ADVANCED ROBOTICS
https://doi.org/10.1080/01691864.2020.1857304

FULL PAPER

The influence of hip joint rotation of a physical assistant robot on curving motion
Yosuke Kuboki, Yasuhiro Akiyama, Shogo Okamoto and Yoji Yamada
Department of Mechanical Systems Engineering, Graduate School of Engineering, Nagoya University, Aichi, Japan
ABSTRACTARTICLE HISTORY

The use of physical assistant robots is expanding to activities of daily living. However, the risk of auser falling which can occur in various environments has not yet been considered despite this being amajor concern for such robots. Therefore, this study focuses on curving motion, during which fallingis more likely to occur, especially when the degree of freedom of the hip joint is restricted by the
robot. We developed a physical assistant robot with an adjustable degree of freedom of hip rotation and observed the curving motions of the wearer under different joint restriction conditions. The
result was statistically tested and the characteristics were extracted using factor analysis. It was notedthat in the trials involving the restriction of hip rotation, the step length, pelvis yaw angle, and speed
were significantly decreased with the decrease in hip rotation. However, as the participants changed
their curving motion to compensate for the effect of joint restriction, the margin of stability varied
slightly. This result suggested the necessity of implementing an assist algorithm that could change
the gait motion to compensate and improve gait stability when curving.

Received 24 March 2020
Revised 23 September 2020
Accepted 18 November 2020

1. Introduction
Recently, physical assistant robots have been developed toprovide assistance in activities of daily living and industrial tasks [1,2]. However, the risk of falling is a criticalhazard for individuals who use physical assistant robots
for various applications, and thus should be carefully considered. When using a physical assistant robot, the ability
to avoid falls likely decreases due to the restriction of
motion caused by the mass of the robot [3,4], a mismatch of the joint mechanism [5], and/or a mismatch of
the assist pattern [6]. Thus, to expand the applicationsof physical assistant robots, it is important to develop amethod to analyze and decrease the risk of falling [7,8].
The complexity of the real life environment also makes
it difficult to utilize physical assistant robots in daily life.
Traditionally, physical assistant robots were used for gait
rehabilitation on the treadmill [9,10]. While this use caseis important and well-studied, the wearer is almost exclusively walking forward and motion in the sagittal plane
dominates, which is not representative of a real-world
environment. Thus, it is required to expand the motion
ability of the physical assistant robot to fit various situations. Generally, it is required to add joints to expand
the degree of freedom (DoF). However, additional joints
potentially diminishes the assist torque because the assist

CONTACT Yasuhiro Akiyama

KEYWORDS

Physical assistant robot; hiprotation; curving gait; gaitstability; factor analysis

torque is possibly absorbed as the motion and deformation of these joints especially when these joints can movefreely and are not so rigid. Furthermore, it increases thesize and mass of the robot, which makes the usability of
the robot worse. Thus, the motion variability and assist
performance may have the trade-off problem, whichmeans that it is required to realize various motions using
less DoF.
Human use various motions such as curving, sitting
and standing, up and down stairs, and so on in thedaily life. Among these motions, it is relatively easy tomove in the sagittal plane because gait assist robots originally equipped the DoF along with this direction. However, in the daily living environment, people changes
walking direction frequently [7,11–14]. The hip rotation and adduction/abduction, which is not critical forstraight gait, are essential for curving motion [15,16].
One study on this topic demonstrated that if joint motion
is restricted, the curving motion of a human wearing aphysical assistant robot may be hindered [17]. However,
although this study compared the wearer’s motion withand without a robotic hip joint, the results did not apply
to industrial applications of the robot as the hip joint
was removed in the free condition. Furthermore, motion
stability was not analyzed in that study. Thus, the effectakiyama-yasuhiro@mech.nagoya-u.ac.jp

Supplemental data for this article can be accessed here. https://doi.org/10.1080/01691864.2020.1857304© 2020 Informa UK Limited, trading as Taylor & Francis Group and The Robotics Society of Japan

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Y. KUBOKI ET AL.

