RESEARCH ARTICLE

Effects of exoskeletal gait assistance on therecovery motion following tripping
Yasuhiro Akiyama ID☯*, Yusuke Fukui☯, Shogo Okamoto‡, Yoji Yamada‡
Department of Mechanical Systems Engineering, Nagoya University, Nagoya, Aichi, Japan☯ These authors contributed equally to this work.
‡These authors also contributed equally to this work.
* akiyama-yasuhiro@mech.nagoya-u.ac.jp

Abstract
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OPEN ACCESS
Citation: Akiyama Y, Fukui Y, Okamoto S, Yamada
Y (2020) Effects of exoskeletal gait assistance on
the recovery motion following tripping. PLoS ONE
15(2): e0229150. https://doi.org/10.1371/journal.
pone.0229150

Physical assistant robots improve the user’s ability to walk. However, they also potentiallyaffect recovery motion following tripping. The assist algorithm should not interfere with therecovery motion, and should enhance the ability of the user to recover after tripping. Thus, inthis study, we investigated the recovery motion affected by the assist robot after tripping.
We compared the recovery motion with different reaction algorithms. Principal component
analysis revealed the effects of the reaction algorithm. Correspondingly, principal components were related to the recovery motion during two steps following tripping. Specifically,
the effects of the reaction algorithm were related to a principal component that represented
the motion of the second step after tripping and that increased the margin of stability. Furthermore, the margin of stability became significantly large when the assistive torque wasapplied during the recovery motion. The result of this study suggests that the assist robot
can potentially enhances the recovery motion of its user following tripping.

Editor: Ning Cai, Beijing University of Posts andTelecommunications, CHINA
Received: October 3, 2019
Accepted: January 30, 2020
Published: February 24, 2020

Introduction

Copyright: © 2020 Akiyama et al. This is an open
access article distributed under the terms of theCreative Commons Attribution License, which
permits unrestricted use, distribution, andreproduction in any medium, provided the original
author and source are credited.

Physical assistant robots are now associated with a broad range of applications in various facetsof daily lives compared to their initial uses for rehabilitation in hospitals [1, 2]. Therefore, assist
robots are required to improve their configurations and algorithms to fit the new environments. In particular, the fundamental problem associated with the introduction of the assist
robot in daily living environments pertains to their abilities to become accustomed with thevariety and flexibility of motion types [3]. Accordingly, the expansion of the range of uses andtypes of environments concomitantly generates new types of risks for assist robots [4].
In the case of the gait assist robot, the risk of falling becomes critical from the viewpoint of
the product’s liability. Even in daily living environments, humans can naturally fall by themselves because they occasionally trip or slip [5, 6]. If a motion mismatch occurs between theassist robot and its user during the recovery motion to avoid the fall, the risk of falling willprobably increase. Thus, it is required that the assist robot does not disturb the reaction
motion induced by perturbations [7]. Furthermore, it is better to enhance the recovery motion

Data Availability Statement: All relevant data arewithin the paper and its Supporting Information
files.
Funding: This work was supported by KAKENHI ofJapan Society for the Promotion of Science. The
Grant Number is 17K01293.
Competing interests: The authors have declaredthat no competing interests exist.

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Effects of exoskeletal gait assistance on the recovery motion following tripping

if this is possible. For this purpose, the evaluation and quantification of the effects of the assistant robot on the recovery motion is required.
The motion characteristics associated with the avoidance of the fall have been studied formany years from the viewpoint of human gait. The two major strategies adopted against tripping during gait are the “elevating” and “lowering” strategies [8]. When tripped in the early tothe middle parts of the swing phase, humans frequently overcome the obstacle by lifting thetripped leg [9, 10]. This is referred to as the elevating strategy. By contrast, when the tripping
occurs in the middle to the late parts of the swing phase, humans typically place the tipped leg
behind the obstacle and step the opposite leg forward. This is commonly referred to as the lowering strategy. Although it is likely that this strategy will be adopted even when an assist robot
is used, this assertion has not been verified yet.
Furthermore, to evaluate the stability of the posture and motion, many methods have been
proposed [11]. Some of these indices are designed to evaluate the periodicity of the gait
motion. However, they are not suitable for the evaluation of the reaction against large perturbation because the recovery motion largely differs from the periodic gait motion. Other methods have been based on the consideration of dynamic stability [12, 13]. However, it is not easy
to evaluate the absolute stabilities of gait and recovery motion using the dynamic stability
index because these types of motions are not inherently physically stable. Therefore, these indices should be used as the relative measures of the degree of imbalance of the motion. These
indices are probably applicable for the evaluation of the recovery motion.
Therefore, the measurement and evaluation of the recovery motion following tripping
could help improve the utility of the assist robot. Specifically, the effect of the assist robot on
the performance of the recovery motion is important. Therefore, in this study, we hypothesized that the reaction algorithm that is based on the estimation of the torque applied by anassist robot during the recovery motion affects the ability to recover following tripping. The
effects of the reaction algorithm could be evaluated by comparing the recovery motions
between different reaction algorithms. Furthermore, the characteristics of the recovery motionin the case of a human robot user could be identified. These are the numerous issues that havenot been considered nor investigated in an exhaustive manner.

