{
  "abstract": "The spring-loaded inverted pendulum (SLIP) describes the center-of-mass (COM) motion of runners but has no trunk. In trunk models, the hip torque couples posture and COM motion and destroys the central-force structure on which SLIP analysis relies. As a result, trunk models have been studied almost only numerically. We show that this structure can be restored. The central pivot point (CPP), a hip-torque law that directs the ground reaction force through the COM, decouples pitch exactly and reduces stance to a planar central-force problem. At upright posture, time-reversal symmetry produces one-parameter families of periodic gaits. A stance-phase pitch law and a stride-level regulator stabilize all computed gaits, also with bounded hip torque and friction. Under CPP, any radial force law in virtual-leg coordinates can be embedded independently of posture. For a linear radial template, the stance radius and the constant-momentum sweep have exact closed forms. With a new gravity correction, the resulting analytic return map, to our knowledge the first for a trunk model, predicts liftoff velocity and apex position with mean errors of 1.6% and 0.9%. The natural gaits of the embedded runner are symmetric and need no force step at touchdown. A near-reversibility argument explains their unit multiplier, and a scalar equation predicts them within 0.8%. A deadbeat stride controller based on the analytic map tracks changes of speed, height and posture. CPP thus makes trunk models accessible to the analytic tools developed for SLIP.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02564",
  "author_total": 3,
  "authors": [
    {
      "name": "İzel Sever"
    },
    {
      "name": "O. Kaan Karagöz"
    },
    {
      "name": "M. Mert Ankaralı"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f718284wf3s4e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02564",
  "fulltext_url": null,
  "id": "f718284wf3s4e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02564",
  "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.DS"
    ],
    [
      "arxiv",
      "physics.bio-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02564",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f718284wf3s4e.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02564",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02564"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    }
  ],
  "title": "Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps",
  "title_text": "Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:10Z",
  "url": "https://research.draconitic.com/paper/f718284wf3s4e",
  "venue": "arXiv",
  "versions": []
}