Research on Tractor Trajectory Tracking Control Based on a Dual-Motor Steer-by-Wire System

doi:10.12133/j.smartag.SA202507027

Abstract

Abstract:

[Objective] Conventional steering systems for autonomous tractors often suffer from insufficient precision and robustness, making it difficult to meet the demands of high-accuracy trajectory tracking. Although single-motor steer-by-wire (SBW) systems proposed in previous studies can improve tracking precision, they are limited by restricted output torque and poor fault tolerance, especially under complex conditions such as low-speed and heavy-load operations. To address these issues, this study aims to develop a high-performance trajectory tracking control method based on a dual-motor SBW system, thereby improving tracking accuracy, robustness, and operational safety under various working conditions. [Methods] A hierarchical control architecture was constructed in this study. At the upper level, a trajectory tracking controller was designed. Based on a two-wheel bicycle dynamic model of the tractor, a linear quadratic regulator (LQR) controller was developed to solve the optimal control problem and compute the desired front-wheel steering angle for trajectory tracking. At the lower level, a steering execution controller was developed for the dual-motor SBW system. First, a mathematical model incorporating both electrical and mechanical components of the system was established. To address nonlinearities and uncertainties, a sliding mode controller (SMC) was designed for each motor to achieve robust control. To mitigate the inherent chattering problem of SMC, a disturbance observer (DOB) was incorporated. The DOB continuously estimated the total disturbance in real time, including both external interferences and internal parameter variations, and provided feed-forward compensation. This compensation enabled a reduction in the switching gain of the SMC, thereby effectively suppressing chattering while maintaining robust performance. For dual-motor coordination, an independent control strategy was adopted, leveraging the identical parameters of both motors. Under this scheme, the two motors received the same steering angle command and operated in parallel, maintaining structural simplicity while enhancing system fault tolerance. The overall control strategy was structured as a hierarchical system, comprising an upper-level LQR trajectory tracking module and a lower-level steering execution module based on SMC+DOB. [Results and Discussions] To validate the effectiveness of the proposed method, both simulations and field experiments were conducted. Simulations were performed on a MATLAB/Simulink–CarSim co-simulation platform, specifically evaluating steering angle tracking performance and the disturbance rejection capability of the DOB. The results showed that, compared with the SMC controller without DOB, the SMC+DOB controller reduced the front-wheel steering angle tracking error by 13.12% while significantly suppressing chattering. Field experiments were carried out on a T954 tractor platform to evaluate the control strategy under realistic operating conditions. A representative working path, consisting of both straight and curved segments, was used, and tests were performed at two speeds: low speed (10 km/h) and high speed (30 km/h). To benchmark performance, three control strategies were compared: LQR+SMC, MPC+SMC+DOB, and the proposed LQR+SMC+DOB, to assess tracking accuracy, robustness, and real-time control effectiveness. The field experimental results showed that: 1) All SBW-based methods significantly outperformed traditional steering in terms of lateral tracking error and heading error. 2) Under low-speed conditions, the proposed LQR+SMC+DOB method reduced the average lateral tracking error, heading error, sideslip angle, and front-wheel steering angle error by 20.0%, 40.0%, 6.5%, and 14.3%, respectively, compared to LQR+SMC. Under high-speed conditions, the corresponding reductions were 23.8%, 52.2%, 4.5%, and 27.3%. 3) Compared with MPC+SMC+DOB, the proposed LQR+SMC+DOB achieved similar trajectory tracking performance while significantly reducing the computation time per iteration. The results showed that the adopted dual-motor SBW system effectively enhanced steering output torque and system fault tolerance, thereby improving trajectory tracking accuracy and thus providing a hardware foundation for resolving the power and safety challenges in tractor heavy-load operations; moreover, the SMC+DOB controller combined strong robustness with smooth control action, effectively suppressing external disturbances and markedly reducing chattering, thereby improving the accuracy and stability of steering execution. [Conclusions] This research proposed and validated a high-precision trajectory tracking control strategy for autonomous tractors. By integrating an upper-level LQR trajectory tracking controller with a lower-level dual-motor SMC+DOB steering controller, a robust and efficient hierarchical control framework was established. This control strategy showed good trajectory tracking performance and real-time capability across different speeds, offering a reliable technological solution for high-performance operations of autonomous tractors. Compared with the MPC control strategy, the control strategy proposed in the study demonstrated exceptionally high computational efficiency, rendering it highly suitable for real-time control applications.

