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Presented at NACOB 98:
North American
Congress
on Biomechanics
Canadian Society for Biomechanics -
American Society of Biomechanics
University of Waterloo
Waterloo, Ontario, Canada
August 14-18, 1998
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ACTIVE AND PASSIVE STABILIZATION OF LATERAL
BALANCE
DURING HUMAN WALKING
A. D. Kuo, C. E. Bauby
Dept. of Mechanical Engineering & Applied
Mechanics, University of Michigan
Ann Arbor, MI 48109-2125
INTRODUCTION
We developed a model of passive dynamic walking
incorporating lateral motion, and found that the
forward modes are stable while the lateral mode is
unstable. We hypothesized that human central
nervous system (CNS) must actively stabilize
lateral motion, but not necessarily forward motion.
As a simple test, we measured variability of foot
placement during natural gait for subjects walking
with eyes open and eyes closed, to see if lateral
variability is increased more than fore-aft
variability when eyes are closed, as would be
predicted by the hypothesis.
REVIEW AND THEORY
Balance is maintained during human walking through
the interaction of CNS control and body dynamics.
Several investigators (cf. McKinnon & Winter, 1993,
Redfern & Schumann, 1994) have hypothesized that
control of lateral balance is of particular
importance, based on evidence such as the high
incidence of sideways falls in the elderly (Hayes
et al., 1996). There is, however, little
understanding of which components of gait are
inherently stable, and which require active
control.
McGeer (1990) showed that a simple two-legged
mechanism can walk stably down a gentle slope with
no external control of energy input, suggesting
that the forward component of human walking may be
passively stable. We extended the passive dynamic
walking model to include lateral motion.
Figure 1. Three-dimensional
passive dynamic walking model. Left: Front view.
Right: View from right.
The three-dimensional passive dynamic walking model
consists of two legs with curved feet which are
geometrically modeled as sections of cylinders (see
Fig. 1). There are three degrees of freedom. The
stance and swing legs rotate about an axis through
the hips, with angles qstance and qswing measured
counter-clockwise from the upright position. The
stance leg also rotates laterally in the frontal
plane about another pin joint between the stance
foot and leg, whose axis runs in the fore-aft
direction when the machine is in the upright
position. This roll angle, , is measured
counter-clockwise from the upright position viewed
from the front. This system will act as two coupled
pendula, with the swing leg swinging forward until
it makes contact with the ground. Assuming a
perfectly inelastic collision and an instantaneous
transfer of weight from the trailing leg to the
leading leg, the states after impact are found
through conservation of angular momentum of the
entire mechanism about the point of impact (along
two axes running fore-aft and laterally), and of
the trailing leg about the hip (along an axis
through the hips). After impact, the trailing leg
becomes the new swing leg, and the leading leg
becomes the new stance leg. A necessary condition
for steady walking is that the system be capable of
a repetitive motion (limit cycle). The search for
the appropriate conditions (a fixed point) involves
the solution of a two-point boundary value problem.
We employed a simple first-order shooting method
search for the fixed point located at
double-support. The stability of the mechanism was
evaluated by forming a discrete linear
approximation of the nonlinear step-to-step
dynamics (PoincarŽ map). Stability of the
approximation is a test of local asymptotic
stability of the nonlinear system.
We found that the passive walking in three
dimensions is unstable, as indicated by the
magnitude of an eigenvalue of the discrete
step-to-step map exceeding unity (see Table 1). The
results show that the unstable mode is primarily
confined to the lateral states, meaning that the
forward motion remains passively stable as in the
planar model. We found that the unstable mode can
be stabilized through a variety of methods,
including small lateral adjustments to placement of
the stepping foot or lateral rotation of the trunk.
We hypothesize that in humans, the CNS must
therefore be concerned with lateral, but not
necessarily forward, stabilization.
| eigenvalues |
-33.335 |
-0.958 |
0.375 |
-0.025 |
-0.003 |
| roll angle |
0.682 |
-0.049 |
-0.008 |
-0.709 |
-0.323 |
| stance angle |
0.238 |
-0.866 |
-0.736 |
-0.009 |
0.352 |
| roll velocity |
0.673 |
0.015 |
0.012 |
0.702 |
0.333 |
| stance velocity |
0.160 |
0.403 |
0.607 |
0.023 |
-0.216 |
| swing velocity |
-0.001 |
-0.291 |
-0.300 |
0.066 |
-0.784 |
Table 1. Eigenvalues and eigenvectors of
step-to-step transition matrix (PoincarŽ map).
Components of associated mode are shown below each
eigenvalue.
PROCEDURES
A simple test of our hypothesis is to compare
relative placement of the feet while walking with
eyes open and with eyes closed. If the CNS actively
stabilizes lateral balance, loss of vision should
result in greater variability in lateral foot
placement. Because the forward walking modes appear
to be passively stable, the CNS need not active
control them, and loss of vision should result in
little or no changes in variability of forward foot
placement.
We measured lateral foot placement in the natural
gait of four normal adult subjects, aged 18-40.
Foot and other body segment kinematics were
measured using a Flock of Birds (Ascension
Technology Inc., VT) magnetic tracking system
mounted on a rolling cart. The cart was pushed
behind subjects who walked at a naturally selected
speed in a subjectively determined straight line.
The absolute location of the cart was measured
using two optical encoder wheels rolling on the
ground, making it possible to reconstruct absolute
position of the feet. When subjects walked with
eyes closed, their trajectory was guided by having
them follow a guide providing a voice cue by
speaking continuously. All subjects walked at least
100 contiguous steps in a trial.
Variability was computed by deriving the absolute
displacment between every two successive steps, and
subtracting the mean displacement. The sample
variance was computed for left-to-right and
right-to-left steps in the lateral and fore-aft
directions.
RESULTS
Each of the four subjects had increased variability
in lateral foot placement with eyes closed, in
comparison to fore-aft foot placement (see Fig. 2).
One subject had lower variability in fore-aft
placement with eyes closed, but still had greater
variability laterally.
Figure 2: Variance of foot
placement for four subjects, shown as difference
between eyes closed and eyes open values. Values
shown include lateral left-to-right and
right-to-left variability, followed by fore-aft
left-to-right and right-to-left variability. For
each subject, compare first two columns with second
two.
DISCUSSION
Preliminary results are consistent with our
hypothesis that lateral balance is actively
controlled by the CNS, and also imply that vision
plays a role in that control. There were also
smaller increases in variability in fore-aft
placement which may indicate a visual role in
forward modes as well, but these differences may be
due to the fact that subjects walked at a less
steady speed with eyes closed. The difference
between fore-aft and lateral variability does
suggest that the inherently stable passive dynamics
of the legs in the passive walking mechanism may
also be present in the human.
REFERENCES
MacKinnon CD & Winter DA (1993) J. Biomech 26:
633-44
Redfern MS, Schumann, T (1994) J. Biomech
27:1339-1346
Hayes WC et al. (1996) Bone 18: 77S-86S
McGeer T (1990) Int J Robot Res 9: 68-82
ACKNOWLEDGMENTS
This work was supported in part by NIH grant
1R29DC02312-01A1, the Whitaker Foundation, and NSF
grant IBN-9511814.
