This paper presents a framework for aerial manipulation of an extensible cable that combines a high-fidelity model based on partial differential equations (PDEs) with a reduced-order representation suitable for real-time control. The PDEs are discretised using a finite-difference method, and proper orthogonal decomposition is employed to extract a reduced-order model (ROM) that retains the dominant deformation modes while significantly reducing computational complexity. Based on this ROM, a nonlinear model predictive control scheme is formulated, capable of stabilizing cable oscillations and handling hybrid transitions such as payload attachment and detachment. Simulation results confirm the stability, efficiency, and robustness of the ROM, as well as the effectiveness of the controller in regulating cable dynamics under a range of operating conditions. Additional simulations illustrate the application of the ROM for trajectory planning in constrained environments, demonstrating the versatility of the proposed approach. Overall, the framework enables real-time, dynamics-aware control of unmanned aerial vehicles (UAVs) carrying suspended flexible cables.

翻译：本文提出了一种用于可伸缩缆索空中操控的框架，该框架将基于偏微分方程的高保真模型与适用于实时控制的降阶表示相结合。偏微分方程采用有限差分法进行离散化，并运用本征正交分解提取降阶模型，该模型在显著降低计算复杂度的同时保留了主导变形模态。基于此降阶模型，构建了非线性模型预测控制方案，能够稳定缆索振荡并处理负载附着与分离等混合过渡过程。仿真结果验证了降阶模型的稳定性、效率与鲁棒性，以及控制器在不同工况下调节缆索动力学的有效性。额外仿真展示了降阶模型在受限环境中轨迹规划的应用，证明了所提方法的通用性。总体而言，该框架实现了对悬挂柔性缆索的无人飞行器进行实时、动力学感知的控制。