Redirection of center-of-mass velocity during the step-to-step transition of human walking

Abstract

SUMMARYSimple dynamic walking models based on the inverted pendulum predict that the human body's center of mass (COM) moves along an arc during each step, with substantial work performed to redirect the COM velocity in the step-to-step transition between arcs. But humans do not keep the stance leg perfectly straight and need not redirect their COM velocity precisely as predicted. We therefore tested a pendulum-based model against a wide range of human walking data. We examined COM velocity and work data from normal human subjects (N=10) walking at 24 combinations of speed (0.75 to 2.0 m s -1 ) and step length. These were compared against model predictions for the angular redirection of COM velocity and the work performed on the COM during redirection. We found that the COM is redirected through angular changes increasing approximately linearly with step length (R 2 =0.68), with COM work increasing with the squared product of walking speed and step length (R 2 =0.82), roughly in accordance with a simple dynamic walking model. This model cannot, however, predict the duration of COM redirection, which we quantified with two empirical measures, one based on angular COM redirection and the other on work. Both indicate that the step-to-step transition begins before and ends after double support and lasts about twice as long -approximately 20-27% of a stride. Although a rigid leg model can predict trends in COM velocity and work, the non-rigid human leg performs the step-to-step transition over a duration considerably exceeding that of double support.

A unified perspective on ankle push-off in human walking

“…It is worth noting that some such explanations have been proposed, but none have been conclusively demonstrated. For instance, the push-off-collision hypothesis (Adamczyk and Kuo, 2009;Kuo, 2002;Kuo et al, 2005;Ruina et al, 2005) has led to a variety of empirical observations, some in apparent support of this hypothesis (e.g. Adamczyk and Kuo, 2015;Houdijk et al, 2009;Huang et al, 2015;Jackson and Collins, 2015;Segal et al, 2012;Soo and Donelan, 2012;van Engelen et al, 2010) and some in apparent contradiction (e.g.…”

“…Dynamic walkers are mechanical systems (or models), often devoid of actuators or controllers, which move dynamically in a stable cyclic motion that resembles human gait (McGeer, 1990). Dynamic walking simulations indicate that push-off by the trailing limb can preemptively accelerate the body's COM upward and forward during the step-to-step transition (Adamczyk and Kuo, 2009;Bregman et al, 2011;Kuo, 2002;Zelik et al, 2014). By redirecting the COM velocity, this push-off can reduce the collisional energy losses associated with landing on the contralateral limb.…”

The strengths and weaknesses of inverted pendulum models of human walking

“…The vertical component of CM velocity is upwards at the start of the step and downwards at the end. A number of studies have addressed the step-to-step transition issue [5,[9][10][11][27][28][29] assuming that it leads to a collision during which energy is lost. The empirical data, however, particularly for the vertical component of the CM velocity, show considerable departures from model predictions over the first and last quarters of the step resulting in minimal vertical velocity at the start and end of the step.…”

The critical phase for visual control of human walking over complex terrain

“…10). Ground contact by the swinging foot marks the end of the single-support phase and the beginning of the double-support phase, during which the COM must be redirected from a downward trajectory to the upward trajectory it will need for the coming step (11). Upon ground contact, the force applied by the leading leg has a horizontal component opposite to the direction of motion of the COM; that is, the leading leg performs negative work on the COM.…”