8th International Conference on Power Electronics - ECCE Asia

May 30-June 3, 2011, The Shilla Jeju, Korea

978-1-61284-957-7/11/$26.00 ©2011 IEEE

[ThD2-4]

Realization of Steer-by-Wire Systemfor Electric Vehicles using Caster Wheels

and Independent Driving MotorsYunha Kim1, Hiroshi Fujimoto2, and Yoichi Hori2

1Department of Electrical Engineering, The University of Tokyo,3-7-1 Hongo, Bunkyo-ku, Tokyo, Japan

2Department of Advanced Energy, The University of Tokyo,5-1-5 Kashiwanoha, Kashiwa-shi, Chiba, Japan

Abstract—Recently many works have been done on elec-tric vehicle motion control. Most of them, however, stillremain in the horizon of the conventional vehicle chassisstructure, which is waste of ability. This paper presents anovel steer-by-wire system for electric vehicles using casterwheels and independent driving motors, which maximizesdegrees of freedom in EV mobility and eventually distin-guishes EVs from the ICEVs. A small-sized experimentalvehicle is introduced and its basic dynamic characteristicsare shown with actual experimental data. It is shown thatthe mobility of the vehicle can be improved by using casterwheels and independent driving motors at low speed, whileit maintains stability at high speed. Feasibilities for futureEV applications are shown with mathematical modeling andanalyses, and control strategies are proposed in the paper.

Index Terms—Caster Wheels, Electric Vehicle, Indepen-dent Driving Motors, Motion Control

I. INTRODUCTION

Recent popularization of electric vehicles (EVs) is re-markable. Some of the leading automobile manufacturersare launching fully electrified vehicles to compete for thepreoccupancy of the market, and many research groupsaround the world are working on the vehicle electrificationand its related issues. Many of them are focusing on theenergy storage system involving batteries, capacitors, orfuel cells for instance [1]. Some of them are into chargingand power transfer techniques [2][3], and many others arefocusing on the infrastructural studies.

From the motion control point of view, it is widelyknown that, compared to conventional vehicles mountinginternal combustion engines (ICEVs), EVs have severalsignificant advantages in vehicle dynamic performancesuch as: electric motors have very quick torque response(1ms or less); electric motors have highly accurate outputtorque; there is no difference between acceleration anddecceleration (i.e. electric motors act as both engine andbrake); electric motors are compact so that they can befitted in each wheel (In-Wheel Motor, IWM); and themotor torque can be measured easily [4].

Among the advantages mentioned above, it is worthnoting that, by using independent driving motors (IDMs),the traction and braking force distribution can be easily

controlled, and thus the vehicle mobility and stability canbe drastically improved with the additional forces andmoments given to the vehicle [5][6].

The aforementioned research works, however, are theones assuming the four-wheeled vehicle frame, whichremains unchanged from the beginning of the mass pro-duction of passenger vehicles. Meanwhile, a very few inliterature have tried to address the chassis configurationwith regard to the new powertrain system, although it isimportant and interesting from the view point of vehiclemotion control.

Focused on this property, the effects of wheel place-ment change on the vehicle dynamics were examinedand evaluated by the author [7] as shown in Figure 1. Itwas shown that, some alternative wheel placements suchas three-wheeled ones can show better performance invehicle motion control while showing equivalent stabilityas that of conventional four-wheel configuration [8][9].Which implies that more studies need to be done on thismatter.

In the same context, this paper proposes a novel steer-by-wire system using caster wheels (Fig. 2) and IDMs asone of the possible chassis configurations for the future

Fig. 1. Yaw rate response to the direct yaw moment input from thedriving motors. 3-wheeled (2 front driving wheels) in blue, 3-wheeled(2 rear driving wheels) in green, and 4-wheeled (2 rear driving wheels)vehicle in red were evaluated.

Fig. 2. A caster wheel (image source: http://advancecaster.com)

passenger electric vehicles. The system consists of twoindependent driving wheels on the rear and two casterwheels on the front. A caster wheel is an undriven wheelthat is free to move or rotate. By choosing caster wheels assteering wheels, the effect of traction and braking forcedistribution generated by driving wheels on the vehicledynamics can be maximized. In addition to this, theunique dynamic characteristics of caster wheel itself canaffect the vehicle motion, which allows the vehicle to haveexpanded mobility.

