modeling, experimenting, and improving skid steering on a...

Modeling, Experimenting, and Improving Skid Steeringon a 6×6 All-Terrain Mobile Platform

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J.-C. FaurouxFrench Institute for Advanced Mechanics LaMI, Clermont University, B.P. 10448, 63000 Clermont-Ferrand, Francee-mail: [email protected]. VaslinClermont University and Laboratory of Informatics, Modeling and System Optimization, Blaise Pascal University, B.P. 10448,63000 Clermont-Ferrand, Francee-mail: [email protected]

Received 1 February 2009; accepted 13 November 2009

Multiple-wheel all-terrain vehicles without a steering system must use great amounts of power when skidsteering. Skid steering is modeled with emphasis put on the ground contact forces of the wheels according tothe mass distribution of the vehicle. To increase steering efficiency, it is possible to modify the distribution ofthe normal contact forces on the wheels. This paper focuses on two aspects: first, it provides a model and an ex-perimental study of skid steering on an all-road 6×6 electric wheelchair, the Kokoon mobile platform. Second,it studies two configurations of the distribution of the normal forces on the six wheels, obtained via suspensionadjustments. This was both modeled and experimented. Contact forces were measured with a six-componentforce plate. The first results show that skid steering can be substantially improved by only minor adjustmentsto the suspensions. This setting decreases the required longitudinal forces applied by the engines and improvesthe steering ability of the vehicle or robot. Skid-steering characteristic parameters, such as the position of thecenter of rotation and absorbed skid power, are also dealt with in this paper. C© 2010 Wiley Periodicals, Inc.

1. INTRODUCTIONThis paper presents a model and experimental results ofskid steering with a 6×6 all-terrain vehicle (ATV). A correctunderstanding of the phenomena that occur during steer-ing would allow the modeling of the contact forces duringskid steering with this vehicle and propose adjustments toimprove steering capabilities and decrease energy loss dueto friction.

Skid is a phenomenon that appears with every type ofground vehicle when the external forces applied to the ve-hicle exceed the capabilities of the vehicle–ground interface(Kececi & Tao, 2006). Skid may be due to longitudinal iner-tial forces when accelerating/braking or to lateral inertialforces when steering at high speed and low radius. It mayalso be due to the design of the vehicle.

Skid always appears with tracked vehicles duringturns, even if some of them have front steering tracks(Watanabe, Kitano, & Fugishima, 1995) because the longcontact surface of the track with the ground requires a giventorque to steer. Conversely, wheels ensure a reduced con-tact surface on a plane ground: a point contact with toroidaltires such as motorbike tires and a linear contact with cylin-drical tires such as those used for cars. In reality, becauseof tire deformation, the contact point or contact line be-comes a contact patch and a moderate steering torque maybe noted. However, wheels give excellent steering capabil-ity while maintaining ground contact. For both tracks and

wheels, grip strongly depends on the normal force valuesand distribution (Mokhiamar & Abe, 2006).

The large majority of wheeled vehicles have steeringwheels, which can be the front wheels on classical cars; therear wheels on power lift trucks or lawn mowers (Besselink,2003, 2004); all the wheels on some types of mobile robotsand sport cars (Shoichi, Yoshimi, & Yutaka, 1986); two frontand two rear wheels of six (FNSS Corp., 2008) or fourfront wheels of eight on military wheeled armored vehi-cles (Patria Corp., 2008) or truck-mounted cranes. The steer-ing mechanism may be complex, particularly when thereare more than two steering wheels. The initial constraintis to respect the Ackermann steering geometry (1817), alsoknown as Jeantaud geometry (1851) in Europe, that mini-mizes skid during low-speed turns. This condition requiresthat all wheels share the same center of rotation in ev-ery position. However, vehicles with more than two axlesgenerally do not completely respect Ackermann geometry(Figure 1). As an example, a semitrailer does not respectAckermann geometry and the three fixed rear axles gener-ate severe wear of the tires. The second constraint is thatthe steering system must be compatible with other func-tions such as transmission and suspension. This increasesmechanical complexity. Another drawback of architectureswith steering wheels is that they generally do not allow therotation of the vehicle on itself (null turning radius). For in-stance,with two steering wheels, this would require a high

Journal of Field Robotics 27(2), 107–126 (2010) C© 2010 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com). • DOI: 10.1002/rob.20333

108 • Journal of Field Robotics—2010

Figure 1. Geometric construction of Ackermann steering with multiple axles: all the wheels share the same center of gyration.However, most of the vehicles with more than two axles do not completely respect Ackermann conditions.

steering angle, which is technically complex to design anddangerous at high speeds.

For this reason, many ATVs still rely on fixed wheelswith no steering mechanism and with an optional suspen-sion system (Figure 2). These vehicles have a robust andreliable behavior on rough terrain. Most of them have a4×4 transmission, such as the Pioneer3-AT robot (RobosoftCorp., 2009), and some have a 6×6 one, such as multi-purpose amphibian vehicles (Oasis LLC Corp., 2009). Theymust turn by skid steering and behave like tracked vehi-cles (Maclaurin, 2007). During skid steering, the wheels thatare not tangent to the curved trajectory have to skid later-ally, which generates friction forces that are opposed to therotation.

The purpose of this work is to model and experimentskid steering in a 6×6 configuration. This paper also ex-plores a solution to reduce energy loss during skid steer-ing. Although lateral friction is a well-known problem ofsuch types of vehicles with nondirectional wheels, it ap-pears that very few studies have tried to reduce lateral

friction forces. Most research is focused on the improve-ment of longitudinal adherence to improve traction and oc-casionally stability on rough terrain, such as the work onthe Gofor Mars exploration robot done by Sreenivasan andWilcox (1994). Reducing steering friction forces could en-hance the interest in this class of simple, robust, and inex-pensive vehicles.

2. DESCRIPTION OF THE 6×6 MOBILE PLATFORM

The Kokoon mobile platform is an all-road 6×6 electricwheelchair (Fauroux, Charlat, & Limenitakis, 2004a) de-signed by several students of the French Institute for Ad-vanced Mechanics (IFMA) from 1999 onward (Figure 3).

Kokoon is made of a modular aluminum frame onwhich are fixed composite body panels (removed dur-ing experiments). Kokoon is driven by two direct-current,permanent-magnet electric motors of 1,330 W each (Moto-vario 24V) and is capable of moving at 8 km/h on 20%slopes and of climbing easily over 15-cm obstacles. Two

Figure 2. Schematic principle of skid steering with several axles that generates lateral friction forces. Many ATVs and robots donot have steering wheels and behave like tracked vehicles.

Journal of Field Robotics DOI 10.1002/rob

Fauroux & Vaslin: Modeling, Experimenting, and Improving Skid Steering on a 6×6 ATV • 109

Figure 3. Overview of the 6×6 Kokoon vehicle developed at IFMA since 1999.

lead-acid batteries (Hawker-Oldham 12 V, 160 Ah, 70 kgeach) ensure 4 h of autonomy. Each motor is controlled bya speed controller (Curtis 1227) that allows current peaksof around 200 A. The driver interface is either a joystick orseparate levers, one for each side.

