MOBILITY CHARACTERISTICS AND CONTROL OF A SKID-STEERINGMICRO-ROVER FOR PLANETARY EXPLORATION ON LOOSE SOIL
*Kenji Nagaoka1 , Kei Nakata2 , Shoya Higa3 , Kazuya Yoshida4
1

Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: nagaoka@astro.mech.tohoku.ac.jp
Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: nakata@astro.mech.tohoku.ac.jp
3
Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: shoya@astro.mech.tohoku.ac.jp
4
Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: yoshida@astro.mech.tohoku.ac.jp
2

ABSTRACTThis paper presents the mobility characteristics of a fourwheel skid-steering micro-rover in loose soil. The characteristics were experimentally investigated in terms of
the eﬀects of wheel grouser’s height, rover’s attitude, andthe inclination angle of sloped terrain. The experimental results showed key relations between the roll angle
and the forward traveling distance of the rover. On thebasis of the relations, we developed two diﬀerent steering controls with and without side-slip compensation forpoint-to-point slope traversal. We confirmed the validityof the control methods by comparative experiments. In addition, the energy consumption of the two steering control
methods was analyzed, and its relationship to the steering
maneuver was experimentally investigated. As a consequence, we found that the skid-steering rover consumed
less energy when combined with spot-turning.

1 INTRODUCTION
Exploration rovers can perform in-situ scientific investigation on an extraterrestrial surface, such as on the Moon orMars. Such robotic exploration technology has become
increasingly important for challenging space missions.
Likewise, low-cost space missions have received a lot of
attention in recent years. Thus far, several light-weightmicro-rover systems have been developed [1, 2] because
an increase in the system weight directly increases launchcosts. Hence, reductions in size and weight are required
for a cost-eﬀective rover mission. One feasible lightweight rover systems is a skid-steering system, which isused for typical tracked vehicles. This system can reduce
the number of actuators needed, resulting in mechanicalsimplicity because a skid-steering rover does not need a
specialized steering mechanism for turning a wheel. The
rover can perform various steering maneuvers by diﬀerent
rotational velocities of the wheels on both sides of its mainbody.
A skid-steering system is often used for mobile
robots. Some researchers have studied their dynamics
modeling and control algorithms [3], which can be ap-

plied to the rover on an ideal flat surface. In actual lunar and planetary missions, however, the rover must travel
over rough terrain covered with loose soil. Such terrain induces wheel slippage and sinkage [4, 5]. Wheel slippagein particular makes it diﬃcult for the rover to follow thedesired path. To facilitate wheeled mobility on loose soil,
Ishigami et al. [6] modeled a rover’s steering characteristics based on soil-wheel interaction mechanics, so-called
terramechanics. They also achieved terramechanics-based
slope traversal control in sand [7]. In this control method,
the wheel’s orientation was controlled to cancel the sideslip of the rover. This approach, however, targeted an allwheel steering system.
This study focused on experimental investigation of
the mobility characteristics of a skid-steering micro-roveron sloped sand. Based on the results, slope-traversal control methods are proposed. We implemented the methods
in a four-wheel skid-steering micro-rover test bed and thenevaluated them experimentally. This paper is organized
as follows. In Section 2 and 3, the experimental mobility
characteristics of the rover on flat and sloped sand, respectively, are presented. Section 4 shows the characteristicbased slope traversal controls and their evaluation. Section 5 summarizes the key results of this study.

2

MOBILITY CHARACTERISTICS ON
FLAT SANDY TERRAIN

We first carried out experiments to understand the mobility characteristics of a skid-steering micro-rover on flatand loose soil. The experiments were performed using
a four-wheel skid-steering test bed.

