Journal of Artiﬁcial Intelligence and Technology, 2021, 1, 153-165
https://doi.org/10.37965/jait.2021.0007

RESEARCH ARTICLE

Proposal of Walking to Prevent a Fall of a Planetary
Exploration Legged Rover Using Effect of Loose Soil
Caused by a Propagation of Vibration
Tomohiro Watanabe1 and Kojiro Iizuka2
1

Graduate School of Engineering and Science, Shibaura Institute of Technology, Saitama City 337-8570, Japan
Department of Systems and Engineering and Science, Shibaura Institute of Technology, Saitama City 337-8570, Japan

2(Received 28 March 2021; Revised 30 June 2021; Accepted 12 July 2021; Published online 15 July 2021)
Abstract: In this study, a walking method that prevents a fall of the planetary exploration-legged rover is proposed. In the
proposed walking method, the leg is sunk by giving vibration to the ground. The posture of the rover is changed to prevent a fallof the rover by sinking the leg. First, the relationship between the kind of vibration and the subsidence of the leg is conﬁrmed. In
this experimental result, the leg is shown to be easy to sink to the ground by giving vibration. Moreover, the larger the vibratory
force is, the easier the leg sinks to the ground. Finally, the legged testbed walks on the loose ground with a slope using the
proposed walking method. In this experimental result, the testbed is difﬁcult to fall down when it uses the proposed walking.
Moreover, the angle of a slope that the testbed can walk becomes large by using the proposed walking.
Key words: planetary exploration legged rover; fall prevention; loose ground; vibration

I. INTRODUCTION
By conducting planetary explorations, we can explore not only theorigins of the planets but also the source of life. Because of that,many missions for exploring the planets have proceeded. Hayabusa2 landed on a surface of an asteroid Ryugu and took the sample
in 2019 [1]. It returned the sample to Earth. The Mars Perseverance
rover successfully landed on Mars in February 2021 [2]. It willcollect samples of rocks and soils. Moreover, concern with theMoon has been growing. In recent years, many missions for
exploring the Moon have also proceeded. For example, there
are launching Smart Lander for Investigating Moon (SLIM) anddeveloping Gateway, which is a platform orbiting the Moon [3,4].
Therefore, these conditions will make many opportunities for
exploring robots to land on the surface of the Moon.
In planetary explorations, exploring robots that are called rovers
were used and obtained various knowledge [5]-[7]. Rovers exploredplanets by moving on surfaces of them. Many rovers were vehicle
type, which consisted of wheels [8,9]. However, the running performance of the wheel-typed rovers is not good. In recent years, thelegged robots are focused on as exploration rovers with high running
performance [10]-[13]. The legged rovers are good at moving onrough terrain which is rocky. Viking 1 and 2 that were the probes andexplored Mars observed the geographical features of Mars. According to the observation results, there were many rocks that were larger
than 30 cm on the ground [14]. Therefore, the running performanceon rough terrain is important for exploration rovers.
The grounds of Mars and the Moon are not only the roughterrain but also the loose ground. The loose ground is covered withthe loose soil called regolith and is easy to deform by receiving
external force. Moreover, there are many craters on Mars and theCorresponding author: Tomohiro Watanabe (e-mail: nb19109@shibaura-it.ac.jp).

