1. Physics of Living Systems
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Humans optimally anticipate and compensate for an uneven step during walking

  1. Osman Darici  Is a corresponding author
  2. Arthur D Kuo
  1. University of Calgary, Canada
Research Article
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Cite this article as: eLife 2022;11:e65402 doi: 10.7554/eLife.65402


The simple task of walking up a sidewalk curb is actually a dynamic prediction task. The curb is a disturbance that could cause a loss of momentum if not anticipated and compensated for. It might be possible to adjust momentum sufficiently to ensure undisturbed time of arrival, but there are infinite possible ways to do so. Much of steady, level gait is determined by energy economy, which should be at least as important with terrain disturbances. It is, however, unknown whether economy also governs walking up a curb, and whether anticipation helps. Here we show that humans compensate with an anticipatory pattern of forward speed adjustments, predicted by a criterion of minimizing mechanical energy input. The strategy is mechanistically predicted by optimal control for a simple model of bipedal walking dynamics, with each leg's push-off work as input. Optimization predicts a tri-phasic trajectory of speed (and thus momentum) adjustments, including an anticipatory phase. In experiment, human subjects ascend an artificial curb with the predicted tri-phasic trajectory, which approximately conserves overall walking speed relative to undisturbed flat ground. The trajectory involves speeding up in a few steps before the curb, losing considerable momentum from ascending it, and then regaining speed in a few steps thereafter. Descending the curb entails a nearly opposite, but still anticipatory, speed fluctuation trajectory, in agreement with model predictions that speed fluctuation amplitudes should scale linearly with curb height. The fluctuation amplitudes also decrease slightly with faster average speeds, also as predicted by model. Humans can reason about the dynamics of walking to plan anticipatory and economical control, even with a sidewalk curb in the way.

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All data generated or analyzed during this study are included in the manuscript and supporting file

Article and author information

Author details

  1. Osman Darici

    Faculty of Kinesiology, University of Calgary, Calgary, Canada
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6217-5656
  2. Arthur D Kuo

    Faculty of Kinesiology, University of Calgary, Calgary, Canada
    Competing interests
    The authors declare that no competing interests exist.


National Science Foundation

  • Osman Darici
  • Arthur D Kuo

ONR ETOWL program

  • Osman Darici
  • Arthur D Kuo

NIH AG030815

  • Osman Darici
  • Arthur D Kuo

The Dr. Benno Nigg Research Chair University of Calgary

  • Osman Darici
  • Arthur D Kuo

NSERC Discovery program

  • Osman Darici
  • Arthur D Kuo

Canada Research Chair program

  • Osman Darici
  • Arthur D Kuo

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.


Human subjects: All subjects provided written informed consent prior to the experiment, according to Institutional Review Board procedures (University of Michigan, Energetics, Balance, and Control of Human Locomotion HUM00020554).

Reviewing Editor

  1. Lena H Ting, Emory University, United States

Publication history

  1. Received: December 3, 2020
  2. Accepted: January 10, 2022
  3. Accepted Manuscript published: January 11, 2022 (version 1)


© 2022, Darici & Kuo

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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