Research Papers

Foot Placement and Balance in 3D

[+] Author and Article Information
Matthew Millard

Department of Bioengineering,  Stanford University, Stanford, CA 94305mjhmilla@stanford.edu

John McPhee, Eric Kubica

Systems Design Engineering,  University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada

J. Comput. Nonlinear Dynam 7(2), 021015 (Jan 26, 2012) (14 pages) doi:10.1115/1.4005462 History: Received January 07, 2011; Revised November 13, 2011; Published January 26, 2012; Online January 26, 2012

Humans use carefully chosen step locations to restore their balance during locomotion and in response to perturbations. Understanding the relationship between foot placement and balance restoration is key to developing useful dynamic human balance diagnostic tests and balance rehabilitation treatments. The link between foot placement and balance restoration is studied in this paper using a simplified monopedal model that has a circular foot, coined the Euler pendulum. The Euler pendulum provides a convenient method of studying the stability properties of three-dimensional (3D) bipedal systems without the burden of large system equations typical of multibody systems. The Euler pendulum has unstable regions of its state-space that can be made to transition to a statically stable region using an appropriate foot placement location prior to contacting the ground. The planar foot placement estimator (FPE) method developed by Wight is extended in this work in order to find foot placement locations in 3D to balance the 3D Euler pendulum. Preliminary experimental data shows that the 3D foot placement estimator (3DFPE) location corresponds very well with human foot placement during walking, gait termination, and when landing from a jump. In addition, a sensitivity analysis revealed that the assumptions of the 3DFPE are reasonable for human movement. Metrics for bipedal instability and balance performance suggested in this work could be of practical significance for health care professionals.

Copyright © 2012 by American Society of Mechanical Engineers
Topics: Pendulums , Stability
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Grahic Jump Location
Figure 1

The 3DFPE calculates a location that will cause an unstable inverted pendulum (shown in black) to transition to a statically stable pose (shown in white). Photo by Muybridge [21].

Grahic Jump Location
Figure 2

The 3DFPE is useful for determining when a biped needs to take a step (or some other action) to stabilize itself (a) and when the center of pressure manipulations ((b) and (c)) are sufficient to stay upright. Photo by Muybridge [21].

Grahic Jump Location
Figure 3

Inverted pendulum parameters. A body with mass and inertia is held up by a massless rigid leg and disc-shaped foot. The ring is always touching the ground. Note that F→ is caused by contact and frictional forces while τ→R and τ→F are due to rolling resistance and spin friction, respectively.

Grahic Jump Location
Figure 4

The 3DOF Euler pendulum has a disc-shaped foot that is tilted relative to the plane at an angle of α about the 2̂ axis. The vector r→p/q rotates with angular velocity β· about the 1̂ axis. Note that frame q is a body-fixed frame centered on the COM of the pendulum.

Grahic Jump Location
Figure 5

Phase portraits of a human-sized Euler pendulum (a = 0.1 m, c = 1 m, m = 75 kg) over α and α·. Regions of stability are shown in white and light gray, while regions of instability are shown in dark gray. The regions of stability are defined in Secs. 33. The first, and to a lesser degree the second, regions of stability (below α = 0.1) are relatively large. The third region of stability (above α = 0.1) shrinks as θ· increases, vanishing in this case before θ· = 0.125 rad/s. The regions of stability increase in size as the rate of energy dissipation (due to rolling resistance and spin friction) increase. The solutions of the 3DFPE are illustrated with the diagonal black line (using the method presented in Sec. 5). Note that the contact location of the 3DFPE would balance the biped when θ· = 0, but not when θ· = 5.

Grahic Jump Location
Figure 6

The 3D foot placement estimator searches for a foot placement location for an unstable body (a) that causes the body to enter the third region of stability (b) and not exit (c).

Grahic Jump Location
Figure 7

The subject’s foot falls, COM and 3DFPE trajectories, and the 3DFPE and CAP locations (at the time of contact) are shown for walking, gait termination, and jumping tasks. The convex hull between the feet during double stance is shown in gray.



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