At present, marine resources, especially the deep-sea resources, are becoming more and more important in resource exploitation globally, and hence, widely used deep-sea cranes are playing essential roles. For such systems, the bridge frames and trolleys are set up above the water, while payloads are transported under the water. In this underwater situation, there exist hydrodynamic forces such as complicated disturbances to the crane systems, making the payload vibration and rope flexibility more obvious. For the sake of improving working efficiency, considering the constraints of all the state variables, an anti-vibration trajectory is designed for the trolley motion, which can not only ensure trolley positioning but also suppress the flexible payload’s vibrations. Then, the state variables are constrained within preset safety ranges. Finally, numerical simulation results prove the satisfactory performance of the designed method.

中文翻译：

---

在深海中工作的灵活起重机系统的点对点运动控制

当前，海洋资源特别是深海资源在全球资源开发中的地位越来越重要，广泛使用的深海起重机发挥着重要作用。对于此类系统，桥架和小车设置在水面上方，而有效载荷则在水下运输。在这种水下情况下，起重机系统存在复杂扰动等水动力，使有效载荷振动和绳索柔性更加明显。为提高工作效率，考虑所有状态变量的约束，为小车运动设计了抗振轨迹，既能保证小车定位，又能抑制柔性有效载荷的振动。然后，状态变量被约束在预设的安全范围内。最后，