Although caster wheels can be found in numerous ap-plications, including shopping carts, chairs, mobile robotsand even the aircraft landing gears, their dynamics has notbeen satisfatorily addressed yet with regard to the vehicledynamics. For instance, it is sometimes neglected as in[10], being described as a point only exerting normal forcefrom the ground to the vehicle body.

In order to fully utilize the advantages of using in-dependent driving motors in vehicle powertrain-chassissystem, the caster behavior needs to be exained beinglinked to vehicle dynamics, which is done in the followingsection.

II. EXPERIMENTAL VEHICLE AND MODELING

A. Experimental Vehicle, CIMEV

CIMEV (Caster-wheeled Independent Motor-drivenElectric Vehicle) is designed to run unmanned. It iscontrolled by a digital signal processor (S-BOX) with twoinput signals transmitted through a radio controller. ThePWM signals interpreted by the receiver are sent intothe DSP, where they are linearized to drive the motors– both driving and steering – to run the vehicle. Fourindependently controlled electric motors are used. Twoare used for steering and the other two for driving. Thevehicle is powered by a 24V Ni-MH battery. Systemconfiguration is shown in Fig. 4.

Measured vehicle parameters are shown below in TableI, and the dimensions and the frame of reference areshown in Fig. 5. The specification of the driving andthe steering motors are shown in Table II and Table III,respectively, and the DSP (S-BOX) I/O setting is shownin Table IV. The sampling time of DSP is set 1 ms.

Four encoders are attached to each of motors to moni-tor the rotation of both the steering and the driving motors.Two encoders for the driving motors have the resolutionof 3600pulse/rotation, and the others for the steeringmotors are with the resolution of 1024pulse/rotation.

Fig. 3. Caster wheeled electric vehicle CIMEV: Two rear wheelsare driven via belt and pulley by two independent driving motors (90Watts each). Two front wheels are casters, connected via gears to twoindependent steering motors (60 Watts each).

Fig. 4. System configuration of the experimental vehicle CIMEV: Thevehicle is controlled by a digital signal processor (S-BOX) with a remotecontroller. Its dynamic behavior is monitored and recorded through anacceleration sensor unit and four endcoders.

Fig. 5. Vehicle dimensions and the frame reference.

Additionally, an acceleration sensor unit (Fig. 6) is usedto monitor the behavior of the vehicle.

TABLE IVEHICLE PARAMETERS (MEASURED)

Parameters Meanings Valuesm Vehicle mass 18.5 kgNf Normal force on each front wheel 39.2 N*Nr Normal force on each rear wheel 51.5 N*Iz Moment of inertia (vehicle) 0.409 kgm2**Iw Moment of inertia (caster wheel) 0.009 kgm2***e Caster arm length 0.040 ml f Distance, from C.G. to front axle 0.247 mlr Distance, from C.G. to rear axle 0.188 mL Wheel base 0.435 md Tire track 0.355 m

*g = 9.8m/s2

**Measured by torsional pendulum method***Calculated

TABLE IISPECIFICATION OF DRIVING MOTOR

Parameters Meanings ValuesPrd Rated power 90 WKτd Torque coefficient 0.093 N ·m/AKed Back EMF coefficient 0.093 V/(rad/s)Rid Internal resistance 0.6 ΩNnd Rotational speed without load 2350 rpmInd Current without load 0.6 AJmd Moment of inertia of roter 0.000071 kgm2

rrd Reduction ratio (belt and pulley) 14 : 25

TABLE IIISPECIFICATION OF STEERING MOTOR

Parameters Meanings ValuesPrs Rated power 60 WKτs Torque coefficient 0.0538 N ·m/AKes Back EMF coefficient 0.0536 V/(rad/s)Ris Internal resistance 2.52 ΩNns Rotational speed without load 8490 rpmIns Current without load 0.0785 AJms Moment of inertia of rotor 0.00000345 kgm2

rrs Reduction ratio (gears) 18 : 120

TABLE IVDSP(S-BOX) I/O SETTINGS

Channel Parameters MeaningsCNT 1 ωL Wheel Speed (L)CNT 2 ωR Wheel Speed (R)CNT 3 δL Steering Angle (L)CNT 4 δR Steering Angle (R)DI1 — Radio Controller CH1DI2 — Radio Controller CH2DI3 — Radio Controller CH3DI4 — Radio Controller CH4AD1 TL Driving Motor Torque (L)AD2 TR Driving Motor Torque (R)AD3 TmL Steering Motor Torque (L)AD4 TmR Steering Motor Torque (R)AD5 γ Yaw RateAD6 ay Lateral AccelerationDA1 TL

∗ Driving Torque Reference (L)DA2 TR

∗ Driving Torque Reference (R)DA3 TmL

∗ Steering Torque Reference (L)DA4 TmR

∗ Steering Torque Reference (R)

Fig. 6. Acceleration sensor unit used in the system. Yaw rate, x-directional, and y-directional accelerations can be measured.

