High Stability Lateral Guided Method forArticulated Vehicle Based on Sensor

Steering MechanismYoshihiro Takita, Shinya Ohkawa and Hisashi Date

Abstract - This paper proposes SSM (Sensor SteeringMechanism) for a lateral guided vehicle with an articulatedbody. Authors demonstrated the simple lateral guiding method

SSM for the front wheel steer type, the reverse phase four-wheelsteer type and the rear wheel steer type vehicle. SSM presents thestable lateral guiding performance for automated vehicle whichfollows a straight and curved path created by guideway. Theother hand, SSM is not established for articulated vehicles suchas wheel loaders and dump trucks used in the mine andconstruction site. This paper leads SSM for an articulated vehiclewith arbitrary position of articulation joint and develops anexperimental robotic vehicle with proposed SSM. Simulated andexperimental data show the advantages of proposed SSM.

Keywords - Mobile robot, SSM, Articulated vehicle, Linefollowing, Dynamics

I. INTRODUCTION

AGVs (Automated Guided Vehicle) are used in variousfields for the labor cost saving. The problem is the movingstability of the vehicle in the lateral direction resulting fromdynamical characteristics by the sensor position and controllingmechanism. The lateral stability of lateral guided vehicles areinvestigated by Abe[1], Minami[2], Makino[3], Shladover [4]and Tsunashima [5]. A practical speed limit of the AGV used inmanufacturing factory is far lower than the drift speed of the tire.The DMT (Dual Mode Truck) has a lateral instability because ofthe geometry of guiding mechanism. In 2005 through 2007, theDARPA (Defense Advanced Research Projects Agency)[6] heldthe grand challenge which spurred many robotics researchers todevelop the autonomous vehicle.

This paper is focusing on industrial vehicles which are usein the construction field, an open mine, etc. In 2008 KomatsuLtd. starts to operate an unmanned large-scale and steering-typedump truck system at the mine in Chile. This is an automateddriving system by using the high accurate GPS, GYROs andMillimeter wave scanners. It will be necessary to automate theloading work in the near future. The lateral guiding system forthe articulated vehicle such as a wheel loaders are investigated byAtafini[7], Bigras[8], Ridley[9], Marshall[10] and Ishimoto[11].

Yoshihiro Takita, Department of Computer Science, National DefenseAcademy, Japan(e-mail: takita@nda.ac.jp)

Shinya Ohkawa, Department of Computer Science, National DefenseAcademy, Japan (e-mail: em50045@nda.ac.jp)

Hisashi Date, Department of Computer Science, National DefenseAcademy, Japan (e-mail: date@nda.ac.jp)

The automated loading is demonstrated by Koyachi[12].Their group calculated the articulation angle under thecondition without slipping. It is need to take into account theside slip of tires when the moving speed is increased. Toimprove the work efficiency for the automated wheel loaderthe stable and simple lateral guiding method for the articulatedvehicle is needed.

Authors proposed and demonstrated SSM (SensorSteering Mechanism) for the front wheel vehicle[13], the four-wheel steering vehicle with reverse phase mechanism[14-17]and the rear wheel steering vehicle[18]. When the vehicle isguided by SSM, no speed limit exists on the straight linetravel, except with respect to the over steer characteristics[13].Experimental results obtained using the developed roboticvehicle revealed that the SSM follows the guideway whileadjusting the centrifugal force and the side force of the tireswhen traveling around corners. For the accurate simulation ofvehicle moving at high speed, the authors proposed thevariable kinetic friction model of the tire and applied it to thederived dynamical equations. The existence of the sensor armprevents the application of SSM to the vehicle operating onordinary road. The senser arm was replaced with aminiaturized 1kHz intelligent camera from 2005. The lastpaper pays attention to the lateral guide of a wheel loader ofwhich articulation joint is located at the center, because SSM isnot applied yet. For the first time application of the articulatedvehicle authors are derived SSM for center articulated typevehicle and developed experimantal setup. Experimental andsimulation results of high-speed moving are presented anddemonstrated the performance of proposed method.

This paper extends the SSM method to the arbitraryposition of articulation joint and develops a 1/25 scaledarticulated dump truck controlled by SSM. Experimental andsimulation results shows the stable high-speed moving and theperformance of proposed method.

II. SSM AND DYNAMICAL MODEL

A. Sensor Steering Mechanism(SSM)SSM for the articulated vehicle is divided into a rear wheel

and a front wheel basis. For the rear wheel basis, the center ofrear axis is moving over the guideway. The front wheel basisis the center of front axis is staying on the guideway. Theserelation is able to use for forward and backward moving of thevehicle. Figure 1 and 2 show schematic of SSM for articulatedvehicle with the rear wheel and front wheel basis, respectively.For the convenient these figures are used bicycle model.