Moon. These craters have slopes. From these features of the loose
ground, there are two problems. First, legged rovers slip on the loose
ground. The loose ground is easy to deform by the motion of theirlegs. Some studies address this problem. Yeomans et al. consideredthat the earth pressure that gives to the legs of rovers is the traction
force of legged rovers [15]. They measured the earth pressure in theexperiment and proposed the model of the earth pressure for leggedrovers. As a result, the earth pressure was strongly dependent on theamount of leg subsidence. The higher the amount of leg subsidence
was, the larger the earth pressure was. Therefore, legged rovers canprevent slipping on the loose ground by increasing leg subsidence.
Moreover, our study group was conﬁrmed that there are two effects
when the loose ground is given vibration [16]. One was to increase
the density of the loose ground, and the other was to increase the leg
subsidence. The walking method that prevents slipping the rover on
the loose ground was proposed using these effects. In the experimental results, the amount of movement using the proposed walking
method became longer compared with one without vibration. Then,
it is the problem that legged rovers fall down by deforming the loose
ground. The posture of the rovers is easy to change on the loose
ground. Some studies address this problem. Komizunai et al.
constructed the simulator about a humanoid walks on the loose
ground [17]. In this simulator, the amount of leg subsidence when
walking was estimated. By estimating the amount of leg subsidence,the posture of a humanoid can be changed before it falls down.
Kamegawa et al. proposed the method that the slope angle of theground is estimated from the positions of rover’s toes and the postureof rovers [18]. Moreover, the gait was changed according to theestimated slope angle of the ground. Shirai et al. proposed thewalking method that legs move preventing a fall of a rover based on
tumble stability margin [19]. The effectiveness of this walking
method was conﬁrmed from the experiment. However, it is needed
to move legs to stabilize the posture of rovers in these methods.
Therefore, these methods cannot be used when legs cannot move by© The Author(s) 2021. This is an open access article published under the CC BY license (https://creativecommons.org/licenses/by/4.0/).

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Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged Roverthe structural restrictions of rovers. Nagaoka et al. developed thegripper that gripped a rock for legged rovers [20]. In this study, alegged rover could walk by using this gripper without falling.
However, this gripper is not effective in the loose ground because
the loose ground is easy to deform by receiving external force.
This study addresses the problem that legged rovers fall downon the loose ground with a slope. Moreover, the walking methodthat prevents a fall of a legged rover is proposed. In the proposed
walking method, legs are sunk by giving vibration to the loose
ground. The posture of legged rovers is changed to prevent to a fallof it by sinking legs. The posture of legged rovers can be changed
without the structural restrictions of them because the proposed
walking method uses changing shape of the loose ground.
In the rest of the paper, a walking method to prevent a fall of a
legged rover using vibration is proposed in Section II. In
Section III, the relationship between the kind of vibration andthe leg subsidence is conﬁrmed. Sinking legs by giving vibration isimportant because the posture of legged rovers is changed bysinking legs in the proposed walking method. Then, the legged
testbed walks on the loose ground with a slope using the proposed
walking method. In this experiment, the effectiveness of the
proposed walking method is conﬁrmed. This experiment is reported in Section IV. Finally, this study is concluded in Section V.
This study’s contribution to knowledge is shown below:• Feature of resistance force that rover’s leg is received from theground in vibrating.
• How to use vibration for walking method that prevents a fall of
the planetary exploration legged rover?
• Effect of a walking method to prevent a fall of a legged roverusing vibration.

II. PROPOSAL OF WALKING METHOD TOPREVENT A FALL OF A LEGGED ROVER
USING VIBRATION
A. MECHANISM THAT ROVER FALLS DOWN ON
THE LOOSE GROUND WITH A SLOPE
In this section, the necessity of a walking method that prevents afall of a legged rover is explained. First, the mechanism that a rover
falls down on the loose ground with a slope is explained. In thisstudy, the moment that is generated by the weight of a rover on aslope is called Mos (moment on a slope). The illustration of theforces that a rover is received on the loose ground with a slope isshown in Fig. 1. Fig. 1 shows the simple forces in a two-dimensional coordinate system. In Fig. 1, Mos is caused around PR (thetouching point between the ground and a rear leg). The term Mos is
calculated from (1)M os = mg cos θR ly − mg sin θR lz ,(1)

where m is the mass of a rover, g is the gravitational acceleration, ly
is the distance from a rear leg to the center of gravity in a y-axis
direction, lz is the distance from a rear leg to the center of gravity ina z-axis direction, and θR is the angle of a rover’s posture andcalculated from (2)θR = θG þ θS ,(2)

where θG is the slope angle of the ground and θS is the angle ofa rover’s posture, which is generated by the leg subsidence andcalculated from (3)Fig. 1. Conceptual diagram of the moment on a slope.

