考虑通信延时的智能汽车非线性路径跟踪控制

doi:10.13229/j.cnki.jdxbgxb.20241003

Abstract

Abstract:

Aiming at the problems of communication delay between controller and actuator in path tracking， strong nonlinearity of the vehicle system， and output constraints of the controller， this paper proposes a nonlinear path tracking controller considering communication delay to improve the performance of vehicle path tracking by taking an electric vehicle as the research object. Firstly， a two-degree-of-freedom vehicle model is established， a tire model is established by using the "magic formula"， and a nonlinear path tracking model with communication delay is established； Secondly， according to the output constraints of the controller， a nonlinear robust controller is designed by using the backstepping adjustment function to meet the system performance indexes and robustness requirements； Finally， the path tracking performance is verified by simulation through MATLAB/Simulink under sinusoidal and double-shifted line conditions， respectively. The results show that： The root mean square （RMS） value of the lateral error of the path tracking of the controller proposed in this paper is reduced by 0.061 9 and 0.010 1 for sinusoidal condition and 0.097 2 and 0.034 7 for double-shift condition compared to the PID and MPC methods， respectively. The robustness of the controller in this paper is better than that of the PID and MPC methods when disturbances are introduced.

Key words: avehicle engineering, intelligent vehicle, path tracking, nonlinear system, time-delay

CLC Number:

U461.6

Yao FU,Chun-shui ZHAN,Ke LIU. Nonlinear path tracking control for intelligent vehicles considering communication delays[J].Journal of Jilin University(Engineering and Technology Edition), 2026, 56(3): 851-859.

Figures/Tables 13

Fig.1

Table 1

"Magic Formula" parameters"

参数	数值
$a 0$	1.413
$a 1$	-23.008
$a 2$	1 010
$a 3$	1 071
$a 4$	1.790
$a 5$	0.199
$a 6$	0
$a 7$	-0.371
$a 8$	0.701
$a 9 ～ a 12$	0

Table 1

Fig.2

Fig.3

Table 2

Vehicle Parameters"

参数	符号	数值
质心到前轴距离/m	$l f$	1.464
质心到后轴距离/m	$l r$	1.672
整车整备质量/kg	$m$	1 528
整车绕z轴转动惯量/（kg·m²）	$I z$	4 178

Table 2

Fig.4

Table 3

Controller parameters"

参数	数值
$λ 0$	0.899
$T$	2.5
$ξ 0$	0.8
$b 1$	10
$b 2$	-0.97
$b 3$	5
$c 1$	100（正弦）、20（双移线）
$c 2$	10

Table 3

Fig.5

Fig.6

Table 4

Table 5

Controller disturbance"

参数	数值
$φ ˙$	$± r a n d 10 % φ ˙$
$β ˙$	$± r a n d 10 % β ˙$
$v y$	$± r a n d 10 % v y$
$β$	$± r a n d 10 % β$