2.1

Experimental Equipment

In the experiments, we used MoonRaker-EM as a fourwheel skid-steering micro-rover test bed, which is an engineering model of a privately funded lunar micro-rover
MoonRaker developed in our laboratory [8]. Figure 1
shows a schematic illustration of MoonRaker-EM and its
wheel with parallel grousers. The rover weighs 8.0 kg including a camera unit, and its size is 0.3 m in width, 0.6 m
in length, and 0.3 m in height. It also has an on-board

BaseWifi antenna

Motion Capture Cameras

Rocker suspension
Wheel&Grouser

0.3 [m]0.6 [m]0.5 [m]Sand Box(a) Overview

Figure 2 : Overview of sandy terrain in experiments.
hGrouser

200 mm(b) Rigid wheel with parallel grousers

Figure 1 : Schematic illustration of MoonRaker-EM.

computer, and thus it can be remotely operated via wireless communication. We measured the rotational velocityof the output torque of each wheel by the embedded motor
controllers during the experiments. In this study, the front
and rear wheels on the same side were controlled have thesame rotational velocity. The rover also has an embedded
gyro sensor, and we measured the rover’s relative attitude
to the direction of gravity. To investigate the eﬀect of thegrousers, we used grouser of diﬀerent heights h (10, 19,
and 25 mm).
Figure 2 shows the overview of the experimental environment. The sand box is 1 × 2 m in size and filled with
Toyoura standard sand. A motion capture camera system
was set up around the sand box to obtain the accurate position and attitude of the test bed during the experiments.
The sampling frequency of the cameras was 5 Hz. We calculated the center of balance position and the attitude of
the rover based on the marker’s position data.

2.2 Evaluation Index
As an evaluation index commonly used, we introduced
the ratio of the rotational velocity of left- and right-side

wheels, γ, as follows: ωr /ωlγ= ωl /ωr

if ωr ≥ ωl(1)otherwise

where ωl and ωr are the rotation velocity of the left- andright-side wheels, respectively. The ratio also satisfies−1 < γ < 1.
A skid-steering rover has three maneuvering modes
reflected in the γ value. When γ = 1, all the wheels rotate with the same velocity and the rover moves forward.
When γ = −1, it performs a spot turn without changing its
center of mass (C.O.M.) position, as shown in Figure 3a.
When −1 < γ < 1, it moves along a circular trajectory, as
shown in Figure 3b.

2.3

Linear Traction Experiment

To experimentally obtain the relationship between slip anddrawbar pull, we carried out the traction experiments using the rover test bed, where traction load is applied to
the rover on flat sandy terrain. Figure 4 illustrates the experimental configurations. The traction load was givenby the pulleys as constant in a direction opposite the linear movement. The applied traction loads of 0, 5.3, 10.6,
15.9, 21.0, 26.1 and 31.1 N correspond to components ofgravity force parallel to a slope surface with angles of 0,5, 10, 15, 20, 25 and 30◦ , respectively. During the experiments, the rotation velocity of all wheels was set to 1 rpm.
In the traction experiments, we used two indexes toevaluate the rover’s mobility characteristics. The first one
is the wheel’s slip ratio, s, which is defined as follows:
s=1−

vrov
rw · ωw(2)

where vrov is the rover’s forward traveling velocity, rw is
the wheel radius, and ωw is the wheel’s rotational velocity.

Traveling Direction
TractionLoadt = 10 [s]t = 20 [s]t = 30 [s]Sandy Terrain(a) γ = −1.0 (where ωr ≥ ωl )Figure 4 : Configuration of traction experiment.
35
h=10 [mm]h=19 [mm]h=25 [mm]30t = 40 [s]t = 60 [s]flinear [J/m]t = 20 [s](b) γ = 0.7 (where ωr ≥ ωl )Figure 3 : Maneuvers of Moonraker-EM on flat sandy terrain.

25
20
15
10
5

In general, s takes a value between 0 and 1 for a tractive
wheel,s = 0 is no slip between wheels and terrain, ands = 1 denotes wheels are stuck.
The second index is total energy consumption per unit
distance traveled, flin , which is calculated as follows:
Wrov
vrov

2.4 Steering Experiment
A steering operation is required for a rover to avoid obstacles and follow a given path. To clarify the steeringcharacteristics of the skid-steering rover, we carried out
steering experiments. Here, we introduce he index f str ,which is defined as follows:
(4)

5

10

15

20

25

30

35

Traction Load [N]Figure 5 : Relationship between energy consumption andtraction load.