s − sFθS = tan−1 R
,
l

(3)

where l is the distance from a rear leg to a front leg, sF is thesubsidence of a rover’s front leg, and sR is the subsidence of a rover’s
rear leg. The risk that a rover falls down is high when the value of
Mos is small. Moreover, a rover falls down when Mos is less than 0.
The reason that legged rovers are easy to fall on the loose
ground is explained here. The term lz is large because the centers ofgravity of legged rovers are higher than that of rovers using othermoving mechanisms. Moreover, the loose ground is easy to deformby receiving external force. On the slope, sR is larger than sF because
the weight of a rover that a rear leg is received is larger than one thatfront a leg is received. Therefore, θs is increased on the slope (eq. (3)). The term Mos is decreased by increasing these values. The
risk that a rover falls down is increased by decreasing Mos. Therefore,
a walking method is needed, which prevents a fall of a legged rover.

B. PROPOSED WALKING METHOD USINGVIBRATION
In this section, a walking method that prevents a fall of a legged roveris explained. It is needed to increase Mos by inclining forward a rover
to prevent a fall of it. In the proposed walking method, Mos isincreased using the feature, which is caused by giving vibration to
the loose ground. The particles of the ground are moved by giving
vibration to the ground as shown in Fig. 2. The shear strength of theground is decreased by moving the particles. The amount of leg
subsidence is increased by decreasing the shear strength. Therefore,a rover inclines forward by giving vibration to the ground.
Details of the proposed walking method are explained. The
proposed walking method is used for the six-legged rover. The
reason is that the six-legged rovers can walk in static walking
without moving the center of gravity. The proposed walking method
is shown in Fig. 3. First, the front legs and the middle legs vibrate(Fig. 3(a)). The rover inclines forward by this motion. Then, therover moves legs forward one by one (Figs. 3(b)-(d)). This motion isbased on wave gait. Fig. 4 shows the movement of each leg and thetiming to vibrate the leg. First, the leg raises and moves forward(Fig. 4(a)). Second, the leg moves down to the ground. Then, the leg
is vibrating when the leg touches the ground (Fig. 4(b)). Moreover,

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increased. Therefore, the traction force of the legged rover isincreased by increasing earth pressure. The effectiveness of thismotion was conﬁrmed. Finally, the body of the rover moves forward(Fig. 3(e)). Moreover, one cycle of this gait is ﬁnished.

III. A PENETRATION EXPERIMENT FOR
MEASURING RESISTANCE FORCEFROM THE GROUND

Fig. 2. Movement particles of the ground when vibration is given to theground.

the leg sinks into the ground. Finally, vibration stops when the leg
ﬁnishes sinking into the ground (Fig. 4(c)). In the previous study, ourstudy group proposed this motion as the walking method that thelegged rover can prevent slipping on the loose ground [16]. This
motion indicates that density of the ground and earth pressure are

The relationship between the kind of vibration and the leg subsidence is conﬁrmed. The smaller the resistance force which isreceived from the ground is, the easier the leg sinks to the ground.
In this experiment, the rod is penetrated in the loose ground.
Moreover, the resistance force that rod is received from the groundis measured. In this section, the experimental machine, the experimental method, and the result are reported.

A. METHOD OF A PENETRATION EXPERIMENTFirst, the experimental machine is explained. The experimental
machine is shown in Fig. 5. It consists of the soil tank part, the leg

Fig. 3. Sequence of proposed walking.

