EVALUATION OF INFLUENCE OF WHEEL SURFACE SHAPES ON TRACTIVEEFFICIENCIES OF PLANETARY ROVERS IN VARIOUS SOIL ENVIRONMENTS
Masataku Sutoh, Kenji Nagaoka, Keiji Nagatani, and Kazuya Yoshida
Department of Aerospace Engineering, Graduate School of Engineering, Tohoku University,
6-6-01 Aoba Aramaki Aoba-ku, Sendai 9808579, Japan

ABSTRACT
Wheels of planetary rovers typically have grousers on
their surface to provide grip for climbing in loose soil
and scrambling over rough terrain. In this study, theinfluence of grousers on the traveling performances ofwheeled rovers is evaluated in various soils. First, the influence of the number of grousers was quantitatively determined by conducting experiments using wheels withdifferent number of grousers in sandboxes covered with
Toyoura sand/lunar regolith simulant. Next, the influence of grouser height was evaluated by conducting experiments using wheels with different grouser heights.
Finally, the experimental results are discussed from thepoint of view of terramechanics. According to the experimental results, it was confirmed that the number ofgrousers and grouser height that a wheel must be at least
required for high traveling performance will be almost
the same for soils having similar pressure-sinkage characteristic.
Key words: Planetary rovers; wheel; grouser.

1.

INTRODUCTION

Mobile robots, also called rovers, have played a significant role in NASA’s Martian geological investigations.
The use of rovers in missions significantly increases thearea that can be explored, and thus increases the scientificreturn from the missions. However, lunar and Martiansurfaces are covered with loose soil, and numerous steep
slopes are found along their crater rims. Wheeled rovers
can be stuck in such conditions and even cause mission
failure.
To avoid such problems, many research groups have studied the traveling performance of planetary rovers on thebasis of terramechanics [1, 2]. Conventionally, terramechanics has mainly been used to study large vehicles,
such as dump trucks, military and agricultural vehicles[3, 4]. Protrusions called grousers (i.e., lugs, cleats) on
the wheels or track of the vehicles have influence on theirtraveling performance. Based on this empirical knowl-edge, grousers have been equipped on wheels of planetary rovers [5], and it was found that they substantiallyinfluence the traveling performance of lightweight vehicles such as planetary rovers [6, 7, 8]. Therefore, it isimportant to evaluate the effect of grousers on the traveling performance of planetary rovers.

There have been some reports on the influence ofgrousers on the traveling performance of lightweight
wheeled rovers. Our group has experimentally evaluated the influence of the number of grousers and grouserheight on the traveling performance of wheeled rovers[6, 7]. Furthermore, Ding et al. reported the influenceof grouser inclination angle on the traveling performanceof a wheel [8]. In addition to the experimental approach,a method for estimating the traveling performance of
wheels equipped with grousers using the discrete element method (DEM) has been proposed [9]. Furthermore, a terramechanics model for wheels with grousers
has recently been proposed [10]. In these studies, however, wheels with short grousers, such as the wheels of
NASA’s Mars Exploration Rovers (MERs), which had
a wheel diameter of 10” and a grouser height of 0.25”[5], were mainly focused. Only a few studies have reported on the behavior of wheels having considerably
taller grousers. Furthermore, these studies reported the
behavior of wheels with different grouser parameters;
however, only one soil type was usually used and the effect of grousers has not been compared for various soils.

In this study, the influence of the number of grousers
on the traveling performance of wheeled rovers was firstevaluated by performing experiments using wheels withdifferent numbers of grousers. Next, the influence ofgrouser height on the traveling performance was evaluated by conducting experiments using wheels having different grouser heights. In the experiments, wheels having
considerably taller grousers are utilized. The experiments
were performed using a two-wheeled rover in sandboxes
covered with Toyoura sand/lunar regolith simulant. In
this paper, a method of evaluating traveling performanceis defined and the above experiments are reported in further detail. Finally, the experimental results are discussed
from the point of view of terramechanics.

2.

TRAVELING PERFORMANCE EVALUATIONMETHOD

2.3.

Resistance torqueIn this section, slip ratio, drawbar pull, resistance torque,and tractive efficiency are introduced for evaluating thetraveling performance of wheeled rovers.

