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A Novel Chassis Structure for Advanced EV Motion ControlUsing Caster Wheels with Disturbance Observer and
Independent Driving Motors
Yunha Kima, Kanghyun Nama, Hiroshi Fujimotob, and Yoichi Horib
aDepartment of Electrical Engineering, The University of Tokyo,3-7-1 Hongo, Bunkyo-ku, Tokyo, Japan
bDepartment of Advanced Energy, The University of Tokyo,5-1-5 Kashiwanoha, Kashiwa-shi, Chiba, Japan
Abstract—This paper presents a novel chassis structurefor advanced EV motion control, using caster wheels withdisturbance observers, and independent driving motors. Thesystem consists of two independent driving wheels andtwo caster wheels. The proposed configuration enables thevehicle to have: a low mechanical stiffness against the directyaw moment input because caster wheels are free to rotate;and high static stability because of the four wheels having alarge base geometry. In addition, by introducing disturbanceobservers, the vehicle was given enhanced mobility andsafety characteristics. Many advantages, which include zero-radius turning, understeer gradient control, load transferestimation, of the proposed system are shown and discussedwith experimental results throughout the paper.
Keywords—Caster Wheels, Electric Vehicle, IndependentDriving Motors, Motion Control
I. INTRODUCTION
Utilizing the advantages of using electric motor [1],many motion control strategies for Electric Vehicles(EVs), such as anti-slip traction control, and roll andyaw stability control, are introduced [2][3]. These con-trol methods turned out to be reasonably effective thatEVs can run more safely than the ICEVs in poor roadconditions. In addition to these properties, vehicle elec-trification enables EVs to excel the conventional ICEVsin terms of vehicle motion, by assigning EVs two kindsof inputs - the steering and the direct yaw moment -while the conventional vehicles have only one input -the steering. However, most of these research works arebased on the four-wheeled vehicle chassis structure withthe conventional mechanical steering system, which hasnot been changed from the beginning of the massiveproduction of the Ford Model T in 1908. It is originallydesigned and optimized for an internal combustion engineto transmit all power to the four driving wheels. Con-sequently it is clear that to use the conventional chassisstructure for the independent motor driven EVs is a wasteof ability, which is the motivation for this paper. Thiswork is on the study and proposal of a novel structure ofEVs for advanced motion control. Despite the underlyingimportance, however, it seems that there has been no
attempt to provide an appropriate and unique structure forthe independent motor driven EVs. In this work a novelchassis structure using caster wheels and independentdriving motors is proposed. Provided with four wheels thesystem is designed to be statically stable, and with casterwheels on the front axle the proposed system is able touse the two kinds inputs - the steering and the direct yawmoment - effectively for two-dimensional motion control.
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. 2. More details about theexperimental vehicle are shown in [4].
B. Mathematical Modeling
As the experimental vehicle having been provided withtwo steering motors, equations can be written as below,considering the torque inputs of the steering motors, andregarding that the liaison moments and the equivalentforces are given by the motors:
IwδL + eC f δL = eC f β +el fC f
Vγ +TmL (1)
IwδR + eC f δR = eC f β +el fC f
Vγ +TmR (2)
Izγ =l f
e(TmL +TmR)−2lrCr(β −
lrV
γ)+Mz (3)
mV (β + γ) =1e(TmL +TmR)+2Cr(β −
lrV
γ) (4)
whereδL: the steering angle of the left wheel;
Fig. 1. 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. 2. 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.
δR: the steering angle of the right wheel;TmL: the torque output of the left steering motor; andTmR: the torque output of the right steering motor.
III. CONTROLLER STRATEGIES ANDADVANTAGES OF CIMEV
The global control scheme for CIMEV is shown inFig. 3. The upper-level controller computes the direct yawmoment reference and the lateral force reference in theform of the steering angles in order to meet the speed andyaw rate requirements. The lower-level controllers whichare the driving controller and the steering controller,assign the motor torques to give the vehicle speed, yawrate, and the steering angles.
Using properly designed controllers, some experimentsare done to show the advantages of the proposed system.In this section, the experiment results are introduced, andthe corresponding advantages of the system are discussed.
