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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
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Novel approach to analyze all-roundkinematic stability during curving steps
YASUHIRO AKIYAMA1 , (Member, IEEE), YOSUKE KUBOKI1 , SHOGO OKAMOTO2 ,(MEMBER, IEEE), AND YOJI YAMADA.1 ,(Member, IEEE)

1
2

Department of Mechanical Systems Engineering, Nagoya University, Aichi Japan
Department of Computer Science, Tokyo Metropolitan University, Tokyo Japan

Corresponding author: Yasuhiro Akiyama (e-mail: akiyama_yasuhiro@shinshu-u.ac.jp).
We thank the support by JSPS KAKENHI Grant Number 17K01293 and the support of our group members, Yusuke Fukui and Takuma
Igami.

ABSTRACT From the viewpoint of the stability of biped walking, the stability for both anteroposterior,lateral, and diagonal directions should be considered owing to the frequent occurrence of turning andcurving motions in the daily environment. In this study, a measure called the all-round margin of stability(MoS) is proposed to evaluate the kinematic balance of the all-round direction. A curving experiment was
performed to analyze the characteristics of the all-round MoS. The curving gait was recorded with andwithout the restriction of hip rotation. The all-round MoS of trials were classified using cluster analysis,
and the characteristics of curving motion were extracted from gait parameters using factor analysis. By
comparing the characteristics of the all-round MoS and factor scores, the features of the all-round MoS
were discussed. The results suggest that the effect of the parameters on the MoS, such as the velocity of thecenter of gravity and step width, matched the characteristics of the all-round MoS. Thus, the effect of therange of motion of hip rotation on curving gait was analyzed using an all-round MoS. The all-round MoS
helps visualize the anisotropy of balance, which then enables estimation of the direction with high fall risk.
Furthermore, the all-round MoS enables to evaluate and improve the performance of gait assist devices suchas exoskeletons. This study proposes the concept of all-round MoS as the method to evaluate balance indiagonal direction especially for complex gait.
INDEX TERMS curving gait, gait stability, margin of stability, range of motion, exoskeleton

I. INTRODUCTION

N increase in the aging population requires improvement in the productivity of aged workers and the ability
to perform routine activities for the elderly. The risk of falls
is a major problem in an aged society because falls are a
critical hazard in both industrial and daily living environments [1], [2]. For improving quality of life and productivity,
exoskeletons are expected to enhance the mobility of theelderly and workers by assisting with gait motion [3], [4].
These exoskeletons emphasize on walking straight at first
because it is the basic requirement of gait. However, thecomplexity of the daily living environment requires humans
to perform various motions. Unlike treadmill training, change
in the walking direction is frequently required in real-world
environments [5], [6]. Furthermore, a study that observed actual falls in the daily living environment reported a variationin the direction of fall, especially when the body direction
is changed [7]. Falls in the lateral direction sometimes causeAsevere injuries, such as hip fractures [8], [9].
Gait assistant robots are equipped with the degree of
freedom (DoF) for hip flexion/extension because they are essential for straight walking. However, the human hip joint hasa DoF of internal/external rotation that allows changes in the
direction of the foot and adduction/abduction to generate themotion of opening or closing the legs in the frontal plane [10].
These DoFs are not only used for straight gait [11], but also
play a key role in performing curving motion.
By observing curving gaits, we revealed that humans use
approximately 30 deg of hip rotation and 10 deg of abduction
when curving corners [12]. Thus, we investigated the effectof the DoFs of the hip joint on the curving gait by restricting
rotation and adduction/abduction of the hip joint using awearable device [13], [14]. The analysis of step positions
and joint angles revealed that the restriction of hip rotation
decreased the step length but did not decrease the physicalmargin of fall in both forward and mediolateral direction.