of joint restriction by a physical assistant robot on thecurving motion and gait stability of the wearer should befurther investigated.
In addition to hip flexion/extension, the internal/externalrotation and adduction/abduction of the hip joint playa key role in performing curving motion [15,18]. In
terms of gait motion, the internal/external rotation of the
hip is the DoF that allows changes in the direction of
the foot, and in turn the direction of the body, during
curving motion. In contrast, adduction and abduction
generate the motion of opening or closing the legs in
the frontal plane. Therefore, even when walking in astraight line, these motions are used to place both feetclose to the center of the body. In the case of curving,
adduction and abduction of the hip are used to perFigure 1. Curving path. The participants were instructed as toform a lateral step, which causes an abrupt change inwhether the left or right foot should be used for the ﬁrst step. This
walking route [15]. Thus, internal/external rotation andﬁgure shows the condition where the ﬁrst step was with the left
adduction/abduction facilitate a smooth curving motion.
foot. The circled numbers denote the number of steps taken. The
Notably, implementation of internal/external rotation
participants walked straight until the second step and performed
a curving motion from the third step.
should be prioritized over adduction/abduction as turning the body is essential to curving motion.
In this study, the change in curving motion in responseto restriction of hip rotation was investigated. A physicalplane by providing an additional DoF, as shown in Figure
assistant robot frame, whose hip rotation joint could be2(b). This sliding mechanism could be fixed to restrict hip
fixed, was used to describe the relationship between joint
rotation. The range of motion of hip rotation was set torestriction, curving motion, and gait stability by factor
30 degree, in accordance with previous work [15].
analysis.
2.2. Participants

2. Experimental method
2.1. Apparatus
The participants walked along the path shown in
Figure 1. The path consisted of a corner section witha radius of 0.5 m and two straight sections which wereused for acceleration and deceleration. The motion of theparticipants in the corner section was recorded using a
motion capture system (MAC 3D System, Motion Analysis Corporation, US). Thirty-five markers were attachedto the body of each participant. The motion capture data
were smoothed using a sixth-order Butterworth filter.
The frame of physical assistant robot, which wascalled MALO (motor actuated lower-limb orthosis), wasattached to the user by the corset around the torso,
belts around the thigh and shank, and shoes. In thisexperiment, actuators were not mounted on the robot
in order to evaluate the effect of the DoF of a joint
on curving motion, independent of stabilizing actuation.
An overview of MALO is shown in Figure 2(a). MALO
had hip, knee, and ankle joints, and all joints could
rotate in the sagittal plane which is generally called flexion/extension. Moreover, the hip joint had an additionalsliding mechanism to allow rotation in the horizontal

Eleven healthy, adult male subjects participated in thisstudy. The participants had an average age of 22.4±2.4
years old (range: 18–25) and an average height and weightof 171.0±5.1 cm and 64.5±7.4 kg, respectively. The bodymass index of the participants ranged between 18.5 and25.2. The experiment was conducted with the approval of
the Nagoya University ethics committee.

2.3. Protocol
Participants were outfitted in the experimental devices
including well-fitting sportswear, motion capture markers, and MALO. Subsequently, participants continuously
walked along the path shown in Figure 1. To control the
gait timing to start curving at the appropriate position,
the starting position was adjusted such that the curving motion started from the participant’s third step. The
participant was instructed to follow the path without
stepping inside the curve.
The hip rotation was sequentially set as free and fixed(unrestricted and restricted) in each trial to observe theinfluence of joint restriction on curving motion. The subject are informed the restriction condition of trials andADVANCED ROBOTICS

3

Figure 2. The frame of physical assistant robot ‘MALO’. The hip, knee, and ankle joints can rotate freely in the sagittal plane, which iscalled ﬂexion/extension. The hip joint has an additional degree of freedom using the sliding mechanism, which allows to rotate in thehorizontal plane. This sliding mechanism can be ﬁxed to restrict hip rotation. (a) Overview. (b) Hip rotation joint.

get used to the device before start recording through several times of training trials. Furthermore, the leg used forthe first step (left/right) was alternated between trials foreach hip rotation condition. Both the left-foot-start andright-foot-start trials were recorded to evaluate the effectof gait timing on when an individual would start curving.
Thus, each participant was tested under four conditions
in total. Ten trials were recorded per condition for eachparticipant, in random order.

3. Data processing
3.1. Parameter definition and calculation
Cycle time (CYtime) is the time between successive heelcontacts (HCs) of the same foot. The timing of the HC
is determined by measuring the minimum height of theheel marker. Step time (STtime) is the time between
the successive HCs of different feet. The step length(STlength) is the distance between the heel markers ofboth feet at the time of HC in the sagittal plane. The
direction of the sagittal plane is the direction perpendicular to the line consisting of the anterior superior
iliac spine (ASIS) markers, which is determined withrespect to the pelvis coordinate system. The center ofmass (CoM) velocity (CoMV) is the velocity of the CoM
at the time of HC; this parameter represents the gait
speed. The motion of the CoM was calculated using Zatsiorsky’s method [19] by fitting the positions of the markers to a human body model (SIMM, Musculographics
Inc., US) [20].

