数据驱动模型预测控制应用于自动驾驶车辆转向

Application of Data-driven Model Predictive Control for Autonomous Vehicle Steering

数据驱动模型预测控制应用于自动驾驶车辆转向

Abstract

With the development of autonomous driving technology, there are increasing demands for vehicle control, and MPC has become a widely researched topic in both industry and academia. Existing MPC control methods based on vehicle kinematics or dynamics have challenges such as difficult modeling, numerous parameters, strong nonlinearity, and high computational cost. To address these issues, this paper adapts an existing Data-driven MPC control method and applies it to autonomous vehicle steering control. This method avoids the need for complex vehicle system modeling and achieves trajectory tracking with relatively low computational time and small errors. We validate the control effectiveness of the algorithm in specific scenario through CarSim-Simulink simulation and perform comparative analysis with PID and vehicle kinematics MPC, confirming the feasibility and superiority of it for vehicle steering control.
Index Terms—data-driven control, autonomous vehicle steering, model predictive control, path tracking
随着自动驾驶技术的发展，对车辆控制的需求不断增加，模型预测控制（MPC）已成为工业界和学术界广泛研究的话题。基于车辆运动学或动力学的现有MPC控制方法面临诸如建模困难、参数众多、强非线性、高计算成本等挑战。为了解决这些问题，本文采用了一种现有的数据驱动MPC控制方法，并将其应用于自动驾驶车辆的转向控制。这种方法避免了复杂的车辆系统建模需求，实现了轨迹跟踪，具有相对较低的计算时间和小误差。我们通过CarSim-Simulink仿真在特定场景下验证了算法的控制效果，并与PID和车辆运动学MPC进行了比较分析，确认了其在车辆转向控制方面的可行性和优越性。
索引术语—数据驱动控制、自动驾驶车辆转向、模型预测控制、路径跟踪。