Fig. 4. Vibration timing when walking.
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Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged RoverFig. 8. Flow of penetration experiment.
Fig. 5. Overview of penetration testing machine.

part, and the actuator part. The size of the soil tank is H 300 mm ×
W 354 mm × L 609 mm. Fig. 6 shows the structure and the size ofthe rod. The vibration motor is mounted in the rod. Fig. 7 shows the
movement of this machine. The leg part is penetrated in the soiltank part by the actuator part. The leg part consists of the force
sensor and the rod. The resistance force from the ground whenpenetrating the rod is measured by the force sensor.
Then, the ﬂow of the experimental method is explained. The
ﬂow of this experiment is shown in Fig. 8. The leg part is set on the
ground (Fig. 8(a)). The ground consists of Silica No. 5. Then, the legpart is penetrated into the soil tank (Fig. 8(b)). The speed of moving
the leg part is 0.55 mm/s. The vibrations are three kinds. These kinds

TABLE I.

Parameters of Table of Vibration

Vibration

Supplyvoltage (V)Vibratory
force (N)Frequency
(Hz)

0
10
20

0.00
0.27
1.32

0
70
153

30

3.04

231

No vibratioon
Weak vibration
Middlevibration
Strongvibration

TABLE II.

Condition for Penetration Experiment

Item
Number of trials
Penetration speed
Amount of subsidence
Kind of sandVibration motor

Conditions (value)10
0.55 mm/s
50 mm
Silica No. 5
TP-2528C-24

of vibrations are prepared by changing the voltage that is supplied to
the vibration motor. Table I shows these vibrations. The force sensor
receives the value of the resistance force from the ground. The
number of trials is 10 times. Table II shows the condition of thisexperiment.
Fig. 6. Overview of rod.

Fig. 7. Movement of penetration testing machine.

B. RESULTS AND DISCUSSION OF APENETRATION EXPERIMENT
Figs. 9–12 show the graphs about the distance of subsidence vsresistance force from the ground in each kind of vibration. In Fig. 9,
the resistance force was shown as a curve and increased in theexperiment without vibration. From Fig. 9, these shapes of thegraphs were hardly different in all trials. This minor difference ingraph shapes is seemingly caused by the irregularity of the loose
ground. As shown from Figs. 10 to 12, graph shapes in theexperiment with vibration were different in comparison with thatin the experiment without vibration. In the experimental results withvibration, the resistance force was low at the beginning of these
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graphs. In the same experimental condition, these shapes of thegraphs were similar, but they have variations. The stronger thevibration was, the larger these variations were. These variations are
seemingly caused by vibration given to the ground. The particles of
the ground are moved by giving vibration to the ground. This
movement of particles is irregular. Therefore, these variations are

Fig. 12. Resistance force vs penetration distance using strong vibration(vibratory force: 3.04 N and frequency: 231 Hz).

Fig. 9. Resistance force vs penetration distance using no vibration(vibratory force: 0.00 N and frequency: 0 Hz).

seemingly caused by moving the particles. In Fig. 13, the resistanceforces are compared in each experimental condition of vibration. In
Fig. 13, the data of median values are chosen because the resistanceforces that were obtained in the same experimental conditions werehardly different in all trials. Fig. 14 shows the difference between the
result in the case of using vibration and one in the case of not using
vibration. At the beginning of this graph, the resistance forces in thecase of using vibration were smaller than one in the case of not using

Fig. 10. Resistance force vs penetration distance using weak vibration(vibratory force: 0.27 N and frequency: 70 Hz).
Fig. 13. Comparison of resistance force in each vibration.

Fig. 11. Resistance force vs penetration distance using middle vibration(vibratory force: 1.32 N and frequency: 153 Hz).

Fig. 14. Overview of difference between resistance force in the case ofusing vibration and one in the case of not using vibration.