Fig. 7. Kinematic relations between parameters during cornering.

B. Mathematical Modeling

In literature, most of the studies regarding the casterwheel dynamics are provided by those who are makingmobile robots or aircrafts. The latter are concerned withthe vibration of an aircraft landing gear during taxiing,thus they are focused on attenuating the phenomenon athigh operation speed [11]. Meanwhile, the former aremore into the kinematics of the system, and more likelyto neglect the transient dynamics. Caster wheels are notseen in vehicle dynamics for passenger vehicles so far.

To establish a simple but accurate mathematical modelof the system, it is reasonable to start with the casterdynamics and its modelling. For the mathematical models,the parameters provided in the previous section are used.Here, it is assumed that the casters are free to rotate onlyunder the effect of the stiffness K and the damping Dabout the king pin. In this model, the vehicle’s corneringis controlled merely by the direct yaw moment input.

Among the dynamic models provided by the afore-mentioned research groups, the model suggested byG. Somieski [11] seems to be compatible for our sys-tem. The system is modelled neglecting the existance ofsteering motors. The governing equations are written as:

Iwδ +Dδ +Kδ = Msa(α)+ eFy(α)−Dt(V )δ (1)

α =

(Vy+l f γVx± d

2 γ−δ)

(2)

where,α: side slip angle of the wheels;K: spring constant about the king pin;

D: damping constant about the king pin;Msa: self aligning torque;Fy: lateral force at the tire-road interface; andDt : damping moment due to tread width.

At constant vehicle speed V , limiting the side slip angleα to 5 degrees where it can be linearized, and using theDugoff’s tire model, and from the kinematic relationsindicated in Fig. 7, we can rewrite the equation (1) as[12][13][14][15]:

(Iws2 +(D+Dt)s+K

)δL

=Csa

(Vy+l f γVx− d

2 γ−δL

)+ eCF

(Vy+l f γVx− d

2 γ−δL

)(3)

for left wheel and

(Iws2 +(D+Dt)s+K

)δR

=Csa

(Vy+l f γVx+

d2 γ

−δR

)+ eCF

(Vy+l f γVx+

d2 γ

−δR

)(4)

for right wheel, where,Csa: coefficient for self aligning torque;CF : coefficient for lateral force.

We can rewrite equation (3) and (4) as below:

δL = Csa+eCFIws2+(D+Dt )s+(K+Csa+eCF )

(Vy+l f γVx− d

2 γ

)(5)

δR = Csa+eCFIws2+(D+Dt )s+(K+Csa+eCF )

(Vy+l f γVx+

d2 γ

)(6)

Moreover, the caster wheels, in relation with the ve-hicle body, are exerting moments through/about the kingpin on the vehicle body, which are noted as:

ML = (Ds+K)δL (7)MR = (Ds+K)δR (8)

These moments can be written in the equivalent formof cornering force, whose direction is along with y−axis,as:

YFL =ML

ecos

(Vy + l f γVx − d

2 γ

)(9)

YFR =MR

ecos

(Vy + l f γVx +

d2 γ

)(10)

When the vehicle speed is low (parking lot maneuvers),the transient caster dynamics can be ignored as in [10].Thus here we investigate the cater-vehicle dynamics as-suming that the vehicle speed is high enough. By addingsome modifications to the bicycle model, the vehicledynamics can be written as:

sIzγ = l fYFL + l fYFR −2lrYR +Mz (11)mV (sβ + γ) = YFL +YFR +2YR (12)

where,Mz: direct yaw moment input from driving wheels;β : side slip angle of the vehicle body;YR: cornering force acting on the rear wheels.

When the vehicle speed is high enough, i.e.:

Vy + l f γVx − d

2 γ≈ Vy + l f γ

Vx +d2 γ

≈ β +l f γV

(13)

Vy − lrγVx − d

2 γ≈ Vy − lrγ

Vx +d2 γ

≈ β − lrγV

(14)

By substituting (5)∼(10) into equation (11) and (12)and using parameters above, we get:

G(s)Mz→γ =γ

Mz=

P(s)Q(s)

(15)

where, P(s) is 4th order polynomial and Q(s) is 5thorder polynomial of s, which can be computed from theequations and the parameters defined above. Note that thetorque input of the steering motors is not considered here.i.e. Caster wheels are free to rotate under influence of Kand D only. The steering angle δ is a state variable.