I. INTRODUCTION

Currently, autonomous driving has matured and is gradually coming into the public eye. Numerous internet and vehicle manufacturing companies are investing increasing efforts into researching autonomous driving technology, which has significantly contributed to improving traffic congestion, reducing traffic accidents, and enhancing economic benefits [1], [2]. Mastinu et al. analyzed the reasons and scenarios in which drivers lose control of the vehicle. They pointed out that after severe lane changes, gusts of wind, or other disturbances, drivers might be unable to regain the intended actions, potentially posing traffic safety hazards [3]. Moreover, Ahangar et al. found that the number of fatalities due to road traffic accidents is continually rising, with many accidents resulting from driver fatigue and distraction [4]. Additionally, the proportion of carbon dioxide emissions from road traffic in the total human carbon dioxide emissions is also increasing [5]. Therefore, research on autonomous driving technology is urgently needed.
目前，自动驾驶技术已经成熟，并逐渐进入公众视野。众多互联网公司和汽车制造企业正在加大对自动驾驶技术研究的投入，这在改善交通拥堵、减少交通事故和提升经济效益方面做出了显著贡献[1]、[2]。Mastinu等人分析了驾驶员失去对车辆控制的原因和场景。他们指出，在剧烈变道、阵风或其他干扰之后，驾驶员可能无法恢复预期动作，这可能会带来交通安全隐患[3]。此外，Ahangar等人发现，由于道路交通事故导致的死亡人数持续上升，许多事故是由于驾驶员疲劳和分心造成的[4]。同时，道路交通产生的二氧化碳排放量在人类总二氧化碳排放量中的比例也在增加[5]。因此，对自动驾驶技术的研究迫在眉睫。
Autonomous vehicles are composed of multiple modules, including perception, prediction, planning, decision-making, and control. Among them, control is one of the most critical modules, and the control methods have always been a key research focus. In the field of autonomous driving control, PID and adaptive control, etc. are widely used in the industry, which do not require mathematical modeling of the system, and the optimal control quantity can be obtained using the vehicle’s state and reference trajectory [6], [7]. In academia, however, Model Predictive Control (MPC) is a widely researched topic. First proposed by Richalet et al. in 1978 [8], MPC have since evolved with various modifications to suit different control scenarios and controlled objects [9]–[11].
自动驾驶车辆由多个模块组成，包括感知、预测、规划、决策和控制。其中，控制是最关键的模块之一，控制方法一直是研究的重点。在自动驾驶控制领域，PID和自适应控制等方法在工业界得到了广泛应用，这些方法不需要对系统进行数学建模，可以直接使用车辆的状态和参考轨迹来获得最优控制量[6]、[7]。然而，在学术界，模型预测控制（MPC）是一个广泛研究的话题。MPC最早由Richalet等人在1978年提出[8]，自那以后，MPC经历了各种改进，以适应不同的控制场景和控制对象[9]–[11]。
However, general MPC require precise modeling of the controlled system. Currently, most MPC methods for autonomous driving steering control are based on vehicle kinematics or dynamics models [12], [13]. Vehicle kinematics models have fewer parameters and simple structures, but they simplify the autonomous vehicle into a two-wheel model, which significantly deviates from the actual vehicle situation and results in low control precision. On the other hand, vehicle dynamics models contain more parameters and require parameter calibration through experiments, and also the strong nonlinearity of the models leads to high optimization computational costs. Therefore, researchers have begun considering how to avoid the cumbersome modeling process and directly use data for system characteristics analysis [14] and controller design [15]– [17].
然而，传统的MPC需要对被控系统进行精确建模。目前，大多数自动驾驶转向控制的MPC方法都是基于车辆运动学或动力学模型[12]、[13]。车辆运动学模型参数较少、结构简单，但它们将自动驾驶车辆简化为双轮模型，这与实际车辆情况相差甚远，导致控制精度较低。另一方面，车辆动力学模型包含更多参数，需要通过实验进行参数校准，而且模型的强非线性导致优化计算成本高。因此，研究人员开始考虑如何避免繁琐的建模过程，直接使用数据进行系统特性分析[14]和控制器设计[15]–[17]。
Currently, Data-driven MPC becomes widely researched. This control method avoids the precise modeling of system, as required by traditional MPC algorithms, and reduces computational time while maintaining high control accuracy. To address existing vehicle control problems, this paper studies the existing Data-driven MPC and, by integrating vehicle system characteristics, applies it to vehicle steering control and verifies the feasibility of this method. The contributions of this paper are presented as follows:
目前，数据驱动的模型预测控制（MPC）被广泛研究。这种控制方法避免了传统MPC算法所要求的系统精确建模，并在保持高控制精度的同时减少了计算时间。为了解决现有的车辆控制问题，本文研究了现有的数据驱动MPC，并通过整合车辆系统特性，将其应用于车辆转向控制，并验证了这种方法的可行性。本文的贡献如下：
1.Based on the research of [18]–[21], a Data-driven Model Predictive Control method is applied to autonomous vehicle steering control.
2.The feasibility of the application of DDMPC to autonomous vehicle steering was verified through simulation experiments, and the superiority of this algorithm was demonstrated by comparing it with other algorithms.
The rest of the paper is organized as follows. Section II provides a brief introduction to our research problem and discusses Willems’ Lemma. In Section III, we introduce the existing research on DDMPC. Based on this, we make minor modifications to make the algorithm applicable to autonomous vehicle control. In Section IV, we validate the effectiveness of the proposed algorithm through CarSim and Simulink simulation experiments and conduct a comparative analysis with PID and vehicle kinematics MPC algorithms. Finally, conclusions are drawn in Section V.
1.基于对文献[18]-[21]的研究，将数据驱动的模型预测控制方法应用于自动驾驶车辆的转向控制。
2.通过仿真实验验证了DDMPC在自动驾驶车辆转向应用的可行性，并通过与其他算法的比较展示了这种算法的优越性。本文的其余部分组织如下：第二节简要介绍了我们的研究问题，并讨论了Willems引理。在第三节中，我们介绍了关于DDMPC的现有研究。基于此，我们进行了小幅修改，使算法适用于自动驾驶车辆控制。在第四节中，我们通过CarSim和Simulink仿真实验验证了所提算法的有效性，并与PID和车辆运动学MPC算法进行了比较分析。最后，在第五节中得出结论。