Fig. 3. Block diagram of the global control scheme for CIMEV.
Fig. 4. Yaw rate responses to the direct yaw moment input versus theconventional steering maneuver at 90 degrees cornering. Vehicle speedis 1m/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.
A. High Mobility at Low Speed
Fig. 4 shows the experimental result of the vehicle yawrate responses to the direct yaw moment input versus theconventional steering maneuver at 90 degrees cornering ata low speed of 1m/s. For the conventional steering case,the steering angle was given by Ackermann geometry at30 degrees which is usually the maximum for passengervehicles.
It is shown that the yaw rate can go over the maximumrate of the conventional one at a given speed, by applyingdirect yaw moment to the driving wheels without causingany energy loss from cornering resistance, which corre-sponds the observation results from the system analyses.This property enables CIMEV to make a more sharpturn than a conventionally steered vehicle does, so thatCIMEV can move more freely in restricted spaces. Thisexperiment result also can be associated with the ICRlocation shown in Fig. 5. Usually a normal passengervehicle has the minimum turning radius of 5 meters,meanwhile CIMEV can turn with zero radius.
At low speed, the advantage of using caster wheels isobvious: as the way they are defined, they freely rotateand so does the vehicle. Vehicles with the normal steeringsystem, need to run in order to make turns. CIMEV, on
Fig. 5. Possible location of ICR (Instant Center of Rotation), coloredblue. CIMEV (upper) and conventional one (lower). Vehicle with normalsteering has usually 5 meters of minimum turning radius, while CIMEVhas zero at zero vehicle speed.
the other hand, can make turns at speed of zero. Thisproperty is advantageous not only for the passenger EVapplications, but also for the vehicles or the mobile robotswhich work in restricted spaces.
Note that, as it can be seen in Fig. 4, the yaw ratetends to have higher response over the given referencevalue when the vehicle is moment steered. This can beexplained by the fact that the inertia to be controlled ismuch larger in the direct yaw moment steer case than theopponent.
B. Making Use of Lateral Force Observer
Since CIMEV is equipped with two independent steer-ing motors, it is possible to apply disturbance observers[5] in the control logic of each wheel. From equations (1)and (2), if we define the disturbance torques for the leftand right as:
TdL = eC f β +el fC f
Vγ− eC f δL = eC f αL ' eYL (5)
TdR = eC f β +el fC f
Vγ− eC f δL = eC f αR ' eYR (6)
the lateral force can be simply calculated by dividingthe caster length e without using any special sensorsto measure it, and moreover, by controlling the steeringangles, the vehicle is allowed to have the controlled lateralforces, which gives a lot of implications to vehicle motioncontrol field.
1) Lateral Force Observer Verification: Fig. 6 com-pares the lateral forces between the one calculated byusing disturbance observers and by using acceleration sen-sor. Since it is a steady state circle running condition (i.e.γ = 0 and Mz = 0), disturbance torques were convertedinto lateral forces (red and blue dashed lines), and thelateral acceleration was converted into the necessary netlateral force to make the turn (black solid line). Exper-imental result shows that the lateral force estimation byusing disturbance observer has reliable accuracy althoughit has some offset, as compared with the calculation using
Fig. 6. Lateral forces calculated by using disturbance observer versusthe one calculated by using lateral acceleration sensor during a steadystate circle running. Vehicle speed was 2m/s, and the steering angle was15 degrees at inner wheel.
acceleration sensor. For better accuracy of the estimationmethod, the offset and its implications need to be furtherinvestigated.
2) Discussion on Load Transfer: As seen in Fig. 6,the outer wheel has larger value in the estimated lateralforce than the inner one. In this thesis, it is assumed thatthe cornering stiffness C f has a fixed value, however, inreality the value changes due to the dynamic change invertical load. It is found, from the experimental resultand from the definition of C f in [6], that the ratio of thevertical load is around 0.63 between the inner and outerwheels.
On the other hand, from the experiment condition, andthe vehicle geometry and parameters, for a given lateralacceleration, the vertical load of the front wheels can beroughly calculated as:
NzFL = 39.2+3.6ay (7)NzFR = 39.2−3.6ay (8)
where, ay of this experiment was 1.87m/s2, thus the ratioNzFL/NzFR should be around 0.69, which is fairly closeto the value from the experiment result. This observa-tion implies that, by using the lateral force observer,the dynamic load transfer of a running vehicle can becalculated without attaching any special sensors such asa potentiometer. More investigation needs to be done forbetter accuracy.