The pelvis yaw angle (PAng) was introduced to evaluate the angle of the pelvis at each step in the horizontal
plane. It is the change in the direction of the pelvis, which
is determined from the rotation of the pelvis coordinate
system in the global coordinate system between the HCs.
The longest (longest dist.) and shortest distances(shortest dist.) are the longest and shortest distances,respectively, between the center of curvature of the walking path and the CoM during the second to fifth steps.
The foot angle (FAng) is defined as the direction of
the foot, which is determined from the line connecting
the toe and heel markers in the pelvis coordinate system. The positive direction is towards the outside of the
body. The hip rotation angle (HRAng) is defined as therotation of the thigh with respect to the pelvis in the horizontal plane. The direction of the thigh is determinedfrom the line of markers attached to the front and rearof the thigh. Since the timing of the HC does not matchthe timing of the maximum (external) and minimum(internal) HRAngs, the maximum and minimum values
during a stride were used. The offsets of both parameters
were adjusted using the data collected from an upright
posture.
Hip flexion (TFlex) and extension (TExt) are calculated in the sagittal plane. The axis of the thigh is determined from the position of the greater trochanter, whichis estimated from the positions of the ASIS and posterior
superior iliac spine [21], and the knee marker. The hipangle is determined as the angle of the thigh axis projected on to the sagittal plane of the pelvis coordinate
system. The offset is adjusted using the data collected

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Y. KUBOKI ET AL.

Table 1. Results of t-test: p-value, median value and quartile range of parameters.
Left-foot-start

Unrestricted
n = 101

Restricted
n = 103

1.58; 1.44 – 2.21
1.54; 1.43 – 1.89

1.57; 1.47 – 1.88
1.54; 1.47 – 1.94

1.55; 1.41 – 2.02
1.55; 1.39 – 2.05

0.81; 0.75 – 1.08
0.79; 0.73 – 1.09
0.81; 0.74 – 0.97

0.82; 0.74 – 1.13
0.79; 0.70 – 1.06
0.75; 0.67 – 0.97

0.79; 0.72 – 1.03
0.80; 0.71 – 0.92
0.79; 0.71 – 1.03

0.78; 0.69 – 1.08
0.78; 0.69 – 0.90
0.78; 0.69 – 1.06

∗∗
∗∗
∗∗

0.46; 0.42 – 0.50
0.43; 0.37 – 0.52
0.44; 0.39 – 0.52

0.40; 0.35 – 0.44
0.36; 0.30 – 0.44
0.24; 0.19 – 0.31

∗∗
∗∗
∗∗

0.52; 0.49 – 0.61
0.82; 0.77 – 0.92
0.46; 0.42 – 0.55

0.46; 0.42 – 0.55
0.94; 0.87 – 1.03
0.41; 0.37 – 0.44

∗∗
∗∗
∗∗
∗∗

0.66; 0.50 – 0.72
0.57; 0.45 – 0.68
0.58; 0.48 – 0.62
0.55; 0.45 – 0.61

0.57; 0.39 – 0.69
0.5; 0.37 – 0.61
0.44; 0.33 – 0.56
0.36; 0.27 – 0.46

∗∗
∗∗
∗∗

0.63; 0.53 – 0.74
0.62; 0.46 – 0.75
0.59; 0.43 – 0.67
0.51; 0.44 – 0.59

0.55; 0.45 – 0.66
0.58; 0.40 – 0.70
0.44; 0.34 – 0.55
0.4; 0.33 – 0.50∗∗∗∗

7.61; 5.42 – 11.38
26.66; 22.51 – 32.65
35.62; 30.55 – 40.15

8.54; 5.20 – 11.81
11.66; 8.84 – 16.76
25.56; 21.74 – 31.08

∗∗
∗∗
∗∗

11.53; 5.13 – 17.23
27.77; 22.66 – 33.41
29.00; 25.35 – 33.48

3.86; 0.21 – 8.99
20.46; 17.26 – 26.00
19.8; 15.68 – 23.92∗∗∗∗

0.84; 0.81 – 0.89
0.58; 0.57 – 0.60

0.82; 0.80 – 0.85
0.6; 0.58 – 0.62∗∗

0.88; 0.84 – 0.92
0.58; 0.57 – 0.61

0.84; 0.80 – 0.89
0.6; 0.59 – 0.62

∗
∗∗
∗∗

7; 2.33 – 17.07
0.84; −3.31 – 10.05−1.48; −10.10 – 5.73
1.93; −1.48 – 8.19

7.41; 3.72 – 17.37−0.98; −3.12 – 1.39
1.29; −4.76 – 7.88
2.08; −1.02 – 4.03

−4.75; −8.72 – −1.48
1.73; −7.88 – 7.17
4.78; −0.18 – 13.79
3.02; −3.46 – 8.32

−4.08; −6.08 – −1.170.80; −2.60 – 9.68
3.52; 1.00 – 6.55
0.21; −3.93 – 7.12

∗∗
∗∗
∗∗
∗∗
∗∗
∗∗

17.83; 14.17 – 25.41
2.28; −5.77 – 5.00
17.59; 14.18 – 19.94
1.78; −1.58 – 4.78
−11.96; −14.04 – −9.65
12.92; 9.90 – 16.96

