Gait & Posture 60 (2018) 15–21

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Gait & Posturejournal homepage: www.elsevier.com/locate/gaitpost

Classiﬁcation and analysis of the natural corner curving motion of humans
based on gait motion

MARK

⁎

Yasuhiro Akiyamaa, , Hitoshi Todab, Takao Ogurab, Shogo Okamotoa, Yoji YamadaaabNagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi, Japan
Mie Prefectural Police, 100, 1, Sakae, Tsu, Mie, JapanA R T I C L E I N F O

A B S T R A C T

Keywords:
Corner turn
Gait motion
Cluster analysis

The curving motion of the human body is more complex than gait motion for straight walking. In particular,when human can freely curve corners, the gait motion varies among and even within individuals. However, is it
not possible to classify natural curving motion using a statistical method? This study investigates the natural
curving motion, encompassing various walking paths selected by subjects, as opposed to previous studies that
focused on speciﬁc stepping strategies or curving motion under precisely controlled conditions. As a result, thenatural curving motions are statistically classiﬁed into ﬁve distinct groups based on certain motion indices. Eachgroup represents a curving strategy and is mainly characterized by the inner inclination of the pelvis, outerrotation of hip joints at the time of heel contact of the inner leg, and inner and/or outer rotation of hip joints atthe time of heel contact of the outer leg. Such strategies are speculated as typical motions within the large
variation in natural curving motion. Another ﬁnding is that, unlike the joint pattern of lower limb joints in thesagittal plane, hip rotation and the abduction/adduction angle drastically change when curving. In particular,
the large inner rotation and abduction angles of the hip joint of both legs, which reached approximately 30° and
10°, respectively, become important when considering the curving gait of a physical assistant robot. Our analysis
and ﬁndings help specify the joint motion required for physical assistant robots.

1. Introduction
Physical assistant robots have recently attracted considerable attention. In addition to being utilized in hospitals, they are also used toaid humans, who do not have serious disorders but are aged or frail, in
performing various daily activities [1,2]. A physical assistant robot fordaily use is sometimes required to be capable of assisting humans in
performing various kinds of movements, which are not required forrehabilitation purposes [3,4]. Turning a corner is one such motion [5],wherein the gait pattern diﬀers from a straight gait.
While the motion of a straight gait mainly occurs in the sagittal
plane [6], three-dimensional joint motion, which includes hip rotation,
hip abduction/adduction, and body inclination, becomes important for
performing a curving motion. However, certain robots do not have
suﬃcient degree of freedom or range of motion (ROM) of the joints [7],which suggests that such robots possibly increase the risk of falling[8,9]. Furthermore, while several robots allow the human to movealong an out-of-sagittal plane [10,11], they do not intentionally assist in
curve motion.
Such curving motion has formed the focus of several studies.
⁎

Previously, the change of heading direction during curving was the
major focus [12–15]. Xu reported a backward leaning of the subject's
body before curving [16], while Orendurﬀ measured the inside shift ofthe center of mass (CoM) during curving around a circle [17]. Stepping
strategies when turning a square corner have also been analyzed, whereclassiﬁed corner turns were studied from the perspective of the stepping
position, direction, and the side of the leg [18–20]. In addition, it
should be noted that many of these studies commonly reported that the
gait speed decreased when turning. However, these studies did notcover curving motion under natural conditions, wherein the start-fromand end-to straight gait and the curving trajectory could be freely selected by the subject, because these studies only focused on a speciﬁc
phase of motion or the shape of the curve. Nevertheless, there is aquestion as to whether the curving strategies used for natural curving
motion are the same as those observed in these particular conditions.
Further inspection of the gait motion during natural curving motion
will help physical assistant robots to assist humans during natural
curving motion. In this study, we identiﬁed and analyzed several curving strategies and their features by recording gait motion such as joint
and body angles, walking path, and ground reaction force (GRF) as a

Corresponding author.
E-mail address: akiyama-yasuhiro@mech.nagoya-u.ac.jp (Y. Akiyama).
URL: http://www.mech.nagoya-u.ac.jp/asi/en/ (Y. Akiyama).

https://doi.org/10.1016/j.gaitpost.2017.10.008
Received 10 February 2017; Received in revised form 3 October 2017; Accepted 5 October 2017
0966-6362/ © 2017 Elsevier B.V. All rights reserved.

