ArticlePLoS computational biology2019
An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal.
Article in PLoS computational biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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14 citing papers in PubMed, 25 citations in OpenAlex.
- How muscle ageing affects rapid goal-directed movement: mechanistic insights from a simple model.PLoS computational biology · 2026Article
- Muscle-Driven Predictive Physics Simulations of Quadrupedal Locomotion in the Horse.Integrative and comparative biology · 2024Article
- Muscle-controlled physics simulations of bird locomotion resolve the grounded running paradox.Science advances · 2024Article
- Optimal Gearing of Musculoskeletal Systems.Integrative and comparative biology · 2024Article
- Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates.Journal of the Royal Society, Interface · 2024Article
- Optimization Design and Performance Analysis of a Bionic Knee Joint Based on the Geared Five-Bar Mechanism.Bioengineering (Basel, Switzerland) · 2023Article
- Legs as linkages: an alternative paradigm for the role of tendons and isometric muscles in facilitating economical gait.The Journal of experimental biology · 2022Article
- Competing Models of Work in Quadrupedal Walking: Center of Mass Work is Insufficient to Explain Stereotypical Gait.Frontiers in bioengineering and biotechnology · 2022Article
- Center of Mass Offset Enhances the Selection of Transverse Gallop in High-Speed Running by Horses: A Modeling Study.Frontiers in bioengineering and biotechnology · 2022Article
- Elastic energy savings and active energy cost in a simple model of running.PLoS computational biology · 2021Article
- Estimating Gaits of an Ancient Crocodile-Line Archosaur Through Trajectory Optimization, With Comparison to Fossil Trackways.Frontiers in bioengineering and biotechnology · 2021Article
- Whole-body kinematic and dynamic modeling for quadruped robot under different gaits and mechanism topologies.PeerJ. Computer science · 2021Article
- Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds.Proceedings. Biological sciences · 2020Article
- The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution.Integrative organismal biology (Oxford, England) · 2020Article
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Authors and funding
2 authors at 1 institution in 1 country.
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No grant is acknowledged in the PubMed record.
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.
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