13.42; 11.31 – 21.10
4.47; −2.62 – 6.19
9.86; 7.71 – 15.05
0.46; −3.59 – 1.73
−5.40; −9.70 – −2.92
5.01; 3.88 – 7.03

∗∗
∗∗
∗∗
∗∗
∗∗
∗∗

1.11; −1.11 – 5.48
−10.03; −12.96 – −7.24
11.63; 8.43 – 15.45
19.97; 11.25 – 29.19−0.37; −5.83 – 2.58
18.86; 15.24 – 25.53

0.33; −1.65 – 2.04
−5.99; −10.52 – −3.80
5.76; 4.54 – 8.64
13.32; 10.99 – 21.99
2.50; −2.87 – 5.98
10.75; 8.18 – 15.39

18.55; 9.29 – 30.63−10.55; −19.72 – 1.71
28.36; 25.42 – 30.76
21.71; 11.93 – 34.37−3.45; −15.15 – 7.28
27.15; 20.40 – 31.61

19.84; 11.65 – 32.06−6.90; −13.43 – 3.97
26.31; 23.11 – 31.46
19.24; 13.46 – 33.07−0.51; −11.5 – 6.31
26.46; 16.88 – 32.52∗∗

22.13; 11.63 – 34.30−6.07; −15.19 – 2.39
28.25; 25.16 – 34.24
18.59; 8.29 – 35.20−7.25; −16.42 – 6.97
25.25; 22.87 – 30.02

20.19; 12.24 – 41.28−5.58; −15.56 – 2.24
28.18; 22.61 – 34.25
18.38; 10.26 – 33.55−1.11; −11.32 – 8.27
22.45; 19.90 – 25.36

∗∗
∗∗
∗∗
∗∗
∗∗

0.08; 0.06 – 0.13
0.09; 0.06 – 0.12
0.12; 0.10 – 0.14
0.12; 0.09 – 0.15
−0.20; −0.22 – −0.15−0.22; −0.27 – −0.16−0.21; −0.27 – −0.17−0.22; −0.26 – −0.18

0.09; 0.06 – 0.12
0.11; 0.09 – 0.14
0.12; 0.10 – 0.16
0.09; 0.06 – 0.13
−0.17; −0.21 – −0.12−0.17; −0.23 – −0.11−0.13; −0.23 – −0.08−0.06; −0.13 – −0.01

∗∗
∗∗
∗∗

0.06; 0.00 – 0.1
0.11; 0.10 – 0.14
0.11; 0.07 – 0.14
0.12; 0.10 – 0.15
−0.19; −0.22 – −0.14−0.26; −0.32 – −0.22−0.17; −0.23 – −0.14−0.23; −0.31 – −0.16

0.08; 0.04 – 0.13
0.13; 0.11 – 0.18
0.11; 0.06 – 0.14
0.14; 0.11 – 0.18
−0.17; −0.21 – −0.12−0.22; −0.29 – −0.17−0.10; −0.16 – −0.05−0.17; −0.23 – −0.11∗∗∗∗