Kokoon is 175 cm long and 103 cm wide, and it isequipped with six wheels of 20-cm radius (denoted r) andwith 7-cm-wide air-inflated tires (Figure 4). The averagewheelbase is denoted e and measures 47 cm, but this mayundergo change when the suspension is compressed. Thetrack width denoted 2v is 93 cm long. This is supposed tobe a fixed value, although the lateral deflection of the sus-pension arms when skid steering may be as high as 2 cm.However, as the suspension arms of the same axle have

Figure 4. CAD model of the Kokoon frame with its main di-mensions.

approximately the same deflection during steering, trackwidth may be considered constant.

Each motor drives synchronously the three wheels ofone side thanks to a belt transmission using six pulleys andfive belts (Figure 5). The motor is directly connected to pul-ley P2 by a clutching system not represented in the figure.Belts B12 and B23 transmit the driving torque to front pul-ley P1 and rear pulley P3, respectively. Belts B1, B2, B3 arelocated on the three independent swing arms and drive thepower to the last pulleys P1w , P2w , P3w that are linked to thewheels. For kinematic compatibility of transmission move-ment with suspension movements, pulleys Pi are mounted

Figure 5. Left-side belt transmission. The electric engine isconnected to pulley P2.



Figure 6. Adjustable swing-arm suspension with oleo-pneumatic shock absorber.

free and coaxial on swing-arm axes. It should be noted thata suspension movement generates an additional couplingtorque on the wheel. However, this phenomenon did notappear in our case as the experiments were made on flatground at constant speed. Pulley-belt transmissions requirecareful belt tension for proper operation.

The six independent swing-arm suspensions use oleo-pneumatic shock absorbers (Figure 6). They are easily ad-justable thanks to the T-slots on the sides of the aluminumprofiles. The top end of the shock absorber is named T andcan be longitudinally translated along the T-slots or verti-cally elevated by spacers. The shock absorbers (Fournales,Inc.) are designed to be inflated at 10 bars using an airpump. Adjusting pressure alters both the preconstraint andthe stiffness.

The first field tests with Kokoon showed excellentclimbing abilities but some steering difficulties. Even withsmall tires (tire tread width 7 cm), the vehicle could notsteer on itself on highly adherent grounds such as tarmac.In this case, steering was still possible with high turningradii and a nonnull longitudinal speed. On less adherentgrounds such as grass or tiled floor, the vehicle could easilyturn on itself.

Initially designed for disabled people, Kokoon is an in-teresting research platform because it has a modular de-sign and can be easily reconfigured (Fauroux, Charlat, &Limenitakis, 2004b). Parameters such as transmission, sus-pension geometry, and mass distribution can be adjustedrapidly. As mentioned above, this 6×6 vehicle shows di-verse behaviors during skid steering according to the typeof ground. This phenomenon is studied in detail in the fol-lowing sections, and the results obtained below are eas-ily transposable to comparable vehicles and mobile robotswith three or more axles.

3. MODELING SKID STEERING

Dynamic modeling of four-wheel vehicles often uses an“equivalent” bicycle model that assumes that the internal

and external wheels of each axle are combined into a sin-gle one. This assumption is acceptable provided that theradius of gyration is large enough and the slip angle small.Apart from the fact that Kokoon has three axles instead oftwo, these hypotheses could not be made during the experi-ments performed with the vehicle as the turning radius wassmall and slip angles were high.

3.1. Symmetrical Skid-Steering Model

A preliminary planar model of the Kokoon platform in-cluding six distinct wheels is shown in Figure 7 (Mendonca& Nait Hadi, 2007), where the vehicle is represented dur-ing a turn of radius R and center O (see Table I). C is thecentral reference point of the vehicle, located in the middleof the second axle. The vehicle has a local reference frame(C, XC, YC,ZC ) with XC directed forward, ZC directed up-ward, and YC to the left so that the frame is direct. Thecenters of external wheels move at speed Vsa , with indexs denoting the side of the vehicle (e for “external” and i for“internal”) and index a standing for the axle number (1, 2,or 3 from front to rear).

Figure 7. Top view of skid-steering model with symmetricalfront and rear slip angles.



Table I. Symbols.

Symbol Type Meaning

αl Scalar Limit of slip angle after which the lateral force Fy stops growing linearlyαsa Scalar Slip angle of the wheel located on side s and axle a

αsa0 Scalar Slip angle of the wheel located on side s and axle a for a null turn radius R

θ Scalar Gyration angle of the vehicle around axis (O,ZO )C Point Center of the middle axle, reference point of the vehicleCsa Point Center of the wheel located on side s and axle a

� Scalar Decrement of the unloaded length of the front and rear suspension springse Scalar Wheelbase of the vehicle (longitudinal distance between consecutive axles)Fsa Vector Force of the wheel-center point Csa

Fxsa Scalar Longitudinal force applied on the wheel-center point Csa

Fysa Scalar Lateral force applied on the wheel-center point Csa

FyMax Scalar Maximal lateral force corresponding to value αl

Fzsa Scalar Normal force applied on the wheel-center point Csa

G Point Center of gravity of the vehicleg Scalar Acceleration of gravityγ Scalar Pitch angle of the vehiclehS Scalar Adjustable distance on suspension that allows change of behaviorhSStd Scalar Standard value of hS

hSMod Scalar Modified value of hS

K Point Projection of the center of gyration O on the sagittal plane (C,XC ) of the vehiclek Scalar Stiffness of suspension springsla0 Scalar Unloaded length of the suspension spring of axle a

la Scalar Loaded length of the suspension spring of axle a

l′a Scalar Loaded length of the modified suspension spring of axle a

l′a0 Scalar Unloaded length of the modified suspension spring of axle a

l0 Scalar Standard unloaded length of a suspension springm Scalar Mass of the vehicleO Point Center of gyration of the vehicle during the turnPskid Scalar Power absorbed by the skid-steering processR Scalar Gyration radius of vehicle during the turnRx,Ry, Rz Scalar Components of the reaction forces measured on the force plater Scalar Wheel radiusTa Point Top fixation point of the suspension spring of axle a

τs Scalar Torques of motors (internal or external according to s value)v Scalar Half track width of the vehicleV sa Vector Speed of the wheel-center point Csa

Vxsa Scalar Longitudinal speed of the wheel-center point Csa

Vysa Scalar Lateral speed of the wheel-center point Csa

xa Scalar Longitudinal position of axle a with respect to point K

xCOP, yCOP Scalar Coordinates of the center of pressure on top of the force platexG Scalar Longitudinal position of the center of gravity G relative to (C,XC )xK Scalar Longitudinal position of the projected center of gyration K relative to (C,XC )

Indicese External side of the turn (where the circle is bigger)i Internal side of the turn (where the circle is smaller)s Side of the turn: can be e for external or i for internala Axle number: can be 1 for front, 2 for middle, 3 for rear

FramesRO (O,XO, YO,ZO ) Global frame connected to the groundRC (C,XC, YC, ZC ) Local frame connected to the vehicle (XC forward, ZC ascending)RP (C,XP , YP , ZP ) Frame connected to the force plate (XP forward, ZP ascending)



Table II. Kokoon slip angles computed from a symmetricalskid-steering model.

