循环空域协调：静止悬挂下的多载体持续飞行
Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension
AI总结：
该研究提出基于循环图的空域协调算法，通过选择内部力方向生成非停轨迹，确保静止悬挂负载下多载体持续飞行，具备可扩展性和稳定性分析。
摘要：
本文证明三个或更多载体的非停飞行可与悬挂负载的恒定姿态兼容。提出算法生成载体协调非停轨迹，方法基于两个支柱：(1) 在负载抓取矩阵的3n-6维空域中选择n个特殊线性无关方向作为哈密顿环的边，相邻方向生成n个在不同2D仿射子空间上演化的力量；(2) 在这些子空间中构造椭圆轨迹，通过适当图着色将哈密顿环的每条边映射到周期坐标，确保相邻坐标无同时零导数。结合负载静力学条件和悬挂点位置，这些选择确保每个力轨迹投影到对应的缆约束球上具有非零切向速度，使负载静止时载体持续飞行。工作提供了一种可扩展的构造设计，适用于n≥3的情况，并量化了灵敏度和单载体故障，提供了兼容固定翼的规划器，在速度/坡度/飞行路径约束下保持负载静力学。理论发现通过四旋翼无人机的仿真和实验室实验得到验证。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
