Received April 14, 2022, accepted May 11, 2022. Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2022.3175409

Gait Stability Index Built by Kinematic
Information Consistent With the Margin of
Stability Along the Mediolateral Direction
TOMOYUKI IWASAKI1 , SHOGO OKAMOTOYASUHIRO AKIYAMA 3 , (Member, IEEE),AND YOJI YAMADA1 , (Member, IEEE)

1,2 , (Member, IEEE),

1 Department of Mechanical Systems, Nagoya University, Nagoya, Aichi 464-0813 Japan
2 Department of Computer Sciences, Tokyo Metropolitan University, Hino, Tokyo 191-0065, Japan
3 Department of Mechanical Engineering and Robotics, Shinshu University, Ueda, Nagano 386-0018, Japan

Corresponding author: Shogo Okamoto (okamotos@tmu.ac.jp)
This work was supported in part by Ministry of Education, Culture, Sports, Science and Technology (MEXT) KAKENHI under Grant
19K21584.

ABSTRACT Gait stability indices that can be easily measured and computed are required in both clinicaland commercial applications. We established a novel gait stability index based on kinematic informationthat was substantially correlated with the margin of stability (MoS); a popular kinetic stability index. The
novel index was computed using the time-series of triaxial velocities from the human body mass center. The
partial least squares regression method was extended to time-series data and applied to the velocity series
to compute the principal motions. These motions were elementary motions constructing the gait motions,and their magnitudes in each gait motion were correlated with the MoS. Gait data from 60 participants(30 males and 30 females; age: 67.6 ± 3.4 years (mean and standard deviation); height: 159.6 ± 7.6 cm;
weight: 60.6 ± 9.3 kg) were analyzed. The combination of three principal motions exhibited a moderatecorrelation with the minimum MoS values in the mediolateral direction at r = 0.68, suggesting that thenovel kinematic index can be used as an easy-to-access alternative to the MoS. The established kinematic
index can be a substitute for the margin of stability.
INDEX TERMS Gait stability, partial least squares regression, principal motion analysis, margin of stability.

I. INTRODUCTION

To date, gait stability and stable walking have been intensively studied by many researchers. It has been shown thatstable gait relies on gait parameters comprising stride length
and walking speed [1]–[6]. In particular, gait stability indices
are useful in judging the risk of falling [7], [8].
There exist two categories of gait stability indices:
kinetic and kinematic. Kinetic indices are computed basedon mechanical dynamics and indicate physical resistancetowards falls; however, they require the positions and angles
of multiple human body parts to be measured, and groundreaction forces are necessary for some kinetic indices. Therefore, the measurement of kinetic indices requires laboratory
settings. The margin of stability (MoS) [9]–[11], feasible
The associate editor coordinating the review of this manuscript andapproving it for publication was Kang Li.
VOLUME 10, 2022

stability region [12], and centroidal momentum [13]1 areexamples of kinetic gait stability indices. Meanwhile, kinematic indices are typically computed using kinematic information from few body parts, which can be easily acquired
through inertial measurements. However, kinematic indices
may not be directly related to kinetic stability indices [6],[12], [14]–[16]. For example, the maximum Lyapunov exponent [17], [18], maximum Floquet multiplier [19], and harmonic ratios [20], [21] are popular kinematic indices.
Kinematic stability indices can be invaluable for clinicaland commercial applications [22], [23] because of their relative ease of measurement outside laboratory environments;
hence, many studies have compared kinetic and kinematic
indices. For example, the short-term Lyapunov exponents
and minimum MoS values in the anterior and mediolateral
1 This index is often applied to bipedal robots.

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

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T. Iwasaki et al.: Gait Stability Index Built by Kinematic Information Consistent