(3)

where Wrov is the total work generated by the motors of
the wheels. Smaller flin values indicate better energy eﬃciency.
Figure 5 shows the experimental result of relationshipbetween flin and the traction load. The horizontal and vertical axes are the traction load and flin , respectively. Whenthe traction load is smaller than 15 N, the grouser height,
h, has no significant impact on flin . In contrast, when the
traction load is over 15 N, the wheels with the higher h exhibits better energy eﬃciency. In addition, Figure 6 showsthe experimental results of the relationship between s andflin . The horizontal and vertical axes are s and flin , respectively. Regardless of the diﬀerence in grouser height h,flin exponentially increases with increasing s. This result
suggests that the slip ratio has more of an eﬀect on energy
eﬃciency than the grouser height.

Wrovflin =
ωrov

035

h=10 [mm]h=19 [mm]h=25 [mm]30
flinear [J/m]flin =

0

25
20
15
10
5
0

0

0.2

0.4

0.6

0.8

1

Slip

Figure 6 : Relationship between slip and energy eﬃciency.
where ωrov is the spot-turning velocity of the rover. f str is
the spot-turning energy per unit angle change of rover attitude. A smaller f str value denotes better energy eﬃciency.
Figure 7 shows the experimental results of the relationship between γ and f str . A smaller γ value shows better energy eﬃciency. No significant diﬀerence was found
for the diﬀerent grouser heights.

2.5

Comparison of Steering Maneuvers

As described, a skid-steering rover can perform the threemaneuvering modes by controlling γ. For point-to-point
locomotion control, the skid-steering rover can perform3

fsteer [J/°]2.5

Energy Consumption [J]3.5h=10 [mm]h=19 [mm]h=25 [mm]

2
1.5
1
0.5
0

-1

-0.5

0

0.5

Method 1
Method 2

3.0
2.5
2.0
1.5
1.0
0.5
0

1

γ

10

19

25

Grouser Height [mm]Figure 7 : Relationship between γ and steering energy efficiency.
two diﬀerent maneuvers. The first method (Method 1) isbased on continuous circular maneuvers by continuous γ
values: −1 < γ < 1. The second one (Method 2) is basedon a combination of discrete γ values: spot-turning (γ =−1: spot-turning in order to head to the target point) andlinear movement (γ = 1: moving linearly to the target
point), which is the so-called bang-bang control.
The energy consumption of the two maneuvers is
discussed. We obtained the energy consumption of
Method 1, E1 , based on the experimental data. In thecomparison, we used the results at γ = 0.7 for the pointto-point maneuver. E1 is here defined as follows:∫E1 =τw · ωw · dt
(5)where ωw is the rotational velocity of the wheel, whichis ωr or ωl , and τw is the corresponding motor’s output
torque of the wheel.
For Method 2, we calculated the total energy consumption, E2 , based on flin and f str . The equation we used
for the second method is shown as follow:
E2 = f str · ∆ζ + flin · ∆L

3.5

(6)

where ∆ζ is an overall attitude change and ∆L is the distance between the initial and final points.
Figure 8 shows the experimental results of the energy
consumption of the two methods. The results confirm thatthe maneuver combining spot-turning and linear movement is a more eﬃcient method compared to the maneuver
based on continuous γ. This advantage is independent of
the grouser height.

3 MOBILITY CHARACTERISTICS ON
SLOPED SANDY TERRAIN
We investigated the mobility characteristics of the skidsteering rover in slope traversal. Thus, we conducted traveling experiments to clarify the relationship between the

Figure 8 : Comparison of energy consumption of steering
maneuvers in flat sand.
slope angle, the grouser height, and motion trajectory. We
simulated a slope by tilting the sand box, as shown in Figure 9. The coordinate system we defined is shown in Figure 10. The x axis is parallel to the slope traversal direction and the y axis is parallel to the slope upward direction.
The origin of the coordinate system is the initial positionof the rover. α is the inclination angle of the sand box. In
these experiments, the linear movement conditions (γ = 1
and ωr = ωl = 1 [rpm]) were input.

