Journal of Robotics, Networking and ArtificialLife, Vol. 1,No. 4 (March 2015), 285­290

Effective rocking motion for inducing sleep in adults- Verification of effect of mother’s embrace and rocking motion Keishi Ashida*,**, Yoshifumi Morita*,**, Ryojun Ikeura**,***, Kiyoko Yokoyama**,****, Ming Ding **, Yuki Mori***Department of Computer Science and Engineering, Nagoya Institute of Technology
Gokiso, Syouwa, Nagoya, Aichi 466-8555, Japan
E-mail: k.ashida.353@stn.nitech.ac.jp / morita@nitech.ac.jp**RIKEN- SUMITOMORIKO Collaboration Center for Human-Interactive Robot Research (RSC RIKEN)
2271-130 Anagahora, Shimoshidami, Moriyama, Nagoya, Aichi 463-0003, Japan***Department of Mechanical Engineering, Mie University
1577 Kurimamachiyacho, Tsu, Mie 514-8507, Japan****Department of Design and Architecture, Nagoya City University
2-1-10 Kitachikusa, Chikusa, Nagoya, Aichi 463-0083, Japan

Abstract
We investigated the most effective rocking motion for inducing sleep in adults. We prepared ten types of rocking
motions, including two types of mother’s rocking motions. The sleep-inducing effect of all the rocking motions wasevaluated using Thurstone’s paired comparison method (Case V). From statistical analysis of the subjective
experimental results we found that, of the ten types of rocking motions, the linear motion component of a mother’srocking motions (Type 2) was the most effective for inducing sleep in adults.
Keywords: Rocking motion, Mother’s rocking motion, Sleep-inducing effect, Thurstone’s paired comparison
method

1. Introduction
Recently, the number of people suffering from highlevels of stress has increased, a phenomenon that has
been called a stressful society.1 Every year, more andmore people suffer from stress-related illnesses.
Moreover, sleep disorders are becoming morewidespread in modern society because stress is one of
the causes of insomnia. In nursing homes, it is a large
burden for caregivers to assist patients to ensure thewellbeing of people who suffer from these problems.2
Therefore, stress reduction and sleep induction arenecessary for many people in modern society. It is
generally known that when a baby is embraced androcked by his or her mother, the baby feels comfortableand falls asleep quickly. Therefore, we hypothesizedthat a rocking motion simulating a mother’s embraceand rocking motion would have the same effects on
adults. Against this background, the aim of our projectis to develop a relaxation machine for reducing stressand inducing sleep by using a rocking motion
simulating that of a mother. We expect that our research
results will be used for other relaxation systems or
robots in the future, for example the Robot forInteractive Body Assistance (RIBA), which is designed
to assist caregivers by lifting patients in and out of theirbeds and wheelchairs.3
In our previous study, we analyzed a mother’sembrace and rocking motion, and we designed andconstructed an excitation apparatus simulating amother’s rocking motion. We found that there are two

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Keishi Ashida, Yoshifumi Morita, Ryojun Ikeura, Kiyoko Yokoyama, Ming Ding, Yuki Mori

types of rocking motions given by a mother, and weconstructed two models of these rocking motions.4 From
analysis of brain signals and subjective assessment, wefound that the mother’s rocking motions were more
effective for inducing sleep in two healthy adults than in
the case without rocking.5 However, there were two
problems with that study. One is that the number ofsubjects was small, and the other is that the sleepinducing effects of different rocking motions have to beinvestigated.
In the work described in this paper, in addition to
the two types of mother’s rocking motions mentioned
above, we prepared eight types of rocking motions tofind the rocking motion that is most effective forinducing sleep in adults. We performed threeexperiments and evaluated the sleep-inducing effect byusing Thurstone’s paired comparison method.

