{
  "abstract": "We study minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds-Shepp pursuer with minimum turning radius $r$. For speed ratio $ν$ and cone half-angle $0<α<π/2$, we prove a global escape/holding classification: straight reversal holds the whole cone for $ν\\le\\sinα$, escape is confined to a barrier-bounded dart for $\\sinα<ν\\le1$, and escape is possible from every state for $ν>1$. For the slower or equally fast evader, $\\sinα<ν\\le1$, we construct the solution with Isaacs' characteristics and verify it in feedback form, using a Filippov pursuer relay and a one-sided evader branch. The finite escape time is the first root of one scalar equation, and the holding region is bounded by the nonusable parts of the rays and a barrier that closes with a convex corner on the front axis. Sample-and-hold counter-controls show that this escape time is the value of the game in nonanticipative strategies at every state except the corner. There the two strategy values differ: the pursuer's is infinite, whereas an evader that chooses which barrier branch to cross from the initial germ of the pursuer's control escapes before the barrier time $τ_I$, which is the evader's exact strategy value. An independent level-set solver, refined on fixed comparison points, agrees with the closed-form escape time and reproduces the holding region at the tested parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27629",
  "author_total": 1,
  "authors": [
    {
      "name": "Ubaldo Ruiz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h24p8waja9az.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27629",
  "fulltext_url": null,
  "id": "4h24p8waja9az",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27629",
  "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.RO"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2202|Guidance and Control Systems"
    ]
  ],
  "openalex": "W7223122673",
  "pdf_url": "https://arxiv.org/pdf/2610.27629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h24p8waja9az.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Minimum-Time Escape from the Conic Field of View of a Reeds-Shepp Pursuer: Classification and Game Value for a Slower or Equally Fast Evader",
  "title_text": "Minimum-Time Escape from the Conic Field of View of a Reeds-Shepp Pursuer: Classification and Game Value for a Slower or Equally Fast Evader",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/4h24p8waja9az",
  "venue": "arXiv",
  "versions": []
}