Methods
The experiments were performed with the permission of the institutional review board of
Nagoya University (approval number: 17–2). Before the onset of the experiment, the subjects
provided informed consent and signed the relevant consent forms.

Apparatus
Assistive devise. A lower-leg exoskeleton which was developed in our lab, referred to as
motor actuated lower-limb orthosis (MALO), was used in this experiment. It consisted of acorset, thigh frames, shank frames, and shoes, as shown in Fig 1. Each neighboring link wasconnected by a single degree-of-freedom (DOF) rotation joint. Hip and knee joints were actuated using direct current motors (RE 40, Maxon Motor AG, Sachseln, Switzerland). The corset
was made of flexible plastic to fit the wearer. A belt was used to fix the frames of MALO to thethigh and to the shank of the user. MALO’s weight was supported by itself through a robotic
frame. Four mobile force plates (M3D, Tec Gihan Co., Ltd., Kyoto, Japan), which could measure 6-DOF forces and torques, were fixed on the sole. They were placed under the toes andheels of both feet. Heel contact (HC) was determined at the time at which the normal component of the ground reaction force (GRF)—as measured by the force plates—exceeded 100 N.

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Effects of exoskeletal gait assistance on the recovery motion following tripping

Fig 1. Structure of the motor actuated lower-limb orthosis (MALO) exoskeleton corset, frames, and shoes withsingle degree-of-freedom rotation joints. Hip and knee joints are equipped with direct current motors.
https://doi.org/10.1371/journal.pone.0229150.g001

The mean time duration of the previous two gait cycles (GCs) was assumed as the gait duration of the subsequent GC. The GC was determined as the time period between the successive
heel contacts of one of the two legs. The current gait phase was calculated as the ratio of thetime from the preceding HC and the estimated gait duration.
The gait assist algorithm of normal walking was designed to help the forward movement of
the body during the stance phase and the leg swing during the swing phase. At the stancephase, the hip joint was assisted toward the direction of leg extension and occurred during theGC (15–45% interval). Furthermore, knee flexion was assisted during the 30–60% interval of
the GC. At the swing phase, hip flexion was assisted during the 65–95% interval of the GC.
The knee extension assist was applied during the 75–95% interval of the GC. The maximum
assistive torque was set at 7 Nm, and corresponded to 20–25% of the inner torque of the lower
limb joints [14, 15]. The upward and downward edges of the assistive torque pattern weresmoothed to achieve comfortable assist using a square sinusoidal function.
Furthermore, the control algorithm of MALO was designed to compensate for the friction
torques of all the joints which were measured a priori. Furthermore, the assistive torque wasinterrupted when the joint started rotating toward the inverse direction to that of the assistive
torque to prevent interference with the user’s motion, even at the time instant at which theassist torque should have been applied.
When the user tripped, there was an option to completely stop the application of the assist
torque. The only exception was the torque which was applied for friction compensation. Thiswas referred to as the “Stop pattern.” This constituted another option for the continuous application of assist torque that was designed for normal gait patterns. This was referred to as the“Continue pattern.” The former pattern was based on the consideration that the robot should
not interfere with the reaction motion of the user in emergency cases. However, the implementation of this strategy is possible only when the tripping could be detected accurately
online. Subsequent pattern is easily installed because the modification or switching from normal assist pattern is not required. However, the assist torque probably affects the recovery
motion although our algorithm was designed in such a way that the torque was not applied to