II. PROBLEM STATEMENT

The development of autonomous vehicle technology relies on efficient and reliable control algorithms. The advantage of MPC lies in its ability to calculate high-precision control inputs within a limited prediction horizon, based on the vehicle model and reference trajectory. Consequently, MPC often depends on accurate vehicle models, but modeling and parameter calibration of traditional vehicle models—especially dynamic models—become extremely challenging. Additionally, vehicle models often have many parameters and strong nonlinearity, which may consume a significant amount of computational time during optimization. Most scholars and engineers address this issue by linearization, but this often leads to a decrease in model accuracy.
自动驾驶车辆技术的发展依赖于高效且可靠的控制算法。模型预测控制（MPC）的优势在于其能够在有限的预测范围内，基于车辆模型和参考轨迹，计算出高精度的控制输入。因此，MPC往往依赖于精确的车辆模型，但传统车辆模型——尤其是动态模型——的建模和参数校准变得极其具有挑战性。此外，车辆模型通常包含许多参数且具有很强的非线性，这可能会在优化过程中消耗大量的计算时间。大多数学者和工程师通过线性化来解决这一问题，但这往往会导致模型准确性的降低。
Based on the Willems’s lemma, which is a data-based method for system identification [22], Jeremy first proposed an algorithmic framework called Data-enabled Predictive Control and applied it on aerial robotics [18]. Thereafter, Berberich et al. designed a robust Data-driven MPC control method [19]–[21]. This method can directly use the Hankel matrix constructed from offline input-output trajectory data of the system to replace complex system models, predicting future states of the system and thereby calculating the optimal control inputs. Lu et al. used this method to complete the data-driven identification of vehicle and designed a DDMPC controller for vehicle lateral stability control [23]. Subsequently, many scholars have expanded and applied this method [24], [25].
基于Willems引理，这是一种基于数据的系统辨识方法，Jeremy首次提出了一个名为Data-enabled Predictive Control的算法框架，并将其应用于空中机器人。此后，Berberich等人设计了一种鲁棒的数据驱动MPC控制方法–。这种方法可以直接使用从系统的离线输入输出轨迹数据构建的Hankel矩阵来替代复杂的系统模型，预测系统的未来状态，从而计算出最优的控制输入。Lu等人使用这种方法完成了车辆的数据驱动辨识，并为车辆横向稳定性控制设计了一个DDMPC控制器。随后，许多学者扩展并应用了这种方法，。
We build on this foundation by applying the data-driven MPC algorithm proposed by [18] and [19] to steering control of autonomous vehicles and provide the algorithm application flowchart, as shown in Fig. 1.
我们在[18]和[19]提出的数据驱动MPC算法的基础上，将其应用于自动驾驶车辆的转向控制，并提供了算法应用流程图，如 图1 所示。

III. APPLICATION OF DDMPC FOR AUTONOMOUS VEHICLE STEERING

A. Willems’ Lemma and Application

Here, we first review the description and application of Willems’ Lemma by [18] and [19].
在这里，我们首先回顾了[18]和[19]对Willems引理的描述和应用。
Suppose the dynamic behavior of a system is described by the following input-output relationship expressed by Eq. 1.
假设系统的动态行为由以下输入输出关系描述，如 方程1 所示。

where u(t) ∈ U ⊂ Rm is the system input at time t, with m being the input dimension; y(t) ∈ Y ⊂ Rp is the system output at time t, with p being the output dimension; G(·) is the system behavior model, generally represented by a transfer function or state-space equations.
其中 $u(t)\in U\subset {\mathbb{R}}^m$ 是系统在时间 $t$ 的输入，$m$ 是输入的维度；$y(t)\in Y\subset {\mathbb{R}}^p$ 是系统在时间 $t$ 的输出，$p$ 是输出的维度；$G(\cdot )$ 是系统行为模型，通常由传递函数或状态空间方程表示。
Apply a set of inputs U to the system, which correspondingly generates a set of outputs Y . The collected open-loop input-output data are represented as two sets of vectors in Eq. 2.
对系统应用一组输入 $U$，相应地产生一组输出 $Y$。收集的开环输入输出数据在 方程2 中表示为两组向量。

where N is the number of data sets, and the selection of this parameter will directly influence the subsequent design of the Data-driven MPC.
其中 $N$ 是数据集的数量，这个参数的选择将直接影响后续数据驱动MPC的设计 。

Process the collected input-output data, which mainly includes data cleansing, continuity checking and noise removal, etc. Then, extend the data into Hankel matrices. The resulting order L Hankel matrix is as Eq. 3 and Eq. 4.
处理收集到的输入输出数据，主要包括数据清洗、连续性检查和噪声去除等。然后，将数据扩展成Hankel矩阵。得到的阶数为 $L$ 的Hankel矩阵如方程3和方程4所示。

where L is the basic prediction horizon of the MPC algorithm. For the input matrix HL(U), we determine whether the input sequence U satisfies the re