In this paper we address the control problem of aerial cable suspended load transportation, using multiple Unmanned Aerial Vehicles (UAVs). First, the dynamical model of the coupled system is obtained using the Newton-Euler formalism, for "n" UAVs transporting a load, where the cables are supposed to be rigid and mass-less. The control problem is stated as a trajectory tracking directly on the load. To do so, a hierarchical control scheme is proposed based on the attractive ellipsoid method, where a virtual controller is calculated for tracking the position of the load, with this, the desired position for each vehicle along with their desired cable tensions are estimated, and used to compute the virtual controller for the position of each vehicle. This results in an underdetermined system, where an infinite number of drones' configurations comply with the desired load position, thus additional constrains can be imposed to obtain an unique solution. Furthermore, this information is used to compute the attitude reference for the vehicles, which are feed to a quaternion based attitude control. The stability analysis, using an energy-like function, demonstrated the practical stability of the system, it is that all the error signals are attracted and contained in an invariant set. Hence, the proposed scheme assures that, given well posed initial conditions, the closed-loop system guarantees the trajectory tracking of the desired position on the load with bounded errors. The proposed control strategy was evaluated in numerical simulations for three agents following a smooth desired trajectory on the load, showing good performance.

翻译：本文研究了使用多架无人飞行器（UAV）进行空中缆绳悬挂载荷运输的控制问题。首先，采用牛顿-欧拉公式建立了"n"架无人机运输载荷的耦合系统动力学模型，其中假设缆绳为刚性且无质量。控制问题被表述为直接在载荷上实现轨迹跟踪。为此，基于吸引椭球法提出了一种分层控制方案：通过计算虚拟控制器实现载荷位置跟踪，由此估计每架无人机的期望位置及其期望缆绳张力，并用于计算各无人机位置的虚拟控制器。该系统属于欠定系统——存在无限种无人机位姿配置可满足期望载荷位置，因此可施加额外约束获得唯一解。进一步地，利用该信息计算飞行器的姿态参考值，并将其输入基于四元数的姿态控制器。通过类能量函数的稳定性分析表明系统具有实际稳定性，即所有误差信号被吸引并包含于一个不变集中。因此，该方案保证了在初始条件适定的情况下，闭环系统能够以有界误差实现载荷期望位置的轨迹跟踪。针对三架智能体跟踪载荷平滑期望轨迹的数值仿真验证了所提控制策略的有效性，展现出良好的控制性能。