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An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal.

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  • Author(s): Polet DT;Polet DT; Bertram JEA; Bertram JEA
  • Source:
    PLoS computational biology [PLoS Comput Biol] 2019 Nov 21; Vol. 15 (11), pp. e1007444. Date of Electronic Publication: 2019 Nov 21 (Print Publication: 2019).
  • Publication Type:
    Journal Article; Research Support, Non-U.S. Gov't
  • Language:
    English
  • Additional Information
    • Source:
      Publisher: Public Library of Science Country of Publication: United States NLM ID: 101238922 Publication Model: eCollection Cited Medium: Internet ISSN: 1553-7358 (Electronic) Linking ISSN: 1553734X NLM ISO Abbreviation: PLoS Comput Biol Subsets: MEDLINE
    • Publication Information:
      Original Publication: San Francisco, CA : Public Library of Science, [2005]-
    • Subject Terms:
      Energy Metabolism/*physiology ; Forecasting/*methods ; Gait/*physiology; Animals ; Biomechanical Phenomena/physiology ; Dogs ; Locomotion ; Models, Biological ; Models, Theoretical ; Running/physiology ; Walking/physiology
    • Abstract:
      It is widely held that quadrupeds choose steady gaits that minimize their energetic cost of transport, but it is difficult to explore the entire range of possible footfall sequences empirically. We present a simple model of a quadruped that can spontaneously produce any of the thousands of planar footfall sequences available to quadrupeds. The inelastic, planar model consists of two point masses connected with a rigid trunk on massless legs. It requires only center of mass position, hind and forelimb proportions and a stride-length to speed relationship as input. Through trajectory optimization of a work and force-rate cost, and a large sample of random initial guesses, we provide evidence for the global optimality of symmetrical four-beat walking at low speeds and two beat running (trotting) at intermediate speeds. Using input parameters based on measurements in dogs (Canis lupus familiaris), the model predicts the correct phase offset in walking and a realistic walk-trot transition speed. It also spontaneously reproduces the double-hump ground reaction force profile observed in walking, and the smooth single-hump profile observed in trotting. Actuation appears elastic, despite the model's lack of springs, suggesting that spring-like locomotory behaviour emerges as an optimal tradeoff between work minimization and force-rate penalties.
    • Abstract:
      The authors have declared that no competing interests exist.
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    • Publication Date:
      Date Created: 20191122 Date Completed: 20200214 Latest Revision: 20240722
    • Publication Date:
      20250114
    • Accession Number:
      PMC6871776
    • Accession Number:
      10.1371/journal.pcbi.1007444
    • Accession Number:
      31751339