Gyration radius Front external slip Front internal slipR (m) angle αe1 (deg) angle αi1 (deg)

0 45.3 −45.30.47 (= v) 26.7 −90/+903 7.7 10.56 4.2 4.8

The slip angle αsa of each wheel is measured betweenthe longitudinal axis of the wheel and the speed vector Vsa .A nonnull slip angle means that the wheel is submitted tolateral ripping. In this model, as the gyration center O islocated on the central axle, the slip angles αi2 and αe2 areboth null. The front and rear slip angles are symmetrical,although the internal and external angles of a single axle arequite different. Their values depend both on the gyrationradius R and on the vehicle dimensions (wheelbase e andtrack width 2v) and are calculated in Eqs. (1):

αe1 = atan(

e

R + v

)= −αe3,

(1)

αi1 = atan(

e

R − v

)= −αi3.

Table II gives the values of the slip angles for theKokoon platform. It can be noted that when the gyration ra-dius R decreases, the slip angles increase, and consequentlythe lateral forces and the energy required to turn also in-crease. Figure 8 represents the graph of the slip angles αi1and αe1 with respect to the gyration radius R, with fixedvalues of e = 0.47 m and 2v = 0.93 m.

It can be noted that each slip angle has a different ex-tremum (2). Two cases must be distinguished:

αi1Max = ±90 deg = −αi30 when R = v,

(2)αe1Max = atan(e/v) = −αe30 when R = 0.

• The first case is when R = v. This forces the internalwheels to move orthogonally to their usual rolling di-rection, which is the worst-case scenario. At the sametime, the external wheels are submitted to a high (butnot extreme) slip angle.

• The second case is when R = 0. The vehicle self-rotatesaround point C. The front and rear slip angles are de-noted asa0(3). They are very high and depend solely onthe vehicle geometry:

αe10 = atan( e

v

)= −αe30,

(3)

αi10 = �/2 + atan(v

e

)= −αi30.

Figure 8. Graph of the slip angles ai1 and ae1 as a function ofthe turning radius R. A singularity appears when R = v.

The absolute value of αe10 increases with the wheelbasee and decreases with the half-track width v. It is the con-trary for αi10. In the case of Kokoon, as e and v have sim-ilar values, the slip angles αsa0 reach around ±45 deg,which is extremely high and largely over the classicalvalues measured for cars.

3.2. Nonsymmetrical Skid-Steering Model

The former symmetrical model would be perfectly accept-able with a balanced vehicle having its center of gravity G

located at the center C of the vehicle. As this is rarely thecase, a more realistic nonsymmetrical skid-steering modelhas recently been introduced (Mousset & Chervet, 2008).

It is important to keep in mind that the vehicle canturn because of the longitudinal and lateral forces. Longi-tudinal forces are provided by the engines, whereas lateralforces result from friction when skid steering. The relationbetween lateral forces Fy and slip angle α is quasi-linear upto a limit value αl , as represented in Figure 9 (Halconruy,1995). The angle αl is of the order of 10 deg for a typical cartire. Above this threshold, there is a transition zone and thetire starts to slip on the ground. So with identical front andrear slip angles, the vehicle should be submitted to equiva-lent front and rear lateral forces and the front and rear slipangles should remain equal throughout the whole process.

But Figure 9 also shows that the lateral force Fy de-pends on the normal force Fz: an increase of Fz generatesan increase of Fy . With a nonbalanced vehicle, the load oneach axle is no longer identical and the lateral forces varyaccordingly. For instance, a vehicle that is heavier on axle



Figure 9. Qualitative graph of the lateral force Fy accordingto slip angle α and normal force Fz (Halconruy, 1995).

3 has an increased lateral force on the rear and the globalequilibrium is altered.

Figure 10 represents the nonsymmetrical model of avehicle with the center of gravity at the rear. Two positionsare shown corresponding to a rotation of angle θ and radiusR around center O. Forces are drawn on the right position,and speeds are represented on the top position. Amplitudesand directions of forces Fsa and speeds V sa are representedqualitatively for wheels of side s and axle a, respectively.All forces and speeds are applied at wheel centers, denotedCsa . Point G is the vehicle center of gravity.

A new point K is introduced and defined as the or-thogonal projection of the gyration center O into the sagit-tal plane (C, XC, ZC ). Point K is now distinct from C. Inthe symmetrical model of Figure 7, the gyration radiuswas segment OC, whereas in the nonsymmetrical model ofFigure 10, it is transformed into segment OK.

On the right of Figure 10, the different reaction forcesof the ground to the vehicle are represented by vectors Fsa ,applied on side s and axle a, that have two components:

• a longitudinal component Fxsa , which is the longitudi-nal reaction of the ground to the vehicle propulsion forceapplied by the engine

• a lateral component Fysa , which is the ground reactionforce opposed to the transversal slipping of the tire, gen-erated because of slip angles (cf. Figure 9)

Concerning the longitudinal reaction forces:

• The longitudinal internal forces Fxia must be smallerthan the longitudinal external forces Fxea in order togenerate a positive torque around the axis (K,ZC ). Fxia

may even be negative if necessary.• The exact value of the longitudinal forces applied on

each axle is unknown because it depends on the localcontact properties. Indeed, the great advantage of syn-

chronous propulsion of all the wheels on the same sideis that the engine torque is automatically distributedwhere the contact is best: i.e., if one wheel is on slip-pery ground, the torque is distributed to the two oth-ers. This principle is similar to differential locking onan all-terrain car, which proves to be extremely efficienton rugged ground. Consequently, the only available in-formation on the longitudinal forces is that they obeyEqs. (4):

Fxe1 + Fxe2 + Fxe3 = τe

r,

(4)

Fxi1 + Fxi2 + Fxi3 = τi

r,

where τe and τi are the torques of the external and inter-nal motors, respectively, and r is the wheel radius.

Concerning the lateral reaction forces, and assumingthat no slip angle is over αl ,

• The lateral internal forces Fyia should be higher with re-spect to Fxia than the lateral external forces Fyea withrespect to Fxea because the slip angles are always largeron the internal side.

• The lateral forces ahead of point K are directed to theoutside of the turn. Those behind point K are directedto the inside of the turn. For a given vertical load on allthe wheels, the higher the longitudinal distance betweenK and Csa projected along XC , the higher the slip angleand the higher the lateral forces Fysa .

In Figure 10, the speeds Vsa are represented on the topposition of the vehicle with a magnitude that is propor-tional to the distance between O and the considered wheelcenter Csa . Generally, this means that external wheels turnfaster than internal ones. Even on the same side, each wheelcenter Csa moves around a separate circle. The speed vec-tors Vsa are constructed tangent to the circular trajectory ofCsa , with the following components:

• The longitudinal speeds Vxsa are oriented to the front ofthe vehicle.

• The lateral speeds are denoted Vysa . Each time Vysa isnonnull, there is lateral slipping of the wheel, whichgenerates a lateral force in the opposite direction.