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Although previous studies revealed the characteristics of
stepping motion during curving, conventional indices andmethods are insufficient for determining the anisotropy of thestability of curving gait in diagonal directions.
Various aspects of gait motion, such as posture, motion
trajectory, joint pattern, variance of motion, and kinematic
margin are used to evaluate the stability of gait. The gaitparameters such as step length, step time, and CoM speed
are used to evaluate the difference of kinematic balance [15].
The statistical method such as factor analysis is also used
to extract the factor related to the physical imbalance [16].
Furthermore, among various indices of gait stability, thelocal dynamic stability and the margin of stability (MoS)
are recommended for evaluating the effect of gait perturbation [17]. The MoS is an index used to evaluate the kinematic
margin from the fall [18]. Although most stability indicesonly cover the motion in the anteroposterior direction, the
MoS is capable of evaluating the kinematic margin in all
the direction of horizontal plane [18]. Thus, some studies
evaluated the balance in mediolateral direction of straightwalking [19]–[21]. Furthermore, other studies suggested thathumans cannot maintain balance without stepping outside if
the MoS becomes negative in the mediolateral direction [22],[23]. They revealed that MoS is more useful as an index ofphysical stability in the mediolateral direction than that in theforward direction because the inverted pendulum concept iswell applicable.
However, humans sometimes fall in the diagonal direction
during curving motion. Thus, the evaluation of balance in anteroposterior or mediolateral direction is insufficient [7]. As
curving progresses, the direction of stepping changes in thehorizontal plane [24], [25]. Furthermore, the component ofground reaction force increases in the lateral direction, whichsuggests the change of the direction of velocity vector [11],[26]. An approach to evaluate gait stability in multiple axes
using inertia measurement units is proposed. The study reported that the gait stability in yaw direction is low compared to the other axes (i.e., pitch and roll directions) [27].
This suggested the importance to consider the interaction ofbalance between anteroposterior and mediolateral directions.
However, the yaw motion does not directly reflect the balance in diagonal direction, and the study did not consider
curving motion. Although we analyzed the MoS of curving
steps, it was done in the forward and mediolateral direction
separately [14]. Thus, it is necessary to develop a stability
index to evaluate kinematic balance in an all-round direction.
In this study, we newly analyzed the curving motion [14]and proposed an index to measure gait stability in an allround direction for evaluating gait motion in a daily living
environment (i.e., corner curving) by expanding the idea of
MoS. Furthermore, the index was applied to evaluate theperformance of the gait assist devices. Thus, we compared
and analyzed the curving gait under different joint restraint
conditions applied by the customized orthosis using the allround stability index.

II. EXPERIMENTAL METHOD

The data of experiment reported previously [14] were used todevelop our balance index, all-round MoS. The experiment
was conducted with the approval of the ethics committee of
Nagoya University.
A. APPARATUS

The participants walked along the path (Fig. 1 (a)), consistingof a corner section with a radius of 0.5 m and two straightsections used for acceleration and deceleration. The motionof the participants in the corner section was recorded using
a motion capture system (Motion Analysis, MAC 3D System). Thirty-five markers were attached to the body of eachparticipant. The motion capture data were smoothed using
a sixth-order Butterworth filter. The joint angle and posture
were estimated by fitting the positions of the markers to ahuman body model (SIMM, MusculoGraphics Inc.) [28]. The
position of the center of mass (CoM) was calculated using
Zatsiorsky’s method [29].
The physical assistant robot, MALO [16], was attachedto the user by the corset around the torso, belts around thethigh and shank, and shoes. The actuators were not mounted
on the robot to evaluate the effect of the DoF of a joint on
the curving motion, independent of stabilizing actuation. An
overview of the MALO is presented in Fig. 1 (b). MALO
has hip, knee, and ankle joints, and all joints can rotate in
the sagittal plane, which is generally called flexion/extension.
Moreover, the hip joint has an additional sliding mechanism
to allow rotation in the horizontal plane by providing an additional DoF, as shown in Fig. 1 (c). This sliding mechanism
could be fixed to restrict the hip rotation. The range of motionof the hip rotation was set to 30◦ , in accordance with previous
work [12].
B. PROTOCOLFor the purpose to record the natural curving gait, elevenhealthy adult male subjects participated in this study. The
average and standard deviation of the age, height, and weightof participants are 22.4±2.4 years old, 171.0±5.1 cm, and
64.5±7.4 kg. The exclusion criteria were gait disorder orlower limb pain, but no participant had these. The participants were fitted to the experimental devices and MALO.
Subsequently, the participants walked continuously along thepath shown in Fig. 1 (a). The starting position was adjusted
such that the curving motion started from the participant’s
third step. The participants were instructed to follow the path
without stepping inside the curve.
The hip rotation was sequentially set as free and fixed (rotfree and rot-restriction) in each trial to observe the influenceof joint restriction on curving motion. Furthermore, the leg
used for the first step (left/right) was alternated between trials
for each hip rotation condition. Thus, each participant wastested under four conditions. Ten trials were recorded per
condition for each participant in a random order.
III. DATA PROCESSING
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Terminal section
2-3 steps