directions were found to exhibit different properties [6], [14]and do not exhibit substantial correlation [15]. In anotherstudy [12], several kinetic and kinematic indices including
the MoS and Lyapunov exponent were compared to predict
falls, and it was concluded that these indices exhibited distinct
properties. In previous approaches, major kinetic and kinematic indices were compared. However, we will employ a different approach by constructing a novel kinematic index thatexhibits a correlation with a major kinetic stability index. One
objective of this study is to find to what extent the value ofa kinetic stability index based on force information including
ground reaction forces can be estimated from motion information including the velocities of body segments. Kinematic
indices can be a partial substitute for kinetic indices because
kinematics and kinetics are physically consistent with eachother.
We utilize the MoS as a referential kinetic index and establish a novel kinematic stability index such that the kinetic
and kinematic indices exhibit a correlation. This kinematic
index is based on the time-series of triaxial velocities atthe center of gravity of a human body. To construct the
proposed index, a partial least squares (PLS) regression [24]is used to compute the principal motion analysis (PMA)[25]–[27]. The PMA decomposes a sample of a multivariate
time-series into several principal motions (which are independent multivariate time-series) to construct a gait motion.
In the case of normal gait, two to three types of principal
motions largely represent the variations of the motion sample set [25], [27], [28]. The combination of PLS and PMA
enables us to compute principal motions whose scores exhibit
a correlation with the MoS values and their meaning canbe interpreted by reviewing the principal motions. In ourprevious work, we applied this method to the MoS in theforward direction for a small sample of 20 people [29]. In thisstudy, we constructed a kinematic gait stability index that
correlated with the MoS in the mediolateral direction andenhanced the validity of the index by using the gait dataof 60 elderly subjects and a cross-validation method. The
number of participants and cross-validation are important
aspects to investigate the generality of the new stability index.
Further, the principal motions were compared with representative gait parameters to validate their meanings.
II. KINETIC GAIT STABILITY INDEX: MARGIN
OF STABILITY

The MoS [9] is a major kinetic index for gait stability withgood validity [7], [31] and experimental demonstration [32].
A larger MoS value indicates a greater resistance to falls
during normal walking. In the present study, we evaluatedthe MoS values along the mediolateral direction of participants on the basis of the extrapolation of the center of mass
(XCoM) [9]. As shown in Fig. 1 (a), the human body was
regarded as an inverted pendulum with a constant leg length l
in a coordinate space defined by the x-axis (right for positive),
y-axis (anterior for positive), and z-axis (upward for positive).
The coordinate vector of XCoM (xcom ) indicates the limits
2

FIGURE 1. Margin of stability (MoS) value and 100% gait cycle.
(a) Definition of the mediolateral MoS. x0com is the point corresponding toxcom on the ground. bos is the coordinate of the support base edge. mosis computed using bos and x0com . (b) Example of the variations in the baseof stability and center of mass in the x-direction (bos , xcom ). The smallest
MoS value can be observed at approximately ∼10% and ∼60% of the gait
cycle. (c) Gait cycle starting from the left-heel contact (0%) and ending at
the following left-heel contact (100%)). Modified from [30].

of the center of mass (CoM) movement at each moment.
If the XCoM is outside the end of the base of support (BoS),a fall will be induced unless a new leading foot touches theground. Since the MoS indicates walking stability at each
instant, it is also used for evaluating perturbation responses
during walking [33], [34] and walking stability in people withmusculoskeletal abnormalities [35], [36].
The position and velocity vectors of the CoM at any
given moment are com and vcom , respectively. xcom is thendefined asxcom = com +

vcom
,
ω

(1)
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T. Iwasaki et al.: Gait Stability Index Built by Kinematic Information Consistentwhere ω is the natural frequency of the pendulum. Here, ω is
calculated as
r
g
ω=
,
(2)
l
where g is the gravitational acceleration and l is the distance from the floor to the CoM in an upright posturefrom [6]. Details of the determination of the CoM position are
described in Section III. As x0com is the point corresponding
to xcom on the ground, the MoS (mos ) is the distance vector
between the end of the BoS (bos ) and x0com :mos = bos − x0com .

(3)

Following earlier studies [6], [9]–[11], we use the minimum
absolute value of mos within the period of a gait cycle as thestability index. The minimum MoS is observed during the
double support phases at approximately 10% or 60% of the
gait cycle, as shown in Fig. 1 (b).

method that extends PMA to find the principal motions whosescores (such as magnitudes) exhibit correlations with the
MoS. The new kinematic stability index is then defined using
a linear summation of several principal motion scores.
Each axial component of the CoM velocities was discretized every 1% of the gait cycle and then normalized(z-score) among all trials. The minimum MoS values werealso normalized among all trials. The samples whose normalized minimum MoS values were greater than 2.58 or
smaller than −2.58 were excluded as outliers. At the k-th trial(k ∈ {1, . . . , k 0 }) for direction j (∈ {x, y, z}), the time-series
vector of the CoM velocity vcom,j,k (∈ R101×1 ) was definedas comprising 101 discretized instances (one value for eachpercentage of the gait cycle):vcom,j,k = (vcom,j,k,1 , vcom,j,k,2 , . . . , vcom,j,k,101 )T .