The slip angles αsa are obtained via Eq. (5) as a functionof xa , which is the longitudinal distance between axle a andthe projected gyration point K. The value of xa depends onwheelbase e and on the longitudinal position xK of point K

relative to (C, XC ), which is negative in Figure 10:⎡⎢⎢⎣αea = atan

(xa

R + v

)

αia = atan(

xa

R − v

)⎤⎥⎥⎦ with xa ∈ {e − xK,−xK, −e − xK }.

(5)



Figure 10. Top-view model of skid steering with nonsymmetrical front and rear slip angles.

3.3. Skid-Steering Modeling

Assuming that the skid-steering vehicle has a constant ro-tation speed, the fundamental principle of dynamics canbe applied with a null rotational acceleration around axis(O, ZO ).

If the friction in the transmission is initially ignored,it can be interpreted in the following way: the steeringtorque generated by the longitudinal forces created bythe motors is used to compensate exactly for the resistingtorque created by the slipping lateral forces. This results inEqs. (6)–(7):

MO,Fxsa+ MO,Fysa

= 0, (6)

[a=3∑a=1

Fxea · (R + v) +a=3∑a=1

Fxia · (R − v)

]

+[

a=3∑a=1

(Fyea + Fyia) · xa

]= 0, (7)

with xa ∈ {e − xK,−xK, −e − xK }.Equation (4) allows us to replace longitudinal forces by

motor torques and to obtain[τe · (R + v)

r+ τi · (R − v)

r

]+

[a=3∑a=1

(Fyea + Fyia) · xa

]= 0,

(8)with xa ∈ {e − xK,−xK, −e − xK }.



Equation (8) governs the skid-steering behavior andmay help to characterize it, provided that sufficient data aregathered from experiments.

In Section 4, we present an original solution to reducethe friction forces Fysa during skid steering. By decreasingthe absolute value of the second term in Eq. (8), which rep-resents the skid-steering resisting torque, it appears that thedriving torque represented by the first term will simultane-ously decrease as an absolute value. This could be an ad-vantageous improvement on this class of vehicles.

Sections 5 and 6 present the experimental part of thiswork. Field tests on the Kokoon vehicle intend to confirmthe nonsymmetrical skid-steering model presented above.

4. IMPROVING SKID STEERING BYSUSPENSION ADJUSTMENT

To improve the steering efficiency of multiaxle vehiclessuch as Kokoon, one solution could be to modify the massdistribution. This could be done by physically adding massor moving existing components and payload in the frame.

Another, simpler solution is to modify the suspensioncharacteristics. In this section, we choose to modify thefront and rear suspensions with respect to the central sus-pension. Our purpose is to increase the vertical load on thecentral axle, which is equivalent to unloading the front andrear axles.

4.1. Model of the Vehicle with StandardSuspensions

To demonstrate this phenomenon, a simplified model ofthe vehicle is considered, with the frame supported bythree suspensions, each one being represented by a verticalspring with linear behavior [Figure 11(a)]. When the vehi-cle is put on the ground, it finds a new equilibrium [Fig-ure 11(b)]. The initial unloaded length la0 of each springchanges to a new loaded value la . The three unknown val-ues of la can be found by solving a set of three equations.

The first equation comes from the fact that the top fix-ation points Ta of the springs remain aligned at the bottom

of the frame, which is assumed to be nondeformable. Thewheel centers Ca also remain aligned because the ground isflat. The angle between both lines is the pitch angle γ of thevehicle and relation (9) can therefore be written

tan (γ ) = l1 − l2

e= l2 − l3

e, (9)

which simplifies into

2l2 = l1 + l3. (10)

As the vehicle is balanced, the fundamental principle ofstatics give the two other equations. The sum of the reac-tion forces Fza and the weight mg gives relation (11):∑

F = Fz1 + Fz2 + Fz3 − mg = 0. (11)

The sum of the moments reduced to the central point C ofthe vehicle gives relation (12):∑

MC = −eFz1 + eFz3 + mgxG cos(γ ) = 0, (12)

with xG the abscissa of G within the local frame (C, XC, YC ),negative in Figure 11(b). Each spring has a linear relation-ship between its force Fza and displacement (la0 − la) viaconstant stiffness k (13):

Fza = k(la0 − la). (13)

Relation (13) is used to replace unknown forces Fza in rela-tion (11) to obtain

k(l10 − l1) + k(l20 − l2) + k(l30 − l3) = mg. (14)

Relation (13) is also used in relation (12) to obtain

−ke(l10 − l1) + ke(l30 − l3) + mgxG cos(y) = 0. (15)

Equations (10), (14), and (15) form a system of three equa-tions and three unknowns la that can be solved to find theequilibrium position of the vehicle. First, Eq. (14) can besimplified into Eq. (16):

l1 + l2 + l3 = l10 + l20 + l30 − mgk

. (16)

e e

γ

Figure 11. Simplified model of a vehicle with three identical suspensions.



Then l2 can be extracted from Eq. (16) with the help ofEq. (10):

l2 = l10 + l20 + l30

3− mg

3k. (17)

On the other hand, Eq. (15) is reformulated into Eq. (18)provided that γ remains small enough:

l1 − l3 = l10 − l30 − mgk

xG

e. (18)

Equations (16) and (17) are condensed into Eq. (19):

l1 + l3 = 2(l10 + l20 + l30)3

− 2 mg3 k

. (19)

Equations (18) and (19) form a system of two equationswith two unknowns (l1, l3) that are extracted:

l1 = 56l10 + 1

3l20 − 1

6l30 − mg

k

(13

+ xG

2 e

), (20)

l3 = −16

l10 + 13l20 + 5

6l30 − mg

k

(13

− xG

2 e

). (21)

If all the unloaded lengths la0 are assumed to be equal tothe same reference length l0, all the unknown lengths la ex-pressed in Eqs. (17), (20), and (21) can be simplified into

l1 = l0 − mgk

(13

+ xG

2 e

)= l2 − mg

k

xG

2 e,

l2 = l0 − mg3k

, (22)

l3 = l0 − mgk

(13

− xG

2 e

)= l2 + mg

k

xG

2 e.

It can be seen that because the center of gravity G islocated at the rear, xG is negative and

l0 ≥ l1 ≥ l2 ≥ l3 > 0. (23)

Using relation (13), the unknown forces Fza can be deducedfrom the lengths la found in Eqs. (22) and expressed inEqs. (24):

Fz1 = mg(

13

+ xG

2 e

)= Fz2 + mg

xG

2 e,

Fz2 = mg3

, (24)

Fz3 = mg(

13

− xG

2 e

)= Fz2 − mg

xG

2 e.

Expression (24) allows us to sort the contact forces by in-tensity on the standard vehicle, which appears to be over-loaded at the rear [relation (25)], which is logical:

Fz3 ≥ Fz2 ≥ Fz1 > 0. (25)

As Fz3 is high, it generates a strong lateral ripping force Fy3during skid steering.

4.2. Model of the Vehiclewith Modified Suspensions

To improve skid steering, the front and rear normal forcesmust be lowered according to their initial value. This can beachieved by modifying the suspensions. For instance, themodified unloaded lengths l′10 and l′30 of the front and rearsprings will be shortened by a given value � with respectto their original unloaded lengths l10 and l30 [Figure 12(a)].After equilibrium is achieved, the unknown spring lengthsare named l′a and the corresponding contact forces F ′

za .The modified unloaded spring lengths are enumerated

in Eqs. (26):

l′10 = l10 − � = l0 − �,

l′20 = l20 = l0, (26)

l′30 = l30 − � = l0 − �.

