1 INTRODUCTION
Robots are considered to be one of the most important
mission devices for planetary explorations and
will be expected to move on planetary surfaces to
collect precise information regarding the origin and
maturing. In the Mars mission by NASA in 1997,
the micro robot Sojourner moved and explored on
the surface of Mars. Sojourner sent the important
data and detailed pictures to the earth.
The Sojourner mission showed the importance of
moving exploration[1]. In planetary exploration, robots
are required to move on rough terrains such as in
craters and rear cliffs where it is scientifically very
important to explore. Further, robots must avoid tipover
and stack even though they move on rough terrains.
In the present, the space agencies around the
world, focuse on on the lunar exploration[1][2][3][4].
On September 2007, the space agency of Japan, JAXA
[5] carried out ranching the Satellite to explore around
the Moon. The mission is named on SELENE Mission.
JAXA is planning SELENE-2 mission[6] as after
mission of SELENE mission. In SELENE-2 mission,
the exploration robots will move on the lunar soil.
However, there is a big problem. Lunar soil is covered
with very soften soil which is named reglith. Exploration
rovers are easy to stack on regolith when they
are traversing on regolith. Therefore, rovers need the
effictive running systems that are not stack on regolith.
To construct high performance locomotion systems,
it is need to study the interaction between locomotion
systems and the soften soil. From this interaction,
this paper extracts some elements to traverse
on soften soil. Then, this paper proposes the design
scheme for locomotion systems of lunar rovers.
In section 2, this paper discusses about terramechanics
between locomotion systems and lunar soil
is considered using model. Section 3 and 4 presents
the experiments and the results. Section 5 is for the
conclusion and the future works of this paper.
2 Terramechanics Consideration
between Locomotion Systems
and Soften Soil
This paper considers the interaction between locomotion
systems and soften soil.
2.1 Model between Locomotion Systems
and Soften Soil
Some researchers have studied robots with interaction
between wheel and soil on a flat terrain [7][8][9][10]
[11][12][13][14][15]. However they do not study the
model on a slope. This paper cosiders the interaction
model between wheel and soil on a slope as shown in
Fig.1.
The line which the wheel runs on slope is shown as
hsoil surfaceh. r! and V! denote the revolution and
velocity of the wheel. Wt means the parallel load of
the wheel to soil surface. Zs denotes the sinkage at
a slope. Ê is used to show the part of the wheel into
soil. Ê1 indicates the inserted angle into soil and Ê2
indicates the escaped angle.
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r??
a
r
Vw
????
????
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????????
????????
Wt
Fig. 1: Interaction Model between Wheel and Soil on
Slope
The slip ratio C is defined by the following formula
here.
C = 8>><>>:
1 !
V!
r!
: drive(r! C V !)
1 !
r!
V!
: brake(r! E V!)
(1)
where,
r : the radius of a wheel
! : angular velocity of a wheel
V! : moving speed of a wheel
2.2 Traction Force produced by Wheel
The traction force of wheel DP is expressed by
the total of force working the wheel. Therefore, the
traction force is expressed by intergrating a shearing
stress ? (Ê) and a normal stress ?(Ê) is intergrated
using contacted area of wheel and soil. Then, the
traction force DP is written as follows using the wheel
radius r and the wheel width b.
DP = rb(Z Ê2
Ê1
? (Ê) cos ÊdÊ ! Z Ê2
Ê1
?(Ê) sin ÊdÊ)
+LjbC Z Ê2
Ê1
Rb cos ÊdÊ (2)
where,
Lj : length of lugs
Rb : pressure given lugs
2.3 Important Elements for Traversability
From model between locomotion systems and soften
soil, this paper extracts the important elements. The
stress between locomotion systems and soil is important
element to traverse on soften soil. Moreover, the
lugs which are installed on surface of locomotion systems
is necessary to get impellent from soften soil.
This paper describes about the reason that these elements
is important from consideration of such locomotion
systems.
