辆的前轮转角约束，前轮转角增量约束和输出量约束将其转换为二次规划问题求解控制时域内控制增量，除此之外，还添加了质心侧偏角约束、侧向加速度约束和轮胎侧偏角约束等车辆动力学约束，从而保证车辆跟踪参考轨迹的精度和稳定性。

最后建立Carsim/Simulink联合仿真平台进行仿真试验。采用控制变量的方法研究预测时域、控制时域和权重矩阵等设计参数的影响规律，并基于此规律反复调整设计参数，使车辆以不同速度在不同附着系数路面上跟踪双移线轨迹时的跟踪性能最优。通过MATLAB做出上述输出量、控制量和约束量的变化曲线，分析速度和附着条件变化对轨迹跟踪性能的影响，试验表明大多数试验工况下车辆跟踪双移线轨迹时都能保持较高的跟踪精度和良好的稳定性，但在极端情况如高速低附着路面上则不能满足横向控制安全性的要求。

关键词：无人驾驶汽车；轨迹跟踪控制；横向控制；Apollo D-kit；模型预测控制器；Carsim/Simulink联合仿真平台

Abstract

Research on autonomous vehicle is of great significance for reducing traffic accidents and congestion, protecting the environment, saving resources and improving the active safety of vehicles. Trajectory tracking control, as a key part in the system of autonomous vehicle, includes longitudinal control and lateral control. It requires the vehicle to accurately track the desired trajectory on the premise of ensuring operational stability, while maintaining good dynamic performance and ride comfort.

Apollo D-kit is the world’s first autonomous driving development kit released by Baidu, which integrates Apollo open source software with wired chassis and sensor hardware. It aims to help developers quickly conduct real car testing and accelerate the research process. This paper designs a transverse controller based on the model predictive control method, which controls the Apollo vehicle to track the double-lane change, and verifies the effectiveness of the control algorithm form the perspective of tracking accuracy and stability. The specific research contents are as follows:

First of all, three basic principles of model predictive control: predictive model, rolling optimization and feedback correction are introduced in detail. I design a technical scheme for trajectory tracking using model predictive controller, and set the vehicle parameters of Apollo D-kit and the simulation condition of double-lane change. On the premise of some idealized assumptions, a vehicle three-degree-of-freedom nonlinear dynamics model based on the assumptions of smaller front wheel angle and linear tire was established and linearized by an approximate method.

Secondly, the model prediction controller is designed from three aspects: prediction model, objective function and constraint condition. Based on the above linear dynamic model, a prediction model is designed to predict the state and output in the predict time domain through the vehicle’s current state and the control increment in the control time domain. I select an appropriate objective function combining with the front wheel angle constraint, the front wheel angle increment constraint and the output constraint, and transform it into a quadratic programming problem to

solve the control increment. In addition, vehicle dynamics constraints such as centroid side angle constraint, lateral acceleration constraint and tire side angle constraint are added to ensure the accuracy and stability of vehicle tracking reference trajectory.

Finally, a Carsim/Simulink co-simulation platform was established for simulation test. The influence law of design parameters such as predict time domain, control time domain and weight matrix is studied by using the method of control variables. And the design parameters were adjusted repeatedly based on this law, so as to optimize the tracking performance when the vehicle tracks the double-lane change at different speeds on the road surface with different adhesion coefficients. MATLAB is used to make the variation curves of the output, control and constraint mentioned above, and the influence of the speed and adhesion conditions on the tracking performance was analyzed. The test results show that the tracking accuracy and stability can be maintained in most test conditions, but the lateral control safety can not be satisfied in extreme conditions such as high speed and low adhesion road surface.

Key Words：autonomous vehicle；trajectory tracking control；lateral control；Apollo D-kit；model prediction controller；Carsim/Simulink co-simulation platform

目 录

摘 要 Ⅰ

Abstract Ⅱ

第一章 绪论 1

1.1. 研究背景与意义 1

1.1.1. 课题研究的必要性及作用 1

1.1.2. 无人驾驶车辆技术路线及架构 2

1.2. 无人驾驶车辆国内外研究现状 4

1.2.1. 国外无人驾驶研究现状 4

1.2.2. 国内无人驾驶研究现状 6

1.3. 无人驾驶车辆循迹控制算法研究综述 8

1.4. 论文的主要研究内容及结构安排 10

第二章 模型预测控制原理及应用于控制器设计思路 11

2.1 模型预测控制原理 11

2.2 车辆应用模型预测控制器自主循迹思路 12

2.2.1. 选择参考轨迹 13

2.2.2. Carsim中获取车辆状态及环境信息 14

2.3 本章小结 15

第三章 车辆动力学模型的建立及线性化 16

3.1 建立车辆非线性动力学模型及轮胎模型 16

3.1.1 建立车辆三自由度单轨模型 16

3.1.2 建立轮胎模型 18

3.2 车辆动力学模型的简化 19

3.3 简化动力学模型的线性化 21

3.4 本章小结 22

第四章 基于MPC的轨迹跟踪控制器设计 23

4.1 基于线性误差方程的预测模型设计 23

4.2 目标函数的设计与求解 25

4.3 约束条件设计 26

4.3.1 前轮偏角、前轮偏角增量和输出量约束 26

4.3.2 质心侧偏角约束 27

4.3.3 附着条件约束 27

4.3.4 轮胎侧偏角约束 27

4.4 本章小结 28

第五章 构建仿真平台及仿真结果分析 29

5.1 构建联合仿真平台 29