An enhanced zero vibration constraint command shaping method for overhead cranes

Load swing suppression remains a critical challenge in underactuated crane systems, especially when arbitrary initial oscillations and strict sway constraints are involved. This paper proposes an enhanced zero vibration constraint command shaping (EZVCCS) method to address this problem. The method explicitly incorporates swing constraints into the shaping process, enabling precise trajectory planning while ensuring terminal state satisfaction. A systematic investigation examines the effects of maneuvering time, velocity constraints, input step number, and sway constraints on system performance. The EZVCCS method supports arbitrary initial and terminal conditions, unlike the traditional ones. This allows maneuvers that are flexible point-to-point even in cases where the sway requirement is stringent. Moreover, it unifies and extends existing command shaping strategies: with a small input step number, it reproduces the acceleration characteristics of zero-vibration (ZV) and zero-vibration-derivative (ZVD) shapers, while delivering improved suppression of initial sway and guaranteed terminal-state accuracy under the imposed constraints. With larger step numbers, the piecewise-constant command attains finer shaping resolution and can closely approximate the closed-form command shaping (CFCS) method, while the embedded constraints enable stricter sway regulation. Overall, the EZVCCS method offers a unified solution that balances sway suppression and computational efficiency, demonstrating strong potential for practical crane applications.