Optimization of energy and time predicts dynamic speeds for human walking
Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual’s movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts dynamic speed vs. time trajectories with inverted U shapes. Model and human experiment (𝑁 = 10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster and dominated by steady-state time and effort. Individual-dependent vigor may be characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone may have similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs can predict transient, steady, and vigor-related aspects of walking.
Data (Carlisle and Kuo, 2023, https://github.com/kuo-lab/short_walk_experiment) and code (Kuo, 2023, https://github.com/kuo-lab/simplelocomotionmodel) for this study are in publicly-accessible archives.
Article and author information
Natural Sciences and Engineering Research Council of Canada (CRC Chair,Tier 1)
- Arthur D Kuo
Natural Sciences and Engineering Research Council of Canada (Discovery award)
- Arthur D Kuo
Dr. Benno Nigg Research Chair
- 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: Informed consent was provided by human participants according to University guidelines. Approval was granted by the Conjoint Health Research Ethics Board (CHREB) of University of Calgary, approval identifier REB21-1497.
- Gordon J Berman, Emory University, United States
- Received: July 17, 2022
- Preprint posted: July 18, 2022 (view preprint)
- Accepted: January 11, 2023
- Accepted Manuscript published: February 13, 2023 (version 1)
- Version of Record published: March 21, 2023 (version 2)
© 2023, Carlisle & 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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