Third step

Corner section
R=0.5 mStraight section
0.7-1.0 m (depends
on the subject)
Initial position(a) Curving path
Hip
Rot
Hip
Flex/Ext

Hip Rot(lock/unlock)Knee
Flex/Ext

Hip
Flex/Ext
Ankle
Flex/Ext(b) Physical assistant robot “MALO”(c) Close-up of hip rotation joint

FIGURE 1. Experimental setups

A. PARAMETER DEFINITION AND CALCULATION

To evaluate the curving motion, the gait parameters that represent the posture and balance in the diagonal direction were
determined, as shown in Table 1. In addition to our previous
study [14], several parameters were newly determined toevaluate the kinematic balance in the all-round directions of
the curving step.
The timing of heel contact (HC) was determined by detecting the bottom height of the heel marker in a time series.
Direction perpendicular to line consisting of the anterior
superior iliac spine (ASIS) markers was determined as the
direction of the sagittal plane, whereas the direction of thefrontal plane was that of the line comprising the ASIS markers. The direction of the sagittal plane was defined as 0◦ ,and the inner direction of the corner was set as the positive
direction for CoMV-dir and Foot-dir in the horizontal plane.
The positive direction of HipAng was toward the outsideof the body. The direction of the thigh was determined fromthe line of markers attached to the front and rear of the thigh.
The angle offset was adjusted using the its value recorded in

the upright posture.
Furthermore, the MoS, which is the index of kinematic
margin from fall, was determined in all-round directions inthis study. Originally, the MoS was calculated as the distance
between the expanded CoM (XCoM), which consists of theposition and velocity of the CoM to account for dynamicbalance and the base of support (BoS) [19]–[21]. A larger
MoS indicates greater stability. Although the MoS is capableof evaluating the balance of any direction in horizontal plane,
it was used only for the anteroposterior and mediolateral
direction [14]. In this study, to evaluate the kinematic margin in diagonal directions, MoS was calculated every 30◦ .
Therefore, we totally obtained value in 12 directions. A
geometrical image of the all-round MoS is shown in Fig. 2.
The direction in the sagittal plane is defined as 0◦ , andcounterclockwise is defined as the positive direction.
B. STATISTICAL ANALYSISThe all-round MoS of the trials was classified using a cluster
analysis. In parallel, a factor analysis was conducted for the4

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Pelvis axis

ー MoS(a) Geometry of all-round MoS(b) Graph of all-round MoS

FIGURE 2. Definition of the all-round MoS

TABLE 1. Curving parameters

Parameter name
StLengPelAngHipAngFront
HipAngBack
StWid
CoMV-norm
CoMV-dirFoot-dist
Foot-dir

BoS-area

Definition
The step length is the distance between the heelmarkers of both feet at the time of heel contact (HC)in the sagittal plane.
The pelvis yaw angle is the change in the frontal
direction of pelvis in the horizontal plane of the global
coordinate system between the HCs.
The hip rotation angle of front and rear leg is definedas the rotation of the thigh with respect to the pelvis
in the horizontal plane at HC.
The step width is the distance between the heel markers of both feet at the time of HC in the frontal plane.
The center of mass (CoM) velocity is the velocity of
the CoM at HC timing. The direction of CoM motionis the CoM velocity direction.
The foot distance is the distance between heel marker
of stepping foot and CoM at the HC timing. The footdirection is the direction of stepping foot from the
CoM
The BoS area is determined as the area of support
polygon consists of heel and toe markers of both feetat the timing of toe contact.

