基于高斯过程回归的无人车辆轨迹跟踪MPC

doi:10.12382/bgxb.2024.0904

摘要/Abstract

摘要：

轨迹跟踪是无人驾驶控制系统中至关重要的功能之一。车辆动力学模型对轨迹跟踪性能有显著影响,但是存在模型复杂度和求解效率之间的矛盾,在非线性工况下无法满足轨迹跟踪精度要求,为此提出基于高斯过程回归(Gaussian Process Regression,GPR)的模型预测控制(Model Predictive Control,MPC) 方法。使用简单模型从而确保求解效率,通过GPR对车辆模型补偿从而提高轨迹跟踪性能。提出基于单轨动力学模型的车辆状态融合估计方法,获得GPR误差补偿模型;构建轨迹跟踪问题模型,推导GPR误差补偿模型在预测时域的迭代方程,对预测时域内的车辆状态进行动态补偿,实现轨迹跟踪控制;通过搭建实车验证平台开展典型工况试验验证,与无补偿MPC方法进行对比。研究结果表明,新方法轨迹跟踪精度得到明显提升,轨迹跟踪横向误差和航向误差分别降低了33.3%和27.9%,同时还兼顾了车辆舒适性的提升,侧向加速度和横摆角速度均值分别下降了17.1%和21.7%。

关键词: 高斯过程回归, 模型预测控制, 轨迹跟踪, 无人驾驶

Abstract:

Trajectory tracking is a crucial functionality of the autonomous driving control system.The vehicle dynamics model has a significant impact on trajectory tracking performance,however,there is a conflict between model complexity and solving efficiency,often leading to insufficient tracking accuracy under nonlinear conditions.To address this challenge,this paper proposes a model predictive control method based on Gaussian process regression (GPR) for trajectory tracking.A simplified model is used to ensure solving efficiency,and GPR model is employed to compensate for the vehicle model,thereby enhancing the trajectory tracking performance.First,a vehicle state fusion estimation method based on the single-track dynamics model is developed to obtain the GPR compensation model.A trajectory tracking error model is developed.Based on the trajectory tracking error from vehicle dynamics model,the iterative equation for GPR error compensation within the predictive horizon is derived to dynamically compensate for model errors in the vehicle state prediction for achieving the trajectory tracking control.Finally,a real-vehicle validation platform is constructed to validate the proposed method under typical driving conditions.The proposed method is compared with other predictive control methods without GPR compensation.The results show the proposed method achieves a significant improvement in trajectory tracking accuracy.Specifically,the lateral and heading errors are reduced by 33.3% and 27.9%,respectively.Furthermore,the vehicle comfort performance is also improved,and the mean lateral acceleration and yaw rate are reduced by 17.1% and 21.7%,respectively.

Key words: Gaussian process regression, model predictive control, trajectory tracking, autonomous driving

中图分类号:

TP275

李秦, 何洪文, 胡满江. 基于高斯过程回归的无人车辆轨迹跟踪MPC[J]. 兵工学报, 2025, 46(8): 240904-.

LI Qin, HE Hongwen, HU Manjiang. Model Predictive Control of Unmanned Vehicle Trajectory Tracking Based on Gaussian Process Regression[J]. Acta Armamentarii, 2025, 46(8): 240904-.

图/表 12

图1 单轨3自由度车辆动力学模型

Fig.1 3DOF Single track vehicle dynamics model

图2 基于GPR和EKF融合的状态估计算法架构

Fig.2 Vehicle state estimation framework based on GPR combined with EKF

图3 轨迹跟踪误差模型

Fig.3 Trajectory tracking error model

图4 轨迹跟踪算法架构

Fig.4 Trajectory tracking algorithm architecture

表1 车辆关键参数

Table 1 Key parameters of vehicle

参数	描述	数值
m/kg	整车质量	2063.4
l_f/mm	前半轴距	1351.8
l_r/mm	后半轴距	1548.2
C_f/(N·rad^-1)	前轮等效侧偏刚度	100640
C_r/(N·rad^-1)	后轮等效侧偏刚度	100640
R_tire/mm	等效轮胎滚动半径	366
I_z/(kg·m²)	绕Z轴的转动惯量	3347.8

图5 实车测试试验

Fig.5 Vehicle test

表2 融合状态估计测试结果

Table 2 The test results of fusion state estimation methods

估计方法	测试工况	β_RMSE/(°)	ω_RMSE/((°)·s^-1)
EKF	蛇形	0.4863	2.6734
EKF	U-Turn	0.1934	1.1264
GPR-EKF	蛇形	0.2528	0.4836
GPR-EKF	U-Turn	0.1403	0.3838

表3 关键模块耗时测试结果

Table 3 Time-consuming test of key modules ms

线程	99%分位耗时	平均耗时	最大耗时
GPR	7.859	6.453	9.370
MPC	1.021	0.976	1.350

图6 不同控制算法比较分析

Fig.6 Comparative analysis of different control algorithms

表4 不同控制器的控制误差对比分析

Table 4 Control errors of different controllers

参数	MPC	MPC+GPR	性能提升/%
e_{1_mean}/m	0.0858	0.0572	33.3
e_{1_max}/m	0.1690	0.1450	14.2
e_{2_mean}/rad	0.0269	0.0194	27.9
e_{2_max}/rad	0.0635	0.0595	6.3

图7 不同控制下车辆状态比较分析

Fig.7 Vehicle states under different control conditions

表5 不同控制器车辆状态结果

Table 5 Analysis of vehicle states under different controllers

舒适性参数	MPC	MPC+GPR	性能提升/%
a_y_{_mean}/(m·s^-2)	0.289	0.240	17.1
a_y_{_max}/(m·s^-2)	1.143	0.831	27.4
ω_mean/(rad·s^-1)	0.114	0.089	21.7
ω_max/(rad·s^-1)	0.291	0.261	10.2

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