3.1

Influence of Grouser Height

Two grousers of h = 10 and 25 mm were used for thisevaluation. Figure 11a and Figure 11b show the results ofthe motion trajectory and heading angle ϕ (i.e., yaw angle), respectively. These confirm that the diﬀerence of hhas little eﬀect on the trajectory and yaw angle. In particular, the yaw angles were almost zero. These results
show that it is diﬃcult to prevent side-slip of the rover bychanging the grouser height and that the rover’s side-slip
is produced without a change of its attitude.

3.2

Influence of Slope Angle

In the next experiments, we investigated the influence ofthe slope angle, α, on the motion trajectory, where we set
α = 0, 5, 10, and 15◦ . Figure 12 shows the resulting trajectories at each slope angle. All the trajectories are linear
and their inclination increases with increasing α. Based onthese results, we approximated the trajectories by a linear
equation as follows:
y=K·x

(7)

where K is constant.
We obtained K by a least squares method. Figure 13
shows the relationship between the obtained K values andthe corresponding sin α values. The results confirm that
K is proportional to sin α. Hence, given a coeﬃcient C,
Eq. (7) can be re-written as follows:y = C sin α · x

(8)

100
0

y [mm]

−100
−200
−300
−400

−24
−26
−28
−30
300

310

320

330
h = 10 [mm]h = 25 [mm]−500

Figure 9 : Overview of slope traversal experiments.

−600
0

100

Heading

Angle (Φ

500

600

700

5

)

h = 10 [mm]h = 25 [mm]

4

[s])

Figure 10 : Definition of inertial coordinate system forslope traversal experiments.

Yaw Angle, φ [ ° ]3αte (t = 0400(a) Motion trajectoryx

Initial Sta

300

x [mm]

y

o

200

2
1
0
−1
−2
−3
−4

We finally determined C = −0.33 from Figure 13.

−5
0

100

200

300

400

500

600

700

x [mm](b) Time history of ϕ

4 SLOPE TRAVERSAL CONTROL

Figure 11 : Experimental results of slope traversal.
Even on sloped sand, the rover is required to autonomously reach a target area while avoiding obstacles
and critical slippage conditions. To meet such requirements, the rover must modify its wheel motion. For slope
traversal, side-slip makes it diﬃcult for the rover to follow
a given path. In this section, we propose point-to-point
slope traversal controls on loose soil based on the experimental mobility characteristics discussed in the previous
sections.

4.1 Discrete Gamma Modulation Control(DGM Control)
As one control method, we propose discrete gamma modulation control (DGM control). Figure 14 shows the coordinate system ( x̄, ȳ) fixed on the rover’s current C.O.M.
position. x̄ indicates the heading direction and ȳ is normal to x̄. θ is defined as the deviation angle from x̄ to thedirectional vector of the target point P. In DGM control,
the rover moves forward with ωr = ωr = 1 [rpm] (γ = 1)
when θ is smaller than a threshold angle θth , where θth isgiven as follows:θth = θth f − θthi ·

|P|
|P0 |

(9)

where θth f and θthi are coeﬃcients for the angle thresholdand |P0 | is the initial distance to the target. In the experiments, θth f and θthi were set to 45◦ and 44◦ , respectively.
When θ > θth , the rover performs the spot turn (γ = −1)
to decrease θ. The control input is selected as a discrete γ
value, i.e., −1 or 1. This method is based on a feedback
loop of the current attitude and C.O.M. position. Figure 15
shows a flowchart of the DGM control. Here, Lth is the tolerable range of the target point, which was set to 100 mm
in subsequent experiments.

4.2

Side-Slip Compensation

Based on the experimental results in Section 3, we appliedside-slip compensation to the DGM control. This compensates for the side-slip distance calculated from equa-Figure 12 : Relationship between α and motion trajectory.

y

Initial Sta

P'

0.02

y

Experimental data

0

lin

ea

-0.04

Φ

pp
rox

ati

on

-0.1
0.05

0.1

0.15
sinα

0.2

0.25

α

Program start

0.3

calculate P

Figure 13 : Relationship between K and sin α.