When a rover travels, a torque is required around the axleof the wheel. This torque is called resistance torque, andit comprises the torque developed by soil compaction andinternal wheel resistance, such as mechanical friction.

2.1.

The resistance torque T can be roughly estimated fromthe current I to a motor that rotates the wheel, using thefollowing equation:

Slip ratio

The slip ratio represents the effectiveness of wheel motion, and in general, it is defined using the actual linear
speed of a vehicle and the radius and angular speed of
the wheel [4]. Wheels with grousers were used in thisstudy. It is difficult to define the effective diameter ofsuch wheels and to define the slip ratio on the basis of theabove method. Therefore, the slip ratio s of a wheel withgrousers is defined as done in [6]:dd − d
d
s=
=1− ,
dd
dd

(1)

where d denotes the actual traveling distance per wheel
rotation, and dd denotes the traveling distance per wheel
rotation on hard ground (i.e., no wheel sinkage condition). Here, dd is geometrically calculated, as previously
reported by our group [6].
The slip ratio has a value between 0 and 1. When thewheel moves forward without slippage, the slip ratio is 0;
when the wheel does not move forward at all because ofslippage, the slip ratio is 1.

2.2.

(3)

where k denotes a torque constant of the motor, and n
and ηg denote gear reduction and maximum efficiency,
respectively. In planetary exploration, resistance torquemust be minimized for low power consumption.

2.4.

Tractive efficiency

Tractive efficiency is defined by the ratio of the input
work to the wheel to the actual work of the wheel. Tractive efficiency η is derived as done in [8]:η=DP (1 − s)rT(4)

where r denotes the radius of the wheel. In this study,
using dd in Eq. 1, r of wheels with grousers is defined as
r=

dd
.
2π

(5)

High tractive efficiency can be achieved if the wheel travels with small slippage and small resistance torque forhigh drawbar pull.

Drawbar pull

The drawbar pull is defined as the difference between the
total thrust and the total external resistance of the vehicle[3], and it varies with wheel slippage. Therefore, a slip
ratio corresponding to the drawbar pull is an important
indicator of the traveling performance of the rover.
The drawbar pull denotes the reserve of ground strengththat can be utilized by motor torque to develop acceleration, move the vehicle on slopes or pull a trailer hitched
to a drawbar [3]. When a rover travels over a slope, itneeds to pull its weight. Therefore, to move the roveron the slope, the drawbar pull DP of wheels satisfies thefollowing equation:
DP = mg sin θ

T = knηg I,

3. EXPERIMENTS
To evaluate the influence of the number of grousers andgrouser height on the traveling performance of wheeledrovers in various soils, slope-climbing tests were performed using a two-wheeled rover with wheels having different number of grousers and different grouserheights. The experiments were conducted in sandboxes
covered with Toyoura sand/lunar regolith simulant. In
this section, the details and results of the experiments arepresented.

(2)

where m is the mass of the rover, g is the gravitational
constant, and θ is the slope angle. According to this equation, the slope angle has the same relation to the slippageas the drawbar pull. Therefore, to evaluate the travelingperformance of a wheeled rover, a slip ratio corresponding to the slope angle was used as the indicator in thisstudy.

3.1.

Two-wheeled rover and wheels

In this study, a lightweight two-wheeled rover with interchangeable wheels (Fig.1) was developed. The wheelbase of the rover was fixed at 600 mm. The roverweight was set to 6.0 kg using additional weights for all
the different wheels. To rotate the wheels and control

Figure 2. Slope-climbing test; the two-wheeled rovertravels in a sandbox covered with Toyoura sand.