0.21; 0.18 – 0.25
0.04; 0.03 – 0.06
0.22; 0.16 – 0.27
0.00; −0.03 – 0.01

0.21; 0.19 – 0.24
0.05; 0.04 – 0.06
0.15; 0.11 – 0.21
−0.01; −0.06 – 0.01

0.19; 0.15 – 0.24
0.00; −0.04 – 0.01
0.16; 0.13 – 0.19
−0.03; −0.06 – 0.00

0.17; 0.14 – 0.22
−0.01; −0.04 – 0.02
0.15; 0.12 – 0.19
−0.03; −0.07 – −0.01

p-value
Cycle time
CYtime:2–4 [s]CYtime:3–5 [s]Step time
STtime:2-3 [s]STtime:3-4 [s]STtime:4-5 [s]Step length
STlength:2-3 [m]STlength:3-4 [m]STlength:4-5 [m]CoM velocity
CoMV2 [m/s]
CoMV3 [m/s]
CoMV4 [m/s]
CoMV5 [m/s]Pelvis yaw angle
PAng:2-3 [deg]PAng:3-4 [deg]PAng:4-5 [deg]Distance
Longest dist. [m]Shortest dist. [m]Foot angle
FAng2 [deg]FAng3 [deg]FAng4 [deg]FAng5 [deg]Hip rotation angle
HRAng:2–4 (Ext) [deg]HRAng:2–4 (In) [deg]HRAng:2–4 (Diﬀ) [deg]HRAng:3–5 (Ext) [deg]HRAng:3–5 (In) [deg]HRAng:3–5 (Diﬀ) [deg]Thigh ﬂexion/extension
TFlex:2–4 [deg]TExt:2–4 [deg]TFlex-TExt:2–4 (Diﬀ) [deg]TFlex:3–5 [deg]TExt:3–5 [deg]TFlex-TExt:3–5 (Diﬀ) [deg]MoS traveling
MoSt2 (Max) [m]MoSt3 (Max) [m]MoSt4 (Max) [m]MoSt5 (Max) [m]MoSt2 (Min) [m]MoSt3 (Min) [m]MoSt4 (Min) [m]MoSt5 (Min) [m]
MoS mediolateral
MoSl:2–4 (Max) [m]MoSl:2–4 (Min) [m]MoSl:3–5 (Max) [m]MoSl:3–5 (Min) [m]Right-foot-start∗∗

Unrestricted
n = 101

Restricted
n = 107

1.59; 1.50 – 2.22
1.60; 1.50 – 2.06

p-value∗

Note: ∗ ≤ 0.05, ∗∗ ≤ 0.01.

from an upright posture. In our analysis, the maximum
flexion angle, maximum extension angle, and their difference were used. In Tables 1 and 2, this difference isexpressed as ‘TFlex-TExt (Diff)’.
The margin of stability (MoS), which is equivalent to
the index of stability, is calculated independently in thetraveling and mediolateral directions using the XCoM
method [22]. XCoM is an index which consists of theposition and velocity of the CoM to account for dynamicbalance. The MoS is calculated as the distance between
the XCoM and the base of support. A larger MoS indicates greater stability.

ADVANCED ROBOTICS

5

Table 2. Factor scores of curving motion.
Left-foot-start: n = 208
Contribution ratio [%]Cycle time
CYtime:2–4
CYtime:3–5
Step time
STtime:4-5
Step length
STlength:2-3
STlength:3-4
STlength:4-5
CoM velocity
CoMV2
CoMV3
CoMV4
CoMV5
Pelvis yaw angle
PAng:2-3
PAng:3-4
PAng:4-5
Distance
Longest dist.
Shortest dist.
Foot angle
FAng2
FAng3
FAng4
FAng5
Hip rotation angle
HRAng:2–4 (Ext)
HRAng:2–4 (In)
HRAng:2–4 (Diﬀ)
HRAng:3–5 (Ext)
HRAng:3–5 (In)
HRAng:3–5 (Diﬀ)
Thigh ﬂexion/extension
TFlex:2–4
TExt:2–4
TFlex-TExt:2–4 (Diﬀ)
TFlex:3–5
TExt:3–5
TFlex-TExt:3–5 (Diﬀ)
Margin of stability traveling
MoSt2 (Max)MoSt3 (Max)MoSt4 (Max)MoSt5 (Max)MoSt2 (Min)MoSt3 (Min)MoSt4 (Min)MoSt5 (Min)
Margin of stability mediolateral
MoSl:2–4 (Max)
MoSl:2–4 (Min)
MoSl:3–5 (Max)
MoSl:3–5 (Min)

