ADVANCED ROBOTICS, 2017https://doi.org/10.1080/01691864.2017.1396251

FULL PAPER

Gait motion for naturally curving variously shaped corners
Yasuhiro Akiyamaa , Shogo Okamotoa , Hitoshi Todab , Takao Ogurab and Yoji Yamadaaa Department of Mechanical Science and Engineering, Nagoya University, Nagoya, Japan; b Mie Prefectural Police, Tsu, Japan

ABSTRACTARTICLE HISTORY

Modeling the curving motion of humans in actual environment is rarely done because of thecomplexity and variability of the turning motion. In this study, various gait motions, includingstraight, round corner, and circular walks, were recorded and analyzed using factor analysis. As aresult, we successfully extracted several factors that represent turning motions, such as long stride
motion, turning motion led by the inner leg, and turning motion led by the outer leg. In particular, wefound that the natural curving motion, which is a motion that results when turning around a roundcorner, is widely and continuously distributed on the factor space. Although several typical stepping
strategies were reported by related studies, we found that the stepping motion changes between
straight and turning gaits in the factor space during natural curving motions. Thus, the classiﬁcation ofcurving motion into several typical distinct stepping patterns is probably insuﬃcient to understandthe natural curving motion. Furthermore, natural curving motions that comprise circular curving
motions that were believed to represent typical curving motions was not validated. On the other
hand, this result also suggests the possibility of generating curving motions for a physical assistantrobot by combining straight gait and circler curving motion.

Received 5 February 2017
Revised 3 August 2017
Accepted 30 September
2017

1. Introduction
The use of physical assistant robots has started spreading
in society because such robots can be used not only forthe rehabilitation on the treadmill [1] but also for gait
assistance of the elderly in daily living [2,3]. Thus, the outof-sagittal motion, which is required in daily activities
such as turning, should be considered. However, many
physical assistant robots have no or limited number ofactuators or joint mechanisms for out-of-sagittal planemotions [4–6], and only few exoskeletons have suﬃcientdegree of freedom and range of motion for such motions[7], although fall is sometimes caused by failure in turning[8–11].
Because of the complexity of human curving motion,
previous studies focused on a limited part of curving motions. Several groups have measured a 180◦ turn [12,13],and the diﬀerence between straight gait and on-site 180◦
turn has been analyzed [14]. Furthermore, some studies
reported that several stepping strategies are available forhumans to turn around a square corner [15–17]. For
example, Taylor et al. [16] indicated the existence of three
types of curving strategies: pivot turning of the inner foot,placing the outer foot in front of the contralateral foot,and directing the inner foot to the curving direction. Xu
et al. [17] separated turning motion around a square anda 45◦ corner to two strategies: step and spin. In addition,
CONTACT Yasuhiro Akiyama

akiyama-yasuhiro@mech.nagoya-u.ac.jp© 2017 Taylor & Francis and The Robotics Society of JapanKEYWORDS

Turning; gait motion; factor
analysis; stepping strategy;
physical assistant robot

the ﬁrst step when the walking direction is altered, which
is probably the transitional motion between a straight
gait and turning motion, was investigated by Patla et al.
[18]. However, in an actual environment, humans rarely
perform such a steep walking path. Furthermore, in theseexperiments, the subjects could not freely select their
walking path and gait timing because the walking path
was strictly controlled by directions and markers on the
ﬂoor. Thus, we anticipated that stepping motions whennaturally turning around corners would be diﬀerent fromthose observed in earlier studies and show more variations.
In contrast, continuous turning around a circler pathwhose radius probably resembled an actual curving path
was also analyzed by other groups [19,20]. These studies
clariﬁed the eye and head direction, ground reaction
force, and lower limb ﬂexion angles when rounding acircler path. However, the transitional motion between
straight gait and circler walk, which appears in the natural
curving motion, was not considered in these studies.
On the other hand, curving motions under more natural conditions were studied by several groups. Olivier andCretual reported the relationship between the curving
radius and speed at a corner section [21]. Reed-Jones
reported the gait motion when turning a blind corner[22]. Okamoto and Yamada studied the stepping strategy

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Y. AKIYAMA ET AL.