Rotary motor

Linear motor

LinearmotionFig. 1. Photograph of excitation apparatus.

order to simulate a mother's rocking motions in the
excitation apparatus.
3. Experimental method

2. Excitation apparatus simulating a mother'srocking motion
In our previous work we analyzed a mother’s embraceand rocking motion to identify the features of the
motion. From the results, we modeled a mother’srocking motion. The model of a mother’s rocking
motion is represented byxref(t)=Ax sin(2fxt),ref(t)=Asin(2ft+)+B,

Rotational motion(1)

where xref(t) and ref(t) are the position and the angle ofthe center of gravity of the baby, respectively, and B
was determined from the angle of a comfortable sitting
position reported in Ref. 6. Then, we realized thisrocking motion using the excitation apparatus shown in
Fig. 1. The excitation apparatus has two degrees of
freedom, one for linear motion and one for rotationalmotion. The rocking chair is driven by a linear motor
and a rotary motor. The rotary motor is connected to thechair through a timing belt for rotation. The drive
systems of the excitation apparatus are composed of
speed-reference-type servo amplifiers for the linear androtary motors, linear and rotary encoders, and a DSP
board (dSPACE DS1104). The DSP board is used to
implement the controllers for the linear and rotary
motors. We designed controllers for the excitation
apparatus using PD control and feed-forward control in

We performed experiments for finding the mosteffective rocking motion for inducing sleep. The sleepinducing effect of each rocking motion was evaluatedon a numerical scale using Thurstone’s paired
comparison method (Case V)7,8. We verified the validityof adopting this method by using Mosteller’s goodnessof-fit test. Moreover, we evaluated the confidence of thescale values.
The subjects were nine healthy males (average age,
25.4 years). The subjects wore ear muffs for soundinsulation during the experiment, had their eyes closed,
and rested in a supine position on the chair which was
rocked by the excitation apparatus. The experimental
protocol is shown in Fig. 2. R1, R2, R3, and R4 denotethe types of rocking motions used in the experiment.
After every two rocking motions, the subjects answered
the question, “Which of the two rocking motions wasmore effective for inducing sleep?”. The evaluation was
performed with six different combinations of four
rocking motions for each experiment. In order to reducethe influence of an order effect, we divided the subjects
into two groups and used six combinations (Types
R1and R2, Types R1 and R3, Types R1 and R4, Types
R2 and R3, Types R2 and R4, and Types R3 and R4) in
two different orders, namely, Procedure 1 andProcedure 2, as shown in Fig. 2.

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Effective rocking motion forTime [min.] 0
Procedure 1(5 subjects)
Procedure 2(4 subjects)

3.5

7.0

10.5

14.0

17.5

21.0

Eye closed and relaxed with the rocking vibration
R1 (1 [min.])R3 (1 [min.])Eye closed and relaxed without rocking (0.5 [min.])R2 (1 [min.])R4 (1 [min.])

Subjective assessment (1 [min.])Fig. 2. Experimental protocol for finding the most-effective rocking motion in Experiments I, II, and III.

position reported in Ref. 6. The Type 3 rocking motion
is shown in Fig. 4.

4. Experiments
We performed three different experiments, Experiments
I, II, and III, which are detailed below.
4.1. Rocking motions used in Experiment I

Fig. 3. Photograph of rocking chair.
0.25
0.25

35

35

0.10

31

31

27

-0.05
-0.05

23

-0.15
-0.15

19

-0.25
-0.25
0
0

15
60

Angle [deg]27

Position [m]

0.05
0.05

23

Angle [deg]Position
Angle

0.15

Position [m]We prepared four types of rocking motions, namely two
types of mother’s rocking motions (Type 1 and Type 2),
a rocking motion imitating the motion of a rocking chair(Type 3), and a rocking motion that has a highcorrelation with motion sickness (Type 4). In Fig. 2, R1,
R2, R3, and R4 correspond to Type 1, Type 2, Type 3,
and Type 4, respectively. Type 3 was added to thecandidates because a rocking chair is known to have arelaxation effect.9 Type 4 was added to the candidates as
an uncomfortable rocking motion in this comparative
study. The parameters of Type 1, Type 2, and Type 4
are shown in Table 1.
In order to produce the motion of a rocking chair
shown in Fig. 3, we first measured the motion of an
actual rocking chair by using a 3D motion capturesystem (Motion Analysis) when an adult male wasseated in the rocking chair. Type 3 is the rocking motion
produced after the experimenter lowered the backrest of
the rocking chair and released it. The motion of therocking chair consists only of rotary motion. We set theamplitude of the rotary motion to as large a value as
possible within a range that was comfortable for the
subject. Moreover, the rotary angle in the steady state
was set to 25 degrees, which is the same as the angle
determined from the angle of a comfortable sitting

19

10

10

20

20

30
Time [sec]

30

40

40

50

50

15
60

Time [s]Fig. 4. Rocking motion (Type 3).

