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.jp2 Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: nakata@astro.mech.tohoku.ac.jp3 Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: shoya@astro.mech.tohoku.ac.jp4 Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Japan, E-mail: yoshida@astro.mech.tohoku.ac.jp

ABSTRACT

This paper presents the mobility characteristics of a four-wheel skid-steering micro-rover in loose soil. The char-acteristics were experimentally investigated in terms ofthe effects of wheel grouser’s height, rover’s attitude, andthe inclination angle of sloped terrain. The experimen-tal results showed key relations between the roll angleand the forward traveling distance of the rover. On thebasis of the relations, we developed two different steer-ing controls with and without side-slip compensation forpoint-to-point slope traversal. We confirmed the validityof the control methods by comparative experiments. In ad-dition, the energy consumption of the two steering controlmethods was analyzed, and its relationship to the steeringmaneuver was experimentally investigated. As a conse-quence, we found that the skid-steering rover consumedless energy when combined with spot-turning.

1 INTRODUCTION

Exploration rovers can perform in-situ scientific investiga-tion on an extraterrestrial surface, such as on the Moon orMars. Such robotic exploration technology has becomeincreasingly important for challenging space missions.Likewise, low-cost space missions have received a lot ofattention in recent years. Thus far, several light-weightmicro-rover systems have been developed [1, 2] becausean increase in the system weight directly increases launchcosts. Hence, reductions in size and weight are requiredfor a cost-effective rover mission. One feasible light-weight rover systems is a skid-steering system, which isused for typical tracked vehicles. This system can reducethe number of actuators needed, resulting in mechanicalsimplicity because a skid-steering rover does not need aspecialized steering mechanism for turning a wheel. Therover can perform various steering maneuvers by differentrotational velocities of the wheels on both sides of its mainbody.

A skid-steering system is often used for mobilerobots. Some researchers have studied their dynamicsmodeling and control algorithms [3], which can be ap-

plied to the rover on an ideal flat surface. In actual lu-nar and planetary missions, however, the rover must travelover rough terrain covered with loose soil. Such terrain in-duces 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 characteris-tics based on soil-wheel interaction mechanics, so-calledterramechanics. They also achieved terramechanics-basedslope traversal control in sand [7]. In this control method,the wheel’s orientation was controlled to cancel the side-slip of the rover. This approach, however, targeted an all-wheel steering system.

This study focused on experimental investigation ofthe mobility characteristics of a skid-steering micro-roveron sloped sand. Based on the results, slope-traversal con-trol methods are proposed. We implemented the methodsin a four-wheel skid-steering micro-rover test bed and thenevaluated them experimentally. This paper is organizedas follows. In Section 2 and 3, the experimental mobilitycharacteristics of the rover on flat and sloped sand, respec-tively, are presented. Section 4 shows the characteristic-based slope traversal controls and their evaluation. Sec-tion 5 summarizes the key results of this study.

2 MOBILITY CHARACTERISTICS ONFLAT SANDY TERRAIN

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

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

0.5 [m]0.6 [m]

0.3 [m]

Base Wifi antenna

Wheel&Grouser

Rocker suspension

(a) Overview

200 mm

h

Grouser

(b) Rigid wheel with parallel grousers

Figure 1 : Schematic illustration of MoonRaker-EM.

computer, and thus it can be remotely operated via wire-less communication. We measured the rotational velocityof the output torque of each wheel by the embedded motorcontrollers during the experiments. In this study, the frontand rear wheels on the same side were controlled have thesame rotational velocity. The rover also has an embeddedgyro sensor, and we measured the rover’s relative attitudeto 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 en-vironment. The sand box is 1 × 2 m in size and filled withToyoura standard sand. A motion capture camera systemwas set up around the sand box to obtain the accurate po-sition and attitude of the test bed during the experiments.The sampling frequency of the cameras was 5 Hz. We cal-culated the center of balance position and the attitude ofthe rover based on the marker’s position data.