Figure 1. Motion capture markers and force sensing shoes wornby the subject.

when a pedestrian avoids another oncoming pedestrian
at a corner [23]. In these studies, the subjects walked
naturally. However, these studies were not intended tomeasure various types of curves, and the observed physical parameters were limited.
Owing to the large degree of freedom or variability, themotion when turning a corner without any constraints inthe walking path and the speed can possibly vary among
diﬀerent corner radii, trials, and subjects. However, suchobservations and analyses were rarely done previously
although such observation could determine varieties ofhuman curving strategies. Thus, we need to experimentally observe various curving motions such as turning
motion around an arc with multiple radii and the transitional phase between turning and straight walk. Understanding the factors that represent the various curving
motions and how the natural walk is composed of thesefactors can possibly enable the design of curving motionsof exoskeletal walking assistant devices by combining
such factors and will be helpful in analyzing its applicability to a variety of natural curving motions. Furthermore, such information will be helpful in determining thespeciﬁcation of the joint coordination and experimental
protocol of the safety and performance test.

2. Method
The experiment was performed with the permission of
the institutional review board of Nagoya University.

Figure 2. Ground mark and walking pathways (black solid lines:
ground mark, foot stamp and gray lines: walking pathways anddirections, dashed lines: scale, cw: clock wise, ccw: counter clockwise).

Corporation, US). A set of critical markers of the SIMM
Motion Module (SIMM, Mulsculographics Inc., US) andsome additional markers were attached (Figure 1(a)). The
ground reaction force was recorded using mobile six-axis
force plates (M3D, Tech Gihan Co., Ltd., Japan) ﬁxed
under the sole (Figure 1(b)). Three types of walking paths,
namely, straight, round corner, and circle, were marked
with tape on the ﬂoor in the recording area (Figure 2). The
total experimental area, which included the accelerationand deceleration areas, was approximately 5 × 8 m. The
radii of the corner sections were 0.5 m (small) and 1.0 m(large). A 1-m radius is common for a round corner[19,20], and a smaller radius, which was closer to a squarecorner, was also used in another study [21].
2.2. Subject

2.1. Apparatus
A series of experiments was conducted in an approximately 4 m × 5 m of recording area in which motion wasrecorded using 10 cameras with three-dimensional motion capture system (MAC 3D system, Motion Analysis

Twelve healthy male subjects participated in the experiment. The average age was 21.2 years old, and thestandard deviation (SD) was 1.7. None of the subjects
reported any disabilities that could aﬀect their gait orbalance. Their mean height and weight were 172.4 cm

ADVANCED ROBOTICS(±3.6 SD), and 61.3 kg (±6.9 SD), respectively. Theiraverage body mass index was 20.6 and ranged from 17.5
to 24.5.
2.3. Protocol
The subjects wore well-ﬁtted sportswear with reﬂective
markers for the motion capture system. During the experiment, each participant walked in self-selected speed
along a straight line, a round corner, and a circle in arandomized order.
The straight-walks were repeated 10 times for eachsubject. The subject was instructed to cross a ground line
in a standing posture. Then, he walked straight to thetarget, which was placed at the extension of the walkinglane.
The corner walks included two circles with diﬀerent
radii. To observe the various curving motions, the starting legs were switched during the trials. A total of 40 trials
were conducted, which consisted of four diﬀerent condition combinations (two radii by two starting legs), andrecorded. The order of the trials was also randomized.
During the trials, the subjects could freely select their gait
speed and walking trajectory except for stepping insidethe drawn curves.
The circular walks consisted of two radii and two
directions. The subject was instructed to walk on eachcircle with four laps and then turn and cover the same
circle for another four times in the opposite direction toprevent dizziness caused by continuous turn. In addition,a suﬃcient interval was introduced between each trial.
The radius of the circle and the starting direction werealso randomized. A total of eight trials, which consisted offour diﬀerent condition combinations (two radii by two
starting directions) were recorded. The subjects were alsoable to freely select their gait speed and walking trajectory
except for stepping inside the ground mark.
2.4. Data processing
Gait motions were recorded at 120 Hz using the motion capture and force plates. To remove the eﬀect ofacceleration and deceleration, the ﬁrst and last 2 m ofthe straight and corner trials and the ﬁrst and last halfcycles of each circle trial were trimmed. Then, the datafrom the motion capture were smoothed using a 6-Hz
Butterworth ﬁlter. The timing of the heel contacts and toe
oﬀs were determined on the basis of the ground reaction
forces with a threshold of 10 N. Trials in which the
tracking markers were critically hidden were not used in
the analysis. Thus, in this study, three trials were unused
for the statistics.
The position of the footprint was calculated as thecenter of the toe and heel markers. The direction of3