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Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged RoverFig. 16. Overview of slope walking experiment on the loose groundusing testbed.
Fig. 15. Situation in each amount of sinkage.

vibration. In this result, the rod was easy to sink to the ground by
giving vibration. Therefore, it is possible that the rover inclines
forward by giving vibration to the ground. Moreover, the larger thevibratory force was, the smaller the resistance force was (Fig. 13). In
this result, it is considered that the larger the vibratory force is, themore effective the proposed walking is. Finally, the resistance forcesin the case of using vibration were increased rapidly and ﬁt one in thecase of not using vibration. The reason is considered that the higher
the subsidence of the rod is, the larger the earth pressure is. The
situation in each amount of subsidence is shown in Fig. 15. The
amplitude of vibration is decreased by increasing the earth's pressure.
Therefore, it is considered that the resistance force in the case ofusing vibration is matched with one in the case of not using vibration
when the earth pressure is higher than the vibratory force.

IV. SLOPE WALKING EXPERIMENT FOR
EVALUATING THE PROPOSEDWALKING METHOD
The slope walking experiment is conducted to conﬁrm the effectiveness of the proposed walking method. In this section, theexperimental method, the testbed, the evaluation method of thewalking methods, and the result are reported.

A. METHOD OF A SLOPE WALKING EXPERIMENTFirst, the experimental method is explained. In this experiment, thetestbed walks on the loose ground with a slope. The experimental
environment is shown in Fig. 16. The ground consists of Silica
No. 5. Two kinds of walking methods are used. There are theproposed walking and the walking without vibration. The proposed

Fig. 17. Details of walking methods.
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TABLE III.

159

Speciﬁcations of Walking Methods

Item

Value (value)

StrideTime of 1 walking cycle
Walking speed
Vibration

47 mm
About 176 s (proposed walking)
About 132 s (walking without vibration)
About 0.27 mm/s (proposed walking)
About 0.36 mm/s (walking without vibration)
Strong vibration
Fig. 18. Overview and structure of legged testbed.

TABLE IV.

Condition for Slope Walking Experiment

Item

Conditions (value)

Slope angle (°)
Number of trails
Walking steps
Motion capture system
Kind of sand0, 5, 10, 15, 20
5
5 steps
OptiTrack Prime 13
Silica No. 5

TABLE V.

Speciﬁcations of Testbed

Item

Conditions (value)

Weight (kg)Size (mm)Servo motor
Vibration motor
Force sensor
Acceleration sensor
Sampling frequency

5.9
H:163 W:422 L:400
KRS6003R2HV ICS
TP-2528C-24
FSR400
ADXL345
2 Hz

walking and the walking without vibration are wave gait. The entire
walking motion is shown in Fig. 3. However, the motion that isshown in Fig. 3(a) is not conducted in the walking without
vibration. Moreover, the details of these walking methods areshown in Fig. 17. In the proposed walking, the leg vibrates andsinks 30 mm to the ground after it touches the ground (Fig. 17(b)).
In walking without vibration, this motion is not conducted after theleg touches the ground. Strong vibration is used in the proposed
walking (Table I). The detail of the walking is shown in Table III.

The slope of the ground changes by 5° between 0° and 20°. The
movement of the testbed is measured by motion capture system(OptiTrack Prime 13). The number of walking steps is ﬁve steps.
The number of trials is ﬁve times in each experimental condition.
Table IV shows the condition of this experiment.
Then, the testbed is explained. Table V shows the speciﬁcations of the testbed. The overview and the structure of the testbed
are shown in Fig. 18. The leg of the testbed consists of three joints.
The vibration motor is mounted in the leg. Judging the contact
between the ground and the legs and measuring the posture of the
testbed are conducted to evaluate the walking methods. The force
sensor (FSR400) is used to judge the contact between the groundand the legs. These force sensors are attached to the toes, as shownin Fig. 19(a). The acceleration sensor (ADXL345) is used tomeasure the posture of the testbed. Fig. 19(b) shows the measuring
direction about the posture of the testbed. The sampling frequencyof these sensors is 2 Hz.

