Online End Deformation Calculation Method for Mill Relining Manipulator Based on Structural Decomposition and Kolmogorov-Arnold Network

Due to the large mass, high end load, and long action distance of a mill relining manipulator, gravity effects inevitably lead to a reduction in end effector positioning accuracy. To solve this problem, an online calculation method is proposed to realize real-time end effector deformation prediction. First, a manipulator is simplified into two cantilever beams: the upper arm and the forearm. Second, a reaction force and moment transformation model is established based on the coupling relationship between the forearm and upper arm. Third, finite element (FE) static analysis and simulation are carried out to obtain the end deformation. A total of 3528 discrete joint configurations are selected to cover the entire joint space, and their corresponding FE solutions are used to establish the end deformation offline dataset. Finally, an online deformation calculation algorithm based on Kolmogorov–Arnold networks (KANs) is developed to predict end deformation in any working condition. Visualization analysis and validation experiments are conducted and demonstrate the superiority of the proposed method in reducing gravity effects and improving computational efficiency. In summary, the proposed method provides support for end position compensation, especially for heavy-duty manipulators.