Right-foot-start: n = 204

1st factor
23.2

2nd factor
14.0

3rd factor
13.4

1st factor
20.2

2nd factor
16.5

3rd factor
12.4

0.92
0.76

0.34
0.51

0.16
0.20

0.92
0.87

0.34
0.31

0.11
0.16

0.93

0.24

0.16

0.91

0.30

0.11

−0.23
−0.26
−0.41

0.53
0.79
0.81

−0.05
0.05
−0.02

−0.22
0.07
−0.31

0.48
0.46
0.18

0.68
−0.49
0.83

−0.83
−0.91
−0.87
−0.81

0.24
0.12
0.33
0.49

0.01
0.01
−0.10
0.04

−0.88
−0.92
−0.76
−0.82

0.08
0.19
0.04
0.10

0.37
0.20
0.59
0.38

−0.30
−0.17
−0.56

0.23
0.73
0.51

0.29
−0.30
0.13

0.00
−0.56
0.01

0.02
0.35
−0.14

0.71
0.44
0.53

−0.22
0.12

0.22
−0.36

−0.19
−0.31

0.47
0.05

0.03
−0.21

0.35
−0.14

0.19
−0.05
0.26
0.07

0.47
−0.20
0.08
−0.43

0.08
−0.94
0.22
−0.76

0.35
0.02
0.21
−0.05

0.22
−0.73
0.36
−0.56

0.03
−0.06
0.19
0.25

−0.22
0.09
−0.61
0.08
0.17
−0.10

0.31
0.06
0.47
0.28
−0.41
0.65

−0.67
−0.80
0.34
−0.02
−0.07
0.06

−0.26
−0.03
−0.21
−0.23
0.05
−0.47

0.14
−0.14
0.27
−0.26
−0.44
0.33

0.07
−0.27
0.34
0.50
0.26
0.38

0.10
0.20
−0.25
0.02
0.20
−0.27

0.07
−0.02
0.27
0.14
−0.18
0.51

0.58
0.46
0.45
0.57
0.36
0.43

−0.06
0.17
−0.33
0.01
0.09
−0.20

0.63
0.36
0.66
0.60
0.47
0.53

0.09
−0.07
0.25
0.11
0.04
0.20

0.62
0.73
0.22
0.42
0.83
0.79
0.51
0.57

−0.07
0.01
0.06
0.48
−0.22
−0.23
−0.52
−0.27

0.42
0.14
0.50
0.33
−0.03
0.06
0.29
0.28

−0.03
−0.48
0.08
−0.36
0.91
−0.22
0.18
−0.02

0.57
0.67
0.75
0.70
−0.18
0.40
0.33
0.76

−0.19
−0.09
0.02
0.40
−0.21
−0.65
−0.59
−0.34

0.08
−0.13
−0.10
0.32

0.06
−0.26
0.01
−0.07

−0.35
−0.11
−0.58
−0.13

−0.05
0.52
0.29
0.55

−0.13
0.01
0.08
−0.16

0.05
−0.23
0.16
−0.01

The MoS in the traveling direction (MoSt) attains its
minimum value shortly before HC and reaches its maximum soon after the whole foot touches the ground. These
values are the minimum and maximum MoS of each step,
respectively. The timings of the maximum and minimum
MoS in the mediolateral direction (MoSl) are determinedfor each stride.

3.2. Analysis method
In advance, logarithmic transformation was performed.
Stride parameters were compared between groups ofdifferent hip rotation restriction condition using MANOVA(Multivariate analysis of variance) [23]. Then, eachparameter was compared using t-test, respectively [24].

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Subsequently, factor analysis was used for both the leftfoot-start and right-foot-start trials to extract the featuresof the curving motion [25].

4. Results
The second to fifth steps of each trial were analyzed,
as all participants performed these steps in a curving motion regardless of restriction condition. Trials inwhich motion capture markers were entirely obstructedfrom view were omitted. Thus, 6–10 trials were analyzed
from the test conditions for each participant with a totalof 101–107 trials analyzed for each condition. The number of trials of each condition are provided in Table 1.
The trajectory of footsteps of representative trials of eachcondition are shown in Figure 3
4.1. Difference in parameters for different joint
restriction conditions
The parameters for each condition are listed in Table 1.
The numbers beside each parameter correspond to thestep number defined in Figure 1. Parameters were statistically compared by MANOVA and t-test between different restriction conditions. According to the result of
MANOVA, significant difference were seen in both Leftand Right foot start conditions (p < .01) between theunrestricted and restricted conditions.
4.1.1. Left-foot-start
As shown in Figure 1, the second and fourth steps correspond to the right foot in this case. Thus, the third andfifth steps correspond to the left foot. In the restrictedcondition, the values of HRAng and TFlex/Ext suggested that hip rotation decreased significantly, unlike
the flexion and extension of the hip joint. With regards
to the gait timing, which was represented by CYtime,
STtime, STlength, and CoMV, the speed and step length
decreased significantly, while there was a non-significant
decrease in step time. Furthermore, it was noted that adecrease in the PAng corresponded to the decrease in step
length. The difference in the MoS depended on the direction and side of the leg. In the traveling direction, the MoS

Figure 3. Position of footstep and CoM trajectory. Representative trials of each condition are displayed. The number placed beside eachfootstep stands for the step number. (a) Unrestricted, start from left step, (b) Restricted, start from left step, (c) Unrestricted, start fromright step, (d) Restricted, start from right step.

ADVANCED ROBOTICSof the left step was more affected by the restriction of the
hip joint compared to the right step.
4.1.2. Right-foot-start
When the trial was started with the right foot, in contrast to the situation shown in Figure 1, the third andfifth steps corresponded to the right foot, and the second and fourth steps corresponded to the left foot. The
trend in the hip angle and gait timing data was similar
to the trend observed in the left-foot-start case. However,the difference between the MoS values was smaller in thiscondition.

