Humans optimally anticipate and compensate for an uneven step during walking

  1. Osman Darici
  2. Arthur D Kuo

  • Curated by eLife

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    Evaluation Summary:

    This study provides experimental evidence supporting an energy optimality principle for walking over uneven terrain. Using a simple rimless wheel model of human walking, the authors previously predicted speed fluctuations to emerge when a step up or down when energy is minimized over the entire walking path. New experimental evidence provides evidence that both anticipatory and reactive adjustments used by the nervous system follow the predictions of an energy minimization principle. The predictive power of an energy-minimization principle during transient, non-steady state behavior is notable. Certain issues regarding the generalizability of the results to variable step lengths and timing, alternative optimality criteria, and limitations of the modeling assumptions should be clarified.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

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Abstract

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 triphasic trajectory of speed (and thus momentum) adjustments, including an anticipatory phase. In experiment, human subjects ascend an artificial curb with the predicted triphasic 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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  1. Version published to 10.7554/elife.65402 on eLife
  2. eLife

    Author Response:

    Reviewer #2 (Public Review):

    The authors evaluated whether their previously published model-based predictions of strategies to take an uneven step during walking agree with new experimental observations. Predictions were obtained under the assumption of optimal control based on a simple mechanical model of walking (rimless wheel). The optimality criterion was minimization of mechanical work. Experimental observations supported the following key model outcomes: (1) compensation steps occurring around the uneven step (as opposed to either after or before), (2) pattern of speed fluctuations before and after the uneven step, (3) scaling of speed fluctuations with gait speed. The paper thereby provides additional support for the optimal control hypothesis. The claim that 'humans compensate with an anticipatory pattern of forward speed adjustments, with a criterion of minimizing mechanical energy input' might be somewhat strong, given that the model relied on a set of limiting assumptions (see also below), reasonable alternative modeling assumptions have not been tested, and only a subset of the model predictions published earlier have been evaluated. The conclusions of the paper could be strengthened by:

    1. demonstrating that the predictions also hold for a model with variable step length;

    We have added predictions for step lengths that increase with speed, according to the pre-ferred step length relationship (Fig. 5c). The optimization shows that “A basic pattern for optimal speed fluctuations retains approximately the same shape across different overall walking speeds, fixed step lengths, or even step length changing according to the human preferred step length relationship (Fig. 5d)… we expect a single basic pattern, treated as a sequence of discrete speed fluctuations (Fig. 5a) to predict optimal responses regardless of an individual’s average speed, step length, or the preferred speed and step length relation-ship.” (Methods, Model)

    1. demonstrating that optimal control also predicts no time lost due to stepping up as compared to walking on even terrain;

    As discussed above, we have clarified that the optimal control was constrained (rather than predicts) to conserve time. (And that subjects were asked to approximately conserve time without feedback.) We have also added a figure demonstrating how the model loses time from the Up-step, if not constrained to do so (Fig. 1b).

    1. demonstrating that the number of compensation steps N that minimizes work corresponds to the observed number of compensation steps;

    As discussed above, we have added explanation that N was not a hypothesis, and was a pa-rameter chosen large enough to capture compensations local to the perturbation. We chose N to be more than large enough to encompass the compensation, for both model and hu-man. We do not hypothesize a particular value for N, because the model very smoothly de-parts from and rejoins steady walking, making it difficult to identify a precise N from noisy human data.

    1. demonstrating that minimal work leads to better agreement between simulations and observations than other plausible optimality criteria;

    We have tested three other plausible criteria that did not match human experiment: No compensatory reaction (constant push-offs, Fig. 1b), reactive feedback after the perturba-tion (Fig. 1c.), and tight speed regulation to avoid speed fluctuations altogether (Fig. 1d). These alternative strategies are rejected in Results.

    1. demonstrating that the predicted dependence of speed fluctuations on step height is in agreement with experimental observations.

    We have reworked the scaling test, and instead of simultaneously testing both speed and step height scaling, these are now performed separately, and the methods explained in more detail. The average Up-step response is shown to approximately predict the fluctua-tions observed for the two other step heights (0 cm and -7.5 cm).

  3. eLife

    Evaluation Summary:

    This study provides experimental evidence supporting an energy optimality principle for walking over uneven terrain. Using a simple rimless wheel model of human walking, the authors previously predicted speed fluctuations to emerge when a step up or down when energy is minimized over the entire walking path. New experimental evidence provides evidence that both anticipatory and reactive adjustments used by the nervous system follow the predictions of an energy minimization principle. The predictive power of an energy-minimization principle during transient, non-steady state behavior is notable. Certain issues regarding the generalizability of the results to variable step lengths and timing, alternative optimality criteria, and limitations of the modeling assumptions should be clarified.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

  4. eLife

    Reviewer #1 (Public Review):

    The study combines theoretical and experimental approaches to probe the laws governing strategy for coping with the control of stepping on uneven terrain. Both congruent results in the anticipatory and reactive adjustments indicate that a simple strategy based on the conservation of energy may be expressed within the neural control pathways. The current version of the manuscript could benefit from the clarification of the study methodology. The development of computational tools supplemented with experimental validation is one of the most effective methods to achieve holistic validity of conclusions and to provide an accurate path to reproducibility and applications.

  5. eLife

    Reviewer #2 (Public Review):

    The authors evaluated whether their previously published model-based predictions of strategies to take an uneven step during walking agree with new experimental observations. Predictions were obtained under the assumption of optimal control based on a simple mechanical model of walking (rimless wheel). The optimality criterion was minimization of mechanical work. Experimental observations supported the following key model outcomes: (1) compensation steps occurring around the uneven step (as opposed to either after or before), (2) pattern of speed fluctuations before and after the uneven step, (3) scaling of speed fluctuations with gait speed. The paper thereby provides additional support for the optimal control hypothesis. The claim that 'humans compensate with an anticipatory pattern of forward speed adjustments, with a criterion of minimizing mechanical energy input' might be somewhat strong, given that the model relied on a set of limiting assumptions (see also below), reasonable alternative modeling assumptions have not been tested, and only a subset of the model predictions published earlier have been evaluated. The conclusions of the paper could be strengthened by:

    1. demonstrating that the predictions also hold for a model with variable step length;

    2. demonstrating that optimal control also predicts no time lost due to stepping up as compared to walking on even terrain;

    3. demonstrating that the number of compensation steps N that minimizes work corresponds to the observed number of compensation steps;

    4. demonstrating that minimal work leads to better agreement between simulations and observations than other plausible optimality criteria;

    5. demonstrating that the predicted dependence of speed fluctuations on step height is in agreement with experimental observations.

  6. eLife

    Reviewer #3 (Public Review):

    Summary. This is an elegant study on predicting and explaining human locomotor choices via optimality principles. The authors find that the humans exhibit stereotypical speed fluctuations when encountering an up or down step in their path, and they argue that the qualitative aspects of these speed fluctuations can be captured by a simple model minimizing energy over the whole walking task. This article adds to the growing literature on predicting human behavior via energy or other optimality, including transient non-steady state behavior.

  7. preLights

    Excerpt

    Maintaining constant speed when walking on an uneven terrain may be possible by minimizing mechanical work. This is observed in a tri-phasic trajectory of speed adjustments by anticipating and using a feedforward approach to the step.

  8. Version published to 10.1101/2020.12.01.407023v2 on bioRxiv
  9. Version published to 10.1101/2020.12.01.407023v1 on bioRxiv