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Effects of exoskeletal gait assistance on the recovery motion following trippingFig 2. Experimental setups. (a) The subject is tripped by an obstacle in the middle of the walking lane. A safety
harness was connected to the gondola to support the subject in the cases of falls. Gait timing is controlled using a guidepole and metronome. (b) The reaction force of the obstacle was used to detect tripping and switch the assist pattern toreaction algorithms. The assist torque was applied based on the gait cycle estimated from the timing of gait events.
https://doi.org/10.1371/journal.pone.0229150.g002

the inverse direction of the joint rotation. These reaction algorithms were designed as the basic
algorithmic tools to evaluate the feasibility and effectiveness of the gait assist process.
Experimental setup. The overview of the experimental setup is shown in Fig 2. The walking and tripping experiment was conducted in a walking lane with dimensions of 5 × 8 m(W × L). Part of this lane (4 × 5 m) was used as the acceleration and deceleration area. In the
middle of the walking lane, the subject who wore the MALO was forced to trip occasionallywith the use of an obstacle which was fixed on the ground, as shown in Fig 2(a).
The gait and recovery motions following tripping were recorded using 10 camera motion
capture system (MAC 3D System, Motion Analysis Corporation, Rohnert Park, CA, US). To
observe the motion of the subject, markers were attached on 24 feature points on the humanvolunteers. The selected feature points were as follows: top head, front head, rear head, sternum, shoulders, elbows, wrists, anterior superior iliac spines (ASISs), posterior superior iliac
spines (PSISs), greater trochanters, knees, ankles, toes, and heels. For some points covered or
hidden by MALO, cluster markers were used.
The subject wore a safety harness which connected the gondola placed above the walking
lane and which moved with the subject to prevent falls. The cable of the harness supported thesubject using air spring but it was usually slacked to avoid interference with the gait motion. In
addition, protectors and supporters were attached to the subject.
The obstacle which was used to trip the subject consisted of a metal plate, as shown in Fig 2(b). The height of the obstacle was 15 cm, and was within the range of obstacles used in tripping experiments [16, 17]. The position of the obstacle was adjusted for each subject so thattripping occurred in the early swing phase.
The timing of tripping and the impact force were measured using four force sensors(M3D-EL-FP-U, Tec Gihan Co., Ltd., Kyoto, Japan) which were fixed behind the tripping
plate. As shown in Fig 2(b), the force applied to the obstacle was monitored by the computer
which executed the assist algorithm and implemented the switching process. The threshold of
the tripping was set to 60 N. Although this tripping detection scheme cannot be used outside

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Effects of exoskeletal gait assistance on the recovery motion following tripping

the laboratory, we selected this method to concentrate on the analysis of the effects of the reaction algorithm.
To prevent the subjects from anticipating the tripping, the subjects wore goggles which covered their lower halves. Furthermore, to stabilize the gait of the subject in all the trials, especially after the tripped trials, two guide poles were placed on the right side of the stepping
position of the acceleration area as indicators. In addition, a mark was placed at the extensionof the walking direction to maintain the walking pattern along a straight line.

ProtocolTen healthy male subjects participated in the experiment. The average age was 23.1 years, andthe standard deviation (SD) was 1.8. Their mean height and weight were 172.9 cm (± 3.5 SD),and 63.6 kg (± 5.1 SD), respectively.
Subsequently, the subjects wore well-fitted sportswear, the MALO, safety gears, and reflective markers, to allow the recording of the motion trajectories. To adapt to MALO, the subject
walked on the walking lane repeatedly until the gait motion became stable. The positions of
the guide pole and the obstacle were determined at the end of this training session. The tripping experiment then began. The subject was allowed to take breaks as needed.
In each trial, the subject stepped in place to initiate gait and adjusted the assist timing before
he moved along the walking lane. The subject then started to walk forward along the lane tothe beat of the metronome and in compliance with the foot indicator.
As mentioned above, one of the two reaction algorithms applied the stop and continue patterns to the MALO after tripping. The reaction algorithm was selected randomly according to
the trial. At the same time, the side at which tripping occurred was changed to eliminate theeffects of the anticipation of tripping. Furthermore, dummy control trials were conducted during which no tripping occurred.
In total, 30 trials were conducted for each subject which included 10 dummy trials. The
number of trials of each condition was controlled and was maintained the same. Furthermore,
the side of tripping (i.e., the selection of the tripping leg) was randomized. Accordingly, thedummy trial was randomly inserted in the sequence of conducted trials.