2.2 Evaluation Index

As an evaluation index commonly used, we introducedthe ratio of the rotational velocity of left- and right-side

Motion Capture Cameras

Sand Box

Figure 2 : Overview of sandy terrain in experiments.

wheels, γ, as follows:

γ =

ωr/ωl if ωr ≥ ωl

ωl/ωr otherwise(1)

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 modesreflected in the γ value. When γ = 1, all the wheels ro-tate with the same velocity and the rover moves forward.When γ = −1, it performs a spot turn without changing itscenter of mass (C.O.M.) position, as shown in Figure 3a.When −1 < γ < 1, it moves along a circular trajectory, asshown in Figure 3b.

2.3 Linear Traction ExperimentTo experimentally obtain the relationship between slip anddrawbar pull, we carried out the traction experiments us-ing the rover test bed, where traction load is applied tothe rover on flat sandy terrain. Figure 4 illustrates the ex-perimental configurations. The traction load was givenby the pulleys as constant in a direction opposite the lin-ear 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 experi-ments, 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 oneis 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 isthe wheel radius, and ωw is the wheel’s rotational velocity.

t = 10 [s] t = 20 [s] t = 30 [s](a) γ = −1.0 (where ωr ≥ ωl)

t = 20 [s] t = 40 [s] t = 60 [s](b) γ = 0.7 (where ωr ≥ ωl)

Figure 3 : Maneuvers of Moonraker-EM on flat sandy ter-rain.

In general, s takes a value between 0 and 1 for a tractivewheel,s = 0 is no slip between wheels and terrain, ands = 1 denotes wheels are stuck.

The second index is total energy consumption per unitdistance traveled, flin, which is calculated as follows:

flin =Wrov

vrov(3)

where Wrov is the total work generated by the motors ofthe wheels. Smaller flin values indicate better energy effi-ciency.

Figure 5 shows the experimental result of relationshipbetween flin and the traction load. The horizontal and ver-tical 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 thetraction load is over 15 N, the wheels with the higher h ex-hibits 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, respec-tively. Regardless of the difference in grouser height h,flin exponentially increases with increasing s. This resultsuggests that the slip ratio has more of an effect on energyefficiency than the grouser height.

2.4 Steering Experiment

A steering operation is required for a rover to avoid ob-stacles and follow a given path. To clarify the steeringcharacteristics of the skid-steering rover, we carried outsteering experiments. Here, we introduce he index fstr,which is defined as follows:

flin =Wrov

ωrov(4)

Traveling Direction

TractionLoad

Sandy Terrain

Figure 4 : Configuration of traction experiment.

0 5 10 15 20 25 30 35

h=10 [mm]h=19 [mm]h=25 [mm]

0

5

10

15

20

25

30

35

f linear

[J/m

]

Traction Load [N]

Figure 5 : Relationship between energy consumption andtraction load.

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1

h=10 [mm]h=19 [mm]h=25 [mm]

Slip

f linear

[J/m

]

Figure 6 : Relationship between slip and energy efficiency.

where ωrov is the spot-turning velocity of the rover. fstr isthe spot-turning energy per unit angle change of rover atti-tude. A smaller fstr value denotes better energy efficiency.

Figure 7 shows the experimental results of the rela-tionship between γ and fstr. A smaller γ value shows bet-ter energy efficiency. No significant difference was foundfor the different grouser heights.

2.5 Comparison of Steering ManeuversAs described, a skid-steering rover can perform the threemaneuvering modes by controlling γ. For point-to-pointlocomotion control, the skid-steering rover can perform

-1 -0.5 0 0.5 1

h=10 [mm]h=19 [mm]h=25 [mm]

0

0.5

1

1.5

2

2.5

3

3.5

f steer

[J/°

]

γ

Figure 7 : Relationship between γ and steering energy ef-ficiency.

two different maneuvers. The first method (Method 1) isbased on continuous circular maneuvers by continuous γvalues: −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 targetpoint), which is the so-called bang-bang control.

The energy consumption of the two maneuvers isdiscussed. We obtained the energy consumption ofMethod 1, E1, based on the experimental data. In thecomparison, we used the results at γ = 0.7 for the point-to-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 outputtorque of the wheel.

For Method 2, we calculated the total energy con-sumption, E2, based on flin and fstr. The equation we usedfor the second method is shown as follow:

E2 = fstr · ∆ζ + flin · ∆L (6)

where ∆ζ is an overall attitude change and ∆L is the dis-tance between the initial and final points.