the footprint was deﬁned as the line that connected thetoe and heel markers. The orientation and position of
the pelvis origin were determined as the center position
between two anterior superior iliac spines. The positionof the center of mass (CoM) of the whole body wascalculated using Zatsiorsky’s method [24]. The position
and inclination of body links were calculated by ﬁtting
the motion of markers to the human model of SIMM
using the least-squares method.
In the curving trials, rotation radius of the subject wascalculated separately from corner radius to evaluate theactual curving radius of the subject. The rotation radius
was determined as the radius of the circle that ﬁt the pathof CoM in the corner section, which consisted of a quarterof a circular area in the horizontal plane. Fitting was doneusing the least-squares method.
Cadence was calculated as the inverse of the time
diﬀerence between successive heel contacts (HC). Double
support phase was calculated as the ratio of the sum oftime distance between HC and toe oﬀ (TO) of both legs
against gait time. Pelvis velocity, which was the parameterto evaluate speed during turning phase, was calculated by
dividing the length of path of the center of pelvis, which
was determined as the center position between sacral andcenter of both anterior superior iliac spines, by gait time.
HC timing of opposite leg was deﬁned as the ratio of
the time distance between HC of leading leg and HC ofanother leg against the gait time of the leading leg. Whenevaluating mean values of gait parameters, all trials wereused.
The parameters used in the later analysis are shownin Figure 3. The following parameters represent the basic
gait parameters.
• Step distance is the distance between the center position of both legs, which was calculated as the centerof toe and heel markers, along the anteroposterior
direction of the pelvis. This deﬁnition allowed us tocompare the step length even when the direction of
motion is altered.
• Step time is the duration between the current andprevious heel contacts.
The following parameters indicate the orientation of
the body, which are used to evaluate the strengthof the curving motion [25]. These parameters were
calculated at the timing when both heel and toe
contacted to the ground to obtain accurate footmark
position.
• CoM-step is the relative position of the CoM of
the subject from the center of both footprints inboth X (lateral) and Y (anteroposterior) axes. The
axes are directed to the front and outer side of thecorner.

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Y. AKIYAMA ET AL.

Figure 3. Coordinate system and parameters used (Minus wasinserted for parameters whose direction was inversed in the
figure.).

• Pelvis-roll is the rotation angle of the pelvis in thefrontal plane. The motion that elevates the innerside of the pelvis is indicated by a positive sign.
• Front step angle is the angle of the line that connects
the front footprint and pelvis against the anteroposterior direction of the pelvis. Similarly, rear step
angle is deﬁned by the rear footprint and pelvis.
The rotation toward the inner side of the corner isindicated by a positive sign.
The following parameters indicate the characteristicsof the stepping strategy when turning curves [16].
• Foot angle is the direction of the footprint along theanteroposterior direction of the pelvis in which thedirection is the same as the step angle.
• Pelvis-yaw-motion is the change in the pelvis-yaw
angle between the current and last heel contacts in
the global coordinate in which the rotation toward
the inner side of the corner is indicated by a positivesign.
Step distance and CoM step were normalized by theheight of each subject. The orientation and position values such as step angle, foot angle, pelvis orientation, andothers at the timing of each heel contacts were used in
the analysis after determining the z-score. These values
such as the step angle, foot angle, and CoM position weredeﬁned in the local coordinate system that located on thepelvis of each subject.
Because of the gait asymmetry between the inner andouter steps due to the turning motion, single stride, whichstarted at the heel contact of the outer leg and ended
at the next heel contact of the same leg, was used as asingle sample. Because of the diﬀerence in the walking
paths, the number of recorded strides diﬀered among
conditions. The range of the number of strides undereach condition and subject was from 15 to 168. Only one
or two valid strides were observed from a single trial ofstraight motion. In the curving cases, two to four strides,
two or three of which overlapped with the curve section,
were recorded in each trial. Thus, the same numbers of
strides, namely, 15, were randomly extracted from each of
the straight, small-corner, large-corner, small-circle, andlarge-circle conditions for each subject. Hence, a total of
900 strides (ﬁve conditions × 12 subjects × 15 strides)
were used in the analysis.
Table 1 shows the correlation matrix of the above mentioned gait-related parameters. Because several parameters showed some extent of correlations, we used factor
analysis to extract fundamentally correlated parametergroups. After each parameter was z-scored, and a factor analysis provided by the MatLab ‘factoran’ function
was applied. This function uses the maximum likelihood
estimation and Bartlett method for factor loading andscoring, respectively. After calculating the factor scores,
major factors were rotated using varimax method, which
is a general procedure to facilitate the interpretation of
the major factors [26].