Data processing
The motion of the subject, GRF, and the interaction force at the obstacle, were acquired at 100
Hz. The recorded motion was smoothed using a 6 Hz Butterworth filter. The joint angle, posture, and the position of the center of mass (CoM) of the subject were calculated based on thefitting of a human model to the position of the markers using the least-squares method. The
biomechanical analysis software SIMM (SIMM, MulsculoGraphics Inc., Evanston, IL, US),was used for this process. The CoM of the entire body was calculated using Zatsiorsky’s
method [18]. Recorded recovery motions of tripped trials were combined across subjects inthe analysis process. In this study, the effects of the contact side differences were ignored.
Regarding the recovery motion following tripping, an elevating strategy was anticipated inthis experiment according to previous research studies which analyzed the relationshipbetween the phase of tripping and reaction strategy [8, 10]. Furthermore, preliminary experiments suggested that the fall avoidance motion could not be completed within a single step.
Thus, in this study, the recovery motion was considered until the landing of the second step
following the onset of tripping. The recovery motion was separated into two phases for analysis. The first phase was determined as the motion between the hit timing (HT) and the firststep (FS), which represented the timing of the landing of the tripped leg. The second phasestarted from the FS and continued to the second step (SS), and was performed by the leg which

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Effects of exoskeletal gait assistance on the recovery motion following tripping

was opposite to the tripped leg. The parameters, which represented the recovery motion ofeach phase were determined as follows:• WS_F(S): Average walking speed of each recovery step
• StT_F(S): Time duration of each recovery step
• TrL_F(S): Normalized length of the trajectory of toe during each recovery phase• ToH_F(S): Maximum toe height during each recovery phase• KA_F(S): Offset maximum knee flexion angle during each recovery phase• StL_F(S): Normalized stride length of each recovery step
• CVx_F(S): Velocity of CoM in the traveling direction at the FS or SS• CVz_F(S): Velocity of CoM in the vertical direction at the FS or SS• MoS_F(S): Margin of stability in the traveling direction at the FS or SS• CPz_F(S): Normalized minimum CoM height of each recovery phase
The average walking speed was calculated as the average speed of the CoM in the traveling
direction within the intervals of successive HCs. The time duration of recovery step was calculated as the time period within the time intervals of successive HCs. The normalized toe trajectory was the moving length of the toe marker of the recovery leg during each recovery phasenormalized by the height of each subject. The maximum toe height and knee angle were themaximum values of the toe marker and the knee angle during each recovery phase, respectively. The knee angle was offset by the mean maximum knee flexion angle of the dummy trialsof each subject. The normalized stride length was determined as the moving distance of theheel marker of the recovery leg through the recovery step in the travelling direction normalized by the height of each subject. The CoM velocities in the traveling and vertical directions
were determined as the CoM speeds of each direction at the timing of each HC.
The margin of stability (MoS) is a parameter which evaluates the dynamic balance by considering the area of the base of support, the position of the CoM, and the CoM velocity [19]. In
this study, the MoS was determined as the distance between the position of the toe marker ofthe forward foot and the extrapolated CoM (XCoM) in the traveling direction. The XCoM wascalculated using the following equation [19].
vCoM
XCoM ¼ CoM þ pffiffiffiffiffiffi
g=l

ð1Þ

The vCoM is the velocity of CoM in the travelling direction. The symbols g and l respectively
denote the gravity coefficient and CoM height. The MoS, which could be successfully used toevaluate the gait balance in the lateral direction [20], was used to compare the stability in thetraveling direction for the different timings and conditions used in this study. The normalized
minimum CoM height was determined as the minimum height of CoM during each recovery
phase normalized by the height of each subject.
The correlations among these parameters were calculated to evaluate the relationships
among them. Representative factors of reaction motion were then extracted using principal
component analysis (PCA) [21]. PCA is a method which is extensively used to compress thedimensions of datasets to extract desired features from them. In the field of gait analysis,
Munuz et al. used PCA to classify various gait motion trajectories [22]. The differences of all

