This paper presents an optimal trajectory generation method for 3D overhead cranes by leveraging differential flatness. This framework enables the direct inclusion of complex physical and dynamic constraints, such as nonlinear friction and collision avoidance for both payload and rope. Our approach allows for aggressive movements by constraining payload swing only at the final point. A comparative simulation study validates our approach, demonstrating that neglecting dry friction leads to actuator saturation and collisions. The results show that friction modeling is a fundamental requirement for fast and safe crane trajectories.

翻译：本文提出一种利用微分平坦性的三维桥式起重机最优轨迹生成方法。该框架能够直接包含复杂的物理与动力学约束，例如非线性摩擦以及负载与绳索的碰撞规避。通过仅在终点处约束负载摆角，本方法允许实现大动态范围运动。对比仿真研究验证了所提方法的有效性，结果表明忽略干摩擦会导致执行器饱和与碰撞事件。研究证实，摩擦建模是实现起重机快速安全轨迹规划的基础性要求。