3. Results
For the circle condition, the gait parameters, gait timings, and stepping geometries were symmetric between
the clockwise and counterclockwise walking directions.
Thus, both directions of rotation were equally treated.
Furthermore, for the straight-walk trials, because no
asymmetry was observed, the gait cycles starting from theleft and right legs were considered in the same manner.
The typical walking pathways of the straight, corner,and circle walk conditions are shown in Figure 4, whichshows the trace of the footprints, position and orientationof the pelvis, trace of the CoM of the whole body, andcenter of consecutive footprints.
3.1. Gait parameters
The gait parameters among the conditions were compared and are listed in Table 2. The speed and step length,
which were typically used in related studies, could notevaluate the curving gait in a correct manner because
these parameters were deﬁned using travel direction,
which was diﬃcult to be determined in the turning gait.
Thus, the pelvis velocity and step distance were deﬁned
and used in this study. In the straight condition, the speed(1.38 ± 0.13 m/s) and step length (72.8 ± 6.2 cm) wereconsistent with newly deﬁned parameters.
The rotation radius is shown in Figure 5. One outlier
trial, whose rotation radius exceeded 10 m, was out ofrange. In all cases, the rotation radius was larger than thecorner radius. Compared to the circle cases, the distribution of the curve cases was skewed because the subject

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Table 1. Correlation matrix of parameters.
Outer stepS-dis
S − disCs − X
Cs − Y
Rsa
Outer step Fsa
Fta
Pr
Py
S − time

Cs-X

Cs-Y

0.32 −0.83
−0.62

Rsa

Fsa

Fta

Inner stepPr

Py

0.34 0.55 −0.33 0.32 −0.54
0.55 0.66 −0.60 0.58 −0.89−0.56 −0.65 0.57 −0.51 0.79
0.09 −0.78 0.58 −0.68−0.32 0.32 −0.58−0.54 0.68
−0.60

S-timeS-dis

Py

S-time−0.36
0.87 0.35 −0.84 0.53 0.15 −0.54 −0.07 −0.49−0.16
0.16 0.69 −0.52 0.34 0.49 −0.36 0.23 −0.61
0.25 −0.73 −0.56 0.92 −0.47 −0.40 0.52 −0.04 0.68
−0.31
0.33 0.63 −0.55 0.49 0.44 −0.48 0.38 −0.78
0.07
0.35 0.51 −0.64 0.34 0.42 −0.31 −0.02 −0.41
0.21 −0.28 −0.76 0.63 −0.47 −0.55 0.45 −0.35 0.87
−0.25
0.25 0.47 −0.46 0.29 0.33 −0.38 0.48 −0.52
0.33 −0.43 −0.62 0.70 −0.52 −0.38 0.52 −0.15 0.70
−0.41 −0.16 0.33 −0.23 −0.01 0.42 −0.10 0.30

−0.29
−0.14
0.21
−0.28
0.15
0.31
−0.09
0.28
0.62

S − disCs − X
Cs − Y
Rsa
Inner step Fsa
Fta
Pr
Py
S − time

Cs-X

Cs-Y

0.29 −0.80
−0.67

Rsa

Fsa

Fta

Pr

0.58 0.16 −0.59 0.01 −0.44
0.32 0.84 −0.51 0.50 −0.92−0.54 −0.51 0.64 −0.15 0.80
0.04 −0.59 0.12 −0.46−0.37 0.52 −0.70−0.45 0.62
−0.44

−0.29
−0.23
0.23
−0.14
0.03
0.36
−0.05
0.34

S-dis: Step distance, Cs-X: CoM step-X, Cs-Y: CoM step-Y, Rsa: Rear step angle, Fsa: Front step angle, Fta: Foot angle, Pr: Pelvis-roll, Py: Pelvis-yaw-motion, S-time:
Step time.

Table 2. Mean and standard deviation of gait parameters of various curving motions.
Unit
Pelvis velocity
Cadence
Step distance (left)
Step distance (right)
Double support ratio
HC timing of opposite leg

