IEEE GCCE 2022 1570820213

1	  2	  3	  4	  5	  6	  7	  8	  9	  10	  11	  12	  13	  14	  15	  16	  17	  18	  19	  20	  21	  22	  23	  24	  25	  26	  27	  28	  29	  30	  31	  32	  33	  34	  35	  36	  37	  38	  39	  40	  41	  42	  43	  44	  45	  46	  47	  48	  49	  50	  51	  52	  53	  54	  55	  56	  57	  60	  61	  62	  63	  64	  65	  Estimation of Mediolateral Gait Postural Stability
using Time-Series Pelvis Angular Velocities
Ziqi Liu, Tomohito Kuroda, Shogo Okamoto

Yasuhiro Akiyama

Department of Computer Science
Tokyo Metropolitan UniversityHino, Japan

Department of Mechanical Engineering and Robotics
Shinshu University
Ueda, Japan

Abstract—Gait stability indices play an important role inboth clinical and commercial applications and are effective forestimating an individual’s fall risk. In general, the computation ofgait stability indices requires motion-capture systems to measure
the positions and angles of multiple body segments. If the stability
indices can be estimated from the time-series data of a single bodysegment, they can be easier to access. We used principal motion
analysis to estimate the margin of stability, which is a popular
gait stability index, based on the time series of the angularvelocities of the pelvis during walking. The linear combinationof three principal motions could estimate the minimum marginof stability along the mediolateral direction with a correlation
coefﬁcient of 0.58. The angular velocities of the pelvis can beused to estimate gait stability independently or in conjunction
with other kinematic information.
Index Terms—Gait stability, pelvis, margin of stability, angularvelocity
Fig. 1. Mediolateral margin of stability from the frontal viewpoint. Posturalstability along the mediolateral direction during walking.

I. I NTRODUCTION
Gait stability indices are used to estimate the risk of falling
during normal or perturbed walking [1]. Several researchers
are trying to establish such indices to screen people withhigh fall risk or evaluate the effect of clinical intervention forpeople with walking disabilities. In this study, we focused on
the gait stability index called mediolateral margin of stability(MoS), which evaluates postural stability using kinematic
information [2].
The computation of the mediolateral MoS requires the timeseries positions of the center of the human body mass (CoM)
and two feet, that is, the measurements of at least three points
are required. The motivation of the present study is to estimate
the mediolateral MoS by using kinematic information of only
one point on the body such that a single inertial measurement
unit replaces motion capture systems for measuring multiple
body points or segments.
One challenging approach was performed by Iwasaki etal. [3], who estimated the minimum mediolateral MoS values
using the time-series of the triaxial velocity of the CoM
with a correlation coefﬁcient of 0.68 between the observed
and estimated mediolateral MoS values. They used principal
motion analysis [4]–[6] to link the mediolateral MoS and thevelocities of the CoM.
In this study, we estimated the minimum mediolateral MoS
values using principal motion analysis and the angular velocities of the pelvis, which is close to the CoM. Although Iwasaki/22/$31.00 ©2022 IEEEet al. [3] used CoM velocities to estimate MoS values, theangular velocities of the pelvis can be easily measured using
an inertial measurement unit. Hence, for practical applications,
it is important to investigate the effectiveness of pelvis angularvelocities in the estimation of MoS values.
II. M EDIOLATERAL M ARGIN OF S TABILITY (M O S)
As shown in Fig. 1, mediolateral MoS is deﬁned as thedistance between the extrapolated position of the CoM andthe boundary of the base of support (i.e., supporting feet) inthe mediolateral direction at any given instant t. This valueindicates the margin against falling in mediolateral direction.
The extrapolated CoM position xcom (t) is its prospective
position in the near future and is deﬁned asxcom (t) = com (t) +vcom (t)
,
ω

(1)

where com (t) and vcom (t) are the position and velocity of theCoM in mediolateral direction, respectively, and ω is computedas√gω=,(2)
l1782

where g is the gravitational acceleration, and l is the heightof the CoM from the ﬂoor in an upright body posture. The
mediolateral MoS is deﬁned as
mos = bos − xcom .