Using this vector, a column vector bk (∈ R303×1 ) is extended
as follows:bk = (vcom,x,k T , vcom,y,k T , vcom,z,k T )T .

III. ANALYSIS OF GAIT MOTIONS

We analyzed a database of gait motion [38]. The analyzed
data included 60 elderly adults (mean age: 67.6 ± 3.4(standard deviation) years; height: 159.6 ± 7.6 cm; weight:
60.6 ± 9.3 kg) without any gait-related abnormalities
declared. Participants walked on a 10 m line, and their two
steps near the center of the course were used for the analysis
described below. The comfortable gait speed was selected,
and five trials were analyzed per participant. The whole-body
motion of the participants was measured using a camerabased motion capture system with a sampling frequencyof 200 Hz. A Butterworth low-pass filter with a cutoff frequency of 6 Hz was applied to the marker positions. The
measurement details are elaborated in [38].
We defined a gait cycle as the steps starting from left-heelcontact to the next left-heel contact, as shown in Fig. 1 (c).
We analyzed three axial CoM velocities, which were computed by differentiating the CoM position for each axis. The
CoM position was defined as the center of the sacral spine
and the two anterior superior iliac spines.
We calculated various gait parameters to understandthe physical meanings of the principal motions that wereobtained. The definitions of each gait parameter are presented
in Table 1. Note that these gait parameters are not necessary
to compute the kinematic index; however, they were used
to discuss the validity of the kinematic index established in
the present study. The parameters were calculated by using
software built in [37].
IV. GAIT STABILITY INDEX BASED ON
KINEMATIC INFORMATION

We established a kinematic gait stability index that correlates with the kinetic gait stability index (MoS) using thetime series of three axial CoM velocities. For this purpose,
we adapted PLS [24] to PMA. In PMA, each gait motion isapproximated using a linear summation of several principal
motions, whereas PLS is a supervised multivariate analysis
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(4)

(5)

The discrete time-series of all of the gait motions are0
expressed by the matrix B (∈ Rk ×303 ) as follows:
B = (b1 , . . . , bk , . . . , bk 0 )T ,(6)

where k 0 is the number of gait samples. k 0 = 291(60 participants × 5 trials − 9 outliers) in this study.
The procedure of the PLS is now shown. The model
formulas of the PLS aresXt l pTl + E
(7)
B=
l=1

and
mos,min =sX

ql t l + e.

(8)

l=1
0

Here, mos,min (∈ Rk ×1 ) stores the minimum MoS values
computed from each of the k 0 trials. s is the number of0
principal motions, t l (∈ Rk ×1 ) is the score of all samples
for the l-th principal motion, pl (∈ R303×1 ) is the load ofthe l-th principal motion, ql is the coefficient for the scoresof the l-th principal motion, and E and e are the regression
errors of B and mos,min , respectively. Based on these formulas,
we determined t 1 such that the covariance with mos,min is
maximized:!
BT mos,min.
(9)t1 = BkBT mos,min k
Here, k k represents the L 2 norm. p1 and q1 are determinedsuch that the sum of the squares of the elements of E and e
are minimized, respectively.
p1 =
q1 =

BT t 1
t T1 t 1
mTos,min t 1
t T1 t 1

(10)
(11)
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T. Iwasaki et al.: Gait Stability Index Built by Kinematic Information Consistent

TABLE 1. Definition of the gait parameters modified from [37]. The joint angles were determined at each instance of the toe-off and heel-contact. These
gait parameters were computed to interpret the principal motions. CoM refers to center of mass.

Next, we determined the scores of the second principal
motions t 2 , such that the covariance with mos,min − q1 t 1 ismaximized. For this computation, matrix B and mos,min are
updated as follows:
mos,min,2 = mos,min − q1 t 1 ,B2 = B − t 1 pT1 .

(12)
(13)

TABLE 2. (a) Correlation coefficients between the principal motion scoresand minimum MoS values in the lateral direction. ** and *** represent a
statistical significance at p < 0.01 and p < 0.001, respectively.
(b) Correlation coefficient between the estimated and observed minimum
MoS values by 2-fold cross-validation. All participants were randomlyclassified into two groups. When the training data were group 1, those forgroup 2 were tested and vice versa.