B. EVALUATION OF WALKING METHODSIn this experiment, Mos is calculated to evaluate the walking
methods. In this section, calculation of Mos is explained. The
term Mos is the moment around the touching point between the
ground and the legs (Fig. 20). In this experiment, the force andthe moment for the acceleration and the deceleration of the testbed
are very small because the testbed walks static. Therefore, gravity is
the primary force that the testbed is received. The term Mos is
calculated from gravity that the testbed is received. The testbed
consists of six legs and a body. The legs have three joints.
Therefore, the testbed consists of 19 links. Each link is called
Lij (Fig. 21). The term i is a leg’s number and j is a joint’s number.
In each link, the mass, the size, and the coordinate of the center ofFig. 19. Sensing system of legged testbed.
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Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged RoverFig. 20. Conceptual diagram of testbed on the slope.

gravity were already measured. The gravity of each link in thecoordinate of testbed is calculated from (4)
1
0
0
C
B
(4)
F gij = Rz ðθYaw ÞRy ðθPitch ÞRx ðθRoll Þ@ 0 A,
−mij gwhere R is the rotation matrix of the x-, y-, and z-directions,θYaw, θPitch, and θRoll are the posture angle of the testbed on aslope, and the x-, y-, and z-directions are shown in Fig. 20. The
term θYaw is approximately 0 because the testbed walks straight.
The directions of θPitch and θRoll are shown in Fig. 19(b). The term
mij is the mass of the link, which is ith of the leg and jth of thejoint, and g is the gravitational acceleration. Then, the moment
around the touching point between the ground and the leg iscalculated. For example, Mk that is the moment around thetouching point between the ground and the leg of kth is calculated
from (5)6 X
4X
M k = F g11 × ðpg11 − pk Þ þ
F gij × ðpgij − pk Þ,(5)
i=1 j=2

where pk is the position vector from the coordinate origin of the
testbed to the point touching the ground and the leg of kth and pgij
is the position vector from the coordinate origin of the testbed tothe center of gravity of the link. These position vectors arecalculated from (6) and (7). For example, Fig. 22 shows these
position vectors in leg 1 (i = 1)
pi = Rðθi2 ÞRðθi3 ÞRðθi4 Þpli4 þ Rðθi2 ÞRðθi3 Þpli3þ Rðθi2 Þpli2 þ pli1 ,(6)Fig. 22. Overview of position vectors in testbed.

8>>> plgi1>>< Rðθi2 Þplgi2 þ pli1
pgij = Rðθi2 ÞRðθi3 Þplgi3 þ Rðθi2 Þpli2 þ pli1>>
> Rðθi2 ÞRðθi3 ÞRðθi4 Þplgi4 þ>>: Rðθi2 ÞRðθi3 Þpli3 þ Rðθi2 Þpli2 þ pli1

#j = 1#j = 2#j = 3 ,(7)#j = 4

where R is the rotation matrix and expressed in (8), θij is theangle of the link, which is ith of the leg and jth of the joint (Fig. 22),and θij consists of the angles in yaw, pitch, and roll directions
Rðθij Þ = Rz ðθijYaw ÞRy ðθijPitch ÞRx ðθijRoll Þ,(8)where plij is the position vector from the coordinate origin of thelink to the joint between Lij and Lij+1 (Fig. 23(a)). The coordinate
origin of the link is the same as the joint of the next link (Fig. 23(a)).
The term plgij is the position vector from the coordinate origin of thelink to the center of gravity of the link (Fig. 23(b)). The moment
Mkn around the line segment connecting point k and point n is
calculated from (9)Fig. 21. Overview of links in the testbed.
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M kn = M k ·ðpn − pk Þ:
jpn − pk j

(9)Their points are that the leg is touched the ground. The terms k
and n are leg’s numbers. Calculation of Mos is divided into threecases because points touching the ground and the legs are changed
in walking. The cases of calculating Mos are shown in (10) and
Fig. 248< M 62
M os = M 53:
M 63

3rd leg is the free leg
6th leg is the free leg :Other cases(10)

When the 3rd leg is the free leg, Mos is M62. When the 6th leg isthe free leg, Mos is M53. In other cases, Mos is M63. The larger the161

value of Mos is, the more difﬁcult the testbed is to fall down.
Table VI shows the symbols used for calculating Mos.
Moreover, the posture of the body in roll direction and theamount of movement by walking are measured to conﬁrm theeffectiveness of the proposed method. The amount of movement ismeasured by the motion capture system.