m/s
step/mincm
cm%%

Straight

Large curve

Small curve

Large circle

Small circle

1.36 ± 0.13
112.1 ± 3.9
71.8 ± 5.6
72.1 ± 6.7
23.4 ± 2.5
50.3 ± 1.3

1.23 ± 0.14
108.8 ± 6.0
68.4 ± 6.3
68.3 ± 6.8
25.3 ± 3.5
50.3 ± 1.7

1.17 ± 0.14
107.9 ± 6.1
66.4 ± 7.2
66.4 ± 7.4
25.9 ± 3.7
50.2 ± 1.7

1.00 ± 0.12
105.9 ± 5.8
59.3 ± 8.6
60.3 ± 7.7
27.5 ± 4.4
49.5 ± 1.5

0.79 ± 0.08
104.1 ± 7.9
51.7 ± 7.1
52.2 ± 6.9
28.7 ± 4.4
49.5 ± 1.7

sometimes deviated from the mark at the start and end
points of the corner section.
3.2. Results of factor analysis
The ﬁrst to third factors collectively explained the 64.8%
of the variances of the samples, and that of the fourth factor was merely 5.4%. Thus, the three major factors wereextracted. After varimax rotation, the contributions ofthese factors were 24.6, 22.8, and 17.4%. The factor loadings of each factor are shown in Figure 6 after being scaledby the contribution ratios. In the case of the straight
gait, the ﬁrst step was treated as the outer step. The
original values of these parameters are listed in Table 3
for comparison among diﬀerent motions.
3.2.1. First factor (long stride factor)
The ﬁrst factor could be considered as a long stride factor,
which aﬀected the orientation and motion of the bodyin the sagittal plane. The large positive step distance of
this factor indicats long strides. The negative CoM-stepY indicats that the CoM position in relation to the footprint was positioned backward. These trends were mainly
observed during the straight gait, as listed in Table 3.

Furthermore, this factor was symmetric between bothlegs, which suggested that the ﬁrst factor did not pertain
to the turning motion.
In addition, in the ﬁrst factor, the pelvis-yaw-motion,
which represents the strength of the turning motion, wassmaller than that in the second and third factors. The
positive step angles should be understood by considering
the relative motion of the stepping leg and the pelvis
orientation. As shown in Figure 4, the step of the straight
gait was located relatively outside the pelvis because thepelvis rotated to the opposite direction at the time of theheel contact, in contrast to the turning motion where
both the pelvis and leg rotated to the turning directions.
3.2.2. Second factor (inner leg turn factor)
The second factor could be considered as the rotation
factor of the inner step. The large positive pelvis-yawmotion directly indicated a turning motion, and the negative CoM-step-X and pelvis-roll indicated the inside tiltof the body. A positive foot angle means that the foot was
directed to the curving direction. These tendencies wereobserved mainly in the parameters of the inner step of
the second factor. The front and rear step angle of theinner step, which were deﬁned by the angular diﬀerence

m/BH
m/BH
m/BH
deg
deg
deg
deg
deg
s
m/BH
m/BH
m/BH
deg
deg
deg
deg
deg
s

Step distance
CoM-step-X
CoM-step-Y
Rear step angle
Front step angle
Foot angle
Pelvis-rollPelvis-yaw-motion
Step time

Step distance
CoM-step-X
CoM-step-Y
Rear step angle
Front step angle
Foot angle
Pelvis-rollPelvis-yaw-motion
Step time

Outer step

Inner step

Unit
0.39 (± 0.04 )–0.12 (± 0.05 )–0.40 (± 0.04 )4.54 (± 4.89 )–24.42 (± 6.84 )–3.17 (± 8.13 )–2.16 (± 2.14 )27.10 (± 11.34 )0.55 (± 0.04 )0.39 (± 0.04 )–0.07 (± 0.04 )–0.39 (± 0.03 )–15.81 (± 4.60 )7.95 (± 7.33 )21.44 (± 6.70 )–3.02 (± 2.06 )10.19 (± 8.86 )0.55 (± 0.03 )0.42 (± 0.03 )0.04 (± 0.03 )–0.44 (± 0.03 )–12.08 (± 3.43 )18.85 (± 4.86 )12.26 (± 5.38 )–0.15 (± 1.58 )–10.94 (± 5.67 )0.53 (± 0.02 )Large curve(N = 462)

0.42 (± 0.03 )–0.04 (± 0.03 )–0.44 (± 0.03 )12.06 (± 3.34 )–19.08 (± 4.86 )–12.27 (± 5.42 )0.08 (± 1.61 )11.16 (± 5.76 )0.54 (± 0.03 )Straight(N = 334)

0.38 (± 0.04 )–0.08 (± 0.06 )–0.37 (± 0.04 )–15.40 (± 5.41 )7.73 (± 8.95 )21.14 (± 9.44 )–2.67 (± 2.52 )12.63 (± 12.12 )0.56 (± 0.04 )0.38 (± 0.04)–0.13 (± 0.06 )–0.38 (± 0.05 )4.10 (± 5.54 )–25.53 (± 8.20 )–1.01 (± 9.51 )–2.35 (± 2.46 )30.18 (± 13.85 )0.56 (± 0.04 )Small curve(N = 440)

Table 3. Mean and standard deviation of gait parameters used on the factor analysis (upper half: outer step, lower half: inner step).