Then, following (9)–(11), t 2 , p2 and q2 are computed by using
B2 and mos,min,2 . In general, the l-th principal motion vector
pl and corresponding score vector t l are computed by using
mos,min,l = mos,min −l−1
X

qu t u ,

(14)

u=1

Bl = B −l−1
Xt u pTu .

(15)

u=1

This process was repeated to compute the third and successive
principal motions.
Using the s principal motions, mos,min was predicted asm̂os,min =sXql t l .

(16)

l=1

We determined s on the basis of the two-fold cross validationsuch that the correlation between the observed and estimatedmos,min became maximized. For this, the sixty participants
were randomly divided into two groups: learning and testing.
Each group included 15 males and 15 females.
V. RESULTS

Table 2 (a) shows the correlation coefficients between thescores of the first to fifth principal motions and the minimum
MoS. The correlation coefficients ranged from 0.58 to 0.10.
Table 2 (b) shows the results of the two-fold cross-validation.
4

These values are the correlations between the observed andestimated MoS values. The MoS was estimated as a linear
sum of the scores based on the multiple principal motions
computed from the learning group. The correlation between
the estimated and observed MoS was the largest when thethree principal motions were included in the analysis. Therefore, we decided to use motions up until the third principal
motion (s = 3).
The estimated MoS for the 60 participants was calculatedusing the linear combination of the three principal motions:m̂os,min = 0.09t 1 + 0.02t 2 + 0.10t 3 .

(17)

Fig. 2 shows a scatter plot of the estimated and observed
values of the minimum MoS. The correlation coefficient
was 0.68 (t(289) = 15.77, p < 0.001, two-tailed t-test),
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T. Iwasaki et al.: Gait Stability Index Built by Kinematic Information Consistent

FIGURE 2. Scatter plot of minimum normalized MoS values (horizontal)
and their estimation using principal motions (vertical).

indicating that our index correlates with the minimum valueof the MoS.
VI. DISCUSSION
A. SEMANTIC VALIDITY OF PRINCIPAL MOTIONSAs described in Section V, the new kinematic index shows
concurrent validity regarding the correlation coefficient withthe minimum MoS, but the semantic validity of this index
is also important. The validity of the measurement index is
discussed from multiple viewpoints, including the concurrent
and content validity [39]. Regarding the content validity,
semantic aspects of the index are discussed. In this section,
we interpret and discuss the meanings of the time-series characteristics of the principal motions and discuss their validity.
Fig. 3 (a) shows the mean time-series variation of the CoM
velocity. Figs. 3 (b)–(d) show the content of the first to thirdprincipal motion vectors. When the value of the principal
motion is zero at a moment, the CoM velocity is the meanvalue among all samples due to the normalization. A positive
value for the principal motion indicates that the CoM velocity
is larger than the mean value. Table 3 shows the correlation
coefficients between the principal motion scores and gaitparameters, and these can be used to interpret the principal
motion.
1) FIRST PRINCIPAL MOTION

For the first principal motion, Fig. 3 (b) shows that thevelocity in the x-axis is large (positive) from the middle of
the right swinging phase to the right stance phase (30%–80%of the gait cycle), and small (negative) from the middle of theleft swinging phase to the left stance phase (80%–30%). This
is in the same phase as the average CoM motion. According toTable 3, the scores of the first principal motion and the step
width are positively correlated (r = 0.43) indicating that a
gait with a large step width involves a greater mediolateral
CoM motion.
In the y-axis, the velocity was large (positive) during
the entire gait cycle, indicating a fast gait. Table 3 showsthat the first principal motion scores are positively correlated
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FIGURE 3. Mean center of motion (CoM) velocity and obtained principal
motions. (a) Mean CoM velocity. (b)–(d) Substance of each principal
motion. (b) 1st principal motion. (c) 2nd principal motion.
(d) 3rd principal motion. A positive or negative load value at a momentmeans that the velocity is larger or smaller than the mean velocity in alltrials, respectively.

