## 1 Introduction  
Autonomous driving technology has advanced rapidly in recent years and has expanding applications in commercial vehicles. Among them, intelligent semi-trailers have become the focus of academia and industry because of their broad development prospects [1]. However, path planning for these articulated vehicles remains a significant challenge in dynamic environments. Unlike passenger vehicles, semi-trailers exhibit complex kinematic behaviors and heightened susceptibility to rollover during lane changes. The risk is exacerbated by variable road conditions (e.g., adhesion coefficients), load distributions, and interactions with surrounding traffic [2]. Academic research on path planning has been conducted for a long time. At present, the common path-planning methods in the industry comprise the artificial potential field method (APF), algorithms based on curve interpolation, algorithms based on sampling, algorithms based on graph searching, and algorithms based on intelligent optimization [3]. The goal of APF is to plan a collision-free path from the starting point to the target point for autonomous vehicles in the environment. It abstracts the movement of vehicles as the movement in a virtual potential field, which is superimposed by a gravitational field and a repulsive field. The gravitational field prompts the vehicle to move toward the target point, and the repulsive field makes the vehicle avoid obstacles. The resultant force received by the vehicle in the potential field determines its movement direction. By continuously calculating the resultant force and updating the vehicle position, a movement path is constructed [4]. There are two main problems with the APF. One is that it is prone to getting trapped at a local minimum, and the other is that it has insufficient adaptability to dynamic traffic conditions. [PERSON] et al. successfully enhanced traditional APF to facilitate collision avoidance for both static and moving obstacles, providing a novel strategy for ensuring the safe operation of autonomous vehicles in complicated environments [5]. [PERSON] et al. implemented a strategy involving the discretization of obstacle boundaries to improve safety during obstacle avoidance. Additionally, a stochastic escape force was integrated to inhibit the vehicle from becoming trapped in local minima [6]. Combining the APF with the model predictive control (MPC) also has a good effect on path planning [7; 8]. However, the application of the APF approach comes with distinct drawbacks. It performs poorly in dealing with the kinematic constraints of vehicles and environmental dynamics, which reduces the driving safety of vehicles to some extent [9]. Algorithms based on curve interpolation can consider the kinematic and dynamic features of the vehicle, which are more common path-planning methods. [PERSON] et al. used the Sigmoid function to generate the lane-changing path to achieve efficient obstacle avoidance and stable path tracking for tractor-trailers [10]. [PERSON] et al. introduced a robust tube model predictive control method based on fifth-degree polynomial trajectories for solving the automatic lane-changing problem of tractor-trailers [11]. Spline curves, such as B-spline curves and Bezier curves, have the advantages of good smoothness and continuous curvature changes, and they are also quite common in path planning [12; 13; 14]. Additionally, the simple curve interpolation method often fails to meet the requirements of vehicles for variable paths. Consequently, in the current stage, the curve interpolation method is customarily integrated with other optimization techniques [15; 16] However, the methods commonly exhibit the problem of elevated computational complexity and demonstrate relative inefficacy when confronted with dynamic obstacles. Algorithms based on sampling include the rapid search random tree algorithm (RRT), the probabilistic roadmap algorithm (PRM), and their improved algorithms (such as R2-RRT*, APG-RRT, etc.) [17; 18; 19].