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arXiv · 2503.03481

Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension

Chiara Gabellieri·Yaolei Shen·Martina Paolucci·Antonio Franchi
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Abstract

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.

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Chiara Gabellieri, Yaolei Shen, Martina Paolucci, Antonio Franchi. 2025-03-05. Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension. https://doi.org/10.1109/tcst.2026.3692228

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