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Fig. 1. Walking lane and typical trajectories. (A) Walking lane, (B) small curve-walk, and (C) large curve-walk. Walking lane and walking pathways (solid line: trace of foot, dashed lines:
trace of center of mass (CoM), square mark: CoM position at each foot contact, diamond mark: center of consecutive foot marks at each foot contact, gray cross lines: pelvis position anddirection, hatched area: corner section, motion in the corner section was analyzed).

speed.
Each subject repeated the walk along the straight-line direction a
total of 10 times. Each subject was instructed to cross a line from astandstill position. Subsequently, the subject walked straight to thetarget, which was placed at the end of the walking lane.
Turning a corner involved walking along two circles of diﬀerent
radii. To observe the various curving motions, the leg used to start the
walk was switched during the trials because the timing when changing
the walking direction was aﬀected by the stepping timing [24]. We
conducted and recorded a total of 40 trials, which consisted of four
diﬀerent condition combinations (two radii × two starting legs). The
order of the trials was also randomized. During the trials, the subjects
were instructed to turn the corner freely, but not to step inside thecorner made by the tape marked on the ﬂoor.

basic research to understand the natural curving motion of humans.
2. Method
Our experiments were performed with the permission of the institutional review board of the Nagoya University.
2.1. Apparatus
Experimental trials were conducted as part of a series of gait measurement experiments. A straight path and a round corner were utilized
for observing the natural curving motions. The round corner wasmarked on the ﬂoor by means of a tape, and the path consisted of astraight line and quarter circle with radii of 0.5 m (small) and 1.0 m(large). The positions of the ground markers and the typical walking
paths are shown in Fig. 1. A 1-m radius is common for a round corner[17,21], and a smaller radius is utilized to evaluate the eﬀect of curving
radii [22].
The gait motion was recorded at 120 Hz by a three-dimensionalmotion capture system (MAC 3D system, Motion Analysis Corporation,U.S.). A total of 22 markers, which consisted of a set of critical markersof the SIMM Motion Module (SIMM, MusculoGraphics, Inc., U.S.) [23],were attached. The GRF was recorded with mobile six-axis force plates(M3D, Tec Gihan Co., Ltd., Japan) aﬃxed under the sole. Four force
plates were separately attached at the toe and heel of each foot.

2.4. Data processing
The walking path and stepping positions varied widely among
subjects and trials because the subjects could freely select them. Thus,
only the motion in the corner section, which consisted of a quartercircular area, was extracted from the corner trial and used for cluster
analysis. The typical walking paths of the natural curving trial are
shown in Fig. 1. Although the curving area did not include all of thecurving motion, it covered the sharpest part of the curving path, which
probably represents the gait pattern of natural curving motion.
The data from the motion capture system were smoothed with theuse of a 6-Hz Butterworth ﬁlter. The timing of the heel contacts (HC)and toe oﬀs (TO) were determined based on the GRF with a threshold of
10 N.
The cadence was calculated as the inverse of the time diﬀerence
between successive HCs. The double support ratio was calculated as theratio of the time when both legs are in the stance phase with gait time.
The pelvis velocity, which was utilized as the parameter to evaluate
speed during the turning phase, was calculated by dividing the length ofthe path of the pelvis center by gait time. When evaluating the meanvalues of the gait parameters, we considered all the trials.
To calculate body inclination and joint angles, especially the hiprotation and abduction/adduction, the human SIMM model was scaled
and ﬁtted to the motion of the markers by means of the least-squares

2.2. Subject
Twelve healthy male subjects participated in the study. The average
age was 21.2 years, and the standard deviation (SD) was 1.7. Theirmean height and weight were 172.4 ± 3.6 cm and 61.3 ± 6.9 kg,
respectively. The body mass index of the subjects ranged between 17.5
and 24.5.
2.3. Protocol
The subjects wore well-ﬁtting sportswear with reﬂective markers.
Then, each participant walked along the straight line, around thecorner, and other walking lanes in a randomized order at a self-selected
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Y. Akiyama et al.

