# Trajectory Planning of a Semi-Trailer Train Based on Constrained Iterative LQR
## 1 Introduction  
With the accelerating trend of economic globalization, e-commerce platforms and import/export trade are flourishing, driving the development of the transport industry. Semi-trailer trains have the advantages of large cargo volumes and low transport costs, making them the first choice for long-distance cargo transport by road. With the development of mobile internet, 5G, and artificial intelligence, autonomous driving technology has become more mature. The trend is to apply self-driving technology to long-haul goods vehicles and to develop self-driving heavy trucks to cope with labor shortages, optimize transport costs, and improve the safety of heavy trucks on the road [1]. Trajectory planning is a key technology to realize automated vehicle driving, which can solve the problem of how the car should go while satisfying traffic rules and obstacle avoidance constraints. The trajectory planning problem for autonomous semi-trailer trains is more challenging than that of ordinary single-unit vehicles [2; 3]. On the one hand, the semi-trailer train has a flexible connection between the tractor and the semi-trailer, and the obstacle avoidance constraints are difficult to handle. On the other hand, the semi-trailer's long body, heavy load, and high center of mass position make the semi-trailer train prone to dangerous working conditions such as drifting, side-slipping, and folding when turning [4]. Therefore, studying the trajectory planning problem for autonomous semi-trailer trains is valuable. Trajectory planning algorithms commonly used for autonomous vehicles are divided into sampling-based, search-based, and optimization-based algorithms. The sampling-based algorithm samples nodes randomly in the state space and generates a planning trajectory by adding constraints. This approach is probabilistically feasible but inefficient for planning complex scenarios. The representative algorithms are the rapidly random tree(RRT) [5; 6; 7] and probabilistic road map methods (PRM). The search-based path planning algorithm [8] searches for the shortest path from the start to the endpoint by traversing neighboring nodes on a raster map to obtain the optimal global solution. However, the A* algorithm [9; 10] and [PERSON]'s algorithm need help planning feasible trajectories in complex scenarios. Additionally, the above two algorithms do not take into account the kinematic characteristics of the vehicle when planning trajectories, which cannot guarantee the feasibility of the planned trajectories in terms of control [11]. These algorithms are more commonly used in the field of mobile robots. The optimization-based trajectory planning method constructs a cost function by introducing evaluation metrics and judges the trajectory's merits according to the cost function's size. A safe trajectory with near-optimal overall performance is planned by calculating the minimum value of the cost function. [PERSON] et al. [12] designed an evaluation function based on the proximity of the driving states of manned and unmanned vehicles. The evaluation function evaluates and filters the initial trajectory clusters to ensure optimally generated trajectories. [PERSON] et al. [13] improved the Pearl model-based trajectory planning algorithm with a multivariate single-objective optimization scheme. Combining the maximum speed constraint, acceleration constraint, and traffic signal length constraint, a window-based trajectory planning method is proposed to improve the smoothness of the planned trajectory. [PERSON] et al. [14] combined the optimality of the genetic algorithm for planning trajectories with the real-time nature of the potential field method for localized planning to improve the quality of the planned trajectories. [PERSON] et al. [15] Based on a comprehensive analysis of sampling-based, search-based, and optimization-based trajectory planning methods, a hybrid planning framework that combines the advantages of both search-based and optimization-based algorithms is proposed.