(3)

We used the minimum value of the mediolateral MoS during
the gait cycle. During normal gait, the mediolateral MoS has
a positive value, and its minimum values appear at approximately 10% and 60% of the gait cycles, which occur at theearly phases of the double stance periods [2]. The MoS values
can be computed for mediolateral and anterior directions. In
this study, we used only the mediolateral MoS. Kuroda et al.
explored the relationship between the mediolateral and anteriorMoSs [7].
III. M ETHODSFig. 2. First principal motion of pelvis angular velocity. Positive (negative)
load indicates that the angular velocity is larger (smaller) than the mean
angular velocity at the moment. Left heel contact is the 0% gait cycle.

A. Gait database
We used the dataset from the AIST Gait database [8], among
which the walking samples of 60 elderly people (30 healthy
women and men with a mean age ± standard deviation of67.6 ± 3.4) were used for this study. Participants walked on
a 10-meter straight line at their own comfortable speeds. Acamera-based motion capture system was used to localize thereﬂective markers attached to the participants at 200 Hz.
B. Principal motion analysis
Principal motion analysis is a supervised multivariate timeseries analysis [3]. It determines the base functions called principal motions such that their linear combination approximates
multivariate time-series samples. Typically, normal human gait
motions can be represented using two to three time-series
bases [3], [9]. The score of a principal motion indicates theextent to which a sample includes that principal motion, andthe scores are determined such that the variance between thescores and objective values is maximized for each principal
motion.
In this study, the objective value was the minimum valueof the mediolateral MoS in a stride sample, which consistedof two successive steps. The multivariate time-series are theangular velocities of the pelvis, as described in Section III-C.

computed the roll and yaw velocities of the line connecting theleft and right ASISs around the y-axis (forward direction) andthe z-axis (gravitational direction), respectively. We did not
use the pitch velocity because it is not considered importantin determining the mediolateral MoS.
IV. R ESULTS
We computed three principal motions, following [3]. As anexample, Fig. 2 shows the motion loads of yaw and roll velocities of the ﬁrst principal motion. The motion loads indicate theyaw and roll velocities of the sample in comparison with themean velocities. For example, the proﬁles of Fig. 2 are nearly
the opposite to those of the mean angular velocities. A sample
with a positive ﬁrst principal score includes relatively smaller
yaw and roll velocities during the gait cycle. That sample may
involve small gait motion.
We estimated the minimum mediolateral MoS values using
regression analysis, with the scores of the three principal
motions as explanatory variables. The correlation coefﬁcient
between the observed and estimated minimum mediolateral
MoS was 0.58. This correlation is slightly smaller than 0.68
reported in the study by Iwasaki et al. [3], where the MoS
values were estimated using triaxial CoM velocities.
V. C ONCLUSION

C. Yaw and roll velocities of pelvis
MoS is computed based on the translational motion of theCoM, which is located beneath the navel and above the pelvis.
Considering the use of an inertial measurement unit, the pelvis
is a potentially good segment to attach the measurement unit tobecause its bone features can be easily palpated. Furthermore,
the measurement unit can be ﬁrmly attached to the body part
because the area near the pelvis contains few muscle and fat
tissues. Hence, we used the yaw and roll angular velocitiesof the pelvis as the time-series postural data for the principal
motion analysis.
In this study, we did not use the inertial measurement unit.
Instead, the angular velocities of the pelvis were computed
using the coordinates of the two bone features of the pelvis:
the left and right anterior superior iliac spines (ASISs). We

The MoS is a popular gait stability index for indicating
fall risk. We estimated the minimum mediolateral MoS values using the temporal variations of the two-axial angularvelocities of the pelvis, considering the potential use of aninertial measurement unit to record human motion data. Noprevious research has attempted to estimate the MoS based on
the angular velocities of single-body segments. On performing
principal motion analysis, the estimated minimum MoS values
exhibited a moderate correlation of 0.58 with the observed
values. The conjunctive use of the velocities along the x,y, and z-directions and the roll, pitch, and yaw angularvelocities will increase the estimation accuracy of MoS values.
The combination of the translational and angular velocitiesof the pelvis may achieve a more accurate estimation than2783

either of the two types of velocities. Further, this study usedmotion data recorded by an optical motion capture to calculate
pelvis motions; however, the quality of motion information
are different between inertial measurement units and opticalmotion captures. Hence, our method needs to be tested byusing inertial measurement units in the future.
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