The Type 4 rocking motion is represented by Eq.
(1). The frequency was determined to be 0.063 Hz,
which has been shown to have a high correlation withmotion sickness10. The amplitude was determined sothat the acceleration was almost the same as those ofother rocking motions and within the range ofacceleration that can be produced by the excitation

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Keishi Ashida, Yoshifumi Morita, Ryojun Ikeura, Kiyoko Yokoyama, Ming Ding, Yuki Mori

Table 1. Parameters of the rocking motions.
Parameter

Type 1

Type 2Type 4

Type 5

Type 6

Type 7

Type 8Type 9Type 10

Ax [m]

0.115

0.098

0.250

0.095

0.100

0.098

0.098

0.060

0

A [deg]

2.455

2.734

10.0

3.136

2.332

2.734

0

0

2.734

B [deg]

25

25

25

25

25

25

25

25

25

fx [Hz]

0.326

0.234

0.063

0.226

0.243

0.234

0.234

0.468

0

f [Hz]0.326

0.234x2

0.063

0.226x2

0.243x2

0.234x2

000.234x2

 [rad]



π/2

π

π/2

π/2

-π/2

π/2

π/2

π/2

apparatus. The parameters of the Type 4 motion are also
shown in Table 1.
4.2. Results in Experiment I

that Type 2 was the most effective for inducing sleep in
adults and Type 4 was the least effective.
Table 2. Frequency distribution matrix in Experiment I.

Type 2 ＞ Type 1 ＞ Type 3 ＞ Type 4.
Moreover, we verified the validity of adopting
Thurstone’s paired comparison method (Case V) by
using Mosteller’s goodness-of-fit test. The goodness-offit, 2, was 3.52, and the flexibility, df, was 3 , meaningthat a 5% significance level was not rejected. Therefore,
Thurstone’s paired comparison method (Case V) can be
adopted for evaluating the sleep-inducing effect.
We examined the significant differences between
the four rocking motions by using the method proposed
in Ref. 11. The result is shown in Fig. 5. We found thatthe 95% confidence interval of Type 1 overlapped withthat of Type 3. The combination of Type 1 and Type 3
showed no significant difference, whereas the other fivecombinations showed significant differences. In otherwords, of the four types of rocking motions, we foundType 1

Type 2Type 3

Type 4

Type 1－6

3

2Type 23－20Type 36

7－

2Type 47

9

7－

Table 3. Scale values of different rocking motions inExperiment I.
Type 1

Type 2Type 3

Type 4

0.19

1.06

-0.11

-1.15

Scale value
2

Scale value and 95%
confidence interval

From the results of the paired comparison method, we
obtained the frequency distribution matrix shown in
Table 2. Table 2 shows the number of subjects whooffered the response “The first rocking motion was
more effective for inducing sleep than the secondrocking motion”. The first and second rocking motions
are shown in the rows and columns of Table 2,
respectively. The scale values for the sleep-inducing
effect of the rocking motions were derived by applying
Thurstone’s paired comparison method (Case V) to
Table 2. The scale values are shown in Table 3. From
Table 3, we can rank the four types of rocking motions
based on their sleep-inducing effects as follows:: Scale value: 95% confidence interval

1
0
-1
-2
0

1

2

3

4

5

Type

Fig. 5. Scale values and 95% confidence intervals of the fourtypes of rocking motions in Experiment I.