2.3.1 Stress Distribution
The stress level is not only problem on considering
to structure locomotion systems with high performance.
The Stress Distribution of the circular wheels
is long to vertical direction. The soften soil under the
wheels are easy to destroy. The shearing strength of
regolith is very small. Therefore the one is easy to
sink into soften soil. On the other hand, the low stress
tires and crawler types are long sideways. If the stress
distribution is long to direction of vertical, because of
the force got to soften soil is too large, the soften soil
under the wheels are broken by these strong force of
vertical direction. If the stress distribution is long
sideways like crawler types, the locomotion systems
has the effect that hardens the soften soil. This paper
considers about the wheel with stress distribution of
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Fig. 2: Stress Distribution of Pentagon Type Wheel
long sideway. If the wheel has the pentagon form,
the one can have stress distribution of long sideway
like shown in Fig 2. Therefore, This paper carries
out experiment to confirm the shearing strength of
soften soil before and after running using the pentagon
typed wheel.
2.3.2 Orbit of Lugs
The lugs installed on the surface of locomotion systems
make the impellent. The locomotion systems
get impellent by rotation of lugs. The lugs of such
locomotion systems have themselves rotation orbit of
lugs. The lugs of the circular wheels have the circular
orbit(Fig.3). On the other hand, the orbit of
lugs of the low-pressure tires and the crawler types is
ellipse(Fig.4). When the lugs of the low stress tires
and the crawler types insert into soften soil, the orbit
of lugs is parallel toward the running surface. This
paper carries out experiment to confirm the effect of
orbit of these lugs.
3 Experiments
3.1 Experimental System
The overview of the experimental system is shown
in Fig.5. In this experiment, the simulant is used
as soil, whose the particle specific gravity is 2.83, the
minimum density is 1.39 [g=cm 3], the adhesive power
is 5.0 [kPa] and the internal friction angle 36.7 [deg].
The depth of the simulant is 0.07 [m]. And the simulant
is dry by the heater. The experimental system
is composed of some mechanics and some sensors as
shown in Fig.6. Here, one wheel, the parallel link,
Fig. 3: Orbit of Lugs on Circular Type
Fig. 4: Orbit of Lugs on Crawler Type
the stator, the guide rail, the load balance and the
balance box are used. The parallel link is attached
between the axis for the wheel and the load balance.
The road balance runs on the guide rail. As sensors,
there are differential transformer to measure the distance
and two encoders. The differential trans-former
measures the horizontal position of a wheel. The
measurable distance of the differential trans-former
is within 20 [mm]. The vertical position of a wheel
can be calculated by the rotary encoder. The velocity
of the wheel is calculated by using vertical and horizontal
position, and time. The rotation of wheel can
be obtained from encoder. Therefore, the slip ratio is
calculated using the velocity and the rotation. The
sinkage is obtained from the present position and position
of the original surface of the soil. Moreover,
the wheel load can be set by some weight into the
balance box.
3.2 Experimental Conditions
In the experiment, the wheel load, the speed of
wheel and slope angle can be changed as parameters.
Experimental parameters are shown in TABLE 1.
Fig. 5: Overview of Experimental System
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Fig. 6: Experimental Setup
3.3 Measurement Item
The measurement items in this experiment are shown
below. The initial shearing strength of soil is measured
by the default of soil. Moreover, the shearing
strength after running are measured for observing
hardening effect.
2 initial shearing strength of soil
2 rotation angle of wheel
2 wheel position
3.4 Wheels for Experiment
3.4.1 Wheels for measurement the shearing
strength of soil
This paper uses pentagon typed wheel (Fig.7 (a)).
The pentagon typed wheel has the stress distribution
that is long sideway. Moreover, the circular
Table 1: Experimental Parameters
Load 2 [kg]
Speed 0.1 [m/s]
Slope 0, 5, 15, 20 [deg]
(a) Pentagon Type (b) Circular Type
Fig. 7: Wheel for Experiment ofg Shearing Stress h
(a) Elastic Wheel (b) Circular Wheel
Fig. 8: Wheel for Experiment ofg Orbit of Lugs h
wheel(Fig.7 (b)) is used to compare. The stress distribution
of the circular wheel is long to vertical direction.