Fig. 2. Classiﬁed curving strategies. The name of groups stands for the feature of the curving motion of each group. The curving motions were characterized by the side of step and leg,
which was used for changing walking direction compared to the other groups. The detail of curving motion of each group was described in Fig. 3. (A) Dendrogram of curving strategies.
(B) Distribution of curving strategies. (C) Angle pattern of each group (the timing when the COM is in the corner area is hatched and vertical lines are the step timing of inner leg (dashedline) and outer leg). (D) Grouping of trials for each subject separated by the corner radius. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the
web version of the article.)method. It should be noted that the human model could not be ﬁtted
perfectly owing to the deformation of skin and clothes. This model wasscaled for each subject. The positive direction of the hip rotation angle
was deﬁned as the inner direction. The posterior and outer inclinationof the body segment was deﬁned as the positive direction of the pitch

and roll angle. The lumbar yaw angle was considered as positive when
the torso rotated along the counterclockwise direction on the pelvis
segment. The GRF of each leg was calculated as the sum of the forces
recorded by both the toe and heel plates. Subsequently, this GRF was
normalized by body mass. The coordinate system of the GRF was ﬁxed
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Fig. 2. (continued)

the use of the Steel–Dwass test [26] because it was presumed that thisclustering illustrated the diﬀerence in curving strategies among groups,
with respect to joint pattern, GRF, and posture.

at the bottom of each foot, and the X-axis was directed to the left side
(inner side of the curve) of the short axis. The Y-axis was directedbackward along the longitudinal axis.
The rotation radius, which probably aﬀected curving motion [22],was deﬁned separately from the corner radius as the radius of the circle
that ﬁt the trajectory of the CoM in the corner section in the horizontal
plane. Although the curvature of the CoM trajectory changed graduallywhen curving, the shape grew closer to the circle in the corner section.
Fitting was performed with the use of the least-squares method. The
maximum and minimum values of body inclination, joint angles, andGRFs in the corner section were calculated as the indices of the curving
trials.
To evaluate the characteristics of the curving strategy, corner trials
were classiﬁed into ﬁve groups by using the three types of parameters
corresponding to pelvis posture. They included the maximum angles ofthe pelvis anterior inclination, pelvis inner inclination, and lumbar yaw
rotation in a direction towards the curving direction, which meant theleft side for each trial. These body inclination parameters possibly reﬂect the pelvis posture at the sharpest part of the curving path of thesubject, whereas the joint angles are related to the timing of speciﬁc
gait events. Next, cluster analysis, which is based on Ward's method[25], was applied for classiﬁcation.
After classiﬁcation, the indices of each group were compared with

3. Result
The means and SDs of the gait parameters during the straight-walktrials were as follows: pelvis velocity, 1.36 ± 0.13 m/s; cadence,
112.1 ± 3.9 step/min; step distance, 72.1 ± 6.7 cm (right) and71.8 ± 5.6 cm (left); and double support ratio, 23.4 ± 2.5%. Here,
we mention that although the pelvis velocity and step distance do notexactly correspond to the speed and step length, the values of theseparameters are similar and consistent with those of previous studies[27,28]. Next, we obtained the abovementioned parameters for thecurving trials with the large radius as follows: pelvis velocity,
1.23 ± 0.14 m/s; cadence, 108.8 ± 6.0 step/min; step distance,
68.3 ± 6.8 cm (right) and 68.4 ± 6.3 cm (left); and double support
ratio, 25.3 ± 3.5%. In addition, for the small-radius case, we obtained
the following values: pelvis velocity, 1.17 ± 0.14 m/s; cadence,
107.9 ± 6.1 step/min; step distance, 66.4 ± 7.4 cm (right) and66.4 ± 7.2 cm (left); and double support ratio, 25.9 ± 3.7%.
The results of the cluster analysis for the corner trials are shown in
Fig. 2. According to Fig. 2B, the ﬁrst (blue) and second (red) groups lie
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Table 1Comparison of motion indices among curving strategies.