4.3. Rocking motions used in experiment II
We prepared three types of rocking motions, namely
Type 5, Type 6 and Type 7, in addition to Type 2. In
Fig. 2, R1, R2, R3, and R4 correspond to Type 2, Type5, Type 6, and Type 7, respectively. Type 5 was arocking motion based on one given to a 5 kg baby inanother study5, and Type 6 was a rocking motion based

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Effective rocking motion foron one given to a 7 kg baby in the same study. Moredetails of these rocking motions are shown in Ref. 5.
Type 7 was the same as Type 2 except for the phase,
which differed by 180 deg. These parameters are shownin Table 4.
4.4. Results in Experiment II
Figure 6 shows the scale values and the 95% confidence
intervals for the sleep-inducing effect of the rocking
motions obtained using Thurstone’s paired comparison
method (Case V) and the method proposed in Ref. 11.
From the scale values in Fig. 6, we can rank the fourtypes of rocking motions based on their sleep-inducing
effects as follows:
Type 2 ＞ Type 6 ＞ Type 5 ＞ Type 7.
Moreover, the validity of adopting Thurstone’s paired
comparison method (Case V) for evaluating the sleepinducing effects was confirmed in the same way as inExperiment I.
In Fig. 6, the combination of Type 2 and Type 7
showed a significant difference, whereas the other fivecombinations showed no significant differences. We
concluded that, of the four types of rocking motions,Type 2 was the most effective for inducing sleep in
adults. As for the reason why no significant differences
appeared, we considered that the evaluations were
uneven because it was difficult for subjects todiscriminate the small differences in the frequency andamplitude. In this situation, Type 7 was chosen as theleast effective rocking motion. With the Type 7 motion,
the subjects reported slight motion sickness.

Scale value and 95%
confidence interval

1: Scale value: 95% confidence interval

0.5
0

-0.5
-1

0

12

25

36

47

5

Type

Fig. 6. Scale values and 95% confidence intervals of the fourtypes of rocking motions in Experiment II.

4.5. Rocking motions used in Experiment III
In order to find a more effective rocking motion for
inducing sleep, in Experiment III, we focused on thecomponents of the Type 2 motion. We prepared three
types of rocking motions, namely, Type 8, Type 9 andType 10, in addition to Type 2. In Fig. 2, R1, R2, R3,
and R4 correspond to Type 2, Type 8, Type 9, and Type10, respectively. Type 8 was a rocking motion
consisting of only the linear motion component of Type
2. Type 9 was also a rocking motion consisting of only
linear motion that was reported to be effective forinducing sleep in babies in Ref. 12. Type 10 was arocking motion consisting of only the rotational motion
component of Type 2.
When the frequency of the rocking motion used inRef. 12 is used instead of the frequency of Type 8, theacceleration is too large. For this reason, the amplitudeAx was set to a smaller value, and the frequency fx was
set to a small value, namely, the frequency f of therotary motion component of Type 7. This rocking
motion is Type 9. These parameters are shown in Table
1.
4.6. Results in Experiment III
Figure 7 shows the scale values and the 95% confidence
intervals for the sleep-inducing effect of the rocking
motions obtained by using Thurstone’s paired
comparison method (Case V) and the method proposed
in Ref. 11. From the scale values in Fig. 7, we can rank
the four types of rocking motions based on their sleepinducing effects as follows:
Type 8 ＞ Type 10 ＞ Type 2 ＞ Type 9.
Moreover, the validity of adopting Thurstone’s paired
comparison method (Case V) for evaluating the sleepinducing effect was confirmed in the same way as inExperiment I.
In Fig. 7, the three combinations including Type 9(Types 2 and 9, Types 8 and 9, and Types 9 and 10)
showed significant differences, whereas the other threecombinations showed no significant differences.
However, there is a significant difference in the
combination of Type 8 and Type 10 if the confidence
interval is changed to 80% instead of 95%. Therefore,of the four types of rocking motions, we concluded that

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Keishi Ashida, Yoshifumi Morita, Ryojun Ikeura, Kiyoko Yokoyama, Ming Ding, Yuki MoriType 8 is the most effective for inducing sleep in adults.
The reason why Type 9 was identified as the least
effective rocking motion was that the acceleration ofType 9 is too large, based on the subjects’ opinions. We
found that the acceleration was related to the effective
motion for inducing sleep.

