Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914549857255424 |
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| author | Gabellieri, Chiara Shen, Yaolei Paolucci, Martina Franchi, Antonio |
| author_facet | Gabellieri, Chiara Shen, Yaolei Paolucci, Martina Franchi, Antonio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension Gabellieri, Chiara Shen, Yaolei Paolucci, Martina Franchi, Antonio Robotics Systems and Control 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. |
| title | Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension |
| topic | Robotics Systems and Control |
| url | https://arxiv.org/abs/2503.03481 |