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. It also presents an algorithm for generating the carriers' 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 work provides a scalable constructive design for any n greater than or equal to 3 with tuning guidelines, quantifies sensitivity and single-carrier failures, and provides a fixed-wing-compatible planner that preserves load statics under speed/bank/flight-path constraints. The theoretical findings are validated through simulations and laboratory experiments with quadrotor UAVs.

翻译：本研究论证了三架或更多载具的非停歇飞行与保持缆索悬挂负载恒定姿态的兼容性，并提出了一种生成载具协调持续轨迹的算法。该方法基于两个核心支柱：（1）在负载抓取矩阵的3n-6维零空间内，选择n个特殊线性独立的内力方向，这些方向对应于负载上缆索连接点所构成的哈密顿环的边。相邻方向对被用于生成在二维仿射子空间上演化的n个力，尽管连接点通常位于三维空间；（2）通过适当的图着色，将哈密顿环的每条边映射为周期坐标，同时确保相邻坐标不会同时出现零导数，从而在这些子空间内构建椭圆轨迹。结合负载静力学条件和连接点位置约束，这些选择确保每个力轨迹投影到对应的缆索约束球面上时具有非零切向速度，从而使载具在负载静止时实现持续运动。该工作为任意n≥3提供了可扩展的构造性设计并附有调参指南，量化了灵敏度与单载具故障影响，还提供了一个在速度/倾斜角/航迹约束下保持负载静力学特性的固定翼兼容规划器。通过四旋翼无人机的仿真与实验室实验验证了理论成果。