For active steering motor control, if we consider themotor torque inputs, and put K = 0 and D = 0, we canrewrite the equations (3), (4), (7), and (8) as:

((Iw + Im)s2 +Dts

)δL

=Csa

(Vy+l f γVx− d

2 γ−δL

)+ eCF

(Vy+l f γVx− d

2 γ−δL

)+TmL (16)

for left wheel and

((Iw + Im)s2 +Dts

)δR

=Csa

(Vy+l f γVx− d

2 γ−δR

)+ eCF

(Vy+l f γVx− d

2 γ−δR

)+TmR (17)

for right wheel, where,Im: moment of inertia of the steering motor;TmL,TmR: steering motor torque.

Equations (7) and (8) become:

ML =−TmL (18)MR =−TmR (19)

III. STABILITY ANALYSIS

Using equation (15), simulations are done to see thesystem response and to determine the system stability.From Fig. 8∼10, we can see that the open loop systemis unstable with any stiffness or damping coefficient atany speed. As we know from our experiences of usingshopping carts, the system should be under a feedbackcontrol by a ‘human controller.’

As it turned out that the open loop system is unstable, itis plausible to see if the closed loop system is stable. First,

Fig. 8. Poles of the open loop system according to varying stiffness K(0 to 10Nm/rad), at D=0.1Nm/(rad/sec), V=10m/s. It is seen that therealways exist a pole in the RHP (marked with red circle) which makesthe system unstable.

Fig. 9. Poles of the open loop system according to varying dampingcoefficient D (0 to 10Nm/(rad/sec)), at K=0.1Nm/rad, V=10m/s. It isseen that there always exist a pole in the RHP (marked with red circle)which makes the system unstable.

Fig. 10. Poles of the open loop system according to varying vehiclespeed V (1 to 20 m/s), at K=0.1, D=0.1. It is seen that there alwaysexist a pole in the RHP (marked with red circle) which makes the systemunstable.

a simple feedback control loop is considered as shown inFig. 11. With this structure, the root-locus of the closedloop system is plotted to obtain stability perspective.

By using a feedback controller, the system poles aremoved to LHP: the system is stabilized. As seen in Fig.12∼14, the stiffness K does not have much effect on thesystem stability while the damping D has the dominant

Fig. 11. A simple feedback controller to check the closed loop stabilitywith a constant gain C.

Fig. 12. Closed loop system poles with varying K (0 to 10Nm/rad)at D=0.1Nm/(rad/sec) and V=10m/s. K does not have much effect onsystem stability.

Fig. 13. Closed loop system poles with varying D (0 to 10Nm/(rad/sec))at K=0.1Nm/rad and V=10m/s. D seems to have the dominant effect onsystem stability.

effect. And as the vehicle speed V increases, the systempoles moves to the fast side, where the system is morestable. Thus it is inferred that the vehicle can be stabilizedwith a simple feedback controller in certain speed range.

From the analyses, however, it can be seen that withonly passive control system, the range of control isrestricted. Due to the existence of the limit in force thata tire-road interface can produce, the direct yaw momentalso has limited value, which results in undesirably lowundersteer gradient. To have sufficient means of motioncontrol, the experimental vehicle CIMEV is provided withtwo steering motors as shown in Fig. 15.

IV. CONTROL STRATEGIES

By using caster wheels and independent driving mo-tors, we can expect the vehicle to have mainly two

Fig. 14. Closed loop system poles with varying V (0 to 20 m/s) atK=0.1Nm/rad and D=0.1Nm/(rad/sec). It can be seen that the systembecomes more stable as the vehicle speed increases.

Fig. 15. Caster wheel with steering motor.

merits: freer vehicle movement at low speed, and theapplication of controlled lateral forces at high speed.Using properly designed controllers with accordance withthe speed range, these advantages can be maximized intheir effects.