Equations (17), (20), and (21) have simply to bereevaluated with the modified unloaded lengths obtainedfrom Eqs. (26). The modified spring-loaded lengths l′a arethen calculated and are presented in Eqs. (27):

l′1 = l1 − 23 �,

l′2 = l2 − 23 �, (27)

l′3 = l3 − 23 �.

Figure 12. Simplified model of a vehicle with modified suspensions. Front and rear springs have shortened unloaded length l′a0.



It appears clearly that adjusting the suspension of value� generates an identical compression of 2�/3 of all thesprings [Figure 12(b)]. This also means that the pitch angleγ remains unaltered. The normal contact forces are derivedfrom Eqs. (13) and (27) and appear in Eqs. (28):

F ′z1 = Fz1 − k

�

3,

F ′z2 = Fz2 + 2k

�

3, (28)

F ′z3 = Fz3 − k

�

3.

Although the sum of the forces is unchanged, the front andrear normal contact forces F ′

z1 and F ′z3 are lowered of k�/3.

This generates a simultaneous lowering of the resisting lat-eral forces F ′

x1 and F ′y3, thus facilitating the skid-steering

process and justifying the type of adjustment made. It alsoallows us to find the required � displacement for a givendecrease in the normal contact forces F ′

z1 and F ′z3.

5. EXPERIMENTAL SETTINGS

The steering process of a vehicle is a complex phenomenonthat may be better understood from an experimental pre-liminary approach (Foster, Ayers, Lombardi-Przybylowicz,& Simmons, 2006; Itoh, Oida, & Yamazaki, 1995). For this6×6 vehicle, it was decided to measure experimentally thecontact forces of the wheels on the ground (Fauroux, Vaslin,& Douarre, 2007).

5.1. The Six-Component Force Plate

During Kokoon displacement, the wheels roll on thetop plate of a six-component force plate (TSR, Merignac,France), rigidly fixed in a wooden box buried in the groundso that the top plate is at ground level (Figure 13).

The six-component force plate used in this study (di-mensions 60 × 80 cm; measurement ranges Rx = 1,000 N,Ry = 900 N, Rz = 2,000 N; resolution 10 N) is composedof a rigid composite top plate (carbon/aluminum) fixedon three two-component strain gauge force transducers Ti

(Figure 14), which are also firmly fixed on the base plate(Couetard, 1993; 2000). Each of these transducers measures

Figure 14. The force plate including the three transducers tomeasure tangential and normal force components.

Figure 13. (a) Placing the force plate in the ground. (b) Integration of the wooden box into the ground. (c) The entire experimentalsystem.



Figure 15. (a) Computing the center of gravity on the CAD model. (b) Measuring the weight distribution with six scales.

one component of the resultant force in the plane of thetop plate (“shearing” component Rx , Ry ) and the other inthe direction perpendicular to the top plate (“compressive”component Rz). The signal values Vi produced by the sixforce transducers are multiplied by the 36 coefficients ofthe sensitivity matrix [S] for calculating the six components(Rx, Ry, Rz, Mx, My, Mz) of the wrench applied on the topplate in the reference frame linked to the force plate:

(Rx Ry Rz Mx My Mz)T = [S](V1 V2 V3 V4 V5 V6)T . (29)

In normal use, the wrench components allow computationof the horizontal coordinates (xCOP, yCOP) of the point offorce application on top of the force plate, which is usuallycalled “center of pressure” (COP). The signals of the force-plate transducers are simultaneously sampled at 100 Hzby a 16-bit A/D conversion card (AT-MIO-16X; NationalInstruments) slotted into a PC, and experimental data arerecorded using acquisition software (LabView 5.1; NationalInstruments). The acquisition PC and signal conditioner arebrought close to the force plate [Figure 13(c)]. Further post-processing is performed in a spreadsheet (Open Office).

5.2. Center of Gravity

The mass distribution on the wheels has a great influenceon the ground contact. It has been determined indepen-dently by the three following different methods with con-sistent results.

The first method uses the computer-aided design(CAD) model of Kokoon [Figure 15(a)]. Each componentis given a uniform density, and the Solid Edge CAD soft-ware can evaluate the volume and calculate the weightof the component. The whole assembly, including severalhundreds of parts, reaches a total weight of 367 kg withoutthe external composite panels.

The second method consists of carefully putting the ve-hicle on six scales using a winch [Figure 15(b)]. The resultsare summarized in Table III and are very close to those ob-tained with the first method. The longitudinal position xG

of the center of gravity G is also given relative to the middleaxle. G is located 133 mm behind the middle axle withoutdriver and only 78 mm behind with a 83-kg driver, for atotal weight of 450 kg. Consequently, the load is higher onthe rear axle and secondly on the middle axle, even if thedriver’s mass contributes to recentering point G.

The third method relies on the force plate to measurestatic loads on each wheel. The results are also consistent

Table III. Mass distribution on the three axles and longitudi-nal position of the vehicle center of gravity.

Front Middle Rear Total xG

axle (kg) axle (kg) axle (kg) (kg) (mm)

Without driver 66 129 171 367 −133With a 83-kg driver 108 158 183 450 −78



Figure 16. Model of the real swing-arm suspension mechanism (a) before and (b) after modification.

with the preceding ones and will be commented on later(Figures 19 and 21).

The results in Table III confirm Eqs. (24) and (25).

5.3. Modifying the Real Swing-Arm Suspension

The real swing-arm suspension mechanism is slightly morecomplex than the single spring used in Sections 4.1 and4.2. It is represented in Figure 16, and its main dimen-sions are provided in Table IV. The shock absorber has anoleo-pneumatic structure and a nonlinear law between thespring force Fs and the spring length ls , with hysteresis. Theswing-arm mechanism also adds nonlinearity to the evo-lution law of the normal contact force Fza with respect tolength la . This double nonlinearity poses no problem forthis work as the vehicle runs only on horizontal ground,with quasi-null variations of the contact force Fza .

For reasons of simplicity, the modification consisted ofdecreasing length hT . This was an easy operation becausethe top-attachment points T of the front and rear shockabsorbers can be adjusted in translation in their T-slot. Dis-tance hT was reduced from hT std = 145 mm to the minimalpossible length hT mod = 45 mm, which is a 100-mm motion

Table IV. Main dimensions of the suspension model.

Parameter Value (mm)

vA 180hT std 145hT mod 45ls 210–280lB 170lC 350d 15

that was performed only on the front and rear suspensions.The consequences of this modification were double:

• The unloaded length la [Figure 16(a)] decreased to l′a[Figure 16(b)] with aε{1, 3}.

• The average stiffness also decreased because of thesmaller moment arm of the spring force FS with respectto the rotation point A of the swing arm.

Because of both simultaneous changes, the vertical forcesFza on the front and rear wheels were noticeably lowered(Figure 17). As a consequence, the central axle was stronglyoverloaded and the central shock absorber underwent visi-ble compression [Figure 17(b)].

