{
  "abstract": "Control allocation for multirotors with bidirectional propellers is commonly formulated in signed-thrust variables, where the wrench map is linear. The signed-quadratic map from physical rotor speed to thrust, however, is not a local diffeomorphism at zero speed. This work derives two distinct consequences. Under nonredundant full actuation, a single-propeller reversal removes one instantaneous task direction; hence, no global continuously differentiable exact static allocator exists over the complete task space. Under redundant actuation, the physical task map may remain regular, yet a transverse pseudoinverse zero crossing requires an unbounded rotor-speed derivative. We define differential realizability as regularity of the physical lift of an actuator-output section, derive exact and first-order validity conditions, and distinguish structural rank loss from an allocator- induced rate singularity. A local nullspace deformation repairs isolated pseudoinverse reversals, while a global fixed-orthant construction establishes existence of regular sections at the cost of persistent task-preserving internal actuation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13588",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Franchi"
    },
    {
      "name": "Mirko Mizzoni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4fmwrh194n9dq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13588",
  "fulltext_url": null,
  "id": "4fmwrh194n9dq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13588",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Adaptive Control of Nonlinear Systems"
    ]
  ],
  "openalex": "W7213325383",
  "pdf_url": "https://arxiv.org/pdf/2609.13588",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4fmwrh194n9dq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13588",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13588"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Differential Realizability of Static Control Allocation in Multirotors: An Impossibility under Nonredundant Full Actuation and a Pseudoinverse Obstruction under Redundant Actuation",
  "title_text": "Differential Realizability of Static Control Allocation in Multirotors: An Impossibility under Nonredundant Full Actuation and a Pseudoinverse Obstruction under Redundant Actuation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4fmwrh194n9dq",
  "venue": "arXiv",
  "versions": []
}