+< 0.1.
* < 0.05.
** < 0.01.

corner motion. The steeper the curving motion, the more step length,
cadence, and speed decreased, as suggested previously [12–14,29].
The common motion observed when curving is demonstrated inTable 1, in addition to the diﬀerence in curving motion strategy amonggroups. The most representative characteristics of curving are the inside
inclination of the pelvis and the torso, appearing as large negative values of the minimum roll angle. This inclination matches the inside
movement of the CoM, as reported previously [17]. At the same time,
the subject directs his head and torso towards the rotation direction
before turning [12–14,30], which was observed as a large maximum
lumbar yaw angle in our study. Across all groups, the GRF in the lateral
direction (Fx), which indicates the centripetal force, is larger on theouter (right) leg, as suggested by Orendurﬀ et al. [17]. A similar trend isobserved regarding the deceleration force (maximum Fy) and normal
force (Fz). This result indicates that the thrust force to turn around thecorner mainly comes from the outer leg.
Although the joint motion becomes asymmetrical between legs, it isdiﬃcult to ﬁnd signiﬁcant diﬀerence in the joint ﬂexion between them.
In addition, our ﬁnding that the gait parameters retain symmetry evenduring curving trials also suggests symmetry of the gait motion in thesagittal plane. Thus, the contribution of the joint ﬂexion to the curving
motion should be small. Instead, the large outer rotation of the hip,followed by its inner rotation and abduction, were commonly observed
as reported previously [29]. This out-of-sagittal-plane motion,

close to each other, and their sizes are larger than those of the othergroups, particularly the fourth (cyan) and ﬁfth (magenta) groups. The
representative pattern of posture parameters used for clustering isshown in Fig. 2C. Even in the dendrogram shown in Fig. 2A, the ﬁrst
and second groups lie close. It should be noted that almost all trials
classiﬁed under the fourth and ﬁfth groups corresponded mostly to one
subject respectively, as can be inferred from Fig. 2D.
The means and SDs of each motion index and the p-value of eachcoupling as calculated by the Steel–Dwass test are indicated in Table 1.
We note from the table that as a common trend, the pelvis inclined
towards the inner side and the lumbar was also directed towards theinner side along the horizontal plane. Although the rotation radius was
not eﬀective as a clustering parameter, the radius diﬀered among
strategies and could be separated into two groups. Speed showed a similar trend and it corresponded to the rotation radius. In contrast, theeﬀect of the diﬀerence in the corner radius appears negligible because
the diﬀerence of the curving strategy within the subject is not the sameamong subjects, as listed in Fig. 2D.

4. Discussion
4.1. Common trends in natural curving motion
A change in gait timing was commonly observed during curving
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Fig. 3. Curving strategy adopted by each group. (A) Image of step angle of each strategy. (B) Curving trajectory of the representative trial of each group (squared step corresponds to thestep in A). (C) Angle pattern of each group (the timing when the COM is in the corner area is hatched and vertical lines are the step timing of inner leg (dashed line) and outer leg).