Proceedings of the World Congress on Engineering and Computer Science 2012 Vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

ISBN: 978-988-19251-6-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2012

A.1 The rear wheel basis SSM:In Fig. 1, a point P and Q is placed at the center of front and

rear wheels, respectively. Ea is a articulation joint of body. Sf isa sensor or guide roller which is located at a top of sensor arm L 'form the center of the front axle, follows smoothly by theguideway of R in radius, and the angle of the sensor arm and thefront body is assumed to be φ. The length of front and rear bodyform Ea are Lf and Lr, respectively. Ea is an intersection of theextension of front body. A relation between ε and φ is as follows:

Lf sin φ = Lr sin ε . (1)A linearized equation at the equilibrium point is obtained asfollows:

δ = Lf +LrLr

φ . (2)

And the sensor arm length PSf is

PSf = L′ = Lf cos φ + Lrcos ε ≈ Lf + Lr = L. (3)This method is applied to a case that an articulation joint islocated in the front half. In this case the articulation angle δ is

assumed to be the virtual steering angle of front wheel vehicle,then the angle of sensor arm P'Sf is 2δ . The stability analysis ofthe front steer type SSM is described in the previous paper, so

this paper leaves out to explain precisely.

A.2 The rear wheel basis SSM Figure 2 shows the rear wheel basis SSM when the front

center axle is moving on the guideway. This method is used forthe backward moving to of the articulated vehicle. In Fig.2, apoint P and Q are a front and rear center of axle, respectively. Eais a articulation joint of body. Sr is a top of sensor arm PSr. Q' isa virtual rear wheel and an intersection of extended line PEa andturning center O to Q. P' is an intersection of extended line PEaand OSr. A relation between a arm angle γ and articulation angleδ is

δ = 2γ . (4)This result is able to use for an arbitrary position of articulationjoint. In this case the sensor arm length has to be change by theturning radius. Then the linear approximation is applied thisrelation if the articulation angle is a range of small:

QSr = 2 R sin δ2

≈ R δ , (5)

PQ ' = R tan δ = Lf

cos δ + Lr ≈ Lf + Lr ≈ R δ

. (6)Finally, the sensor length is able to use the same length as wheelbase. When the articulation angle is located at Q' this system isas same as the rear steering vehicle. The stability analysis ofstraight line moving of the rear steering vehicle controlled bySSM is shown by the author. In this case this paper leaves out toexplain the stability problem.

B. Dynamical Equation of MotionFigure 3 shows the rigid body bicycle vehicle model moving

at V . It is assumed that the right and left tires have samecharacteristics. In figure 3, N is the Newton reference frame.Dextral sets of mutually perpendicular unit vectors n1 and n2 arefixed in N . The reference frame A is fixed on the vehicle,

R

δ

δ

rear

front

Q

P

O

sensorS f

δ

E f

E a

L fL r

δ

L'

δ

P' φ

ε

guideway

L'

Fig. 1 Rear wheel basis SSM for articulated vehicle

R

δ

δ

rear

front

Q

P

O

sensor

E a

L r δ

L f

Q'

δ

S r

γ

P'

guideway

R*

S * r

Q*

L*

L*δ

δ

δ

γ

Fig. 2 Front wheel basis SSM for articulated vehicle

A*

β

β

2U

2U

dy

dt

ddt

(x

,y )

θ

r

a Aa

dydt n

b dxdt

n

ndt

a

F

V

V

D

D

dxdt

n 1

2

r

l ff

l rl rr

l rf

θ b

B*

l frl f

1

-l rr b

2a

l ffa

f

f F f a

b

b b

a

bδ a

δ r

2 1

b

B b2

1

n

Nn

2

1

cd

(x ,y

)

aa

k d

τ c

τ c

f

f

r

r

2

1

θ

dθ

(x, y)

r

Fig. 3 Schematic model of articulated vehicle

and the mutually perpendicular unit vectors a1 and a2 are fixed inA. Here, θ is the body position angle, g is the yaw angle, δf andδr are the steering angles of the front and rear tires, respectively,βf and βr are the slip angles of the front and rear tires,respectively, γf and γr are the angles between n1 and the velocityvector of the front and rear axles, respectively. In addition, Ufand Ur are the cornering forces of the front and rear tires,respectively, lf and lr are the distances from the center of gravityto the front and rear axles, respectively, m is the mass, and I isthe moment of inertia about the yaw-axis of the vehicle. Finally,Ff and Fr are the driving forces, and Df and Dr are the rollingresistance forces of the front and rear tires which are acting in theopposite direction of velocity vector V f and Vr , respectively.