This suspension adjustment is equivalent to change inmass distribution, as summarized in Table V. Front and rear

Figure 17. (a) Standard suspension configuration. (b) Modi-fied configuration after adjustment.



Table V. Effects of suspension adjustments on the equivalentmass distribution (including an 83-kg driver).

Front axle Middle axle Rear axle TotalConfiguration (kg) (kg) (kg) (kg)

Standard 108 158 183 450Modified 80 (−26%) 250 (+58%) 120 (−34%) 450

Figure 18. Experimental field with reference frame and trajec-tories.

axles were offloaded by 26% and 34%, respectively, andmiddle axle loads 58% more.

Adjusting the suspensions was an extremely interest-ing option because of the small amount of work requiredand the significant changes generated. The following sec-tion presents the real experiments with and without sus-pension adjustments.

6. EXPERIMENTAL RESULTS

The experimental field can be seen in Figure 18. Lines show-ing the desired trajectories were drawn on the ground us-ing flour. Three types of trajectories have been consideredin this study: a straight line (which is equivalent to a turnwith infinite radius), a turn with a 6-m radius, and a turnwith a 3-m radius.

Several experiments were performed with the aim offollowing as closely as possible the desired trajectories(Douarre, 2006). Results are summarized in Figures 19–21.

The force-plate sample frequency was set at 100 Hz,which was sufficient for a slow vehicle such as Kokoon.Test duration varied according to the trajectory: driving ina straight line took generally no more than 1.5 s, whereasturning was slower and required up to 2.5 s because steer-ing demanded greater power from the electric motors, andthis power had to be adjusted on each side of the vehiclein real time by the driver if the correct path was to be fol-lowed.

Figure 19. A typical graph obtained when the 6×6 vehicle drives over the force plate. The time axis can be divided into fiveintervals according to the number of wheels simultaneously present on the force plate.



Figure 20. Trace of the center of pressure for the modified ve-hicle and for three types of trajectories.

Figure 19 is a zoom of Figure 21(b) and shows the typ-ical reaction forces applied to the vehicle when it drivesover the platform. Because the vehicle wheelbase (47 cm)is smaller than the force-plate width along the rolling di-rection (60 cm), sometimes only one and sometimes twowheels may be on the force plate at the same time. This ex-plains the shape of the curves of the reaction forces appliedto the vehicle when it crossed the force plate (Figure 19).The time axis of each trial can be divided into five intervals:

1. First, only wheel 1 applies efforts on the force plate;2. Then wheel 2 climbs onto the force plate (left transpar-

ent area), and the vertical component of reaction forceRz increases suddenly;

3. After that, wheel 1 leaves the force plate and only wheel2 remains on it;

4. Then, it is up to wheel 3 to cross the force plate (righttransparent area) and a second peak on Rz appears;

5. Finally, wheel 2 leaves the force plate and only wheel 3remains on it until the end of the crossing.

Another type of experimental result is representedin Figure 20: the trace of the center of pressure on theforce plate for various trajectories of the modified vehicle.Phases 1, 3, and 5 are represented by curve segments di-rected upward. Phases 2 and 4, during which two wheelsare present at the same time on the force plate, are repre-sented by a sudden downward inflexion of the curve. It isinteresting to see that the center of pressure follows almostperfect circular arcs during phases 1–3–5. This confirms thatthe trajectory was correctly followed by the vehicle (see ar-rows in Figure 20).

Figure 21 gives typical results obtained with standardsuspensions (panels a, b, c on the left) and modified sus-pensions (panels d, e, f on the right) for different values ofthe gyration radius R. Tables VI and VII are obtained byaveraging the Rx , Ry , Rz values on the single-wheel inter-vals and give an order of magnitude of the reaction com-ponents, thus eliminating the small variations in the sig-nal due to electrical perturbations and vehicle vibrations onsmall pieces of gravel.

6.1. Reference 6×6 Vehicle withStandard Suspension

For normal force Rz in standard configuration, it can beseen in Figure 21(a) and Table VI that wheel 3 (930 N) bearsmore weight than wheel 2 (848 N), which, in turn, bearsmore weight than wheel 1 (635 N). These results includethe driver’s weight and confirm the previous calculationsof the center of gravity. Assuming that the grip coefficient

Table VI. Average forces on the right wheels for standard suspensions.

Wheel 1 (front) Wheel 2 (middle) Wheel 3 (rear)Standardsuspensions Rx (N) Ry(N) Rz(N) Rx(N) Ry(N) Rz(N) Rx (N) Ry(N) Rz(N)

Straight line 23 10 635 −17 −67 848 −30 −40 930Turn R = 6 m 70 −270 627 454 −36 972 68 438 905Turn R = 3 m 74 −321 534 553 −146 1,016 86 532 914

Table VII. Average forces on the right wheels for modified suspensions.

Wheel 1 (front) Wheel 2 (middle) Wheel 3 (rear)Adjustedsuspensions Rx (N) Ry(N) Rz(N) Rx(N) Ry(N) Rz(N) Rx (N) Ry(N) Rz(N)

Straight line 69 −105 446 −155 −33 1,393 −43 −95 671Turn R = 6 m 49 −194 468 282 −80 1,382 3 281 671Turn R = 3 m 8 −331 563 450 49 1,533 −55 398 666



Figure 21. Forces on the right wheels. (a) (b), and (c) For the standard suspension; (d) (e), and (f) for the modified suspension.

is identical on every wheel, this means that the rear andcentral wheels are able to apply a higher propulsion forceRx and to undergo a higher lateral force Ry . When the tra-jectory varies [Figures 21(b) and 21(c)], the overall shape ofthe normal force Rz does not differ considerably: the firstpeak is identical; the second peak changes slightly, proba-bly due to transient phenomena.

Propulsion force Rx has an original shape: it appearsthat only the central wheel applies a propulsion force. Thismay be caused by insufficient tension in the front andrear transmission belts. This problem must be correctedin future work because the central belts cannot transmitthe complete torque; hence only one-third of the poten-

tial propulsion force is currently used by the vehicle. Theplanned solution is to replace belt transmission by chaintransmission. Another interesting result is the evolution ofRx with respect to the steering radius R: when R decreases,Rxmust increase to make the vehicle rotate, as expectedfrom Eq. (7). Along a straight line, Rx does not need tobe very high in order to generate vehicle movement. Butduring a turn with R = 6 m (respectively, 3 m), Rx reaches454 N (respectively, 553 N). This increase in Rx force wasclearly experienced by the driver, who needed to increasethe power during short turns.

As expected, the lateral force Ry has a negligiblevalue when driving in a straight line. However, this value



increases particularly on the front and rear wheels when theturning radius R decreases. For instance, for the 3-m turn,Ry reaches −321 N (respectively, 532 N) on wheel 1 (respec-tively, wheel 3). The opposite signs of Ry between wheels1 and 3 logically reflect the opposite lateral efforts appliedon these wheels during the turn. The absolute values of Ry

are not symmetrical on front and rear wheels. One explana-tion is that axle 3 loads more weight than axle 1. This is alsothe case for the 3-m turn, where Ry is nonnull on the cen-tral wheel (−146 N). These results seem to confirm that thecenter of gyration of the vehicle is not located on the cen-tral axle, as predicted by the nonsymmetrical skid-steeringmodel presented in Section 3.2.