Based on a further comparison of the peak rotation angles of theouter and inner hips, we depict the curving strategy of each group in
Fig. 3. In the case of straight walking, the hip rotation is close to zero at
the time of HC and is maximum in the early stance phase [6]. In contrast, during the curving motions, a large hip rotation occurs in theearly stance phase. The manner of this hip rotation determines thecurving strategy. However, the validity of the fourth- and ﬁfth-groups
should be certiﬁed by testing additional subjects because of the limited
number of samples. The curving motion of the ﬁrst and second groups isparticularly foot rotation, is necessary to alter the pelvis direction.
4.2. Characteristics of the curving motion of each group
As shown in Fig. 2B, the main parameter that separates the various
groups is the maximum lumbar yaw angle. Furthermore, the fourth andﬁfth groups can be mainly identiﬁed by the minimum pelvis roll andpitch angles, which become positive when the pelvis inclines in theposterior and outer direction.
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Conﬂict of interest statement

characterized by a large outer rotation of the hip joints. A large outerrotation of both legs at the timing of HC of the inner foot alters thewalking direction to execute the curve. In contrast, the third groupdisplayed a large inner rotation of the outer leg in the stance phase. The
fourth group exhibited the same characteristics, but for the inner leg.
The ﬁfth group displayed a relatively large inner rotation in both legs.
These trends indicate that the ﬁfth-group uses the inner rotation of bothlegs, whereas those third- and fourth-group use only one leg to turn. As
previously discussed, the curve motion of all groups can be mostly
characterized by the hip rotation.
Although many parameters of the ﬁrst and second groups are similar, there are several parameters that also deﬁne their diﬀerences. In
the ﬁrst group, the pelvis inclined to the inner side of the curve during
the swing phase of the inner leg via a combination of certain features,such as the large maximum pelvis inclination towards the inner side,which comes from a large abduction angle of the inner leg, andasymmetrically large hip and knee maximum ﬂexion angles of the innerleg. In other words, the subjects’ upper body leaned towards the curving
direction. However, those in the second group did not show such rolling
motion of the pelvis and upper body.

The authors declare no conﬂict of interest.
Acknowledgments
We thank the support by JSPS KAKENHI Grant Number 26750121
and the support of Tsubasa Goto.
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4.3. Practical implications of curve motion classiﬁcation
In brief, the strategies shown in Fig. 3 can be separated as curving
with the inner step and curving with the outer step. In this experiment,
the “spin” motion was not observed to be the same as in the study,
which recorded the curving motion in a simulated daily living environment [5]. Furthermore, the stepping motions were separated more
precisely than in previous studies [18] and connected to the joint motions. The existence of groups with large numbers of trials, such as theﬁrst, second, and third groups, suggests that there are several strategies
commonly used by the subjects. However, it should be noted that theexistence of unique strategies is also suggested from the result.
In this study, although further analysis is required to characterize
the motion of each stride during curving, it appears probable that the
gait cycle, whose curve angle is steepest, can be extracted from thisanalysis. In addition, the extracted curving strategies determine the
ROM required for a natural curving motion, which also should beequipped in a physical assist device as shown in Table 1 and Fig. 3C.
Furthermore, the analysis of speciﬁc curving strategies can aid in determining the assist pattern of each joint.
The change in speed accompanied by the curving motion also possibly causes the motion mismatch, because some physical assistant robots require several gait cycles to ﬁt the change in gait timing. Thus, it
is also important to control the gait timing along with the progression ofcurving motion.
5. Conclusion
In this study, the natural curving motion, which is the motion obtained when freely turning around corners, was recorded, and several
curving strategies were identiﬁed using cluster analysis. The ﬁve
identiﬁed curving strategies were characterized by motion indices suchas the inclination of the pelvis, maximum and minimum joint angles,
and peak GRFs. The curving strategy can be largely summarized by thepeak inner and outer rotation angles of the hip joints. In most trials,
subjects used the outer rotation of both legs when stepping on the inner
foot; however, the inner rotation of the outer foot was also used in sometrials. Although these strategies suggest a large variation in the curving
motion within and among subjects, it is possible to categorize suchmotions into one of the ﬁve representative strategies. Such identiﬁcation of motion characteristics can aid in analyzing the natural curving
motion of humans, which has not thus far been suﬃciently understood.
Furthermore, it can also help physical assistant robots to match natural
curving motion in daily living environments.

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