{
  "abstract": "We address robust trajectory-planning problems with state constraints and with control/state-dependent uncertain inputs and measurements. Uncertain inputs and measurements satisfy quadratic inequalities with rank-2 indefinite multipliers; measurements depend on the uncertain-state realization and on the uncertain inputs. By means of Lagrangian duality, we derive finite nonsmooth constraints that guarantee robust satisfaction of the state constraints, yielding a formulation that can be addressed without bilevel solvers. We develop a two-step convex heuristic for the resulting nonconvex nonsmooth formulation, using a convex relaxation followed by a convex feasibility-recovery step. We test the two-step approach on a rendezvous scenario with state-dependent navigation uncertainty, and we reduce by a factor 13.8 the computation time with respect to the commercial solver Gurobi, while maintaining robust satisfaction of constraints.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38803",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabio Spada"
    },
    {
      "name": "Behçet Açıkmeşe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rdbvxhma4xw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38803",
  "fulltext_url": null,
  "id": "9rdbvxhma4xw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38803",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.38803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9rdbvxhma4xw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Robust Planning with Quadratically Constrained State-Dependent Uncertainties",
  "title_text": "Robust Planning with Quadratically Constrained State-Dependent Uncertainties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/9rdbvxhma4xw8",
  "venue": "arXiv",
  "versions": []
}