4.2. Factor analysis
The results of the factor analysis are presented in Table 2.
Three major factors were identified for each condition.
To improve the accuracy of the analysis, the step time wasconsolidated as a single parameter.
4.2.1. Left-foot-start
The first factor was primarily related to the CYtime,
STtime, CoMV, MoSt, and HRAng of the right stride(between the second and fourth steps). The parametersdescribing gait timing, except for STlength, were represented by this factor. The second factor primarily consisted of the STlength, PAng, and HRAng of the left
stride (between the third and fifth steps). The third factor
was represented by the FAng, HRAng of the right stride(HRAng:2–4), and TFlex/Ext. Notably, the second factor pertained to the parameters that significantly differed
between the restriction conditions. Furthermore, HRAng
was related to each of the three factors.
Subsequently, the relationship between the restriction
condition and the factors was evaluated by performing
the t-test. The results indicated that both the first and second factors differed significantly (p < .01) between theunrestricted and restricted conditions. In the restrictedcondition, the first factor became big whereas the second
factor was small.

7

restriction conditions indicated that only the third factor was significantly reduced (p < .01) in the restrictedcondition.

5. Discussion
5.1. Curving motion under unrestricted condition
5.1.1. Left-foot-start
Although the participant entered the corner section fromthe third step (left step), the direction of the pelvis
changed only slightly, according to the value of PAng:23 in Table 1. However, the slight internal rotation of theright hip (indicated by HRAng:2–4 (In)) suggested thatthe stepping leg was directed along the curve rather than
the straight section.
At the fourth step, the participant started turning. To
place the fourth step (right step) inside the curve, thestance leg rotated inward, as indicated by the rotation of
the left hip (HRAng:3–5 (In)). Thus, PAng:3-4 increased
at this step. Furthermore, the large PAng of the fifth step
(PAng:4-5) suggested that the curving motion continued
at the fifth step.
5.1.2. Right-foot-start
The participant started to curve from the third step (rightstep) in this case as well. The large internal rotation of theleft hip (HRang:2–4 (In)) suggested that the third step
was toward the inside of the curve, although PAng:2-3
was less than in successive steps. This motion resembled that of the fourth step in the left-foot-start case, andcorresponded to the outside (right) leg.
Next, at the fourth step, PAng:3-4 increased, indicating the change in body direction had begun. At this step,
the step length (STlength:3-4) was greater than that of theother steps. The long fourth step required the small external rotation of the left hip (HRang:2–4 (Ext)) to preventto separate from the path.

5.2. Effect of the restriction of hip rotation
4.2.2. Right-foot-start
The first factor was related to the CYtime, CoMV, andMoSt, similar to in the left-foot-start case. However,the second factor consisted of the MoSt, FAng, andTFlex/Ext, which differs from the left-foot-start case.
The third factor consisted of the STlength, PAng, andMoSt, and appeared to be similar to the second factor of
the left-foot-start case, as it consisted of the parametersthat significantly differed between the restriction conditions. The comparison of the factors between the different

5.2.1. Left-foot-start
It appears obvious that the decrease in the HRAng
is a consequence of joint restriction. Accordingly, thedecrease in the PAng is likely caused by the decrease in
hip rotation because hip rotation is essential to chang
the direction of the pelvis. Furthermore, the CoMV and
STlength decreased, which indicate a change in gait. The
decrease in these parameters could be attributed to thefact that the participant walked with a short stride due torestriction of hip rotation.

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According to the factor analysis, both the first andsecond factors were considerably affected by the restriction of the hip joint and included the HRAng. However,the parameters included in each factor were different.
The first factor was related to the STtime, CoMV, MoSt,
and HRAng:2–4(Diff)), which represents the stride of
the outer leg. It is interesting to note that these parameters are not directly related to the curving motion. In
contrast, the parameters of the second factor, such as
the STlength and PAng, are parameters representative of
curving motion. Furthermore, HRAng:3–5(Diff)), which
denotes the stride of the inner leg, was included in thisfactor. Thus, according to the first factor, the restrictionof the outer leg led to a slow gait, which corresponded
to a decrease in speed and the STlength. In contrast, thesecond factor suggests that the restriction of the inner leg
diminished the curving motion of each step, corresponding to a small PAng and STlength.
5.2.2. Right-foot-start
Although the trend of the parameters appears to be similar to that of the left start case, the effect of restriction
seems to be smaller, especially for the MoS. In the factor
analysis, the parameters of the first factor partly resembled those of the left start case, as the STtime and CoMV
were related to this factor. However, the hip rotation was
weakly related to this factor, and the effect of the joint
restriction was not significant. The parameters related
to the curving motion (i.e. STlength and PAng) were
included in the third factor and the effect of the joint
restriction was significant. Furthermore, the HRAng was
also weakly related to this factor. Thus, in the right startcase, the relationship between the restriction of a specificside and change in the motion is more obscure comparedto that of the left start case.