3) Understeer Gradient Control: Furthermore, it isalso possible at a high vehicle speed to change the under-steer characteristics by using the lateral force feedbackcontrol. Let us call it the understeer gradient control.The understeer gradient Kus is one of the major vehicledynamic characteristics during cornering.
CIMEV inherently is a severely understeered vehicledue to the free rotation of the casters, however, by usingthis control it becomes close to a neutral steered one. Theundersteer gradient controller makes α f smaller by givingthe positive feedback of the estimated lateral force Y to
Fig. 7. Understeer gradient controller.
Fig. 8. Understeer gradient control: Change in slope (understeergradient Kus).
the direct yaw moment Mz, and thus it virtually makes thecornering stiffness C f larger: refer to [6]. ConsequentlyKus can be controlled to go closer to zero. The controlscheme is shown in Fig. 7, and the experimental resultsare shown in Fig. 8 and 9. The vehicle ran on a circleand was accelerated from 0 to 4 m/s.
Usually a passenger vehicle is an understeered one,and has a peak in yaw rate gain at a certain vehicle speed– the characteristic speed Vchar, like the red dotted casein Fig. 8 and 9, so the radius of cornering gets biggeras the vehicle accelerates. On the other hand, the neutralsteered vehicle can run on a circle of a constant radiusregardless of its speed, which gives the driver a natural(linear) feeling during cornering. By using the understeergradient control, the cornering characteristics of CIMEVcan be tuned to the driver’s favor, i.e. the value can becontrolled by changing the gain Clat as shown in Fig. 8.
4) Bank Angle Estimation: Another advantage of us-ing the lateral force observer is the estimation of the roadbank angle on which the vehicle is running. It is basedon a simple kinematic relation between the gravitationalforce and the lateral force of the front wheels as shown inFig. 10 without using any special sensors. When a vehicleis running straight on a road which has a bank angle ofϕ , from the kinematic relation it is written as:
Y =lrL
mgsinϕ (9)
thus ϕ can be estimated as:
ϕ = sin−1 Y Llrmg
' Y Llrmg
(10)
Fig. 9. Understeer gradient control: Vehicle trajectory during anaccelerating circle run.
Fig. 10. Kinematic Relations of Bank Angle Estimation.
Fig. 11. Bank where the experiment was carried out. The bank angleis 10.5 degrees.
Fig. 12. Lateral acceleration signal from the acceleration sensor andthe lateral force observer. Vehicle is released at t = 2, and the vehiclespeed increases upto 2m/s.
It can be seen in the Fig. 12 that the two lateralacceleration signals agree well, and the estimated and
measured values are acceptable. The bank angle of theroad is 10.5 degrees, which assigns 1.79m/s2 of lateralacceleration due to gravity. The vehicle was released att = 2 by hand, and the vehicle speed increases upto 2m/s.As the vehicle starts to run, the lateral force observerworks properly.
It is a simple and cost effective method, howeverin order to apply this method in a passenger vehicleapplication, decoupling the effects of the bank angleand the lateral acceleration during cornering needs to beinvestigated.
IV. CONCLUSION
In this paper, a novel chassis structure for electric vehi-cles is proposed using caster wheels and independent driv-ing motors. An actual experimental vehicle is introduced,and its system configuration is shown. Feasibility andthe advantages of the system is shown with experimentresults. At low speed, CIMEV shows high mobility. It isapplicable in various fields such as passenger EVs, mobilerobots, military and space rovers which work in limitedspaces. Additionally, utilizing lateral force observer, thelateral force during cornering can be estimated and pos-sibly controlled. By doing this it is possible to reduceenergy loss from the cornering resistance, or to controlthe characteristics of the vehicle such as the understeergradient.
V. ACKNOWLEDGMENT
The authors wish to acknowledge the assistance andsupport of the preparing group for the student sessions ofthe SNU-UT Joint Seminar 2011.
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