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A Reachability-based Safety Certificate for Dynamical System Motion Policies — arXiv:2609.38421

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.38421
License (as archived): CC0-1.0
Archived: 2026-10-07T15:11:28.280Z
SHA-256 of the archived text: 7d51a45ab4702c917ec0b32c3f4be0749b0df5eab2ece0669b7b934893619973
Stable URL of this page: https://metraipolis.com/documento/dc_ef74f883bcbc

How to cite

A Reachability-based Safety Certificate for Dynamical System Motion Policies — arXiv:2609.38421 — arXiv (en), https://arxiv.org/abs/2609.38421 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ef74f883bcbc (Metraipolis archive dc_ef74f883bcbc, sha256 7d51a45ab4702c917ec0b32c3f4be0749b0df5eab2ece0669b7b934893619973)

BibTeX

@misc{dcef74f883bcbc,
  title = {A Reachability-based Safety Certificate for Dynamical System Motion Policies — arXiv:2609.38421},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.38421},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ef74f883bcbc; sha256 7d51a45ab4702c917ec0b32c3f4be0749b0df5eab2ece0669b7b934893619973},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.38421. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Dynamical Systems (DS) are reactive motion policies representing vector fields trained with theoretical guarantees of stability and convergence. To ensure safety during deployment in unknown environments they must be locally reshaped, either through modulation or geometric control barrier function strategies. However, depending on the geometry of the obstacles and the complexity of the DS, these local strategies can lead the system to unavoidable collisions or spurious attractors. In this work, we certify safety with a value function drawn from the notion of backward reachability tube, which measures the worst-case safety along a rollout trajectory of the nominal DS. Usually, such a value function is intractable for a controlled system due to curse of dimensionality. We show that in the DS-based learning-from-demonstration setting, the absence of a control input collapses the reachability problem to a deterministic rollout, and the presence of certain stability conditions truncates the infinite horizon to a finite one, resulting in a well-defined value function. We further show that the value function we devised is the maximal forward-invariant subset of the obstaclefree region for the nominal DS flow. The application of this certificate function is validated across five DS constructions - analytical, Neural ODE, diffeomorphic latent space, LPV-DS, SE(3)and validate it on a Franka manipulator. Modulation and geometric CBFs also suffer from saddle point in cases of headon approach towards an unsafe zone. We show that CBF-on-V avoids this pitfall entirely.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-10-01 in cs.RO).
Categorie arXiv: Robotics (cs.RO).
Pagina del lavoro: https://arxiv.org/abs/2609.38421 — 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 2026-10-07T14:44:47.337Z dalla pagina https://arxiv.org/catchup/cs.RO/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).