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Effects of exoskeletal gait assistance on the recovery motion following tripping

the extracted parameters and factor scores between reaction algorithms were tested using theMann–Whitney U test [23].
Furthermore, the relationship between the contact condition and recovery motion wasmodeled using multiple regression analysis [24]. The MoS and each principal component wereselected as the objective variables and as the indices of balance after tripping. The parameterswhich represented the contact condition were selected as explanatory variables. The candidate
parameters of the explanatory variables were determined as follows:• Bspeed: Body speed before HT (m/s)• Gphase: Gait phase at HT (%)• Tangle: Trunk angle at HT (˚)• Pforce: Peak contact force (N)• Rassist: Reaction algorithm (Stop: 0, Continue:1)
The speed of the body was determined as the average speed of the CoM from 0.1 s before
tripping to the tripping in the traveling direction. The trunk angle was determined as the angle
of forward tilt of the trunk axis in the sagittal plane. The trunk axis was determined as the line
which connected the center of the shoulder markers and the center of ASISs and PSISs. The
peak contact force was the maximum load applied to the tripping plate. The parameters of thereaction algorithms were modeled as discrete values.
To avoid multicollinearity, the correlations among the explanatory variables were checked
preliminarily. Moreover, the regression model was adjusted based on the selection of parameters whose contributions were significant.

ResultOverview of the gait and recovery motions
In total, 200 tripped trials were conducted for ten subjects. However, there were error trials inwhich a) the tripping phases completely differed from the early swing phases, b) the subjects
collided with the obstacles multiple times, and c) the collision was partial. These error trials
were not analyzed. Thus, in total, 110 tripped trials were analyzed. Among these, 53 trials werestop patterns and 57 trials were continue patterns.
Gait parameters, such as the velocity, stride length, and cadence of normal gait were calculated from five dummy trials which were randomly extracted from each subject. The averagevalues of the gait parameters of each subject were distributed in the ranges of 0.99–1.20 m/s(walking speed), 48.2–54.8 strides/min (cadence), and 1.16–1.42 m (stride length).
The timing of tripping was distributed within the range of 65–80% of the GC, and corresponded to the early swing phase. In all the trials, the elevating strategy was selected. This selection was consistent with the relationship between the tripped timing and recovery strategy
reported previously [10] A typical recovery motion pattern is shown and described in Fig 3. As
one of the features of the elevating strategy, the tripped leg stepped forward at the FS. Furthermore, the recorded reaction motion suggested that the tripping affected the motion of the
opposite step, i.e., the SS. This meant that the subject needed to take multiple steps to compensate for the effects of tripping.

Reaction parameters
The median and interquartile range (IQR) values of recorded parameters are shown in
Table 1. During the recovery motion, the subjects decelerated. Thus, WS decreased in the

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Effects of exoskeletal gait assistance on the recovery motion following tripping

Fig 3. Typical reaction motion against tripping. Stick picture of the recovery motion in the sagittal plane. The left leg
was tripped in this figure. The subject stepped the tripped leg forward. Then, the recovery leg was stepped.
https://doi.org/10.1371/journal.pone.0229150.g003

second phase. The large ToH and KA values in the first phase clearly indicate that the subject
had to lift his foot to exceed the obstacle. Furthermore, the MoS increased in the second phase,
which meant that the stability increased owing to the recovery motion. By contrast, the broad
distribution of the KA values in the second phase suggests the existence of a variety of recovery
motions.
The correlation matrix of these parameters is listed in Table 2. According to the definitionof the MoS, it is obvious that the MoS is highly negatively correlated to the WS. However, StL
is not correlated to MoS although the stride length is probably related to the expansion of thebase of support. Instead, StT, which is the duration of the recovery step, is more correlated to
the MoS. Although rapid and large steps tend to help avoid falls [25, 26], the same trend was
not identified in this experiment. It is likely that the lengthy step time was accompanied by asufficient step length in this experiment because subjects were sufficiently strong.
Table 1. Median and interquartile ranges of tested parameters.
Parameter

UnitFirst phase

Second phase

WS

m/s

1.03; 0.98—1.09

0.95; 0.84—1.03

StTs

0.67; 0.64—0.76

0.55; 0.50—0.62

TrL/height

0.67; 0.61—0.74

0.70; 0.61—0.76

ToHm

0.32; 0.28—0.34

0.14; 0.11—0.18

KA

deg

28.11; 20.92—37.85-0.40; -7.50—7.76

StL/height

0.57; 0.52—0.62

0.52; 0.46—0.57

CVx

m/s

1.08; 0.98—1.20

0.96; 0.83—1.08

CVz

m/s

-0.41; -0.47 - -0.32-0.23; -0.31 - -0.15

MoSm-0.09; -0.16 - -0.01-0.01; -0.06—0.05

CPz/height

0.53; 0.51—0.54

0.54; 0.52—0.55

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PLOS ONE | https://doi.org/10.1371/journal.pone.0229150 February 24, 2020

-0.38

StT_F
0.43

-0.08

TrL_F

0.42

0.62
0.59

0.60

-0.30

KA_F

0.18

-0.10

ToH_F

https://doi.org/10.1371/journal.pone.0229150.t002

CPz_S

MoS_S

CVz_S

CVx_S

StL_S

KA_S

ToH_S

TrL_S

StT_S

WS_S

CPz_F

MoS_F

CVz_F

CVx_F

StL_F

KA_F

ToH_F

TrL_F

StT_F

WS_F

WS_F

Table 2. Correlation coefficients of studied parameters.