Proceedings of the World Congress on Engineering and Computer Science 2012 Vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

ISBN: 978-988-19251-6-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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When the displacement vector is used as follows:

X= x y θa θb T. (7)

The dynamical equation of motions are derived as follows:

MX+CX+D(X) = F (8)

M=

M11 0 M13 M14 0 M11 M23 M24 M13 M23 M33 M34 M14 M24 M34 M44 ,

C=

C11 0 C13 C14 0 C11 C23 C24 C13 C23 C33 C34 C14 C24 C34 C44 ,

D(X) = [D1 D2 D3 D4]T,

F= F1 F2 F3 F4T.

Where

M11= -ma-mb , M13= - (lf mb+lff ma) sin θ a,

M14= - lrf mb sin θ b, M23= - (lf mb+lff ma) cos θ a,

M24= lrf mb cos q b, M33= - Ia - lrf2ma - lf2mb,

M34= - lf lrf mb cos δ a, M44= - Ib - lrf 2mb,

C11= Df/ x 2+y 2 +Dr/E , C13= Dr lf sin θ a/E ,

C14= Dr lr sin θ b/E , C23= - Dr lf cos θ a/E ,

C24= - Dr lr cos θ b/E , C33= Dr lf2/E ,

C34= Dr lf lr cos δ a/E , C44= Dr lr 2/E ,

D1= (lf mb - lff ma)θ a2cos θ a - lrf mbθ b

2 cos θ b

D2= (lf mb - lff ma)θ a2 sin θ a - lrf mbθ b

2sin θ b

D3= - lf lrf mbθ b2 sin δ a, D4= lf lrf mbθ a

2 sin δ a,

F1= 2Uf sin θ a + 2Ur sin θ b - Ff cos θ a- Fr cos θ b,

F2= - 2Uf cos θ a - 2Ur cos θ b - Ff sin θ a- Fr sin θ b,

F3= 2Ur lf cos δ a - Fr lf sin δb + τ c ,

F4= 2Ur lr -τ c and

E=x 2+y 2+lf 2θ a

2+lr2θb

2+ 2lf xθ a sinθ a+ 2lrxθ b sinθ b

+ 2lf lr θ aθ b cos δ a - 2lf yθ a cos θ a - 2lryθ b cosθ b .(9)

The control torque of PD controller is as follows:

τc= -(δ a -δ r)kd - δ acd . (10)In this case, the cornering forces are regarded as a linear functionof the slip angle and are written as follows:

Uf = - 2Kf βf , Ur = - 2Kr βr (11)where Kf and Kr are the cornering power of the front and reartires, respectively.

III SIMULATION RUNNING ON THE COURSE

A. Tire characteristicsIn the previous paper, the relationship between the lateral

force and the slip angle were measured using a test equipment.These data are also used in the present paper. The lateral forcesgenerated by the tire are measured when the contact forces are setat 3.63N and 4.12N. These data are approximated to the fourthpolynomial by using the least squares method as follows:

U1 static(β) = -2.146 × 10-5β 4

+ 1.824 × 10-3β 3

-5.923 × 10-2β 2 + 0.958 β + 8.391 × 10-2

, (12)

U2 static(β) = -2.542 × 10-5β 4

+ 2.183 × 10-3β 3

-7.066 × 10-2β 2 + 1.118 β + 5.146 × 10-2

. (13)Equation (12) is equivalent to equation (13) multiplied by thecontact force ratio 4.12/3.63. In this case the cornering force isproportionate to the contact force of the tires. For the simulationtwice the cornering force is applied to the body because the frontand rear axles have two tires.

B. Simulation conditionsThe course, which consists of two semicircles of radius

0.5m connected by straight segments of 0.7m in length, wasused to analyze the turning motion, including drifting, of alaterally guided vehicle by the SSM. The dynamical analysis ofthe vehicle was performed by integrating equations (1) to (3)with the Runge-Kutta method. While the numerical calculation ofdynamical motions the contact point of the guideway and thesensor is determined, and the articulation angle is derived byusing SSM relation which is proposed in this paper and appliedto dynamical equations. In addition, the calculated velocityvectors and the rolling direction angle of the front and rear tireswere used to determine the slip angles and cornering forces.

In order to simulate the drifting maneuver when the vehicleis turning at the corner, the variable kinetic model[15] is used inthe cornering force calculation. And the other remainingsimulation conditions are the same as the previous paper[19].Simulation results of running on the test track are shown with theexperimental results. Table 2 shows friction parameters whichare founded in the simulation.