Figure 8 shows the experimental results of the energyconsumption of the two methods. The results confirm thatthe maneuver combining spot-turning and linear move-ment is a more efficient method compared to the maneuverbased on continuous γ. This advantage is independent ofthe grouser height.

3 MOBILITY CHARACTERISTICS ONSLOPED SANDY TERRAIN

We investigated the mobility characteristics of the skid-steering rover in slope traversal. Thus, we conducted trav-eling experiments to clarify the relationship between the

3.5

3.0

2.5

2.0

1.5

1.0

0.5

010 19 25

Grouser Height [mm]

Ene

rgy

Con

sum

ptio

n [J

]

Method 1Method 2

Figure 8 : Comparison of energy consumption of steeringmaneuvers in flat sand.

slope angle, the grouser height, and motion trajectory. Wesimulated a slope by tilting the sand box, as shown in Fig-ure 9. The coordinate system we defined is shown in Fig-ure 10. The x axis is parallel to the slope traversal direc-tion 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. Inthese experiments, the linear movement conditions (γ = 1and ωr = ωl = 1 [rpm]) were input.

3.1 Influence of Grouser HeightTwo 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 an-gle), respectively. These confirm that the difference of hhas little effect on the trajectory and yaw angle. In par-ticular, the yaw angles were almost zero. These resultsshow that it is difficult to prevent side-slip of the rover bychanging the grouser height and that the rover’s side-slipis produced without a change of its attitude.

3.2 Influence of Slope AngleIn the next experiments, we investigated the influence ofthe slope angle, α, on the motion trajectory, where we setα = 0, 5, 10, and 15◦. Figure 12 shows the resulting tra-jectories at each slope angle. All the trajectories are linearand their inclination increases with increasing α. Based onthese results, we approximated the trajectories by a linearequation 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 sinα values. The results confirm thatK is proportional to sinα. Hence, given a coefficient C,Eq. (7) can be re-written as follows:

y = C sinα · x (8)

Figure 9 : Overview of slope traversal experiments.

x

y

o

αInitial State (t = 0 [s])

Heading Angle (Φ)

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

We finally determined C = −0.33 from Figure 13.

4 SLOPE TRAVERSAL CONTROL

Even on sloped sand, the rover is required to au-tonomously reach a target area while avoiding obstaclesand critical slippage conditions. To meet such require-ments, the rover must modify its wheel motion. For slopetraversal, side-slip makes it difficult for the rover to followa given path. In this section, we propose point-to-pointslope traversal controls on loose soil based on the exper-imental mobility characteristics discussed in the previoussections.

4.1 Discrete Gamma Modulation Control(DGM Control)

As one control method, we propose discrete gamma mod-ulation control (DGM control). Figure 14 shows the co-ordinate system (x, y) fixed on the rover’s current C.O.M.position. x indicates the heading direction and y is nor-mal to x. θ is defined as the deviation angle from x 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 is

0 100 200 300 400 500 600 700−600

−500

−400

−300

−200

−100

0

100

x [mm]

y[m

m]

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

300 310 320 330

−30−28−26−24

(a) Motion trajectory

0 100 200 300 400 500 600 700−5

−4

−3

−2

−1

0

1

2

3

4

5

x [mm]

Yaw

Ang

le, φ

[ ° ]

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

(b) Time history of ϕ

Figure 11 : Experimental results of slope traversal.

given 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 experi-ments, 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 γvalue, i.e., −1 or 1. This method is based on a feedbackloop of the current attitude and C.O.M. position. Figure 15shows a flowchart of the DGM control. Here, Lth is the tol-erable range of the target point, which was set to 100 mmin subsequent experiments.

4.2 Side-Slip CompensationBased on the experimental results in Section 3, we appliedside-slip compensation to the DGM control. This com-pensates for the side-slip distance calculated from equa-

Figure 12 : Relationship between α and motion trajectory.

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0 0.05 0.1 0.15 0.2 0.25 0.3

Experimental data

sinα

linear approximation

K

Figure 13 : Relationship between K and sinα.

