Time-optimal motion trajectory generation incorporating an input shaper for overhead cranes operated by industrial servo systems

This paper proposes a motion trajectory generation method that achieves time-optimality under input shaping constraints for overhead cranes operated by industrial servo systems. The proposed approach formulates a constrained trajectory optimization problem that minimizes motion time while suppressing residual vibration by embedding a zero-vibration (ZV) or zero-vibration-and-derivative (ZVD) input shaper into the trajectory generation process. By using a simplified model that requires only the natural frequency and damping ratio to characterize vibration, this approach enables practical implementation even when full system identification is difficult. The effectiveness and robustness of the proposed method are demonstrated through simulations and experiments using an overhead crane apparatus. The results demonstrate that the proposed method achieves shorter motion times with effective vibration suppression compared to conventional input shaping and maintains robustness against modeling errors in natural frequency and damping ratio.