C. RESULTS AND DISCUSSION OF A SLOPEWALKING EXPERIMENT
Table VI shows the result of the slope walking experiment. In
Table VII, success means that the testbed could walk without
falling down in all trials. Fall means that the testbed fell down in alltrials. The testbed fell down on the loose ground with a lean of 15°
and 20° when it used the walking without vibration. The testbed
could walk using the proposed walking on all slopes without falling
down. In this result, the proposed walking prevented a fall of theFig. 23. Overview of position vectors in the link.

Fig. 24. Calculation cases of Mos.
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Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged RoverTABLE VI. List of Symbols That Used Calculating
Moment on a Slope
Description

SymbolLeg number
Joint number
Gravity of link
Posture of testbed in yaw direction
Posture of testbed in pitch direction
Posture of testbed in roll direction
Mass of link
Gravitational acceleration
Leg number that a leg touches ground
Moment around point that a leg touches ground
Position vector from coordinate origin to point that a
leg touches ground (coordinate of testbed)
Position vector from coordinate origin to center ofgravity (coordinate of testbed)
Angle of joint
Position vector from coordinate origin to joint(coordinate of link)
Position vector from coordinate origin to center ofgravity (coordinate of link)
Moment around the line segment connecting two
points that a leg touches ground (coordinate of testbed)
Moment on a slope

i
j
Fgij
θYaw
θPitchθRollmijgn and kMk
pi

TABLE 7.
Slope angle
0°
5°
10°
15°
20°

Fig. 25. Moment vs time on a slope with 0°.

pgij
θij
plij
plgij
Mkn
Mos

Result of Slope Walking Experiment
Proposed walking

Walking without
vibration

Success
Success
Success
Success
Success

Success
Success
Success
Fall
Fall

testbed. Moreover, the angle of a slope that the testbed can walk
became large by using the proposed walking.
From Figs. 25 to 29, there are the graphs of time vs Mos inwalking. In these graphs, the data of one trial are chosen because
Mos, which was obtained in the same experimental conditions, washardly different in all trials. Fig. 30 shows the change of Mos in one
cycle of the walking. The term Mos was decreased at the beginningof this graph because the testbed raised the rear legs (Fig. 30). The
term Mos was increased in the ending of this graph because the bodyof the testbed moved forward. From Figs. 25 to 27, time isexpressed in percentage because the walking times are different
in each walking method. These values of Mos were not different ona slope with 0° (Fig. 25). In Figs. 26 and 27, Mos in the proposed
walking was larger than one in the walking without vibration on aslope with 5° and 10°. In this result, the testbed was difﬁcult to fall
down when it used the proposed walking. In Figs. 28 and 29, only
Mos in the proposed walking is shown because the testbed fell downusing the walking without vibration. In Figs. 28 and 29, Mos in the
proposed walking is not decreased in each walking cycle. In theseFig. 26. Moment vs time on a slope with 5°.

Fig. 27. Moment vs time on a slope with 10°.

graphs, the larger the slope angle was, the smaller the Mos was.
However, the testbed could walk using the proposed walking on all
slopes without falling down. The reason for this result is consideredthat the resistance forces that prevent a fall of the testbed arecaused. The friction force between the leg and the ground and theearth pressure is caused by sinking the legs in the ground (Fig. 31).
Therefore, it is considered that the actual Mos is larger than thecalculated Mos. In this result, falling down of the testbed was

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seemingly prevented by not only the effect of gravity but also othereffects.
From Figs. 32 to 36, there are the graphs of time vs testbed’s
posture. In these graphs, the data of one trial are chosen because theposture of the testbed, which was obtained in the same experimental conditions, was hardly different in all trials. In these graphs, theposture of the testbed is the angle in roll direction (Fig. 19(b)).
Their values of the testbed’s postures were not different on a slopewith 0° (Fig. 32). In Figs. 33 and 34, the posture of the testbed in the
proposed walking was smaller than one in the walking without
vibration on slopes with 5° and 10°. In Fig. 35, the posture of theFig. 28. Moment vs time on a slope with 15°.