with the step width and length, gait speed, and CoM positionin the forward direction, and negatively correlated with thecadence and upper body pitch angle. A gait with a large firstprincipal motion score can be a fast walking motion with alarge step width and length, small cadence, and forward leanof the upper body.
The positive correlation between the first principal motion
scores and minimum MoS indicates that the gait is themost stable in terms of the MoS if the gait is performed
as described above. It is natural that a larger step width
will result in a larger fall margin in the lateral direction.
However, it is unclear whether other gait parameters, such as
the upper body angle and gait speed, directly affect the MoS.
In terms of the effect of the gait speed on the lateral MoS,
earlier studies are not fully consistent [6], [11], [40], [41].
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T. Iwasaki et al.: Gait Stability Index Built by Kinematic Information Consistent

TABLE 3. Correlation coefficients between the principal motion scoresand gait parameters. Only significant values (p < 0.05) are shown. PM:
principal motion, CoM: center of mass, HC: heel contact, TO: toe off.

in the mediolateral MoS. In contrast, for the second principal
motion, the scores exhibited a negative correlation coefficientwith the gait speed, and slower walking was more stable thanfaster. Gait samples with large scores of the second principal
motion involve greater cadences and small stride lengths
that may contribute to increase in the MoS. Earlier studies[6], [11] also reported that gaits with high cadences tend
to exhibit large mediolateral MoS. If only the relationshipbetween the gait speed and mediolateral MoS is considered,
the two principal motions contradict each other. Note thatolder people tend to adopt large step widths and small stride
lengths for lateral stabilization, which is a combination of thefirst and second principal motions [43].
3) THIRD PRINCIPAL MOTION

For example, Alamoudi et al. [11] and Gill et al. [40] reported positive correlation coefficients between the gait speed
and lateral MoS, whereas little correlation was found in[6], [41]. Caderby et al. [41] thought that the increase in step
width associated with an increase in gait speed is a postureadjustment to remain the lateral MoS. Following this idea, theincrease in step width and not in gait speed directly influences
the lateral MoS. The step width may become greater at gait
speeds higher than those preferred by individuals [42].
2) SECOND PRINCIPAL MOTION

Fig. 3 (c), which displays the second principal motion, showsthat the velocity in the y-axis was small (negative) for theentire gait cycle. However, the CoM velocity in the z-axis wasat its minimum at toe-off (∼15% and ∼65% of the gait cycle)
and maximum before heel contact (∼40% and ∼90% of the
gait cycle), which is the opposite of a normal CoM motion.
The second principal motion canceled a change in the velocity
in the vertical direction.
According to Table 3, the second principal motion scores
were negatively correlated with step length and walking
speed, and positively correlated with cadence. The second
principal motion can be interpreted as a slow motion witha large cadence and small step. Joint angles such the thighangles at heel-contact and toe-off also present the featuresof small steps. When the step length is small, the CoM
movement in the lateral direction is small [41], [42]. In suchcases, XCoM and CoM are relatively similar, and the MoS
is large. Therefore, the gait motions with large scores for thesecond principal motion exhibit reasonably large MoS values.
Interestingly, the correlation between the principal motion
scores and gait speed, and the scores and cadence, were
opposite in the first and second principal motions. For the firstprincipal motion, the scores exhibited a positive correlation
coefficient with the gait speed, and faster walking was morestable than slower. As discussed above, greater step widths
accompanied by greater speeds may contribute to the increase
6

Fig. 3 (d) shows the loads of the third principal motion. In thefirst half of the gait cycle (0%–60%), the velocity along thex-axis is positive, while in the second half it is negative. This
profile corresponds to the differential curve of the average
x-velocity, as shown in Fig. 3 (a). The large score of the thirdprincipal motion leads to the forward phase of the x-velocity.
The z-velocity is at its maximum at the instance of toeoff and minimum around the instance of heel-contact, which
is close to the characteristics of the average motion of thez-velocity. This indicates a large CoM motion along thevertical direction and large step lengths.
As listed in Table 3, the scores of the third principal motion
exhibit positive correlation coefficients with the step lengths,
kick-up angles, and minimum foot clearance. Furthermore,a negative correlation was exhibited with the lower thighangle at the instance of toe-off. These correlations indicatethat the motions with large third principal motion scores
involve an intense kick at the instance of toe-off and large
step lengths. However, it is difficult to explain how thesecharacteristics pertain to the MoS values.
B. LIMITATIONS OF THE STUDY