6.2. Modified 6×6 Vehicle

With the modified vehicle, the duration of turn trials wasonly 2 s instead of 2.5 s with standard suspensions, becausesteering and power control were much easier for the vehi-cle and the driver, respectively. These improvements wereclearly experienced by the driver during these trials. Re-sults are summarized in Table VII.

In Figures 21(d)–21(f), it can be noted that the Rz curvedoes not change a lot with the turning radius R. As ex-pected on the modified vehicle, the highest normal load issupported by axle 2. During the straight-line trajectory [Fig-ure 21(d)], the normal force Rz shows a strange shape witha peak during Phase 3. This could be caused by the driverleaning forward or by the vehicle tilting on a small obsta-cle. Apart from this phenomenon, the total of normal forceson the external wheels remains constant at around 2,500 N(Figure 22). The total weight of the vehicle was supposedto be 4,500 N, as shown in Table III. This means that the ex-ternal wheels bear approximately 56% of the weight of thevehicle, which was probably not perfectly horizontal, witha little roll angle. Figure 22(b) clearly shows the important

Figure 23. Total propulsive forces Rx due to external wheelsfor standard and modified suspensions.

part of the load borne by wheel 2 with the modified sus-pensions.

The curves of force Rx still show that only the centralwheel applies an effective propulsion force. However, themodified suspension seems to have decreased the requiredpropulsion force. This could mean that a smaller longitu-dinal force is able to generate the same movement of thevehicle. For a 6-m turn, Rx decreases from 454 to 282 Non the central wheel, which means a gain of 38% with re-spect to the initial suspension adjustment. The sum of thepropulsive forces Rx of all the external wheels is visible inFigure 23. The driver clearly needs to inject less energyinto the electric motors. The force decrease is quantified at43.5%, for radius 6 m as well as radius 3 m. The overallturning time was observed to be shorter than with a clas-sical suspension. This suggests that the global turning effi-ciency is improved with the modified suspension. Furtheranalysis is required to quantify this improvement.

Rz (

N)

Rz (

N)

Figure 22. Total of normal forces Rz borne by external wheels with repartition for standard and modified suspensions.



The lateral force Ry has approximately the same shapein the initial and adjusted configurations. For a 6-m turnwith the modified vehicle, there is a 28% decrease of Ry

on the front axle and a 36% decrease on the rear axle. Thismeans that less energy is dissipated during skid steeringwith the modified suspensions.

6.3. Important Parameters to CharacterizeSkid Steering

From the skid-steering model and the corresponding exper-imental results, it appears that the nonsymmetrical modelfor skid steering on the Kokoon vehicle is verified. Toquantify this nonsymmetry, it is important to find the pro-jected center of gyration K and its longitudinal position xK .

xK becomes a characteristic parameter that can be ex-tracted by first developing Eq. (8) into Eq. (30):[

τe · (R + v)r

+ τi · (R − v)r

]

+⎡⎣ (Fye1 + Fyi1) · (e − xK )

+ (Fye2 + Fyi2) · (−xK )+ (Fye3 + Fyi3) · (−e − xK )

⎤⎦ = 0. (30)

Then xK is factorized and extracted:

xK = {[τe · (R + v) + τi · (R − v)]/r} + e · (Fye1 + Fyi1 − Fye3 − Fyi3)Fye1 + Fyi1 + Fye2 + Fyi2 + Fye3 + Fyi3

. (31)

However, obtaining xK theoretically from Eq. (31) isslightly awkward as the values of Fysa are not preciselyknown and depend on the model used for slip angles. Thebest way would be to ascertain xK experimentally by mak-ing the vehicle turn on itself (with a zero turning radius)and finding the invariant point of its sagittal plane. Thiswould require high-resolution photographs of the vehicletaken from the top and will be done in future work.

Section 5 introduced the concept of suspension modi-fication in order to lower friction forces during skid steer-ing. This decrease can be quantified by introducing thesupplement of power Pskid absorbed by skid steering:

Pskid =[τe · (R + v)

r+ τi · (R − v)

r

], or

Pskid = −[

a=3∑a=1

(Fyea + Fyia) · xa

](32)

with xa ∈ {e − xK, −xK, −e − xK }. Equation (32) gives twoways of calculating Pskid:

• The first one is to measure the torque of the enginesthrough experimentation. This will be done in futurework by measuring current inside the engines withhook-on ammeters.

• The second one is based on the knowledge of all thelateral forces. A simple solution would be to use a sec-ond force plate buried in the ground to obtain experi-mental results. But an even better solution would be tointegrate force sensors into each wheel for continuousmeasurement. This would provide precise knowledgeof the law f that governs lateral forces Fy , as shown inEq. (33) and Figure 9:

Fy = f (α, Fz). (33)

As the slip angles αsa are fixed for a given gyration ra-dius R, as the mass distribution on the axles and the val-ues of Fz may be considered constant at uniform speed,the knowledge of this law would allow the predictionof the power consumption for skid steering. It requires,however, a careful fitting of the law to as many experi-ments as possible.

These preliminary results are very encouraging andconfirm that turning efficiency is highly sensitive to thenormal component Fz of the contact force, as expected inEq. (33). Fz can be adjusted either by the mass distribu-tion in the vehicle or by suspension adjustments. Changingmass distribution requires either adding ballast or moving

sufficient masses inside the vehicle using a suitable mech-anism. In both cases, the adjustment is not very practicaland not suitable to selectively overload only the central axleof the vehicle, which is required to improve skid-steeringability. On the other hand, suspension adjustments can leadto the expected results with only simple modifications thatmay concern spring stiffness or the fixture position of thespring. Future work will have to confirm this result and toquantify it more precisely by using parameters xK and Pskidfirst introduced here in Eqs. (31) and (32).

More generally, it now appears feasible to improveskid steering of many comparable vehicles by using thismethod. The main idea presented in this work is to reducethe energy loss due to friction during skid steering by over-loading the axle that is closest to point K , whereas the otheraxles are underloaded proportionally to their distance frompoint K . Knowledge of parameter xK is therefore critical inadopting a correct strategy for adjusting the suspensions.The sum of normal forces Fz remains constant but theirdistribution changes, and likewise for the lateral forces Fy .This allows the steering torque to decrease.

For vehicles with two axles, it appears to be difficult toimprove skid steering with our method if the vehicle is bal-anced (i.e., with the same mass on the front and rear axles)as point K is in the middle of the vehicle and no axle is



closer to K . So it should be noted that this method is par-ticularly suitable for vehicles and robots with three or moreaxles.

7. CONCLUSION

This work has presented models and experiments of theskid-steering phenomenon on a 6×6 vehicle. It character-ized the lateral skid forces that are responsible for a highlevel of energy dissipation during steering. It also char-acterized the projected center of gyration K and its po-sition relative to the vehicle. This center depends on thevehicle mass distribution as well as its propulsion andsuspension systems. Preliminary results seem to confirmthat point K is not located on the central axle of the vehi-cle. This suggests that the proposed nonsymmetrical skid-steering model is correct. Locating point K is thus a priorityin order to achieve an efficient control of the vehicle or mo-bile robot during skid steering.