Key words: autonomous tractor, trajectory tracking, steer-by-wire, LQR, SMC, disturbance observer

CLC Number:

S219

LI Lei, PAN Liang, DONG Jiwei, CAO Zhonghua, LUO Xingfa, ZHAN Xiaomei, LI Yali, SUN Zhiqiang. Research on Tractor Trajectory Tracking Control Based on a Dual-Motor Steer-by-Wire System[J]. Smart Agriculture, 2026, 8(5): 169-181.

Figures/Tables 18

Fig. 1

Fig. 2

Table 1

Model parameters of the dual-motor SBW system

参数	含义	单位
$U 1$ ， $U 2$	两个电机的控制电压	V
$L 1$ ， $L 2$	两个电机的电枢电感	H
$I 1$ ， $I 2$	两个电机的电流	A
$K 1$ ， $K 2$	两个电机的反电动势系数	V·s/rad
$K 12$	两个电机的转矩系数	N·m/A
$θ 1$ ， $θ 2$	两个电机的转角	rad
$R 1$ ， $R 2$	两个电机的电阻	Ω
$T m$	两个电机的合力矩	N·m
$T 1$ ， $T 2$	两个电机的力矩	N·m
$J$	等效转动惯量	kg·m²
$b m$	等效阻尼系数	N·m·s/rad
$G$	减速器减速比	无量纲
$η$	减速器传动效率	无量纲
$M a, M x, M y, M z$	分别为回正力矩、车轮在纵向、横向和垂向方向产生的阻力矩	N·m
$M r$	总转向阻力矩	N·m
$ω 1, ω 2$	两个电机的角速度	rad/s

Table 1

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 2

Parameters of tractor and control system

参数	值	参数	值
m	3 425 kg	b _m	0.42 N·m·s/rad
$L f$	1 150 mm	K ₁=K ₂	320 V·s/rad
$L r$	1 100 mm	K ₁₂	0.09 N·m/A
$C f$	13 125 $N / d e g$	L ₁=L ₂	2.12e-3 H
$C r$	15 500 $N / d e g$	R ₁=R ₂	0.04 Ω
Q	diag（1，1，1）	G	30
R	diag（0.3，0.3）	η	0.98
J	0.09 kg·m²

Table 2

Fig. 9

Table 3

Fig. 10

Fig. 11

Fig. 12

Table 4

Fig. 13

Table 5

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方法	跟踪误差
方法	均方根/deg	最大误差/deg
方法1 （SMC）	0.256 0	3.821 1
方法2 （SMC+DOB）	0.222 4	3.764 2

	LQR+SMC	MPC+SMC+DOB	LQR+SMC+DOB
横向跟踪误差/m	0.070 0	0.053 0	0.056 0
纵向跟踪误差/m	0.100 0	0.041 0	0.070 0
航向角误差/deg	0.500 0	0.280 0	0.300 0
纵向速度跟踪误差/（km/h）	0.600 0	0.410 0	0.500 0
平均质心侧偏角/deg	1.201 0	1.116 0	1.123 0
前轮转角误差/deg	0.350 0	0.270 0	0.300 0
单次计算用时/s	0.015 2	0.321 2	0.016 1

性能指标	LQR+SMC	MPC+SMC+DOB	LQR+SMC+DOB
横向跟踪误差/m	0.130 0	0.077 0	0.099 0
纵向跟踪误差/m	0.120 0	0.071 0	0.083 0
航向角误差/deg	2.300 0	0.900 0	1.100 0
纵向速度跟踪误差/（km/h）	0.900 0	0.660 0	0.700 0
平均质心侧偏角/deg	2.864 0	2.776 0	2.735 0
前轮转角误差/deg	2.200 0	1.300 0	1.600 0
单次计算用时/s	0.016 2	0.331 2	0.016 8