0.33

0.09

0.39

0.50

0.14

StL_F

0.39

-0.04

-0.01

0.15

0.05

0.76

CVx_F

-0.35

-0.41

-0.38

-0.29

-0.34

-0.34

-0.25

CVz_F

-0.14

-0.04
0.19

0.07

0.46

0.28

0.25

0.23

0.14

0.00

CPz_F

-0.55

0.29

0.32

0.07

0.35

0.38

-0.62

MoS_F

-0.04

-0.52

-0.04

0.51

0.03

-0.06

-0.05

-0.08

-0.02

0.41

WS_S

-0.53

0.06

0.72

0.04

-0.40

0.24

0.29

0.07

0.24

0.28

-0.47

StT_S

0.28

0.29
0.47

0.09

-0.15

-0.03

0.05

0.07

-0.06

-0.35

-0.27

-0.24

-0.34

0.24

ToH_S

0.52

0.08

0.02

-0.23

0.39

0.39

0.19

0.00

0.16

0.32

0.25

TrL_S

0.77

0.51

0.28

0.14

-0.13

0.11

-0.01

0.03

0.04

-0.25

-0.16

-0.09

-0.07

0.07

KA_S

0.42

0.36

0.87

0.20

0.51

0.27

-0.01

-0.15

0.35

0.50

0.19

0.04

0.08

0.24

0.16

StL_S

0.49

0.22

0.17

0.46

-0.40

0.87

-0.05

-0.44

0.12

0.19

-0.15

-0.08

-0.04

-0.23

-0.11

0.23

CVx_S

-0.57

-0.15

-0.41

-0.51

-0.24

0.19

-0.50

0.24

0.26

-0.10

-0.01

0.33

0.21

0.11

0.28

0.32

-0.15

CVz_S

0.19

-0.38

0.24

0.24

0.11

0.34

0.49

-0.31

0.05

0.48

-0.12

-0.14

0.14

0.13

0.04

0.27

0.32

-0.23

MoS_S

0.12

0.35

-0.20

0.18

-0.21

-0.24

0.05

0.03

-0.06

0.87

0.21

-0.37

0.23

0.53

0.37

0.28

0.43

0.31

0.04

CPz_S

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Furthermore, the CPz, which is the minimum CoM height of the second phase, wasstrongly correlated to the parameters of the first phase. Given that the increased CoM height
helped avoid the fall, the lengthy step time and stride length of the first phase probably helped
recover the body balance. At the same time, the increased CVz value negatively affected theCPz. This corresponded to an insufficient recovery process. By contrast, the effects of theparameters of the first phase on the MoS of the second phase were not so large compared toCPz.

Principal components
The factor loadings of the principal components are shown in Fig 4. The three major principal
components which were associated with the respective proportions of variance of 22.3, 18.9,
and 16.2%, were extracted. Thus, these major parameters explained 57.4% of the sample
variance.
First component (early recovery). This component is characterized by the large positive
values of the parameters of the first phase. By contrast, the absolute values of the parameters in

Fig 4. Factor loading of each principal component. The three major principal components which were associated with therespective proportions of variance of 22.3, 18.9, and 16.2%.
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the second phase were relatively small. These features suggest that this component represents
the recovery motion of the first step. Therefore, the large value of the first component corresponded to the recovery in the early phase, that is, the first phase of the recovery motion. However, it should be noted that the MoSs of both the FS and SS are positive. This means that therecovery motion of the first phase improves the balance of successive steps. Furthermore, thepositive CVz and CPz values of the second phase also suggest the improvement of the balanceof this phase.
Second component (forward movement). This component was characterized by a positive WS, TrL, StL, and CVx, at the timing of the SS. Furthermore, the StL and CVx of the FS
also contributed to this component. The movement of the subject in the traveling direction isrepresented by these parameters. Therefore, the large value of the second component corresponded to the forward movement during the recovery motion. In addition, the small magnitudes of the MoSs for both the FS and SS suggest that this component is not related to therecovery of balance.
Third component (assisted recovery). This component is characterized by the large positive value of the second phase. It seems that this component represents the recovery motion of
the second phase. However, the MoS of the first phase becomes large in value and positive.
This contradiction could be explained by considering the large negative WS at the first phase.
The slow body movements of the first and second phases increase the MoS according to thedefinition. Furthermore, as mentioned below, the value of this component increased in the“continue” trials. Therefore, this component corresponded to the recovery motion induced by
the assist pattern.