A. Low Speed Range Control

At low speed (parking lot maneuvers) the tires do notdevelop lateral forces. They roll without any slip angle,and thus the vehicle turning is determined only by thegeometrical relations. As shown in the Fig. 16, the instantcenter of rotaion (ICR) of the vehicle, which is a criterionevaluating the vehicle mobility, can be placed at any pointon the line passing through the rear axle by using casterwheels and independent driving motors, while that of theconventional vehicle cannot. The minimum turning radusof a vehicle with normal steering configuration is usuallyaround five meters, on the other hand, that of the casterwheeled vehicle is zero. For this case, we can use thetarget ICR location determining process defined by Lamet al. [16].

In low speed range, the steering motors do not needto work actively; only with the direct yaw moment inputand passive caster wheels, the vehicle movement can bemanaged satisfactorily. Fig. 17 shows the experimentalresult of the vehicle yaw rate responses to the direct yaw

Fig. 16. Possible location of ICR, colored blue. Caster wheeled vehicle(upper) and conventional one (lower). Vehicle with normal steering hasusually 5 meters of turning radius, while with caster wheels it is zero.

Fig. 17. Yaw rate responses to the direct yaw moment input versus theconventional steering maneuver at 90 degrees cornering. Vehicle speedis 2m/s in all cases. The steering angle is 30 degrees at inner wheel forthe conventional steering case. Direct yaw moment is given by wheelspeed controller.

moment input versus the conventional steering maneuverat 90 degrees cornering. For the conventional steeringcase, the steering angle was given at 30 degrees which isusually the maximum for passenger vehicles. It is shownthat the yaw rate can go over the maximum rate of theconventional one, by applying direct yaw moment to thedriving wheels.

B. High Speed Range Control

At high speed, tires produce lateral forces in ac-cordance with the tire slip angle. These lateral forcesare crucial because they provide the vehicle with thecentripetal force during cornering. Thus, in passenger ve-hicle applications, the steering motors should be activelycontrolled for safety and stability reasons.

Since CIMEV is equipped with two independent steer-ing motors, it is possible to control the lateral forcevectors by controlling the steering angle of each steeringwheel. If we put:

Td =Csa

(Vy + l f γVx ± d

2 γ−δ

)+ eCF

(Vy + l f γVx ± d

2 γ−δ

)(20)

Fig. 18. Lateral forces calculated by using disturbance observer versusthe one calculated by using lateral acceleration sensor during a steadystate circle running. Vehicle speed was 4m/s, and the steering angle was15 degrees at inner wheel.

Fig. 19. Controller configuration

where, Td is the disturbance torque, the lateral force

CF

(Vy + l f γVx ± d

2 γ−δ

)(21)

can be instantaneously calculated (Csa, CF are knownvalues.) by using a disturbance observer [17], and more-over, by controlling the steering angles independently, thevehicle is allowed ‘the controlled lateral forces,’ whichhave never been controlled in the conventional steeringsystems. Fig. 18 shows the lateral forces which werecalculated by using disturbance observer and accelerationsensor. Since it is a steady state circle running, i.e. γ = 0and Mz = 0, equations (11) and (12) become:

0 = l fYFL + l fYFR −2lrYR (22)may = YFL +YFR +2YR (23)

Using these equations, disturbance torques were con-verted into lateral forces (red and blue dashed lines inFig. 18), and the lateral acceleration was converted intothe ‘necessary’ net lateral force to make the turn (blacksolid line in Fig. 18). Experimental result shows that thelateral force estimation by using disturbance observer hasreliable accuracy as compared with the calculation usingacceleration sensor. The controller configuration is shownin Fig. 19.

V. CONCLUSION AND FUTURE WORKS

In this paper, a novel steer-by-wire system is proposedusing caster wheels and independent driving motors. An

actual experimental vehicle is introduced, and its sys-tem configuration is shown. The mathematical model isdiscussed with simulations, and the system stability isanalyzed. The open loop system turned out to be unstable.However it is shown that, with feedback controller andadditional actuators, the system can be more powerfulthan the conventional one. Feasibility of the system isshown with experiment results in the low and high speedranges.

By using various control strategies including cost func-tion minimization, it is possible to contorl the vehicle mo-tion in a certain desired fashion such as: yaw stabilizingcontrol, energy saving control [18], and etc.. Utilizing thehigh degrees of freedom of CIMEV, many possible controlapplications will be examined.

VI. ACKNOWLEDGMENT

The authors would like to thank Dr. Sehoon Oh, Mr.Toshiyuki Uchida, and other research group members fortheir sincere academic and technical supports. Also theywould like to send sincere condolences to the victims ofthe earthquake and the tsunami, and believe that Japanwill recover soon from the tragic disaster vibrantly.

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