Table 5

Fig.7

Table 6

References 21

[1]	Lei Y L, Wen G Z, Fu Y, et al. Trajectory-following of a 4WID-4WIS vehicle via feedforward-backstepping sliding-mode control[J]. P I Mech Eng D-J Aut, 2022, 236(2/3): 322-333.
[2]	谢宪毅, 王禹涵, 金立生, 等. 基于改变控制时域时间步长的智能车轨迹跟踪控制[J]. 吉林大学学报: 工学版, 2024, 54(3): 620-630.
	Xie Xian-yi, Wang Yu-han, Jin Li-sheng, Intelligent vehicle trajectory tracking control based on adjusting step size of control horizon[J]. Journal of Jilin University (Engineering and Technology Edition), 2024, 54(3): 620-630.
[3]	常胜, 刘宏飞, 邹乃威. 汽车变曲率路径循迹H_∞回路成形鲁棒控制[J]. 吉林大学学报:工学版, 2024, 54(8): 2141-2148.
	Chang Sheng, Liu Hong-fei, Zou Nai-wei. H∞ loop shaping robust control of vehicle tracking on variable curvature curve[J]. Journal of Jilin University (Engineering and Technology Edition), 2024, 54(8): 2141-2148.
[4]	靳欣宇, 张军, 刘元盛, 等. 基于Stanley算法的自适应最优预瞄模型研究[J]. 计算机工程, 2018, 44(7): 42-46.
	Jin Xin-yu, Zhang Jun, Liu Yuan-sheng. Research on adaptive optimal pre-scanning model based on Stanley's algorithm[J]. Computer Engineering, 2018, 44(7): 42-46.
[5]	Melkou L, Rezoug A, Hamerlain M. PID-Terminal sliding mode control of aircraft UAV[C]∥Proceedings of the 8th UKSim-AMSS European Modelling Symposium on Computer Modelling and Simulation, New York, The United States, 2014: 21-23.
[6]	Zhai L, Wang C P, Hou Y H, et al. MPC-based integrated control of trajectory tracking and handling stability for intelligent driving vehicle driven by four hub motor[J]. IEEE Trans Veh Technol, 2022, 71(3): 2668-2680.
[7]	Pang H, Liu M H, Hu C, et al. Practical nonlinear model predictive controller design for trajectory tracking of unmanned vehicles[J]. Electronics, 2022, 11(7): 18-25.
[8]	Zhang J X, Xu K D, Wang Q G. Prescribed performance tracking control of time-delay nonlinear systems with output constraints[J]. IEEE-CAA J Automatica Sin, 2024, 11(7): 1557-1565.
[9]	Zhang Z Q, Xu B, Tan C, et al. Adaptive control of uncertain nonlinear time-delay systems with external disturbance[J]. IEEE Trans Syst Man Cybern-Syst, 2022, 52(2): 1288-1295.
[10]	Sun W W, Wu Y, Lv X Y. Adaptive neural network control for full-state constrained robotic manipulator with actuator saturation and time-varying delays[J]. IEEE Trans Neural Netw Learn Syst, 2022, 33(8): 3331-3342.
[11]	Peng C, Yue D, Tian Y C. New approach on robust delay-dependent h_∞ control for uncertain t-s fuzzy systems with interval time-varying delay[J]. IEEE Trans Fuzzy Syst, 2009, 17(4): 890-900.
[12]	Tang H Y, Wang Q Y, Feng X Y. Robust stochastic control for high-speed trains with nonlinearity, parametric uncertainty, and multiple time-varying delays[J]. IEEE Trans Intell Transp Syst, 2018, 19(4): 1027-1037.
[13]	Jiao X H, Shen T L. Adaptive feedback control of nonlinear time-delay systems: The LaSalle-Razumikhin-based approach[J]. IEEE Trans Autom Control, 2005, 50(11): 1909-1913.
[14]	Wang T C, Luo X X, Li W Q. Razumikhin-type approach on state feedback of stochastic high-order nonlinear systems with time-varying delay[J]. Int J Robust Nonlinear Control, 2017, 27(16): 3124-3134.
[15]	Sachan K, Padhi R. Barrier lyapunov function based output-constrained control of nonlinear euler-lagrange systems[C]∥Proceedings of the 15th International Conference on Control, Automation, Robotics and Vision. Singapore, Singapore, 2018: 18-33.
[16]	Song M S, Zhang F, Huang B X, et al. Anti-disturbance control for tethered aircraft system with deferred output constraints[J]. IEEE-CAA J Automatica Sin, 2023, 10(2): 474-485.
[17]	Zhao K, Wen C Y, Song Y D, et al. Adaptive uniform performance control of strict-feedback nonlinear systems with time-varying control gain[J]. IEEE-CAA J Automatica Sin, 2023, 10(2): 451-461.
[18]	Mayne D Q. Model predictive control: recent developments and future promise[J]. Automatica, 2014, 50(12): 2967-2986.
[19]	Biegler L T. A perspective on nonlinear model predictive control[J]. Korean Journal of Chemical Engineering, 2021, 38(7): 1317-1332.
[20]	Alavilli A, Nguyen K, Schoedel S, et al. TinyMPC: model-predictive control on resource-constrained microcontrollers[C]∥IEEE International Conference on Robotics and Automation, Yokohama, Japan, 2023: 1-7.
[21]	郑香美, 高兴旺, 赵志忠. 基于"魔术公式"的轮胎动力学仿真分析[J]. 机械与电子, 2012(9): 16-20.
	Zheng Xiang-mei, Gao Xing-wang, Zhao Zhi-zhong. Simulation analysis of tire dynamics based on the "magic formula"[J]. Machinery and Electronics, 2012(9): 16-20.

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工况	本文控制器	PID	MPC
正弦	0.344 9	0.406 8	0.355 0
双移线	0.025 1	0.122 3	0.059 8

项目	本文控制器	PID	MPC
增长率/%	2.030 0	5.383 0	3.521 0
干扰前	0.344 9	0.406 8	0.355 0
干扰后	0.351 9	0.428 7	0.367 5

Nonlinear path tracking control for intelligent vehicles considering communication delays

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