0.35 (± 0.05 )–0.10 (± 0.03 )–0.33 (± 0.03 )–19.28 (± 4.19 )2.86 (± 6.85 )26.33 (± 6.02 )–3.21 (± 2.15 )22.62 (± 5.49 )0.57 (± 0.04 )0.35 (± 0.04 )–0.14 (± 0.04 )–0.34 (± 0.03 )–1.44 (± 4.31 )–26.04 (± 6.59 )5.02 (± 5.95 )–3.64 (± 2.12 )35.58 (± 6.94 )0.58 (± 0.04 )Large circle(N = 1344)

0.30 (± 0.04 )–0.13 (± 0.03 )–0.24 (± 0.02 )–21.50 (± 5.81 )0.34 (± 10.39 )33.41 (± 6.52 )–2.71 (± 2.21 )35.38 (± 7.63 )0.57 (± 0.05 )0.30 (± 0.04 )–0.15 (± 0.04 )–0.26 (± 0.03 )–2.01 (± 4.83 )–32.57 (± 9.11 )11.67 (± 7.14 )–3.85 (± 2.10 )47.00 (± 7.65 )0.59 (± 0.05 )Small circle(N = 1209)

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Figure 4. Walking pathways (solid line: trace of foot, dashed lines: trace of CoM, square mark: CoM position at each foot contact, diamondmark: center of consecutive foot marks at each foot contact, gray cross lines: pelvis position and direction).

between the pelvis and foot step, were not large, whichmeant that the subjects changed the directions of thepelvis and inner step when altering the walking direction.
3.2.3. Third factor (outer leg turn factor)
In contrast, the third factor was mainly related to therotation of the outer step. This factor was very similar tothe second factor except that the variables related to theturning motion were largely prominent at the outer step.
3.2.4. Sample distribution in factor space
The factor score of each consecutive step is shown in
Figure 7. The stride samples were distributed along withthe rotation radius. The strides of the straight walk (dark8

Y. AKIYAMA ET AL.

Figure 5. Probability density of rotation radius.

green with edge) were located in the area with positiveﬁrst factor and negative second and third factors. In
contrast, the small-circle walks (scarlet with edge), forwhich the rotation radii were smaller than 0.8 m, werelocated in the area with high negative ﬁrst factor andsmall negative or positive second and third factors. The
large-circle walks (purple with edge in most cases), forwhich the rotation radii were 0.8 to 1.2 m, were located between the straight and small-circle trials. The
general observations in the present study are consistent
with those in the earlier studies. The distribution of thesmall and large circle trials matched the phenomenon
observed by Orendurﬀ et al. [19], where the CoM moved
inside when turning, and this inside shift in the CoM
increased as the turn became sharp. The inside shift of
the CoM corresponded to large second and third factor
scores. Positive front foot angles, which means the inward
direction of the front foot, in the positive second andthird factors matched the stepping strategy, i.e. putting
the pivot foot toward the curving direction, when thewalking direction is altered [16].
The corner walks (yellow with black edging for thesmall radius and chartreuse for the large radius) were
widely distributed between the circle and straight trials
and were especially spread on the second and third factor
planes. The order of distribution, namely, small-circle,
large-circle, corner, and straight walks, which is clearlyshown in Figure 7(a), suggested that the three factors
indicated the strength of the turning motion, which isrelated to the corner radius.

4. Discussion
4.1. Validity of gait motion
The gait parameters for the straight walk shown in Table 2
were compared with those reported in previous studies[27,28] because the types of gait parameters for the cornerand circle walks were not uniﬁed across previous studies. Speed, cadence, and step length were not criticallydiﬀered from that of the present studies. The double
support ratio also matched that of the previous study[29]. Previous study [29] also reported that the value of

Figure 6. Factor loading vectors (upper half: outer step, lower half:
inner step).

the foot angle of the straight walk was approximately 6.3◦
from the travel direction. We note that the deﬁnitionsof the foot angles are diﬀerent between the two studies.
Our result were close to these values when considering
the several degrees of pelvis-yaw angle, which aﬀected
the foot angle in our analysis. The pelvis-roll angle at theright heel contact was approximately 0.1 ± 0.7◦ , and thatat the left heel contact was –0.1 ± 0.9◦ . The values were
smaller than 1◦ as previously reported in previous study[30], and motion symmetry was retained. Although thesoles of the shoes used in the present study was thicker
than general soles, their eﬀect was minor at least on the
gait parameters.
According to Table 2, the gait parameters of the curving cases are located in between the straight and circle
cases. However, it is unclear that which parameters arecausal and dependent. In addition, although the curve
trials included transitional motion between the straight
gait and turning motion, the standard deviation of the
gait parameters of the curve trials were not larger thanthat of the other trials, which suggested that the gaitparameters did not change during the corner turning
motion.
The change in the pelvis velocity can probably describe the change in the gait parameters among the conditions. Previous studies, which compared the gait timing
among straight gaits with diﬀerent speeds, reported that

