ArticlePloS one2015
The cost of leg forces in bipedal locomotion: a simple optimization study.
Article in PloS one, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- How muscle ageing affects rapid goal-directed movement: mechanistic insights from a simple model.PLoS computational biology · 2026Article
- Muscle-controlled physics simulations of bird locomotion resolve the grounded running paradox.Science advances · 2024Article
- Center of mass kinematic reconstruction during steady-state walking using optimized template models.PloS one · 2024Article
- Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates.Journal of the Royal Society, Interface · 2024Article
- Humans plan for the near future to walk economically on uneven terrain.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Mechanical work accounts for most of the energetic cost in human running.Scientific reports · 2022Article
- Article
- 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
- An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal.PLoS computational biology · 2019Article
- Article
- Robotic lower limb prosthesis design through simultaneous computer optimizations of human and prosthesis costs.Scientific reports · 2016Article
- Children and adults minimise activated muscle volume by selecting gait parameters that balance gross mechanical power and work demands.The Journal of experimental biology · 2015Article
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2 authors.
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Abstract
Simple optimization models show that bipedal locomotion may largely be governed by the mechanical work performed by the legs, minimization of which can automatically discover walking and running gaits. Work minimization can reproduce broad aspects of human ground reaction forces, such as a double-peaked profile for walking and a single peak for running, but the predicted peaks are unrealistically high and impulsive compared to the much smoother forces produced by humans. The smoothness might be explained better by a cost for the force rather than work produced by the legs, but it is unclear what features of force might be most relevant. We therefore tested a generalized force cost that can penalize force amplitude or its n-th time derivative, raised to the p-th power (or p-norm), across a variety of combinations for n and p. A simple model shows that this generalized force cost only produces smoother, human-like forces if it penalizes the rate rather than amplitude of force production, and only in combination with a work cost. Such a combined objective reproduces the characteristic profiles of human walking (R² = 0.96) and running (R² = 0.92), more so than minimization of either work or force amplitude alone (R² = -0.79 and R² = 0.22, respectively, for walking). Humans might find it preferable to avoid rapid force production, which may be mechanically and physiologically costly.
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