P = P − C sin α · |P| · ȳ

yes

If

tion Eq. (9) and modifies the target point upward. The position vector from the C.O.M. to the modified target point,
P′ , is given as follows:′

TargetPoint

Figure 14 : Schematic of DGM control.

-0.08
0

P

ra

im

-0.06

int

θ'
θ

x
o

-0.02

Target P
o

x

o

K

Modifiedtenomove forward

If
no

yes
turn rightturn left(10)

where ȳ is a unit vector of ȳ.
Figure 16 shows a flowchart of the DGM control withthe side-slip compensation. In every calculation cycle, P′
is updated and the heading angle is modified based on
θ′ . Here, the slope angle α is measured by a gyro sensor
inside the rover. This compensation utilizes the experimental characteristics as feedforward control based on the
feedback data of the rover’s position and attitude.

yes

If
no
stop
Program end

Figure 15 : Flowchart of DGM control system.

4.3 Evaluation of Side-Slip Compensation for
DGM Control
The slope traversal experiments were carried out to evaluate the eﬀectiveness of the DGM control with the side-slip
compensation. The slope angle and target point were set
α = 15 [◦ ] and (x, y) = (1300 mm, 0 mm), respectively.
The grouser height of 10 mm was used in the experiments.
Figure 17 shows the resulting trajectories that we obtained from the evaluation experiments. The variation of
the C.O.M. position in the y axis based on the control withcompensation is smaller than that without compensation.
The results confirm that the compensation law works effectively.

4.4 Continuous Gamma Modulation Control(CGM Control)
We also propose point-to-point slope traversal control asa continuous gamma modulation control, i.e., the control
input is selected as −1 < γ < 1. In the first step, the radius
r of the circular maneuver, which can go through both thecurrent C.O.M. position and the target point, is calculated

based on the rover’s attitude and position. Figure 18 is aschematic of the CGM control. Given the center positionof the circle locates on the same line of ȳ, we calculate r
as follows:
1 |P|2r= ·(11)
2 P · ȳOn the basis of Eq. (11) and a bicycle model on a flat
surface [9], we can compute γ as a control input to realize
the desired radius as follows:γ=−brov + 2r
brov + 2r(12)where brov is the distance between the right-side and leftside wheels, as shown in Figure 18. This method is also
based on the same feedback loop with the DGM control.

4.5

Comparative Evaluation of CGM and
DGM Control

A slope traversal experiment was performed to evaluate
the DGM control. The experimental conditions were theCenter Positionof Circular Curve

Program startr

Side-Slip Compensation

calculateyes

IfTarget
Point

y

If

ωl
no
move forward

x

no

yes
turn rightbrovturn left

ωr

Figure 18 : Schematic of CGM control model.

yes

If
no

DGM Control
CGM Control

400

stop
Program end

Figure 16 : Flowchart of DGM control system with sideslip compensation.

y [mm]

200

Target Area

0
−200
−400

w/o Side-Slip Compensation
w/ Side-Slip Compensation

400

y [mm]

200

Target Area

0
−200
−400
0

200

400

600 800x [mm]

1000 1200 1400

Figure 17 : Trajectories of slope traversal based on DGM
control with and without side-slip compensation.
same as those used to evaluate the CGM control. In
the DGM control, side-slip compensation was also implemented. Thus, the modified target point was given in its
control loop.
Figure 19 shows the motion trajectories of the DGM
and CGM controls for comparison. A snapshot of theseexperiments is shown in Figure 20. The CGM control’s
trajectory shows some variation of the C.O.M. position ascompared to that of the DGM control
Furthermore, to compare the energy consumption ofeach system, we normalized the energy by the total traveling distance. The energy eﬃciency is defined as η =Et /Lt , where Et and Lt are the total energy consumption
and the total traveling distance, respectively. Figure 21
shows the energy eﬃciency η of each control. The result-

0

200

400

600 800x [mm]

1000 1200 1400

Figure 19 : Trajectories of slope traversal based on CGM
and DGM controls with side-slip compensation.
ing values were averaged by three trials under the same
conditions, and thus, the error bars are shown in Figure 21.
From this comparison, we found that the DGM control isslightly more eﬃcient than the CGM control as a slope
traversal control method. This result indicates the sametendency as the steering experiments in flat sandy terrain.