Fig. 31. Overview of resistance forces by subsidence.

Fig. 29. Moment vs time on a slope with 20°.

Fig. 30. Change of Mos in 1 walking cycle.

Fig. 32. Posture of testbed vs time on a slope with 0°.

Fig. 33. Posture of testbed vs time on a slope with 5°.
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Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged Rover

testbed in the proposed walking was not increased. However, theposture of the testbed in the proposed walking was increased inFig. 36. Therefore, the proposed walking method has the featurethat the posture angle of the testbed is decreased. However, thelarger the angle of a slope is, the less effective this feature is.
Fig. 37 shows the graph comparing the amounts of movement.
The amount of movement in the proposed walking is larger thanFig. 37. Amount of movement in each walking.

Fig. 34. Posture of testbed vs time on a slope with 10°.

one in the walking without vibration. The testbed slipped and did
not move forward in a slope of 10° when it walked using thewalking without vibration. In this result, the running performance
was improved by using the proposed walking.
Finally, we discuss the advantage and weaknesses of the
proposed walking. On the advantage, a legged rover is difﬁcult
to fall down because the posture angle of a legged rover isdecreased by using the proposed walking. Moreover, the amountthat a legged rover walks becomes large by using the proposed
walking. On the weakness, the time during one cycle of walking
motion in the proposed walking is longer than one in the walking
without vibration. The reason is that the time of vibrating legs is
added in the proposed walking. In this study, shortening ofvibrating time is not addressed yet. This weakness will be solved
when the relationship between vibrating time and running performance is conﬁrmed in the future study.

V. CONCLUSION

Fig. 35. Posture of testbed vs time on a slope with 15°.

Fig. 36. Posture of testbed vs time on a slope with 20°.

In this study, a walking method that prevented a fall of the leggedrover was proposed. In the proposed walking method, the leg was
sunk by giving vibration to the ground. The posture of the rover
was changed to prevent a fall of the rover by sinking the leg. First,
the relationship between the kind of vibration and the subsidence ofthe leg was conﬁrmed. In this experiment, the rod was penetrated
into the loose ground. Moreover, the resistance force that the rod
was received from the ground was measured. The experimental
results are shown below:• The rod is easy to sink to the ground by giving vibration.
• The larger the vibratory force is, the smaller the resistanceforce is.
In these results, it was possible that the rover inclines forward
by giving vibration to the ground. Finally, the legged testbed
walked on the loose ground with a slope using the proposed
walking method. The experimental results are shown below:• The testbed is difﬁcult to fall down when it used the proposed
walking.
• The angle of a slope that the testbed can walk becomes large byusing the proposed walking.
• The posture angle of the testbed is decreased by using the
proposed walking.
• The amount of movement in the proposed walking is larger
than one in the walking without vibration.
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Watanabe and Iizuka

In these experimental results, it was conﬁrmed that the proposed walking method was effective.
The value of Mos was decreased in high angle slopes but the
testbed could walk without falling down. The reason for this result
is considered that the resistance forces that prevent a fall of the
testbed are caused. In the future study, Mos that includes these
resistances will be calculated. The proposed walking will be able tobe evaluated accurately by including these resistances. Moreover,
the time during one cycle of walking motion in the proposed
walking was longer than one in the walking without vibration.
Running speed can be increased by shortening the time during one
cycle of walking motion. Therefore, the time during one cycle ofwalking motion should be short. In future study, the relationshipbetween vibrating time and running performance will be conﬁrmed
to short vibrating time.

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