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Figure 7. Factor score vectors (dark green: straight; scarlet: rotation radius of less than 0.8 m; purple: rotation radius is between 0.8 and
1.2; orange: rotation radius is between 1.2 and 1.6; pink: rotation radius is between 1.2 and 2.0; black: rotation radius is larger than 2.0;
and edged marks: straight and circle cases).

the cadence and step distances decreased, and the double support ratio increased when the pelvis velocity decreased [29,31]. The small deviation of the gait parameters of the natural curving cases probably be consideredthat the deceleration and acceleration phase around thecorner was not observed because of the limitation of thelength of the walking lane.
Previous studies [29,31] reported that when the walking speed decrease to approximately 70%, the cadence
drops to approximately 80%, and the step length drops toapproximately 85%. At the same time, the double support
ratio increases by approximately 57%. However, in thesmall-circle case, although the pelvis speed decreases toapproximately 58% from the straight case, the cadence
drops to approximately 93%, and the step distance drops
to 72%. Because of the body inclination, the pelvis velocity
became smaller than the speed calculated from the step
distance and cadence. In addition, the double stance ratio
approximately increases by 23%. Thus, it appears that thechange of the cadence is small compared to that of theprevious studies.
The ﬁrst factor is related to the walking velocity andthe curve motion is not solely explained by this factor.
However, because the walking velocity was not controlled
in this study to observe the natural motion of the subject,separating the eﬀect of walking velocity and curving condition is impossible. Thus, another study is required to
identify the eﬀect of such parameters.

4.2. Gait parameters do not become asymmetricwhen curving
As listed in Table 2, asymmetry in the step distance was
not observed even during the natural and circler curving
conditions. Although it was unexpected that the step
distance of left and right legs were almost the same evenwhen turning-left the curve or circle, these data suggestthat the asymmetry foot angle did not aﬀect the stride
in the sagittal plane. In addition, the timing of the HCof the opposite leg was nearly 50%, which also suggested
the symmetry of the gait timing in the turning motion.
These facts suggest that gait parameters are not related tothe second and third factors, which are the turn factorsof the inner and outer legs.
4.3. Circle rotation partially simulates the natural
turning motion
Figure 7 shows that the strides could be separated among
the straight and diﬀerent radii of the circle walks in thefactor space. However, they were widely distributed, andthe strides of the corner walks overlapped with the straightand circle walks. In particular, the distribution became
wider in the corner walks than that in the other conditions and was distributed between the straight and circle
walks. An explanation for these distribution characteristics is that the data for the corner walks included somewalking phases such as straight and circle-curve gaits

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Y. AKIYAMA ET AL.

Figure 8. Factor score vectors of the curve trials (dark green: straight; scarlet: rotation radius of less than 0.8 m; purple: rotation radius
is between 0.8 and 1.2; orange: rotation radius is between 1.2 and 1.6; pink: rotation radius is between 1.6 and 2.0; black: rotation
radius is larger than 2.0; edged marks: straight and circle cases; black line: connection between the first and second steps; and gray line:
connection between the second and third steps).

and their transitional motion that appeared during thenatural curving motion.
The strides of some subjects on the factor space whereconsecutive three gait cycles were observed during thecorner walks are shown in Figure 8. In the plane of thesecond and third factors, the corner walk started near
the area of the straight gaits (dark green) and approached
the area of the circle walks (scarlet, purple, and orange
with edge) as the subject entered the corner section. Then,it moved back toward the straight gait as the subject
ﬁnished turning.
However, the values of the ﬁrst factor signiﬁcantly
diﬀered between the corner and circle walks as shownin Figure 7. Figure 6 shows that the low ﬁrst factor,
which means the small step distance and large CoMstep-Y, of the circle walk indicates the gait motion of
the short step and forward leaning, which was a trendthat did not occur in the straight and corner walks. Thisdiﬀerence between the corner and circle walks probably
indicate the qualitative diﬀerence between them. In thecircle walk, the subject continuously turned; hence, theirturning motions might have been adjusted to the circle
walk. On the other hand, the turning motion is temporalin the corner walk.
When developing an exoskeleton, which covers thecurving motion, the curving performance should betested. As a test method, continuous rotation around acircle is probably more convenient than corner curving
due to the small deviation in motion, compact experimental space, and ease in controlling the rotation radius.