5

CONCLUSION

In this paper, we discussed mobility characteristics andcontrol methods of a four-wheel skid-steering micro-rover
for slope traversal. From the traveling experiments onflat loose soil, it was found that the linear movement energy eﬃciency of the rover is dependent on the slip ratioof the wheels. We also calculated the energy consumption of two steering maneuvers and compared their energy
consumption. The results confirmed that a more eﬃcientsteering maneuver can be achieved by combining spotturning and linear movement. From the traveling experiments on sloped terrain, we clarified the key relationshipbetween the slope angle, the grouser height, the rover attitude, and the rover’s side-slip. As one of the key experimental characteristics, we introduced a relational equation for estimation of the side-slip. Based on these travel-start0s

60sEnergy Efficiency [J/m]

start

5
4
3
2
1
0

30 s

30 s

DGM Control

CGM Control

Figure 21 : Comparison of energy eﬃciency of CGM andDGM controls.

References

60 s

60 s

90 s

90 s

stop

stop

112 s
DGM Control

119 s
CGM Control

Figure 20 : Snapshots of CGM and DGM control experiments in sloped sand.

ing experiments on the slope, we proposed two point-topoint control methods, the CGM and DGM controls, andalso side-slip compensation was applied to each control
method. Comparing the motion trajectories of the CGM
control with and without the side-slip compensation, thevalidity of the side-slip compensation was evaluated. The
experimental comparison of the energy eﬃciency showedthat the DGM control using discrete γ was more eﬃcientthan that using continuous γ. As a result, it is concluded
that the skid-steering rover can achieve eﬃcient maneuvers with less side-slip on sloped sandy terrain by combining spot-turning and linear movement.

[1] M. Post, B. Quine, and R. Lee, “Beaver MicroRover Development for the Northern Light Mars
Lander”, Proceedings of the 16th Bi-Annual Astronautics Conference of the Canadian Aeronautics andSpace Institute, 2012.
[2] A. Wedler et al., “LRU - Lightweight Rover Unit”,
Proceedings of the 13th Symposium on Advanced
Space Technologies in Robotics and Automation,
2015.
[3] K. Kozłowski and D. Pazderski, “Modeling andControl of a 4-Wheel Skid-Steering Mobile Robot”,
International Journal of Applied Mathematics andComputer Science, vol. 14, no. 4, pp. 477–496, 2004.
[4] R. Irani, R. Bauer, and A. Warkentin, “A Dynamic
Terramechanic Model for Small Lightweight Vehicles with Rigid Wheels and Grousers Operating in
Sandy Soil”, Journal of Terramechanics, vol. 48,
no. 4, pp. 307–318, 2011.
[5] J. MacLennan, P. Jayakumar, C. Senatore, M.
Wulfmeier, and K. Iagnemma, “Investigation ofStress and Failure in Granular Soils for Lightweight
Robotic Vehicle Applications”, Proceedings of the2012 NDIA Ground Vehicle Systems Engineeringand Technology Symposium, 2012.
[6] G. Ishigami, A. Miwa, K. Nagatani, and K. Yoshida,“Terramechanics-Based Model for Steering Maneuver of Planetary Exploration Rovers on Loose Soil”,
Journal of Field Robotics, vol. 24, no. 3, pp. 233–
250, 2007.
[7] G. Ishigami, K. Nagatani, and K. Yoshida, “Path Following Control with Slip Compensation on Loose
Soil for Exploration Rover”, Proceedings of the2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5552–5557, 2006.
[8] K. Yoshida, N. Britton, and J. Walker, “Development and Field Testing of Moonraker, a Four-Wheel
Rover in Minimal Design”, Proceedings of the 12th
International Symposium on Artificial Intelligence,
Robotics and Automation in Space, 2013.
[9] F. Solc and J. Sembera, “Kinetic Model of a Skid
Steered Robot”, Proceedings of the 7th WSEAS
International Conference on Signal Processing,
Robotics Automation, pp. 61–65, 2008.