set of gait parameters shown in Table 1 to extract the characteristics of the curving gait. By comparing factor scores
across cluster groups, the relationship between the all-round
MoS and the features of the stepping motion were discussed.
Both the all-round MoS and gait parameters of each stepping foot (left and right steps) were analyzed separately.
Then, the all-round MoS and factor scores with and without
joint restraints were compared. Multivariate analysis of variance (MANOVA) and the Tukey-Kramer method were used
for comparison.
IV. RESULTS

The single inner (left) step and single outer (right) steps
were obtained from each trial. Trials in which the motion
capture markers were entirely obstructed from the view wereomitted. Thus, six to ten trials were analyzed based on thetest conditions for each participant. In total, 204 and 209 trials were analyzed for rot-free and rot-restriction conditions,
respectively.

TABLE 2. Number of samples in each cluster of inner (left) stepRot-freeRot-restriction
Total

1st cluster 2nd cluster 3rd cluster Total
37
141
26
204
19
21
169
209
56
162
195
413

TABLE 3. Number of samples in each cluster of outer (right) stepRot-freeRot-restriction
Total

1st cluster 2nd cluster 3rd cluster 4th cluster Total
20
69
73
42
204
19
32
73
85
209
39
101
146
127
413

A. CLUSTER ANALYSISThe all-round MoS, consisting of MoSs in twelve directions,at the time of HC was classified using cluster analysis. The
inner and outer steps were analyzed separately.
The inner step cases were separated into three clusters,
and the outer step cases were separated into four clusters
considering the number of samples included in each cluster.
The number of samples in each group is shown in Tables 2
and 3, respectively.
The average all-round MoS of each cluster is shown in
Fig. 3 (a) and (b). In the left step, the MoS increased in
the front-left direction, which is the direction of the footstep.
Moreover, the MoS in the posterior right direction, which isthe direction of the support limb, was also high. The differences among clusters appeared in the MoS of the posterior
half. In the right step, as in the left step, MoS increased in the
direction of the footstep and support limb. The differencesamong the clusters also appeared in the posterior half. Furthermore, in few trials, the MoS became negative in a specificdirection (i.e., 60◦ on the right step). In addition, the allround MoS is compared between the restriction conditions in
Fig. 3 (c) and (d). In the rot-free condition, the MoS increasedin the posterior half. Occasionally, it decreased in the anterior
half. The result of MANOVA suggested that the all-round
MoS of each cluster differed significantly. The p-values of
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each pairs of clusters are shown in Tables 4 and 5.

As a result of factor analysis, three factors were extracted
for each step. The factor loading vectors, weighted by thecontribution rate, are shown in Fig. 4. The characteristics
of clusters of all-round MoS are investigated using factor
scores associated with each cluster. The factor scores of eachcluster are shown in Fig. 5 (a)(b). The comparison of factor
scores with and without joint restraint conditions is shown in
Tables 6 and 7, and Fig. 5 (c) and (d).

The second cluster of the all-round MoS was placed
between the first and third clusters, excluding the second
factor. Although the CoMV tends to move to the front-right
direction as the first cluster, the slower speed diminishes theeffect of CoMV-dir.
The characteristics of the third cluster of the all-round
MoS are opposite to those of the first cluster. The slower
speed, suggested by the negative first factor, corresponds tothe larger MoS in the anterior half. Furthermore, the positive
second factor indicates a large step width that results in alarge MoS in the lateral direction.

1) Inner step2) Outer step

According to the factor loading shown in Fig. 4, the first
factor is strongly related to PelAng, CoMV-norm, and negative CoMV-dir. This factor contributes to rapid walking andalteration of body direction. Furthermore, the CoM did not
move in the inner direction of the pelvis. The second factor
consists of StWid, CoMV-norm, CoMV-dir, and Foot-dir. A
larger second factor corresponds to the step towards the innerdirection of the corner, implying that the body moves to theleft side without altering the pelvis direction. The third factor
was characterized by positive PelAng, Foot-dist, and negative
StLeng. However, the magnitude of PelAng was less than thatof the first factor.

