Multi-Objective Dimensional Optimization of n-3UPS Mooring Robot Configuration with Linear Layout

To address the challenge of coupled optimization between global parameters and local performance in multi-robot mooring systems under ultra-long linear layouts, this study focuses on the n-3UPS mooring robot configuration and explores the influence law of long-distance layout on the force transmission performance of the generalized parallel mechanism. First, a generalized parallel mechanism model of multi-robot-ship systems is constructed, and the inverse force Jacobian matrix is derived to describe the force transmission relationship. Second, a multi-objective evaluation system is established, including the workspace index, the Global Conditioning Index, and the Global Anisotropy Index. Further, the Cuckoo Search algorithm is used to optimize key parameters such as robot spacing, relative rotation angle of the moving platform, offset, and diameter ratio of the hinge-point circumcircle. The results reveal the influence of spacing on force transmission efficiency in surge, sway, and yaw directions: as spacing increases, the fitness for surge and sway decreases due to enhanced workspace constraints, while yaw fitness significantly improves. Based on this, a multi-robot layout strategy is proposed: “Robot groups with large spacing provide yaw torque, robot groups with moderate spacing provide surge force, and robot groups with small spacing provide sway force.” Simulation results validate the effectiveness of the method, providing theoretical support for the dimensional design of ultra-long linear multi-mooring robot systems.