However, the diﬀerence between the natural curving andcircle rotation motions should be considered.
Figures 7 and 8 show that the natural curving motion
will probably be considered as the combined motion ofstraight gait and circle rotation in the plane of the second
and third factors. In contrast, the ﬁrst factor of the circle
cases diﬀers from that of the straight and curve cases.
According to Table 3 and Figure 6, the diﬀerence in theﬁrst factor mainly resulted in the diﬀerence of the motionin the sagittal plane. Although such diﬀerence probably
comes from the diﬀerence in the walking velocity, theeﬀect is not very clear. Thus, when the circle rotation
motion is tested instead of the natural curving motion, we
should consider that the natural walking speed changes
depending on the walking path, and the gait parameters and posture, such as the step distance and CoMstep-Y, diﬀer between natural curving and circle rotation
motions. From our study, it is also suggested that thisdiﬀerence become smaller when the curve radius becomelarger.
4.4. Natural turning motions are highly variable inthe space including representative curving
strategies
Figure 8 shows that the distributions of the strides of
the corner walk were widely spread even for the same
subject, especially in the plane of the second and third
factors. The wide and seamless distribution of the second
steps is attributed to the diﬀerence in the walking course,

ADVANCED ROBOTICS

the side of the leg they used to turn around the corner, thestrength of turning of each leg, and the behavior adaptive
to these subtle diﬀerences in the curving motions. In
contrast to the straight and circular walks, the gait motion
varied among the subjects and trials in the corner walks
because the subjects could select the position, direction,and timing to enter and exit the corner, in contrast toturning around the small circles.
Because of such enormous degree of freedom in thenatural curving motion, determining the “typical” curving motions that were reported in earlier studies [16,17] under limited experimental conditions is diﬃcult.
Instead, it appears that the strides of the curving gaitseamlessly distributed in the factor space and the natural
curving motion can probably be considered as the connection of such strides. In addition, part of such curving
motions possibly includes stepping strategies previously
reported in related studies [16,17,19,25].

5. Conclusions
To determine the characteristics of a natural curving motion, gait experiments, which included a straight gait anda continuous looping motion, in addition to the natural
curving motion, were conducted. As a result of the factor
analysis, the curving motions were found to be composedof three major factors: long-stride factor, rotation factorof the inner step, and rotation factor of the outer step.
According to the distribution of the factor score vectors,
the straight and circle walks could be separated, andthe corner walks, which represent the natural curving
motions, can be understood as the motion trajectory thatmoved between the straight and circle turning gaits in theplane of the second and third factors of factor space.
The turning patterns of the strides in the factor spacevaried and were widespread due to the unconscious selection of the walking course. Such corner-curving motions
might not be categorized into a few patterns that wereconsidered in some of the previous studies. Instead, theyshould be expressed in a continuous space such as thefactor space used in this study.
Because of the gradual change in the gait motion whencurving a corner, employing several typical curving motions in a physical assistant robot may not be eﬀective.
On the other hand, the distribution of the curving motions between straight gaits and circler walks suggests theprobability of generating curving motions by combining
these motions. In addition, by comparing the motion
distribution in the factor space of actual curving and thatof the assistant robot, robot applicability can be evaluated.

Disclosure statement
No potential conﬂict of interest was reported by the authors.

11

Funding
We thank the support by JSPS KAKENHI [grant number# 26750121]; the support of Mr. Tsubasa Goto.

Notes on contributors
Yasuhiro Akiyama received the BE degree in engineering from
Tokyo Institute of Technology, Tokyo, Japan, in 2006, and the
MS and the PhD degree in engineering from the Universityof Tokyo, Tokyo, Japan, in 2008 and 2011, respectively. Since
2016, he has been an assistant professor at the Graduate Schoolof Engineering, Nagoya University. His main areas of researchinterests are mechanical safety, human-robot interaction, andmanned space mission.
Shogo Okamoto received MS and PhD degrees in information
sciences in 2007 and 2010, respectively, from the Graduate
School of Information Sciences, Tohoku University. Since 2016,he has been a senior lecturer at the Graduate School of Engineering, Nagoya University. His research interests include
haptics and human-assistive technology.
Hitoshi Toda received MS degree from Nagoya University in
2000. In 2000, he joined Forensic Science Laboratory of Mie
Prefectural Police Headquarters. His main areas of researchinterests are human engineering, traﬃc engineering and safetyengineering.
Takao Ogura received BE degree from Nagoya University in
1996. In 1996, he joined Forensic Science Laboratory of Mie
Prefectural Police Headquarters. His main areas of researchinterests are human engineering, computer vision and image
processing.
Yoji Yamada received a doctor degree from Tokyo Institute ofTechnology in 1990. He had been with Toyota Technological
Institute since 1983 and became an associate professor in the
Graduate School of the Institute. In 2004, he joined Intelligent
Systems Research Institute of National Institute of Advanced
Industrial and Science Technology (AIST). In 2009, he moved
to the Department of Mechanical Science and Engineering,
Graduate School of Engineering, Nagoya University as a professor. His current research interests include safety and intelligence technology in human/machine systems, their robotic
sensing and control.

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