Figure 1. Two-wheeled rover.

their angular speed, the rover has a microcontroller (H83048one; Renesas Technology Corp.), and a motor embedded with an encoder (RE-max 25 with GP32C planetary gear and MRenc encoder; Maxon Co., Ltd). A
motion measurement system using an optical sensor andlaser source [11] was mounted on the rover to measure
the actual rover traveling distance/speed. The slip ratios is determined from the distance using Eq. 1. Furthermore, a current sensor module (ACS712; Sparkfun Electronics) was mounted on the rover to measure the current
to the motor that rotates the wheel. From the current, theresistance torque T is determined using Eq. 3.
Five wheel types, which have different numbers ofgrousers (configuration 1 in Tab. 1), were developed.
This wheel has a diameter of 250 mm, including thegrouser height, and a width of 100 mm. Each grouser
was made of aluminum and has a thickness of 1 mm andheight of 25 mm. In addition, five wheel types, whichhave different ratios of grouser heights (hd ) to wheel inner diameters (D) (configuration 2 in Tab. 1), were developed. The wheel has a diameter of 250 mm, including thegrouser height, and a width of 100 mm. Each wheel was
equipped with twelve grousers placed at equally spaced
intervals. The wheel surface was covered with sandpaper having a roughness corresponding to that of the target
soil.

3.2.

Experimental conditions

A two-wheeled rover, with the above ten types of wheels,
was used to conduct slope-climbing tests in sandboxes(Fig.2). Each sandbox had a length, width, and depth of
1.5 m, 0.30 m, and 0.20 m, respectively, and was filledwith Toyoura sand/lunar regolith simulant. Toyoura sand(JIS R 5200) has very low cohesion and its particle size isalmost uniform. Lunar regolith simulant (FJS-1; Shimizu
Corp.) has almost the same mechanical properties as real
lunar regolith [12]; it is cohesive and its particle size is
non-uniform. The soil parameters of each soil are listed
in Tab. 2. The sandbox could be manually inclined tochange its slope angle. In the experiments, the slope
angles were set at up to 24◦ at 4◦ intervals. The angular speed of the wheel was fixed at 2.50 rpm, and theslip ratio/resistance torque was obtained using the meanvalue after the wheels stopped sinking. Each trial was
conducted under identical soil conditions, and three trials
were conducted for each condition.

Table 1. Wheels with different number of grousers and different grouser heights; except for the wheel with 0 grousers, theother wheels have a diameter of 250 mm, including the grouser height, and a width of 100 mm.

Configuration 1
Grousers : 0

Grousers : 3

Grousers : 6

Grousers : 12

Grousers : 24

D:25cm;hd :0.0cm

D:24cm;hd :0.5cm

D:20cm;hd :2.5cm

D:15cm;hd :5.0cm

D:10cm;hd :7.5cm

Configuration 2

1

1
0 grousers
3 grousers
6 grousers
12 grousers
24 grousers

0 grousers
3 grousers
6 grousers
12 grousers
24 grousers

0.8
Slip ratio [-]Slip ratio [-]

0.8
0.6
0.4
0.2

0.6
0.4
0.2

0

0
0

5

10
15
Slope angle [deg]

20

25

0

(a) Toyoura sand

5

10
15
Slope angle [deg]2025(b) Lunar regolith simulant

Figure 3. Slope angle versus slip ratio (for different numbers of grousers).

3.3.

3.3.1.

Evaluation of the number of grousers influenceon traveling performance
Influence of the number of grousers on slip ratio

To evaluate the influence of the number of grousers on
slip ratio, the data for the cases with different number ofgrousers were plotted in the graphs shown in Fig.3.
The wheels showed small slip ratios over slopes with angles up to 4◦ (Fig.3(a)) on Toyoura sand, while on lunar
regolith simulant, the slip ratios were small over slopes
with angles up to 8◦ (Fig.3(b)). This means that thewheels can travel with a small amount of slippage overa steeper slope on lunar regolith simulant than on Toyoura sand. Over the slopes, there were slight differencesin slip ratio values for different number of grousers. Thatis, over flat/gentle terrain, it is not necessary for a wheel
to be equipped with grousers for high traveling performance.
On Toyoura sand, wheels with 6, 12, and 24 grousers generally showed smaller slip ratios than those with 0 and
3 grousers over slopes with angles greater than 4◦ (Fig.
3(a)). Meanwhile, on lunar regolith simulant, the sametendency was observed over slopes with angles greaterthan 8◦ (Fig. 3(b)). Over the slopes, an increase in thenumber of grousers contributes to wheel slip improvement if the number of grousers is up to 12; wheels with
12 and 24 grousers showed slight differences in slip ratio