Difference of recovery motion among reaction algorithm
According to the Mann–Whitney U test, the reaction algorithm affected some reaction parameters and a principal component. The boxplots of these parameters are shown in Fig 5.
Among the principal components, the reaction algorithm only affected the third component. Furthermore, the parameters of the second phase were affected to a greater extent by thereaction algorithm, whereas only the MoS differed significantly among the parameters of thefirst step. It seems reasonable that the torque applied during the first phase affected the motionof the second phase.

Relationship between contact condition and reaction motion
The MoS at FS could be modeled according to Eq (2) based on multiple regression analyses.
MoS ¼ 0:90

0:59Bspeed

0:49 � 10 2 Gphaseð2Þ

0:63 � 10 2 Tangle þ 0:43 � 10 1 Rassist
� 2 value of this model was 0.29 and the p-values of all the parameters were less than 0.01.
The R
Although the first, second, and third components of PCA were also modeled, the p-valuesof the explanatory variables suggested that these parameters could not be explained by theparameters mentioned above.

Discussion
Recovery strategies and their performancesMultiple steps were required for the recovery from tripping as mentioned above. However,
the ratio of the strength between the first and second steps differed among trials. The first

PLOS ONE | https://doi.org/10.1371/journal.pone.0229150 February 24, 202011 / 16Effects of exoskeletal gait assistance on the recovery motion following tripping

Fig 5. Boxplot of reaction parameters and principal component parameters which were affected by the reaction
algorithm (p < .05) were extracted. Box represents the first and third quartiles. Outliers, which are separated from thequartile more than 1.5 times the interquartile range, are marked with crosses.
https://doi.org/10.1371/journal.pone.0229150.g005

PLOS ONE | https://doi.org/10.1371/journal.pone.0229150 February 24, 202012 / 16Effects of exoskeletal gait assistance on the recovery motion following trippingFig 6. Step motion of recovery strategies. The recovery motion could be classified based on the length of recovery
steps. (a) The first step after tripping was large, whereas the second step was small. (b) The first step was small and thesecond step was large.
https://doi.org/10.1371/journal.pone.0229150.g006

principal component could be considered as the most representative parameter for the distinction of the recovery strategy.
In the trials whose first principal component were positive, the first step after tripping waslarge, whereas the second step was small, as shown in Fig 6(a). The increase of the MoSs at the
FS and SS that occurred in conjunction with the increase of the first principal component, suggested that the large first step effectively recovered the gait balance. By contrast, when the firststep was not sufficiently large to recover balance, the subject had to increase the step length ofsuccessive step to continue to recover balance, as shown in Fig 6(b).
Thus, from the viewpoint of balance recovery, it seemed more appropriate to place the firststep at a distant location. Previous studies also suggested the effectiveness of this strategy [26,27]. Even when the assist robot was used, this strategy was effective in improving balance.

Effects of the reaction algorithm on the recovery motion
Among the three principal components, only the third principal component—which was
related to MoS—and the gait motion of the second step, differed significantly in the comparison of the reaction algorithms, as shown in Fig 5(g). Considering the similarities of the motion
patterns between the normal swing and recovery steps observed in the experiment, the assist
torque applied in the recovery phase probably helped the step motion. Specifically, the applied
torque during the swing phase could contribute to the increase of the foot height and step
length.
However, the third principal component did not affect the motion of the FS in comparison
to the SS. In the case of the elevating strategy, the FS was executed soon after the tripping.
Thus, the change of motion caused by the assist torque could not become so large. By contrast,
the assist torque applied in the recovery phase affected the SS because there was sufficient assist
time. Additionally, even though the effects of the reaction algorithm on specific parameters of
the first phase were not significant, it should be noted that the MoS of the first phase was also
improved in the continue condition. This trend was consistent in the cases of the componentof the third principal component and the multiple regression model.
By contrast, the first principal component did not differ between the reaction algorithms.
Furthermore, although we attempted to describe the first principal component from the contact condition and the reaction algorithm using the multiple regression model, this process did

PLOS ONE | https://doi.org/10.1371/journal.pone.0229150 February 24, 202013 / 16Effects of exoskeletal gait assistance on the recovery motion following tripping

not work efficiently. This result suggested that the effects of the reaction algorithm on theselection of the reaction strategy were minor. However, the direct detection of the intended
motion of the wearer with the use of a sensing device, such as an electromyogram, may contribute to assist the reaction motion.