The first cluster of the all-round MoS is characterized by ashort MoS in the front-left direction, as shown in Fig. 3 (b).
The scores of the first and second factors shown in Figs. 4(b) and 5 (b) suggest high speed, long step length, small step
width, and CoMV toward the inner direction. As mentioned
above, in the frontal direction, the fast speed decreases the
MoS [31]. Furthermore, the long step length also decreases
the MoS in the forward direction according to the gait experiment [31] whereas the short step width does not affect the
MoS in the lateral direction [32]. In addition, pelvic rotationis also high according to the first factor. Therefore, the resultsof this cluster suggest that the rapid curving motion causes a
decrease in MoS in the front-left direction. In contrast, thesecond cluster of the all-round MoS was placed in the middleof other clusters, and did not have notable characteristics.
The MoS of the third cluster was large on the left side. The
large second factor suggests a large step width that increases
the MoS in the lateral direction [31]. The weaker internalmotion amplifies this tendency.
The MoS of the fourth cluster was large in the anterior halfarea. According to the factor score, a smaller speed and shortstep length increased the MoS [31]. This is the likely reason
for the largest margin among all clusters.

B. FACTOR ANALYSIS

2) Outer step

Unlike the inner step, the first factor of the outer step isstrongly related to the positive StLeng and related to the
CoMV-norm. These parameters represent the strong forward
step. Furthermore, a positive PelAng indicates body rotation
towards the corner. The second factor is strongly related tothe positive StWid as the inner step. However, the effect on
CoMV-dir and Foot-dir is negative, implying that the bodymoves toward relatively outside of corner. The third factor isrelated to the PelAng, BoS-area, and negative HipAngBack.
The positive PelAng suggests that this factor works similar to
the first factor.
V. DISCUSSION
A. RELATIONSHIP BETWEEN ALL-ROUND MOS ANDSTEPPING MOTION
1) Inner step

According to Fig. 3 (a), the first cluster of the all-round
MoS can be characterized by a short MoS in the forward
direction. Especially in the front right direction, the MoS
became negative, which sometimes occurred in the forward
direction during gait [30]. Meanwhile, the factor score andfactor loading of each factor shown in Figs 4 (a) and 5 (a)suggest that this cluster tends to perform large rotation withhigh speed according to the large positive first factor. The
high speed can be directly related to the short MoS in theforward direction [31]. Furthermore, the negative CoMV-dir
indicates the direction of CoMV towards relatively outsideof the corner, which decreases the MoS in the front right
direction.

B. EFFECT OF JOINT RESTRAINT
1) Inner step

Based on the distribution of samples for each condition in theclusters shown in Table 6, some clusters probably represent
the characteristics of each of the restriction conditions. The
second and third clusters mainly consist of strides with rotfree and rot-restriction conditions, respectively as shown in
Table 2. Thus, the characteristics of these clusters represent
one condition each. The factor scores of each condition
shown in Fig. 5 (c) correspond to those of each cluster, as
shown in Fig. 5 (a). According to Fig. 3 (a) and (c), theall-round MoS of the rot-restriction condition is large in thefront-right direction, which corresponds to the third cluster.
In contrast, it appears that the first cluster consists of a rapid
curving motion, regardless of the restriction.
2) Outer step

Unlike the inner step cases, none of the clusters reflected thecharacteristics of the restriction conditions because both rot-

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Cluster 1
Cluster 2
Cluster 3

Cluster 1
Cluster 2
Cluster 3
Cluster 4(b) Clusters of the right step(a) Clusters of the left stepRot-freeRot-restriction

Rot-freeRot-restriction(c) Restriction conditions of the left step(d) Restriction conditions of the right step