The experimental work also suggested that skid-steering efficiency of a 6×6 ATV can be substantiallyimproved by only minor adjustments on the vehicle sus-pension. An important modification in contact force distri-bution was obtained with a 10-cm adjustment of damperfixtures. The driver reported that he felt a substantial im-provement in the steering capacity during the trials per-formed with the modified vehicle. This minor adjustmentof the suspensions allowed reduction of the propulsionforces by around 40% and also brought down the lateralforces in the same proportion.

The absence of any steering system on a vehicle is aguarantee of robustness and control simplicity, but it hasthe major drawback of consuming too much power dur-ing steering phases. The method and solutions presented inthis paper could be generalized to many types of multiaxlevehicles and robots in order to improve their skid-steeringperformance. Indeed, on vehicles with three or more axles,one can imagine an adaptive suspension capable of modi-fying the normal force distribution on the wheels withoutchanging either mass or payload distribution in the vehi-cle. This is currently done manually in the Kokoon vehicle.In a future version, the suspension adjustment could be au-tomatically performed only during turns by using a dedi-cated mechanism, resulting in lower energy consumptionduring skid steering. When driving in a straight line, theadjusting mechanism would reset the initial normal forcedistribution for better balancing of traction forces on all theaxles together with improved pitch stability.

Further work will focus on extended experimental re-sults and improved modeling. The first thing for experi-ment will be to film the vehicle motion from a top viewduring self-rotation with a zero turning radius in order toprecisely locate point K .

A new version of the vehicle is also currently beingconstructed with chain transmissions instead of belts. Thiswill prevent sliding inside the transmission and will al-

low us to obtain more precise experimental results. An-other work in progress concerns the measurement of con-tact forces, because the force plate buried in the groundcannot simultaneously measure the contact forces on all sixwheels. Moreover, when the wheel is rolling over the forceplate instead of on the normal ground, there is also a changein contact parameters. For these reasons, a more sophisti-cated experiment is planned in the short term, with eachwheel including a six-component force sensor. Hopefully,these two improvements should allow us to refine our skid-steering models and to obtain more precise experimentalresults.

ACKNOWLEDGMENT

The Kokoon prototype was designed, built, tested, and con-tinuously improved with the extensive help and constantmotivation of IFMA (French Institute for Advanced Me-chanics) and UBP (Blaise Pascal University) students. Theauthors also acknowledge the financial support of OSEO-ANVAR (French National Agency for Development of Re-search), the Michelin Company, and the TIMS ResearchFederation. The other sponsors and people involved inKokoon development are given on the Kokoon Project Webpage: http://www.kokoon.fr.st.

REFERENCES

Besselink, B.C. (2003). Computer controlled steering system forvehicles having two independently driven wheels. Com-puters and Electronics in Agriculture, 39(3), 209–226.

Besselink, B.C. (2004). Development of a vehicle to study thetractive performance of integrated steering-drive systems.Journal of Terramechanics, 41(4), 187–198.

Couetard, Y. (1993). Capteur de forces a deux voies et applica-tion notamment a la mesure d’un torseur de forces. INPI,Patent 96 08370 (France).

Couetard, Y. (2000). Caracterisation et etalonnage de dy-namometres a six composantes pour torseur associe a unsysteme de forces. Ph.D. thesis, Universite Bordeaux 1.

Douarre, G. (2006). Caracterisation du vehicule a 6 roues motri-ces Kokoon. Final semester engineering project, IFMA.

Fauroux, J.C., Charlat, S., & Limenitakis, M. (2004a,September). Team design process for a 6×6 all-roadwheelchair. In Proceedings International Engineeringand Product Design Education Conference, IEPDE’2004,Delft, The Netherlands (pp. 315–322). Available athttp://jc.fauroux.free.fr.

Fauroux, J.C., Charlat, S., & Limenitakis, M. (2004b, June). Con-ception d’un vehicule tout-terrain 6×6 pour les person-nes a mobilite reduite. In Proceedings 3eme ConferenceHandicap 2004, Paris Expo, Porte de Versailles, France(pp. 59–64). Available at http://jc.fauroux.free.fr.

Fauroux, J.C., Vaslin, P., & Douarre, G. (2007, June). Improv-ing skid-steering on a 6×6 all-terrain vehicle: A prelimi-nary experimental study. In Proceedings of IFToMM 2007,the 12th World Congress in Mechanism and Machine



Science, Besancon, France (Paper A100.pdf). Available athttp://jc.fauroux.free.fr.

FNSS Corp. (2008). PARS 6×6 and 8x8 wheeled armoured ve-hicles. Retrieved January 29, 2009, from http://www.fnss.com.tr.

Foster, J.R., Ayers, P.D., Lombardi-Przybylowicz, A.M., &Simmons, K. (2006). Initial effects of light armored vehicleuse on grassland vegetation at Fort Lewis, Washington.Journal of Environmental Management, 81, 315–322.

Halconruy T. (1995). Les liaisons au sol. Boulogne-Billancourt,France: Editions E.T.A.I.

Itoh, H., Oida, A., & Yamazaki, M. (1995). Measurement offorces acting on 4WD-4WS tractor tires during steady-state circular turning in a rice field. Journal of Terrame-chanics, 32(5), 263–283.

Kececi, E.F., & Tao, G. (2006). Adaptive vehicle skid control.Mechatronics, 16(5), 291–301.

Maclaurin, B. (2007). A skid steering model with track pad flex-ibility. Journal of Terramechanics, 44, 95–110.

Mendonca, C., & Nait Hadi, H. (2007). Modelisation etexperimentation du vehicule a six roues motrices Kokoon.Master’s thesis, Universite Blaise Pascal.

Mokhiamar, O., & Abe, M. (2006). How the four wheels shouldshare forces in an optimum cooperative chassis control.Control Engineering Practice, 14(3), 295–304.

Mousset, C.H., & Chervet, T. (2008). Modelisation etexperimentation du vehicule a six roues motricesKokoon. Master’s thesis, Universite Blaise Pascal.

Oasis LLC Corp. (2009). The Max 6×6 ATV. RetrievedJanuary 29, 2009, from http://www.oasisllc.com/english/max.htm.

Patria Corp. (2009). The armoured modular vehicle. RetrievedJanuary 29, 2009, from http://www.patria.fi.

Robosoft Corp. (2009). The Pioneer 3 ATRV. Retrieved January29, 2009, from http://www.robosoft.fr.

Shoichi, S., Yoshimi, F., & Yutaka, T. (1986). Steering apparatusfor a vehicle having steerable front and rear wheels. PatentUS4614351, 1986-09-30, Honda Motor Co. Ltd. (Japan).

Sreenivasan, S.V., & Wilcox, B.H. (1994). Stability and trac-tion control of an actively actuated micro-rover. Journalof Robotic Systems, 11(6), 487–502.

Watanabe, K., Kitano, M., & Fugishima, A. (1995). Handlingand stability performance of four-track steering vehicles.Journal of Terramechanics, 32(6), 285–302.


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