Optimal regulation of bipedal walking speed despite an unexpected bump in the road

Osman Darici*, Hakan Temeltas, Arthur D. Kuo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Bipedal locomotion may occur over imperfect surfaces with bumps or other features that disrupt steady gait. An unexpected bump in the road is generally expected to slow down most types of locomotion. On wheels, speed may be regained quite readily with “cruise control” performed in continuous time. But legged locomotion is less straightforward, because the stance leg may be under-actuated, and the continuous-time dynamics are periodically disrupted by discrete ground contact events. Those events may also afford good control opportunities, albeit subject to the delay between discrete opportunities. The regulation of walking speed should ideally use these opportunities to compensate for lost time, and with good economy if possible. However, the appropriate control strategy is unknown. Here we present how to restore speed and make up for time lost going over a bump in the road, through discrete, once-per-step control. We use a simple dynamic walking model to determine the optimal sequence of control actions—pushing off from the leg at the end of each stance phase—for fast response or best economy. A two-step, deadbeat sequence is the fastest possible response, and reasonably economical. Slower responses over more steps are more economical overall, but a bigger difference is that they demand considerably less peak power. A simple, reactive control strategy can thus compensate for an unexpected bump, with explicit trade-offs in time and work. Control of legged locomotion is not as straightforward as with wheels, but discrete control actions also allow for effective and economical reactions to imperfect terrain.

Original languageEnglish
Article numbere0204205
JournalPLoS ONE
Issue number9
Publication statusPublished - Sept 2018

Bibliographical note

Publisher Copyright:
© 2018 Darici et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


U.S. Department of Defense (W81XWH-09-2-0142), http://cdmrp.army.mil/Office of Naval Research (ETOWL), https://www.onr.navy.mi National Institutes of Health (AG0308), https://www.nih.gov/ Defense Advanced Research Projects Agency (M3 Atlas Program), https://www. darpa.mil/ The Dr. Benno Nigg Chair at University of Calgary The Canada Research Chair program, http://www.chairs-chaires.gc.ca/home-accueil-eng. aspx The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. This research was funded in part by the U.S. Department of Defense (W81XWH-09-2-0142), Office of Naval Research (ETOWL), National Institutes of Health (AG0308), Defense Advanced Research Projects Agency (M3 Atlas Program), the Dr. Benno Nigg Chair at University of Calgary, and the Canada Research Chair program.

FundersFunder number
National Institutes of HealthAG0308
U.S. Department of DefenseW81XWH-09-2-0142
Office of Naval Research
Defense Advanced Research Projects Agency
University of Calgary
Canada Research Chairs


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