FIGURE 3. All-round MoS of each step

TABLE 4. Statistical comparison of all-round MoS of of inner (left) step

1-2 clusters
1-3 clusters
2-3 clusters
Rot-free/
Rot-Restriction

0
deg
**
**
0.29

30
deg
**
**
*

60
deg
**
**
**

90
deg
0.18
**
**

120
deg
**
**
**

150
deg
**
**
**

180
deg
**
**
**

210
deg
**
**
**

240
deg
**
**
**

270
deg
**
0.10
**

300
deg
**
**
**

330
deg
**
**
**

**

*

0.74

**

**

**

**

**

**

**

**

0.11

∗≤0.05, ∗∗≤0.01

free and rot-restriction conditions were not prominent for all
clusters of the outer step, as shown in Table 3. Furthermore,
the difference in the shape of the all-round MoS in theanterior half between the conditions is slight, as shown in
Fig. 3 (d).
However, Fig. 5 (d) suggests that the factor scores differ
significantly between the two conditions. Compared to therot-free condition, a smaller first factor and a larger second
factor suggest a shorter step length and step width in the
rot-restriction condition. Furthermore, the CoMV and pelvic
rotation were small. These characteristics correspond to theresult of direct comparison of gait parameters with and with-out restriction of hip rotation [14].
C. MEANING OF ALL-ROUND MOS

The all-round MoS is an idea that expanded the MoS to all the
direction of horizontal plane. The all-round MoS of each direction consists of the distance between the edge of BoS and
XCoM, respectively. According to this definition, the fasterthe component of gait speed, the smaller the MoS becomes.
Furthermore, the MoS tends to become small towards theshort axis direction of BoS. If the MoS becomes negative,
an additional step is required to prevent fall.
We determined the all-round MoS to evaluate the kine7

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Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALSTABLE 5. Statistical comparison of all-round MoS of of outer (right) step

1-2 clusters
1-3 clusters
1-4 clusters
2-3 clusters
2-4 clusters
3-4 clusters
Rot-free/
Rot-Restriction

0
deg
0.16
**
**
**
**
**

30
deg
*
**
**
0.13
**
**

60
deg
**
**
**
**
**
**

90
deg
**
**
1.00
**
**
**

120
deg
**
**
**
**
**
**

150
deg
**
**
**
**
**
**

180
deg
N/A
N/A
N/A
N/A
N/A
N/A

210
deg
**
**
**
**
**
0.96

240
deg
**
**
**
**
**
0.8

270
deg
1.00
*
*
**
**
0.95

300
deg
0.50
*
**
**
**
*

330
deg
0.82
**
**
**
**
**

*

0.59

*

**

**

**

N/A

**

0.84

*

**

**

∗≤0.05, ∗∗≤0.01

1st factor
3rd factor-4-2

1st factor
3rd factor

2nd factor
0

2

4

-6

6

StLengStLengPelAngPelAngHipAngBack

HipAngBack

HipAngFront

HipAngFront

StWid

StWid

CoMV-norm

CoMV-norm

CoMV-dir

CoMV-dirFoot-dist

Foot-dist

Foot-dirFoot-dir

BoS-area

BoS-area(a) Factor loadings of the left step-4

-2

2nd factor
0

2

4

6

(b) Factor loadings of the right step

FIGURE 4. Factor loadings

TABLE 6. Factor score of each cluster and condition of inner (left) step

1st cluster
Rot-free
2nd cluster
3rd cluster
1st cluster
Rot-restriction 2nd cluster
3rd cluster
1st clusterAll
2nd cluster
3rd cluster

1st factor-0.26 (± 0.72 )0.01 (± 1.18 )-0.29 (± 0.67 )0.38 (± 0.61 )-0.29 (± 0.30 )0.08 (± 1.04 )-0.04 (± 0.74 )-0.03 (± 1.11 )0.03 (± 1.00 )2nd factor
1.65 (± 0.61 )0.23 (± 0.53 )-0.55 (± 0.68 )2.12 (± 0.35 )0.48 (± 0.43 )-0.76 (± 0.67 )1.81 (± 0.58 )0.26 (± 0.53 )-0.74 (± 0.67 )3rd factor-0.59 (± 0.90 )-0.67 (± 0.69 )-0.38 (± 0.78 )1.27 (± 0.67 )-0.31 (± 0.32 )0.64 (± 0.82 )0.04 (± 1.21 )-0.62 (± 0.67 )0.50 (± 0.88 )matic margin of the curving gait. Because the walking direction gradually changes between the forward and lateral
directions during curving, the definition of the margin in

