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Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields — arXiv:2609.19726

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19726
License (as archived): CC0-1.0
Archived: 2026-10-10T05:25:31.883Z
SHA-256 of the archived text: 53bd504c9b040a8136faac7a7e22cd9d6ca831aba9af4a6951fec23fa4bd383a
Stable URL of this page: https://metraipolis.com/documento/dc_daf39541dc4e

How to cite

Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields — arXiv:2609.19726 — arXiv (en), https://arxiv.org/abs/2609.19726 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_daf39541dc4e (Metraipolis archive dc_daf39541dc4e, sha256 53bd504c9b040a8136faac7a7e22cd9d6ca831aba9af4a6951fec23fa4bd383a)

BibTeX

@misc{dcdaf39541dc4e,
  title = {Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields — arXiv:2609.19726},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19726},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_daf39541dc4e; sha256 53bd504c9b040a8136faac7a7e22cd9d6ca831aba9af4a6951fec23fa4bd383a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19726. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The existing singularity-free guiding vector field (SF-GVF) with an additional virtual coordinate can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-intersecting desired paths. However, the desired speed given by the GVF along the desired path in the original lower-dimensional space cannot be arbitrarily specified but depends on path parameterizations. One possible workaround is to partially normalize the physical projection of the SF-GVF and assign a user-designed speed. However, we show that this workaround may introduce new singularities since the normalization denominator can become zero. To address this issue, we propose a new SF-GVF with prescribed physical speed (PPS). The integral curves of the new SF-GVF converge exponentially to the desired path from any initial condition in the higher-dimensional space (including virtual dimension); more importantly, the robot's physical speed converges to the PPS, while the path-error dynamics remain invariant under regular reparameterizations of the desired path. We further develop a saturated acceleration control law for second-order kinematic models. Finally, comparative simulations and 3D path-following experiments with a quadrotor under different PPS profiles validate the theoretical results and demonstrate the effectiveness of the proposed approach.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-18 in cs.RO).
Categorie arXiv: Robotics (cs.RO).
Pagina del lavoro: https://arxiv.org/abs/2609.19726 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:47:38.849Z dalla pagina https://arxiv.org/catchup/cs.RO/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).