Factors which affect the recovery of balance
It seems obvious that the posture and motion before tripping affected the recovery motion.
The result of multiple regression analysis suggested that the MoS could be described from
Bspeed, Gphase, Tangle, and Rassist, as shown in Eq (2).
The MoS decreased when the walking speed increased as mentioned above. Thus, the effectof Bspeed of this model seems reasonable. The model also suggested that the MoS decreased
when the tripping occurred at a later phase. The CoM moved forward from the support leg as
the gait phase progressed during the early to the middle parts of the swing phase (during
which the tripping occurred in this study). Thus, the initial condition of the recovery motion
worsened when the tripping occurred at a later timing.
The trunk angle was a posture parameter at the time of tripping. The forward tilt of thetrunk possibly disturbed hip flexion. This was essential to exceed the obstacle given that it limited the range of foot lifting. In addition, the forward tilt of the trunk was also equivalent to theforward movement of the CoM. Similar to the reason provided for the tripping phase, thetrunk angle made the initial condition of the recovery motion worse.
Rassist was one of the parameters of the reaction algorithm and represented the reaction
motion after tripping whereas other parameters represented the contact condition. Considering the values of the coefficients and the ranges of all the parameters, it seemed that the degreeof the effect of the reaction algorithm used in this experiment on the MoS was the same as thatevoked by the other parameters.
Additionally, it should be noted that the first to the third principal components, which also
represented the recovery motion, could not be modeled using the parameters of posture andmotion before the tripping. This result suggested that either the effects of these parameters on
the recovery motion could not be described by the simple linear model, or that there wereother factors which were more essential for the description of the recovery motion.

Conclusion
The recovery motion against tripping during assisted walking was observed and analyzed inthis study. When physical assistant robots are used in the daily living environment, it is likelythat the wearer may trip and fall. Accordingly, the effect of the assistive torque applied by the
robot during the recovery motion was evaluated in this study.
For the in-depth understanding of the responses evoked after tripping, it is essential to consider a variety of robots and assist patterns. To maximize the contribution to improve theserobots, in this study, the structure of the assist robot and the assist algorithm were set to follow
the general specifications of the assist robot. Subsequently, the effects of the two types of reaction algorithms that either stopped assisting after tripping, or continued to apply assistive torques, were experimentally tested. The observed recovery motions were analyzed statistically.
The result suggested that the effects of the reaction algorithm were related to a principal
component which represented the motion of the SS after tripping and increased the MoS. Furthermore, the MoS became significantly large in the cases at which the assistive torque wasapplied. Overall, the evoked results suggested that the assistive torque applied during therecovery motion could help the subject step forward and recover balance after tripping.

PLOS ONE | https://doi.org/10.1371/journal.pone.0229150 February 24, 202014 / 16Effects of exoskeletal gait assistance on the recovery motion following tripping

Supporting information
S1 Dataset.
(CSV)
S2 Dataset.
(CSV)

Author Contributions
Conceptualization: Yasuhiro Akiyama, Yoji Yamada.
Data curation: Yasuhiro Akiyama, Yusuke Fukui.
Formal analysis: Yasuhiro Akiyama, Yusuke Fukui, Shogo Okamoto.
Funding acquisition: Yasuhiro Akiyama.
Investigation: Yasuhiro Akiyama, Yusuke Fukui.
Methodology: Yasuhiro Akiyama, Yusuke Fukui, Shogo Okamoto.
Project administration: Yasuhiro Akiyama, Yoji Yamada.
Resources: Yoji Yamada.
Software: Yasuhiro Akiyama, Yusuke Fukui.
Supervision: Yasuhiro Akiyama, Shogo Okamoto, Yoji Yamada.
Validation: Yasuhiro Akiyama, Shogo Okamoto, Yoji Yamada.
Writing – original draft: Yasuhiro Akiyama, Yusuke Fukui.
Writing – review & editing: Yasuhiro Akiyama.

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