Table 2. Soil parameters and values; bulk density (ρ),
cohesion (c), angle of internal friction (φ), and pressuresinkage parameters (kc , kφ , and n).
Toyoura sand Lunar regolith simulant
ρ [kg/m3 ]1.5×103
1.7×103c [kPa]0
0.8
φ [◦ ]
38.0
37.2
kc [kN/mn+1 ]0.9
1.4
kφ [kN/mn+2 ]
1500
820
n [-]
1.1
1

values.
Over the steep slopes, it was observed that for the caseswith wheels with small number of grousers, the rover
moved forward only when grousers contact with theground; a linear speed of the rover changed periodicallyin a cycle corresponding to grouser intervals. With atleast 12 grousers, the rover could constantly move forward. This is why an increase in the number of grousers
contributed to wheel slip improvement.
According to the above observations, it was concluded
that over steep slopes, an increase in the number ofgrousers greatly contributes to improving the travelingperformance if the number of grousers is up to 12. Inother words, this wheel must be equipped with at least 12
grousers for high traveling performance. It is noteworthy
that this number is the same for both soils.

3.3.2. Influence of the number of grousers
on tractive efficiency
To evaluate the influence of the number of grousers on
tractive efficiency, the data for the cases with different
number of grousers were plotted in the graphs shown in
Fig.4. Tractive efficiency was obtained from the slip ratio
and resistance torque using Eqs. 1 – 5.
The wheels with 0 and 3 grousers showed a slightly
higher tractive efficiency over slopes with angles up to 4◦(Fig.4(a)) on Toyoura sand, while on lunar regolith simulant, their tractive efficiencies were high over slopes with
angles up to 8◦ (Fig.4(b)). This is because all the wheels
show slight differences in slip ratio values over the slopes
and wheels with small numbers of grousers have smaller
resistance torques.
On Toyoura sand, the wheels with 6, 12 and 24 grousers
have a high tractive efficiency over slopes with angles
greater than 4◦ (Fig.4(a)). Meanwhile, on lunar regolith
simulant the same tendency was observed over slopes
with angles greater than 8◦ (Fig.4(b)). This is because

0.5
0 grousers
3 grousers
6 grousers
12 grousers
24 grousers

0.4

Tractive Efficiency [-]Tractive Efficiency [-]

0.5

0.3
0.2
0.1

0 grousers
3 grousers
6 grousers
12 grousers
24 grousers

0.4
0.3
0.2
0.1

0

0
0

5

10
15
Slope angle [deg]2025(a) Toyoura sand

0

5

10
15
Slope angle [deg]2025(b) Lunar regolith simulant

Figure 4. Slope angle versus tractive efficiency (for different numbers of grousers).

the wheels with 6, 12, and 24 grousers have a smaller slip
ratio than those with 0 and 3 grousers over the slopes.
According to the above discussion, for both soils, it was
concluded that wheels with small number of grousers
have high tractive efficiencies over gentle slopes. On theother hand, wheels with large number of grousers havehigh tractive efficiencies over steep slopes.

3.4.

Evaluation of grouser height influenceon traveling performance
3.4.1.

Influence of grouser height on slip ratio

To evaluate the influence of grouser height on slip ratio,
the data for the cases with different grouser heights wereplotted in the graphs shown in Fig.5.
The wheels showed small slip ratios over slopes with angles up to 8◦ (Fig.5(a)) on Toyoura sand, while on lunar
regolith simulant, the slip ratios were small over slopes
with angles up to 12◦ (Fig.5(b)). Over the slopes, there
were slight differences in slip ratio values for different
grouser heights.
On Toyoura sand, the slip ratio over slopes with angles
greater than 8◦ (Fig.5(a)) was seen to decrease with anincrease in grouser height, although the wheels with 2.5
cm, 5.0 cm and 7.5 cm high grousers showed slight differences in slip ratio values. Meanwhile, on lunar regolith
simulant, the same tendency was observed over slopes
with angles greater than 12◦ (Fig.5(b)).
For the wheels with 0.5 cm high grousers, the grousers
bulldozed soil close to the surface of the ground, which
resulted in generating a small shearing stress. On theother hand, for wheels with 2.5 cm, 5.0 cm, and 7.5 cm
high grousers, the grousers bulldozed soil deep under the
ground; shearing stress generated is large. This is why anincrease in grouser height generally contributed to a hightraveling performance.
In the experiments, it was observed that when the wheels

