{
  "abstract": "Many spatial (3D) vehicles, including AUVs and fixed-wing aircraft, are effectively nonholonomic and subject to limited actuation, such that continuous time-invariant stabilization is fundamentally obstructed by Brockett's necessary condition. To overcome this obstruction, we exploit the geometric singularity of spherical coordinates to design a backstepping continuous, time-invariant feedback law that exponentially stabilizes a 3D nonholonomic vehicle actuated solely by forward surge velocity, pitch rate, and yaw rate. The resulting closed-loop region of attraction excludes only the coordinate singularity, codimension-two, measure-zero set of initial conditions in which the vehicle lies on the line through the target orthogonal to the target plane, thereby covering the largest possible domain. We further construct a strict control Lyapunov function to prove global exponential stability of the origin on this domain with a user-specified decay rate, while simultaneously preventing the system from approaching the singular set. Finally, we show that the closed-loop system is exponentially attractive to the origin in Cartesian coordinates. Numerical simulation examples in both spherical and Cartesian coordinates illustrate the effectiveness of the control law.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24192",
  "author_total": 3,
  "authors": [
    {
      "name": "Kwang Hak Kim"
    },
    {
      "name": "Velimir Todorovski"
    },
    {
      "name": "Miroslav Krstic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mcfctrhdnwtx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24192",
  "fulltext_url": null,
  "id": "6mcfctrhdnwtx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24192",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Control and Dynamics of Mobile Robots"
    ]
  ],
  "openalex": "W7214017135",
  "pdf_url": "https://arxiv.org/pdf/2609.24192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mcfctrhdnwtx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Global Exponential Stabilization of a 3D Nonholonomic Vehicle in Spherical Coordinates",
  "title_text": "Global Exponential Stabilization of a 3D Nonholonomic Vehicle in Spherical Coordinates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6mcfctrhdnwtx",
  "venue": "arXiv",
  "versions": []
}