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Human walking contains variability due to small intrinsic perturbations arising from sensory or motor noise, or to promote motor learning. We hypothesize that such stride-to-stride variability may increase the metabolic cost of walking over and above a perfectly periodic motion, and that neglecting such variability in simulations may mis-estimate the metabolic cost. Here, we quantify the metabolic estimation errors accrued by neglecting the stride-to-stride variability using human data and a musculoskeletal model by comparing the cost of multiple strides of walking and the cost of a perfectly periodic stride with averaged kinematics and kinetics. We find that using an averaged stride underestimates the cost by approximately 2.5%, whereas using a random stride may mis-estimate the cost positively or negatively by up to 15%, ignoring the contribution of measurement errors to the observed stride-to-stride variability. As a further illustration of the cost increase in a simpler dynamical context, we use a feedback-controlled inverted pendulum walking model to show that increasing the sensory or motor noise increases the overall metabolic cost, as well as the variability of stride-to-stride metabolic costs, as seen with the musculoskeletal simulations. Our work establishes the importance of accounting for stride-to-stride variability when estimating metabolic costs from motion. 

Abstract Human biomechanical data are often accompanied with measurement noise and behavioral variability. Errors due to such noise and variability are usually exaggerated by fewer trials or shorter trial durations and could be reduced using more trials or longer trial durations. Speeding up such data collection by lowering number of trials or trial duration, while improving the accuracy of statistical estimates, would be of particular interest in wearable robotics applications and when the human population studied is vulnerable (e.g., the elderly). Here, we propose the use of the James–Stein estimator (JSE) to improve statistical estimates with a given amount of data or reduce the amount of data needed for a given accuracy. The JSE is a shrinkage estimator that produces a uniform reduction in the summed squared errors when compared with the more familiar maximum likelihood estimator (MLE), simple averages, or other least squares regressions. When data from multiple human participants are available, an individual participant’s JSE can improve upon MLE by incorporating information from all participants, improving overall estimation accuracy on average. Here, we apply the JSE to multiple time series of kinematic and metabolic data from the following parameter estimation problems: foot placement control during level walking, energy expenditure during circle walking, and energy expenditure during resting. We show that the resulting estimates improve accuracy—that is, the James–Stein estimates have lower summed squared error from the ‘true’ value compared with more conventional estimates.