Tractor Semi-Trailer Off-Tracking and Stability Approximate Bi-Level Policy Optimization

Trajectory tracking control of tractor semi-trailer vehicles poses significant challenges due to inherent off-tracking behavior and roll instability risks. While existing approaches have demonstrated effectiveness, they often rely on computationally intensive numerical solvers and require time-consuming manual tuning of cost function weights. This paper presents an approximate bi-level policy optimization (ABPO) framework that simultaneously optimizes the cost function and synthesizes an explicit control policy to minimize off-tracking while reducing computational complexity. The proposed framework employs a hierarchical structure: the upper level updates cost weights based on the trailer’s stability trajectory, while the lower level derives an approximate optimal policy by solving the tractor’s control problem. By leveraging Pontryagin’s Maximum Principle (PMP), we have developed a novel method to analytically compute cost weight gradients through differentiation of the PMP conditions. This enables the formulation of a related optimal control problem (OCP) whose solutions directly yield gradients for cost parameter updates. The ABPO framework achieves automatic weight coefficient adjustment, enhances trajectory tracking accuracy for both tractor and trailer units, and significantly reduces computational burden. Simulation and experimental validation across 4 classical scenarios demonstrates that the learned policy reduces rearward amplification by 17.82%, lateral tracking errors by 84.15%, and rollover by 64.19%, respectively. Notably, the control policy computation requires less than 10ms, making it suitable for real-time applications. The source code for the algorithms described in this paper is publicly available at https://github.com/TroyResearch/ABPO.git Note to Practitioners—This paper addresses a challenge in the autonomous driving industry: efficient and safe trajectory tracking control for tractor semi-trailer vehicles. Current industrial solutions typically require significant computational resources and time-consuming manual tuning of control parameters, limiting their practical implementation. Our proposed ABPO framework offers a practical solution by automating the parameter-tuning process and reducing computational complexity while maintaining safety standards. The framework can be readily integrated into existing complex control systems with minimal hardware requirements, making it suitable for real-time applications. However, when applying this framework to other control problems, the specific formulation of upper and lower-level problems needs to be carefully redesigned based on the particular problem characteristics to ensure the effectiveness of the control architecture. Future research will focus on extending this methodology to a broader range of control applications, like multi-robot control systems, autonomous fleet navigation, and imitation learning scenarios.