## 1 Introduction  
Currently, thanks to the rapid development of navigation technology, particularly the Bei Dou System (BDS) navigation, unmanned agricultural vehicles have been widely promoted in China, as they can achieve efficiency, high standards, lower costs, etc. [1; 2]. It is worth noting that tractor-trailers possess the qualities of flexible combination and heavy loads, which can be utilized in harvesting, plowing, spraying, etc. [3]. However, in contrast to the structured environment, farmland often contains unanticipated disturbances, which significantly increase the challenge in controlling unmanned agricultural vehicles. In addition, unlike the tractor, the tractor-trailer model is a typical high-order underactuated system, i.e., only one control input but multiple output variables. Some traditional control methods hardly address this underactuated problem. Hence, the path-tracking control of agricultural tractor-trailers is still a hot research issue [4; 5]. Numerous studies on the path-tracking control of agricultural vehicles have emerged recently, mainly focusing on control based on kinematics, dynamics, and model-free techniques [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. Research on sophisticated control techniques, including fuzzy control, intelligent control, and sliding mode control (SMC), has also been conducted by relevant academics. A dynamic model of a traction unit and a nonlinear controller were created in [6], but an additional control system was required at the connecting shaft. A pure-pursuit tracking technique for rice transplanters was developed in [7], which employed fuzzy rules to achieve a dynamic adjustment of the forward-looking distance. The path tracking control problem of a boom sprayer in a paddy field was addressed in [10] using a composite terminal sliding mode control based on a disturbance observer. An adaptive proportional-integral-differential control (PID) was presented in [13] to handle the path tracking control of a tractor, and the nonlinear constructor approach was utilized to update the PID parameters in real time. To address the issue of the variable speed tracking control of agricultural vehicles, the linear-chain feedback approach was adopted in [15], and a straight-line path tracking test was conducted. Tractor-trailers are restricted by non-holonomic kinematics, which makes the aforementioned chain model feedback control approach ineffective for controlling a tractor-trailer. Due to measurement error, installation error, tire deformation, the road adhesion coefficient, and other factors, it is difficult to avoid model parameter perturbation and external disturbance during tractor-trailer path tracking. Thus, it remains necessary to develop a method for controlling tractor-trailer path tracking that is reliable. To our knowledge, few papers have paid attention to the path tracking control of agricultural tractor-trailers, and the existing methods all show poor tracking accuracy. Sliding mode control is one of several advanced control theories that has received a lot of interest due to its simplicity of implementation and insensitivity to parameter perturbation and external disturbances. A sliding mode control approach based on fixed high gain was proposed in [18] for tractor-trailers. However, this approach exhibited chattering phenomena, which can easily damage the mechanical structure. To handle the chattering problem, [19; 20; 21] proposed various approaches to address this problem, including boundary-layer-based methods, high-order sliding modes, adaptive control, and integral sliding modes, but none of these methods have been applied to agricultural tractor-trailers. Fuzzy control has developed rapidly in recent years, and numerous worthwhile studies have been conducted [22; 23], which provide an idea of how to optimize control parameters.