The strengths and weaknesses of inverted pendulum models of human walking

McGrath, MP; Howard, D; Baker, RJ

Abstract

An investigation into the kinematic and kinetic predictions of two ‘inverted pendulum’ (IP) models of
gait was undertaken. The first model consisted of a single leg, with anthropometrically correct mass and
moment of inertia, and a point mass at the hip representing the rest of the body. A second model
incorporating the physiological extension of a head–arms–trunk (HAT) segment, held upright by an
actuated hip moment, was developed for comparison. Simulations were performed, using both models,
and quantitatively compared with empirical gait data. There was little difference between the two
models’ predictions of kinematics and ground reaction force (GRF). The models agreed well with
empirical data through mid-stance (20–40% of the gait cycle) suggesting that IP models adequately
simulate this phase (mean error less than one standard deviation). IP models are not cyclic, however, and
cannot adequately simulate double support and step-to-step transition. This is because the forces under
both legs augment each other during double support to increase the vertical GRF. The incorporation of an
actuated hip joint was the most novel change and added a new dimension to the classic IP model. The hip
moment curve produced was similar to those measured during experimental walking trials. As a result, it
was interpreted that the primary role of the hip musculature in stance is to keep the HAT upright. Careful
consideration of the differences between the models throws light on what the different terms within the
GRF equation truly represent.

Citation

McGrath, M., Howard, D., & Baker, R. (2015). The strengths and weaknesses of inverted pendulum models of human walking. Gait & Posture, 41(2), 389-394. https://doi.org/10.1016/j.gaitpost.2014.10.023

• Journal Article Type: Article
• Acceptance Date: Oct 22, 2014
• Online Publication Date: Oct 30, 2014
• Publication Date: Feb 1, 2015
• Deposit Date: Jun 17, 2015
• Publicly Available Date: Apr 5, 2016
• Journal: Gait & Posture
• Print ISSN: 0966-6362
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 41
• Issue: 2
• Pages: 389-394
• DOI: https://doi.org/10.1016/j.gaitpost.2014.10.023
• Publisher URL: http://dx.doi.org/10.1016/j.gaitpost.2014.10.023
• Related Public URLs: http://www.sciencedirect.com/science/journal/09666362