{
  "abstract": "Full actuation is commonly valued for independent position and attitude tracking. This work establishes a complementary principle: when only a position trajectory is prescribed, minimizing a positively homogeneous allocation cost selects underactuated-like behavior on a fully actuated multirotor. This cost class includes norms and power laws, including standard minimum-norm pseudoinverse allocation. We use fiberwise infimization to transport the actuator-output cost to wrench space, yielding a homogeneous infimal allocation cost. Restriction to unit zero-moment forces defines a directional landscape whose minimizing directions are independent of force magnitude. We show that aligning any fixed minimizing direction with the required world-frame force minimizes instantaneous and integrated zero-moment allocation costs. The resulting body force remains in a fixed one-dimensional subspace without transverse components. We derive an exact optimality-gap decomposition quantifying the additional cost of every other attitude trajectory and characterizing the minimum-cost class. When a disturbance or prescribed-motion change modifies the required-force direction, a fully actuated platform can immediately generate the modified force using transverse authority and reorient toward the new minimum-cost family. A structurally underactuated platform must reorient before generating that force. Thus, homogeneous allocation-cost minimization explains why optimal nominal motion can be underactuated-like, while full actuation remains valuable for disturbance rejection and transient force generation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04726",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Franchi"
    },
    {
      "name": "Barbara Bazzana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09ch056etsv9w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04726",
  "fulltext_url": null,
  "id": "09ch056etsv9w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04726",
  "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.OC"
    ],
    [
      "openalex",
      "2207|Control and Dynamics of Mobile Robots"
    ]
  ],
  "openalex": "W7220681005",
  "pdf_url": "https://arxiv.org/pdf/2610.04726",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09ch056etsv9w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04726",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04726"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Emergent Underactuation in Fully Actuated Multirotors by Minimizing a Homogeneous Allocation Cost",
  "title_text": "Emergent Underactuation in Fully Actuated Multirotors by Minimizing a Homogeneous Allocation Cost",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/09ch056etsv9w",
  "venue": "arXiv",
  "versions": []
}