TABLE 7. Factor score of each cluster and condition of outer (right) step

1st cluster
2nd cluster
Rot-free
3rd cluster
4th cluster
1st cluster
2nd cluster
Rot-restriction
3rd cluster
4th cluster
1st cluster
2nd clusterAll
3rd cluster
4th cluster

1st factor-0.14 (± 0.66 )0.07 (± 1.37 )0.00 (± 0.83 )-0.61 (± 0.57 )0.58 (± 0.47 )-0.12 (± 0.74 )0.46 (± 1.30 )-0.20 (± 0.62 )0.21 (± 0.68 )0.01 (± 1.21 )0.23 (± 1.11 )-0.34 (± 0.63 )2nd factor
1.81 (± 0.46 )0.91 (± 0.75 )0.23 (± 0.62 )0.18 (± 0.71 )0.96 (± 0.29 )-0.16 (± 0.30 )-0.40 (± 0.66 )-1.26 (± 0.54 )1.40 (± 0.57 )0.57 (± 0.81 )-0.09 (± 0.71 )-0.79 (± 0.91 )3rd factor
0.94 (± 0.71 )0.00 (± 0.73 )-0.98 (± 0.71 )0.61 (± 0.91 )1.86 (± 0.56 )0.60 (± 0.54 )-0.59 (± 0.60 )0.18 (± 0.85 )1.38 (± 0.79 )0.19 (± 0.73 )-0.78 (± 0.68 )0.32 (± 0.89 )diagonal direction becomes an advantage in this method to

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Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS

2.50

**

2.00

2.50

**
**

2.00
**

1.50
Factor score

**
**
**

3.00

**
**

1.00
1st cluster

0.50

2nd cluster

0.00

3rd cluster

-0.50

1.00

**

**
*
1st cluster
2nd cluster

**

0.50

3rd cluster

0.00

4th cluster

-1.50

-2.00
1st factor
Mean

2nd factor
Mean

-2.00

3rd factor
Mean

1st factor(a) Clusters of the left step****

2nd factor

3rd factor(b) Clusters of the right step
2.00

*

**

1.50

1.00

**

**

1.00

0.50
0.00

Rot-free-0.50

Rot-restriction

Factor score

Factor score

*
**

-1.00

-1.50

1.50

**
**

-0.50

-1.00

2.00

**
**

**
**

1.50
Factor score

3.00

0.50
Rot-free

0.00

Rot-restriction

-0.50

-1.00

-1.00

-1.50

-1.50

-2.00
1st factor
Mean

2nd factor
Mean

1st factor
Mean

3rd factor
Mean(c) Restriction conditions of the left step

2nd factor
Mean

3rd factor
Mean(d) Restriction conditions of the right step
FIGURE 5. Factor scores