Here, we address the limitations and concerns of the present
study. As mentioned in Section I, many representative gaitstability indices do not substantially correlate with eachother [6], [12], [14]–[16], [44]–[47]. This is because eachindex evaluates a different aspect of gait. However, the index
based on the principal motion score showed a moderate correlation with the MoS, possibly because both indices are basedon the CoM velocity. PMA and PLS can be applied to thetime-series of other body parts. It remains to be investigatedwhich body part’s velocity or acceleration information is bestin terms of the correlation with MoS. Further, it would bepossible to increase the correlation between the MoS andkinematic index based on the principal motions by employing the velocities of multiple body segments. Although it isunderstandable how the first and second principal motions
may increase the MoS values, it should be noted that thecharacteristics of the principal motions are only correlatedwith the MoS values and are not necessarily causally related.
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T. Iwasaki et al.: Gait Stability Index Built by Kinematic Information Consistent

We estimated the position of the CoM from the marker
positions measured using a motion capture system and differentiated it to obtain the CoM velocity. If we use the CoM
velocity measured by an inertial measurement unit, we may
not be able to obtain the same results that were obtained inthis study because of the influence of the sampling rate andthe integration of the error. Our method should be tested usinginertial measurement units because methods to assess gaitstability and performance using these units are currently popular, as indicated by previous studies [16], [45], [48]–[51],and have promising accessibility.
Additionally, fall risks or abnormal walking may be more
related to gait variability than to mean gait features [8],[22], [52]–[55]. For example, the variability of minimum footclearance may be used to differentiate between those with andwithout trip-related histories [54] and the variability of step
width can be related to fall history [55]. Our proposed method
is not for evaluating the variability of gait patterns; instead,
it evaluates the stability of individual strides.
The gait database we used in the present study [38]included only healthy participants. To determine the clinicalvalidity of the kinematic index developed in this study, it isimportant to test individuals with a history of falls and thosedeemed at risk by clinical experts. Finding or establishingstability indices that can accurately estimate fall risks is a
primary concern among the researchers.
VII. CONCLUSION

We developed a novel kinematic gait stability index thatis consistent with the MoS in the lateral direction. Many
earlier studies reported that no substantial correlation existed
between currently used kinetic and kinematic gait stability
indices. We applied PLS to PMA and statistically constructed
an index that was correlated with the minimum value of the
MoS using time-series data of the CoM velocity. Based on
the three principal motions, the constructed index showeda moderate correlation coefficient of 0.68 with the MoS.
Although this correlation coefficient is not very high, it can befurther improved by involving the kinematic information ofmultiple body segments, among other methods. Furthermore,part of the principal motions can be reasonably linked withthe fall margin. These results suggest that this gait stability
index can be an easy-to-access alternative to the MoS.
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TOMOYUKI IWASAKI received the B.S. and M.S.
degrees in mechanical engineering from Nagoya
University, in 2019 and 2021, respectively. He iscurrently a Mechanical Engineer. His researchinterest includes human motion analysis.

SHOGO OKAMOTO (Member, IEEE) received
the Ph.D. degree in information sciences fromTohoku University, in 2010. From 2010 to 2021,
he was with Nagoya University as an AssistantProfessor and an Associate Professor. He is currently an Associate Professor with the Departmentof Computer Sciences, Tokyo Metropolitan University. His research interests include haptics,
assistive robotics, human-centered informatics,
and affective computing.

YASUHIRO AKIYAMA (Member, IEEE) received
the B.E. degree in engineering from the Tokyo
Institute of Technology, Tokyo, Japan, in 2006, andthe M.S. and Ph.D. degrees in engineering fromThe University of Tokyo, Tokyo, in 2008 and 2011,
respectively. He was an Assistant Professor with
the Department of Mechanical Systems, Nagoya
University, until 2022. He is currently an Associate Professor with the Department of Mechanical Engineering and Robotics, Shinshu University,
Japan. His main research interests include mechanical safety, human–robot
interaction, and biomechanics.

YOJI YAMADA (Member, IEEE) received the
Ph.D. degree from the Tokyo Institute of Technology. Since 1983, he has been at the Toyota Technological Institute, Nagoya, Japan. In 2004, he joined
the National Institute of Advanced Industrial Science and Technology, as a Leader of the Safety
Intelligence Research Group. In 2009, he joined
the Department of Mechanical Systems Engineering, Graduate School of Engineering, Nagoya University as a Professor.

VOLUME 10, 2022