Multirotor UAVs have been typically considered for aerial manipulation, but their scarce endurance prevents long-lasting manipulation tasks. This work demonstrates that the non-stop flights of three or more carriers are compatible with holding a constant pose of a cable-suspended load, thus potentially enabling aerial manipulation with energy-efficient non-stop carriers. It also presents an algorithm for generating the coordinated non-stop trajectories. The proposed method builds upon two pillars: (1)~the choice of $n$ special linearly independent directions of internal forces within the $3n-6$-dimensional nullspace of the grasp matrix of the load, chosen as the edges of a Hamiltonian cycle on the graph that connects the cable attachment points on the load. Adjacent pairs of directions are used to generate $n$ forces evolving on distinct 2D affine subspaces, despite the attachment points being generically in 3D; (2)~the construction of elliptical trajectories within these subspaces by mapping, through appropriate graph coloring, each edge of the Hamiltonian cycle to a periodic coordinate while ensuring that no adjacent coordinates exhibit simultaneous zero derivatives. Combined with conditions for load statics and attachment point positions, these choices ensure that each of the $n$ force trajectories projects onto the corresponding cable constraint sphere with non-zero tangential velocity, enabling perpetual motion of the carriers while the load is still. The theoretical findings are validated through simulations and laboratory experiments with non-stopping multirotor UAVs.

翻译：多旋翼无人机通常被考虑用于空中操控任务，但其有限的续航能力阻碍了长时间持续操控的实现。本研究证明，三个或更多载具的不间断飞行与保持缆绳悬吊负载的恒定姿态是相容的，从而可能实现利用高能效不间断载具进行空中操控。本文同时提出了一种用于生成协调不间断轨迹的算法。所提出的方法基于两大支柱：(1) 在负载抓取矩阵的 $3n-6$ 维零空间中，选择 $n$ 个特殊的线性无关内力方向，这些方向被选为连接负载上缆绳附着点所构成图中一条哈密顿环的边。利用相邻的成对方向生成 $n$ 个在互异二维仿射子空间中演化的力，尽管附着点通常位于三维空间中；(2) 通过适当的图着色映射，将哈密顿环的每条边对应到一个周期坐标，从而在这些子空间中构造椭圆轨迹，并确保相邻坐标不会同时出现零导数。结合负载静力学和附着点位置的条件，这些选择保证了每个 $n$ 个力轨迹在对应的缆绳约束球面上投影具有非零切向速度，使得载具能够实现持续运动而负载保持静止。理论结果通过仿真和实验室中不间断多旋翼无人机的实验得到了验证。