with 0.5 cm and 2.5 cm high grousers traveled, theirwheel surfaces made contact with the ground. On theother hand, when the wheels with 5.0 cm and 7.5 cm highgrousers traveled, only their grousers made contact withthe ground and they penetrated a few centimeters below
the surface of the ground. That is, the effective grouserheight of the wheels with 5.0 cm and 7.5 cm high grousers
were almost the same as that of the wheel with 2.5 cm
high grousers. This is why an increase in grouser height
does not contribute much to a high traveling performanceif grouser height is greater than 2.5 cm.
According to the above discussion, it was concluded thatover steep slopes, an increase in grouser height greatly
contributes to improving the wheel slip if grouser height
is up to 2.5 cm. In other words, this wheel must be
equipped with at least 2.5 cm high grousers for high traveling performance. It is noteworthy that this height is thesame for both soils.

3.4.2. Influence of grouser height on tractive efficiency
To evaluate the influence of grouser height on tractive
efficiency, the data for the cases with different grouserheights were plotted in the graphs shown in Fig. 6.
The wheels without grousers and 0.5 cm high grousers
showed a slightly higher tractive efficiency over slopes
with angles up to 8◦ (Fig.6(a)) on Toyoura sand, whileon lunar regolith simulant, their tractive efficiencies werehigh over slopes with angles up to 12◦ (Fig.6(b)). This isbecause all the wheels show slight differences in slip ratio values over the slopes and wheels with short grousers
have smaller resistance torques.
On Toyoura sand, the wheels with 2.5 cm, 5.0 cm, and7.5 cm high grousers has a high tractive efficiency overslopes with angles greater than 8◦ (Fig.6(a)), while on lunar regolith simulant, their tractive efficiencies were highover slopes with angles greater than 12◦ (Fig.6(b)). Thisis because the wheels with 2.5 cm, 5.0 cm, and 7.5 cm
high grousers have a smaller slip ratio than those without

1

1
D:25cm; hd:0.0cm
D:24cm; hd:0.5cm
D:20cm; hd:2.5cm
D:15cm; hd:5.0cm
D:10cm; hd:7.5cm

D:25cm; hd:0.0cm
D:24cm; hd:0.5cm
D:20cm; hd:2.5cm
D:15cm; hd:5.0cm
D:10cm; hd:7.5cm

0.8
Slip ratio [-]Slip ratio [-]

0.8
0.6
0.4
0.2

0.6
0.4
0.2

0

0
0

5

10
15
Slope angle [deg]

20

25

0

(a) Toyoura sand

5

10
15
Slope angle [deg]

20

25

20

25

(b) Lunar regolith simulant

Figure 5. Slope angle versus slip ratio (for different grouser heights).

0.5
D:25cm; hd:0.0cm
D:24cm; hd:0.5cm
D:20cm; hd:2.5cm
D:15cm; hd:5.0cm
D:10cm; hd:7.5cm

0.4

Tractive Efficiency [-]Tractive Efficiency [-]

0.5

0.3
0.2
0.1

D:25cm; hd:0.0cm
D:24cm; hd:0.5cm
D:20cm; hd:2.5cm
D:15cm; hd:5.0cm
D:10cm; hd:7.5cm

0.4
0.3
0.2
0.1

0

0
0

5

10
15
Slope angle [deg]2025(a) Toyoura sand

0

5

10
15
Slope angle [deg](b) Lunar regolith simulant

Figure 6. Slope angle versus tractive efficiency (for different grouser heights).

grousers and 0.5 cm high grousers, although the former
wheels have relatively large resistance torques.
According to the above discussion, for both soils, it was
concluded that wheels with short grousers have high tractive efficiencies over gentle slopes. On the other hand,wheels with tall grousers have high tractive efficiencies
over steep slopes. These results indicate that the optimum
wheel shape differs according to the goal of the exploration mission. A wheel with short grousers is suitable fora mission in which rovers are required to travel long distances over flat/gentle terrain. On the other hand, wheels
with tall grousers are suitable and essential for missions
in which rovers are required to climb steep slopes such as
crater rims.