3.4.2 Wheels to confirm the traversability by
differents of horbit of lugsh
As the wheels to confirm the traversability by the
effect of orbit of lugs, this paper uses the elastic wheel
(Fig.8 (a)). The elastic wheel is made from elastic
material of iron. And the elastic wheel has ellipse
orbit of lugs. Moreover, the circular wheel (Fig.8(b))
is used to compare.
4 Experimental Results
This paper carried out the experiments to grasp
three important elements, the effect of lugs, the hardening
effect and the effect by orbit of lugs.
4.1 Shearing Strength
The shearing stress is shown in Table.2. The shearing
stress were measured by the vane shearing tester.
Table 2: Shearing Stress Before and After Running
Wheel Before[cNm] After[cNm] Tendency
Normal 0.43 0.30 &
Pentagon 0.40 0.53 %
The shearing stress of the circular wheel after running
on soften soil is down compared with before running.
This means that the soften soil under the wheel was
destroyed. On the other hands, the shearing stress of
the pentagon typed wheel after running on soften soil
increased compared with before running. The soften
soil was harden by the pentagon typed wheel was running.
Therefore, the soften soil under the pentagon
typed wheel is not easy to destroy. Moreover, to be
wide the contacting area to soften soil is effective.
4.2 Orbit of lugs installed Locomotion
systems
Figure.9 shows the experiment result using the elastic
wheel to confirm the influence by orbit of lugs
when slope is 20 [deg]. Moreover, the sinkage of both
wheels at running is shown in Fig.10. In the case
of the circular wheel runs on slope, the slipping phenomenon
remarkably increases. On the other hands,
the running condition of the elastic wheel is good.
The sinkage of both wheel at running on soften soil
with slope is shown in Fig.10. The elastic wheel is not
easy to sink because of having the structure of low
stress and wide hardening area. And then, the wheel
with ellipse orbit got enough impellent to traverse
on soften soil compared with the wheel with circular
orbit. Therefore, the slipping phenomenon of the
elastic wheel is not easy to increase. Figure.11 shows
the result of slip ratio at slope. From this results,
the elastic with ellipse orbit is effective to traverse on
soften soil with slope.
5 Conclusion and FutureWorks
In this paper, the design scheme of the locomotion
systems for the lunar robots was discussed. From
the theoretical approach, the elements for the design
scheme are extracted using the representative locomotion
systems, the vehicles with circular wheel, the
vehicle with the low-pressure tires and crawler types.
These elements areg stress distribution between the
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250 300 350
Circle
Elastic
Distance [mm]
Slip Ratio
Circular Wheel
Elastic Wheel
Fig. 9: Experimental Result:Slip Ratio(2[kg], 20[deg],
0.1[m/s])
0
10
20
30
40
50
60
70
0 50 100 150 200 250 300 350 400
Circle
Elastic
Distance [mm] S
i
n
k
a
g
e
[
m
m
]
Elastic Wheel
Circular Wheel
Fig. 10: Experimental Result:Sinkage(2[kg], 20[deg],
0.1[m/s])
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Circle
Elastic
Slope [deg]
Elastic Wheel
Circular Wheel
Slip Ratio
Fig. 11: Experimental Result(2[kg], 0.1[m/s])
locomotion systems and soil handg orbit of lugs h.
The experiments to confirm the influence these parameters
for design schemes were carried out. The experimental
results showed that there were important
to make large the contacting area between wheels and
soften soil, and to have the ellipse orbit of lugs. As
future works, the new locomotion systems will be developed
from important elements that this paper proposed.
Moreover, this paper will make vehicle with
locomotion systems, and the running experiment will
be carried out.
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