{
  "abstract": "This paper studies intrinsic path following for fully actuated rigid-body attitude dynamics over a broad class of attitude paths, namely arbitrary smooth embedded closed curves on $\\mathsf{SO}(3)$. We construct a tangential--transverse state decomposition on a tubular neighborhood using normal and pullback bundle geometry. The resulting second-order dynamics admit a smooth feedback transformation that independently assigns tangential and transverse covariant accelerations. A transverse proportional--derivative law renders the path-following manifold invariant and locally uniformly exponentially stable on an explicit forward-invariant neighborhood, while leaving the tangential dynamics freely assignable. This allows independent regulation of progression along the path, stabilization of a selected attitude on the path, or tracking of a time-varying motion. For a representative fiber path, the tubular coordinates are obtained in closed form up to the natural cut-locus obstruction, and simulations illustrate point stabilization and trajectory tracking.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04332",
  "author_total": 1,
  "authors": [
    {
      "name": "Adeel Akhtar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x4et9q4gtv7h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04332",
  "fulltext_url": null,
  "id": "5x4et9q4gtv7h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04332",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
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    [
      "arxiv",
      "math.OC"
    ],
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      "openalex",
      "2207|Control and Stability of Dynamical Systems"
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  "openalex": "W7220713687",
  "pdf_url": "https://arxiv.org/pdf/2610.04332",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x4et9q4gtv7h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04332",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04332"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Intrinsic Path Following on $\\mathsf{SO}(3)$",
  "title_text": "Intrinsic Path Following on SO(3)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/5x4et9q4gtv7h",
  "venue": "arXiv",
  "versions": []
}