{
  "abstract": "This paper studies path-following control for a kinematic unicycle evolving on a smooth manifold embedded in \\(\\mathbb{R}^3\\). The objective is to stabilize a one-dimensional path on the manifold without imposing a temporal parameterization, thereby distinguishing the problem from trajectory tracking. Working in a geometric framework, we propose two feedback laws: a static controller for prescribed nonzero translational speed and a dynamic controller based on a dynamic extension of the translational speed. By lifting the path to the unit tangent bundle of the surface, we characterize the corresponding path-following manifold and establish its control invariance. We then show that the proposed controllers render the path-following manifold locally exponentially stable under suitable regularity conditions. A numerical simulation illustrates the proposed controller. Code and animations are publicly available at https://gradslab.github.io/UnicycleOnManifolds/.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23878",
  "author_total": 2,
  "authors": [
    {
      "name": "Adeel Akhtar"
    },
    {
      "name": "Mohamed Al Lawati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fd8xctn6ygfjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23878",
  "fulltext_url": null,
  "id": "fd8xctn6ygfjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23878",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Control and Dynamics of Mobile Robots"
    ]
  ],
  "openalex": "W7214032682",
  "pdf_url": "https://arxiv.org/pdf/2609.23878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fd8xctn6ygfjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Modeling and Control of a Unicycle Robot on Manifolds",
  "title_text": "Modeling and Control of a Unicycle Robot on Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/fd8xctn6ygfjw",
  "venue": "arXiv",
  "versions": []
}