Scale value and 95%
confidence interval

2: Scale value: 95% confidence interval

1
0
-1
-2

0

12

28

93

4
10

5

Type

Fig. 7. Scale values and 95% confidence intervals of the fourtypes of rocking motions in Experiment III.

5. Conclusion
From subjective experimental results, we found that, of
the ten types of rocking motions examined, the linear
motion component of a mother’s rocking motion (Type2) was the most effective rocking motion for inducing
sleep in adults.
In future work, we plan to confirm that the Type 8
rocking motion, which is the linear motion componentof a mother’s rocking motion (Type 2), is effective forinducing sleep and reducing stress in adults by using
electroencephalogram (EGG) analysis. We will also
compare the Type 8 rocking motion and aromatherapy,
which is a popular natural way of inducing sleep andbringing about relaxation.
References
1. Ito, H. and Ishino, Y., Adverse Effects of Sleep
Deprivation, Iho Fuji, No.124 (2003) (in Japanese), p.1.
2. Mishima, K., Sleep Problems in Dementia, Proceedingsof the Annual Meeting of the Japanese Research Groupon Senile Dementia, Vol.17 (2010) (in Japanese), pp.109113.

3. RIKEN-TRI Collaboration Center for Human-Interactive
Robot Research (RTC), World’s first robot that can lift
up a human in its arms, RIBA, (online), available from<http://rtc.nagoya.riken.jp/RIBA/index-e.html>,(accessed on 13 June, 2014)
4. Yamaguchi, K., Kobayashi, H., Morita, Y. Sakaida, Y.
Ikeura, R. and Yokoyama, K., Motion Analysis ofMother's Embracing and Rocking a Baby andDevelopment of Excitation Apparatus, Proc. of Int. Conf.
on Control, Automation and Systems 2011 (ICCAS2011)(2011) pp.1792-1796.
5. Morita, Y., Yamaguchi, K., Ashida, K., Ikeura, R. andYokoyama, K., Verification of Sleep-Inducing Effect by
Excitation Apparatus Simulating Mother's Embrace andRocking Motion, Proceedings of the 9th International
Workshop on Robot Motion and Control (RoMoCo '13)
(2013) , pp.80-85.
6. Sasaki, Y., Kawamoto, T. and Ymazaki, N.,
Development of an Experiment Bed for Searching
Comfort Semi-Sitting Position, Japanese Journal ofErgonomics, Vol.42, No.6 (2006), pp.373-380.
7. Research Committee of Sensory Evaluation, Sensory
Evaluation Handbook, JUSE ed., JUSE Press, Ltd., Japan(1973), pp.471-476.
8. Ichikawa, H., A Study of Representing Content for aSpecial 3D Display (2010) (in Japanese), pp.34-41.
9. Tamakoshi, S., Yamamoto, N., Morimoto, F., Nagae, S.,
Ichiba, H. and ISO, H., Engineering Psychology on the
Relaxation Effects of a Rocking chair, Behavioral
Science Research, Vol.50, No.2 (2012) (in Japanese),
pp.101-105.
10. Siroto, H., Evaluation Method of Motion Sickness inTrains Using Low-frequency Lateral Vibration, Railway
Research Review, Vol.130 (2006) (in Japanese), pp.3839.
11. Tabata, Y., Ohga, Y., Kakuta, M., Nakamae, M.,
Morioka, M., Uto, F., Okunishi, T., Oti, T. and Maeda,
K., Confidence Coefficient of Subjective Scale Value in
Method of Paired Comparisons (Case V), JapaneseSociety of Radiological Technology, Vol.51, No.4 (1995)(in Japanese), pp.445-449.
12. Fuji, T., Furusawa, T., Takenouchi, T. and Tomotari, M.,
Development of Electric Bed for Babies for Parenting
Support, Japan Society for Design Engineering (2006) (inJapanese), pp.19-20.

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