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

P′ = P −C sinα · |P| · y (10)

where y is a unit vector of y.Figure 16 shows a flowchart of the DGM control with

the side-slip compensation. In every calculation cycle, P′

is updated and the heading angle is modified based onθ′. Here, the slope angle α is measured by a gyro sensorinside the rover. This compensation utilizes the experi-mental characteristics as feedforward control based on thefeedback data of the rover’s position and attitude.

4.3 Evaluation of Side-Slip Compensation forDGM Control

The slope traversal experiments were carried out to evalu-ate the effectiveness of the DGM control with the side-slipcompensation. The slope angle and target point were setα = 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 ob-tained from the evaluation experiments. The variation ofthe 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 ef-fectively.

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 controlinput is selected as −1 < γ < 1. In the first step, the radiusr of the circular maneuver, which can go through both thecurrent C.O.M. position and the target point, is calculated

TargetPoint

α

Modified Target PointInitial State

x

y

y

xθ

o

o

θ'P'

PΦ

Figure 14 : Schematic of DGM control.

P

Program start

calculate

If Ifyes

no yes no

turn right turn left

yesIf

move forward

no

Program end

stop

Figure 15 : Flowchart of DGM control system.

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 y, we calculate ras follows:

r =12· |P|

2

P · y (11)

On the basis of Eq. (11) and a bicycle model on a flatsurface [9], we can compute γ as a control input to realizethe desired radius as follows:

γ =−brov + 2rbrov + 2r

(12)

where brov is the distance between the right-side and left-side wheels, as shown in Figure 18. This method is alsobased on the same feedback loop with the DGM control.

4.5 Comparative Evaluation of CGM andDGM Control

A slope traversal experiment was performed to evaluatethe DGM control. The experimental conditions were the

Program start

calculateSide-Slip Compensation

If Ifyes

no yes no

turn right turn left

yesIf

move forward

no

Program end

stop

Figure 16 : Flowchart of DGM control system with side-slip compensation.

0 200 400 600 800 1000 1200 1400

−400

−200

0

200

400

Target Area

x [mm]

y [m

m]

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

Figure 17 : Trajectories of slope traversal based on DGMcontrol with and without side-slip compensation.

same as those used to evaluate the CGM control. Inthe DGM control, side-slip compensation was also imple-mented. Thus, the modified target point was given in itscontrol loop.

Figure 19 shows the motion trajectories of the DGMand CGM controls for comparison. A snapshot of theseexperiments is shown in Figure 20. The CGM control’strajectory 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 trav-eling distance. The energy efficiency is defined as η =Et/Lt, where Et and Lt are the total energy consumptionand the total traveling distance, respectively. Figure 21shows the energy efficiency η of each control. The result-

TargetPoint

Center Positionof Circular Curve

ωr

ωlx

y

r

brov

Figure 18 : Schematic of CGM control model.

−400

−200

0

200

400

x [mm]

y [m

m]

0 200 400 600 800 1000 1200 1400

DGM ControlCGM Control

Target Area

Figure 19 : Trajectories of slope traversal based on CGMand DGM controls with side-slip compensation.

ing values were averaged by three trials under the sameconditions, 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 slopetraversal 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-roverfor slope traversal. From the traveling experiments onflat loose soil, it was found that the linear movement en-ergy efficiency of the rover is dependent on the slip ratioof the wheels. We also calculated the energy consump-tion of two steering maneuvers and compared their energyconsumption. The results confirmed that a more efficientsteering maneuver can be achieved by combining spot-turning and linear movement. From the traveling exper-iments on sloped terrain, we clarified the key relationshipbetween the slope angle, the grouser height, the rover at-titude, and the rover’s side-slip. As one of the key exper-imental characteristics, we introduced a relational equa-tion for estimation of the side-slip. Based on these travel-

DGM Control CGM Control

119 s

stopstop

startstart

90 s

60 s

30 s

0 s

112 s

90 s

60 s

30 s

0 s

Figure 20 : Snapshots of CGM and DGM control experi-ments in sloped sand.

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

DGM Control CGM Control

Ene

rgy

Effi

cien

cy [J

/m]

0

1

2

3

4

5

6

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

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