balance naturally, the MoSt tended to increase in the
restricted condition. It is possible that this arose from theparticipants compensating for the effect of joint restriction to maintain a balanced gait. Although the reduction of pelvis yaw angle in each step tended to decrease
the MoS by decreasing the step length, the participants
recovered from this effect by decreasing the gait speed.
Furthermore, the MoSl was related to the CoMV rather
than the STlength, as indicated by the first factors of boththe left- and right-foot-start cases. It should be considered that MoS cannot currently be used as an absolutemeasure of stability because gait motion is fundamentally
unstable. Thus, the value of the MoS is a relative index,
and the qualitative difference in gait motion caused bycompensation for joint restriction should be considered.
5.4. Limitations
For statistical analysis, the subjects with similar attribution, young male adults, were recruited in this experiment. However, the effect of joint restriction on the curving motion probably differs among various gait motionsof different attribution of subjects. For example, it wasreported that the elderly sometimes performes a different
stepping strategy [26]. The experiment of subjects withvarious gait motions is required to generalize the result.
The curving motion maybe depends on the configuration of physical assistant robot because the mass, inertia,
stiffness and other design parameters potentially affectgait motion [3,4,27]. In this study, the joint restriction
was focused. Thus, the curving motion under the restriction of hip rotation were compared. Furthermore, common type of joint mechanism and fixation method are
selected for generality. To evaluate the effect of configuration of assistant robot, another study, which compares
the motion under different configurations, is required.

5.3. Stability
According to the definition of the MoS, to improve the
MoS, the step foot must be placed far from the CoM andthe CoM height and velocity should be decreased [22].
However, none of the participants attempted to control
their CoM height in this experiment. Thus, the change in
the MoS was caused by changes in foot position and CoM
velocity.
During the curving motion, the change in CoM velocity and step position was predominantly observed in thesagittal plane. Thus, the MoSl was slightly affected by
restriction, especially in the right start case. Furthermore,
the MoSl was not strongly related to the three major
factors.
In the traveling direction, despite the joint restriction making it difficult for the participants to maintain

6. Conclusion
In this study, changes in gait and stability caused by aphysical assistant robot were observed and analyzed during curving motion. Factor analysis was used to reveal
important features of curving motion with and without
joint restriction. The results suggested that restriction of
hip rotation which is required for curving motion caused
a significant decrease in the step length, speed, and pelvis
yaw angle of each step. Furthermore, it was revealed
that the participants changed their curving motion tocompensate for the effects of joint restriction. However,considering gait stability, the MoS sometimes increasedin the restricted condition. This trend can be ascribedto the fact that the participants maintained gait stability when compensating for joint restriction. The results

ADVANCED ROBOTICSof this study indicate that an assist algorithm for curving motion should be formulated for physical assistantrobots. In particular, this algorithm should match thecharacteristics of curving motion, which differs according to the actuation mechanisms of different joints in thephysical assistant robot. Therefore, the result of this study
suggests the direction of the improvement of the joint
structure and assist algorithm of the physical assistantrobot, which will be used in the daily living environment.

Acknowledgments
We thank the support by JSPS KAKENHI Grant Number
17K01293 and the support of our group members, Yusuke
Fukui and Takuma Igami. We also thank Ms. Xuan Yang.

Disclosure statement
No potential conflict of interest was reported by theauthor(s).

Funding
This work is support by JSPS KAKENHI Grant Number
17K01293.

Notes on contributors
Yosuke Kuboki received the B.E. and M.S. degree in engineeringfrom Nagoya University, in 2018 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.
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. Since
2016, he has been an assistant professor of Nagoya University, Japan. His main areas of research interests are mechanicalsafety, human–robot interaction, and manned space mission.
Shogo Okamoto received M.S. and Ph.D. degrees in information sciences in 2007 and 2010, respectively, from the Graduate
School of Information Sciences, Tohoku University. Currently,
he is an associate professor at the Department of Mechanical
Systems Engineering, Nagoya University. His research interests include haptics, affective engineering, and human-assistive
technology.
Yoji Yamada received a doctor degree from Tokyo Institute ofTechnology in 1990. In 2004, he moved 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 of Intelligent
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, and assistive robotics.

9

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