4.

DISCUSSION FROM THE POINT OF VIEWOF TERRAMECHANICS

As presented in subsections 3.3 and 3.4, the number ofgrousers and grouser height that a wheel must be at least
required for high traveling performance were almost thesame for Toyoura sand and lunar regolith simulant. In
this section, their reasons are discussed from the point ofview of terramechanics.

When a terrain is considered to be homogeneous within
the depth of interest, its pressure-sinkage relationship isexpressed [3] asp=(kc+ kφ )z nl(6)where p is pressure, l is the smaller dimension of the contact patch, that is, the width of a rectangular contact area,z is sinkage, and kc , kφ , n are pressure-sinkage parameters. The value of kc , kφ , and n can be derived from
penetration tests using plates.
Using the soil parameters of Toyoura sand and lunar regolith simulant shown in Tab. 2, the pressure-sinkage relationship of the soils were obtained, as shown in Fig.7.
In the figure, l was fixed at 2.0 cm. In a case that a loadof 3 kg uniformly acts on a rectangular plate having awidth of 2.0 cm and length of 10.0 cm (i.e., in a casethat a wheel has a contact patch of 2.0 cm in our experiments), the pressure would be 14.7 kPa over the contact
area. Assuming that a plate and wheel would follow thesame pressure-sinkage relationship, for a contact pressureof around 14.7 kPa, sinkage of wheel would be almost thesame on Toyoura sand and lunar regolith simulant (Fig.
7). This means that both soils have the similar pressuresinkage characteristic for the rover/wheels conditions inthis study.

wheels with conventional grouser heights. Finally, it was
concluded that for soils having a similar pressure-sinkage
characteristic, the number of grousers and grouser heightthat a wheel must be at least required for high travelingperformance will be almost the same.

30
Toyoura sand
Lunar regolith simulant
p=14.7[kPa]

Pressure[kPa]

25
20
15
10

REFERENCES

5
0
0

0.005

0.01

0.015
Sinkage[m]

0.02

0.025

0.03

Figure 7. Pressure-sinkage relationship for Toyoura sandand lunar regolith simulant (for fixed l of 2.0 cm).

In the experiments using wheels with different numberof grousers (subsection 3.3), over steep slopes, the wheel
were required at least 12 grousers for high traveling performance. Over the slopes, the wheel would obtain thrust
only when grousers travel in a range where a normal
stress is generated beneath it [7]. Considering this range,
the minimum required number of grousers would be determined for a wheel; this range is derived from the sinkage of the wheel. According to the above discussion, on
Toyoura sand and lunar regolith simulant, wheel sinkage
would be almost the same; this leads a normal stress tobe generated in the same range beneath a wheel. This is
why the number of grousers required for a wheel was thesame for both soils.
In the experiments using wheels with different grouserheights (subsection 3.4), the wheel was required at least
2.5 cm high grouser for high traveling performance. Thisis because the effective grouser heights of the wheels
with 5.0 cm and 7.5 cm high grousers were determinedby depths of grouser penetration and they were almost
the same as that of the wheel with 2.5 cm high grousers.
According to the above discussion, on Toyoura sand andlunar regolith simulant, which have the similar pressuresinkage characteristic, a depth of grouser penetration is
expected to be almost the same. This leaded the grouserheight required for a wheel to be the same for both soils
in this study.

5.

CONCLUSIONSIn this study, slope-climbing tests were performed using
a two-wheeled rover with wheels equipped with grousers
in sandboxes covered with Toyoura sand/lunar regolith
simulant. The influence of the number of grousers on thetraveling performance of wheeled rovers was also evaluated. Next, the influence of grouser height on travelingperformance was evaluated. According to the experimental results, it was confirmed that an increase in the number of grousers generally contributes to improved tractive
efficiency over steep slopes on both soils. Furthermore,
it was found that over steep slopes, wheels with considerably much taller grousers travel more efficiently than[1] K. Iagnemma, S. Kang, H. Shibly, and S. Dubowsky.
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