analyze the imbalance of curving steps. As a general trend,
the shape of the all-round MoS was small on the opposite
side of the stepping foot of the anterior half. This trend
matches the fall in the lateral direction, reported as actual
falls [7]. Because the direction of fall affects the severityof fall injuries, it is important to estimate the fall directionof a specific gait motion. Furthermore, the results suggested
that the all-round MoS reflected the difference in gait motion
caused by gait variability and restriction conditions, as shownin Figs. 3 and 5. This result encouraged us to develop an
index to estimate not only the risk of falls, but also theseverity of fall injury during the curving gait.
However, when calculating the all-round MoS, the direction of the CoM velocity vector and the direction of the MoS
were mismatched in the backward direction. The all-round
MoS was simply determined as the distance between the
XCoM and BoS in each direction. However, the posterior halfof the all-round MoS may not have reflected the kinematic
margin against backward fall because the subject could move
the CoM forward by decreasing the ground reaction force,
which decelerates the CoM motion. However, the margin forthe backward fall could be evaluated using MoS. Yang et al.
used the rear edge of the supporting leg as the BoS to evaluate
the backward margin of the swing phase [33]. Furthermore,
Sivakumaran et al. evaluated the kinematic margin in theanteroposterior and mediolateral directions during the swing
phase as well as during the double stance phase [34]. Furthermore, the expansion of the MoS to evaluate the kinematic
margin in the backward direction is another challenge toestimate the risk of backward fall.
D. LIMITATIONSIn this study, the BoS was determined as a quadrangle thatconnected the position of the toe and heel markers of bothfeet. Although the results of our analysis were consistent
with the characteristics of gait parameters, the simplificationof the BoS shape made the area of the BoS narrower than
the actual support polygon. For the actual usage of all-round
MoS such as diagnosis of gait balance, an elaborate model of
support polygon consists of feet may be required. Thus, the
BoS should be expanded considering the shape of the foot,especially in the lateral direction of the foot.
In this study, the variance of gait motion used was limited
compared to that of general population because the gait
motion of only healthy young men was observed. Thus, thedevelopment of the general classification model of the allround MoS is another work for future. In the current analysis,
the trials of each subject tended to belong to several clusters
together. It can be considered that the characteristics of the
gait of individuals was reflected to the classification. For the
analysis of all-round MoS in the general population, the affil9

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Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS

iation of subjects should be considered for the classification,
whereas we focused on the correspondence between clustersof all-round MoS and gait characteristics.
VI. CONCLUSION

It is difficult to evaluate the risk of fall of the motion thatchanges the walking direction because the current stability
measures can evaluate the kinematic stability in the anteroposterior or mediolateral direction independently. In thisstudy, the novel all-round MoS is developed and introduced
to quantify the kinematic margins in all directions and analyze the kinematic instability in the diagonal direction of the
body during curving gait.
By expanding the concept of the margin of stability, we
determined the all-round MoS as a measure of the kinematic
margin in the diagonal direction in addition to the forward
and lateral directions. Curving gait was observed with andwithout the restriction of hip rotation. Furthermore, the gaitparameters were calculated and analyzed using factor analysis. By comparing the all-round MoS and gait parameters,
the characteristics of the all-round MoS were discussed.
In this study, the effects of the range of motion of hiprotation on curving gait were analyzed using the all-round
MoS. The results confirmed that the characteristics of groups
classified according to the all-round MoS could be describedby their stepping motions involved in the factor scores. The
investigation of change of the all-round MoS caused by
the exoskeleton enables evaluation and improvement of its
performance.
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YASUHIRO AKIYAMA received the B.E. degree
in engineering from Tokyo Institute of Technology, Tokyo, Japan, in 2006, and the M.S. and the
Ph.D. degree in engineering from the Universityof Tokyo, Tokyo, Japan, in 2008 and 2011, respectively. Then, he was an assistant professor of
Nagoya University, Japan till 2021. Currently, heis an associate professor of Shinshu University,
Japan. His main areas of research interests aremechanical safety, human-robot interaction, andmanned space mission.

YOSUKE KUBOKI received the B.E. and M.S.
degree in engineering from Nagoya University, in2018 and 2020, respectively. Since then, he has
been working for HITACHI, Ltd. as an engineer.
His research interests are human-robot interaction,
wearable robotics, and safety engineering.

SHOGO OKAMOTO received MS and PhD degrees in information sciences in 2007 and 2010,
respectively, from the Graduate School of Information Sciences, Tohoku University. Currently, heis an associate professor at the Department ofComputer Sciences, Tokyo Metropolitan University. His research interests include haptics, affective engineering, and human-assistive technology.

YOJI YAMADA received a doctor degree from
Tokyo Institute of Technology in 1990. In 2004, hemoved from Toyota Technological Institute to National Institute of Advanced Industrial and Science
Technology (AIST), as a group leader of Safety
Intelligence Research Group in the Department ofIntelligent Systems. In 2009, he moved to the Department of Mechanical Science and Engineering,
Graduate School of Engineering, Nagoya Unversity as a professor. His current research interests
include safety and intelligence technology in human-machine systems, andassistive robotics.

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