Trajectory Tracking Control for a Container Transferring Mobile Robot Based on an Improved NMPC

Abstract

Container Transferring Mobile Robots are widely used in container handling, narrow-aisle transfer, workstation delivery, and automated loading and unloading tasks. These robots usually operate in environments with dense shelving, narrow passages, and clearly defined boundaries. During practical operation, they also frequently perform start-stop motions, pickup tasks, and delivery tasks. These factors make trajectory tracking more challenging, especially when the robot is affected by motion-state switching, reference-path curvature variation, and limited aisle space. In such conditions, attitude fluctuations and control instability may occur, increasing the risk of collision between the robot body and the aisle boundaries.To address this problem, this paper proposes a constrained trajectory-tracking control method for a Container Transferring Mobile Robot based on a discretized model derived from Lagrangian dynamics. First, the dynamic model of the robot is established using the Lagrange method, and a prediction model is obtained through discretization. Then, considering the vehicle width, aisle width, and safety-margin requirements, a virtual safety corridor is constructed to describe the allowable motion range of the robot body. This corridor is introduced into the trajectory-tracking optimization problem as a geometric boundary constraint, so that the operating region of the robot can be limited during prediction and control.The hard-constraint formulation can prevent the robot from crossing the aisle boundary when the optimization problem remains feasible. However, in cases with large initial deviations, rapid changes in reference-path curvature, or further restricted aisle space, the feasible region of the optimization problem may shrink significantly. This may lead to optimization infeasibility and affect the continuous operation of the controller. To improve the applicability of the controller under such conditions, nonnegative slack variables are introduced to soften the geometric boundary constraints, and a linear penalty term is added to the cost function. In addition, an adaptive penalty mechanism based on the degree of constraint violation is designed to enhance constraint recovery near the boundary.Simulation and hardware experimental results show that the proposed method maintains optimization feasibility when the initial lateral deviation exceeds the prescribed corridor threshold. Compared with the standard NMPC and the fixed-weight soft-constrained NMPC, the proposed controller reduces the corridor-violation duration and improves boundary-recovery performance, while maintaining acceptable tracking accuracy and real-time computational performance.