IV. EXPERIMENT AND SIMULATION

A. Dump truck type articulated robot vehicleBefore the designing of the articulated dump truck, the

articulation position of commercially sealing dump truck areinvestigated. 1:3 is the most popular articulation ratio in a wheelbase. Figure 4 shows an outside view of SSM robotic vehiclewith articulate body which is developed for the experiment.Figure 5 shows outline and dimension of this robot. The wheelbase is 0.21m, the tread is 0.135m, and the gross weight is1.78kg. Three reflective markers are pasted at the front, rear axleand articulation joint, and are measured the positions by 3Dmeasurement system. 1kHz CMOS camera located at the frontaxle follows a 0.02m white line pasted on a black face course.The physical parameters of this vehicle are shown in table 1, andare the same as in simulations.

The rotational angle of CMOS camera and articulation angleare controlled by servo motors through the deceleration gears.Rotational angle of the camera φ is sensed by the rotary encoder,and the target value of PD controller for articulation angle is set at-4/3φ when the rear wheel basis SSM and -2φ when the frontwheel basis SSM. The vehicle body is a double-layered structureby flat aluminum plates and is not combined with suspensionmechanism. The vehicle is equipped with tread-patterned tenderrubber tires, the insides of which were filled with sponge in

Proceedings of the World Congress on Engineering and Computer Science 2012 Vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

ISBN: 978-988-19251-6-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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order to produce soft contact with the load surface. The outsidediameter and width of the tires were 0.059m and 0.023m,respectively. The data of the tire characteristics were measuredand applied to the simulation. The power source is used Ni-MHAAA type 10 cells (12 Volt) and installed inside of the body.

B. Simulation and experimental resultsFigure 6 and 7 show experiment and simulation data

running on the test track when the vehicle is controlled by therear wheel basis SSM moving at 2.5m/s. In each figure, (a) isthe trajectories of front, middle and rear point, (b) is the velocity,(c) is the articulation angle, and (d) is the slip angle. And alsoFig. 8 and 9 show data when the vehicle controlled by the frontwheel basis SSM.

These figures show that the proposed SSMs for articulatedvehicle are achieved the lateral guide at high-speed moving. InFig. 6(a) and 7(a) the front and rear axle is passing away fromthe guideway. The other hand Fig. 8(a) and 9(a) show that thefront tires are passing near the guideway and the drift of rear tiresis reduced. The big difference between the rear and front wheelbasis SSM is the minimum speed at the corner. The minimumspeed is over the 2m/s in Fig. 8(b) and 9(b), and is lower the2m/s in Fig. 6(b) and 7(b). Each slip angle data showsdifferences between SSMs. The slip angle of front wheel basisSSM is smaller than the rear wheel basis SSM. A slow-speedmoving is not shown here, but the trajectory of rear tires by thefront wheel basis SSM pass inside of the track. As a resultssimulated and experimental results are well coincide with eachother. In these stimulations the control delay of PD-controller forthe articulation angle is set at 15ms of which value is measuredby the experiment.

V. CONCLUSIONS

This paper proposed SSMs which are a lateral guidedmethod for a vehicle with articulated body. The idea of SSM arethat the sensor is located at the tip of the sensor arm of whichlength is the same as the wheel base of vehicle, and anarticulation angle is decided by SSMs relation. In this paper aSSM robotic vehicle is developed and the dynamical model ofarticulated vehicle is derived and calculated. The experimentaland simulation results are shown that SSMs achieve the steadystate tracking even if the drift condition is occurred at the corner.These results are well correspond with each other. Finally,advantages of SSM are that the system is a simple and the stablebehavior is obtained. And SSMs are available for not only thefront steering vehicle, reverse phase four-wheel steering and rearsteering vehicle but also the articulated vehicle.

References

[1] Abe, M., Vehicle Dynamics and Control, pp.192-213. kyoritsuPublication(in Japanese), 1979.

[2] Minami, M., et al., Magnetic Autonomous Guidance by IntelligentCompensation System, Vol.31, No.5, pp.382-391, 1987.

[3] Makino, T., et al., High-Speed Driving Control of an Automatic GuidedVehicle Using an Image Sensor, Transactions of the Society ofInstrument and Control Engineers, Vol.28, No.5, pp.595-603, 1992.

Fig. 4 Outside view of developed SSM robot vehicle

φ

Lamp

���

motor 3

�����

motor 1

battery

motor 2

������

���������������

1kHz smart camera

Observed point

control system

diff

eren

tial g

ear

�������

L = 0.21L = 0.21

�����

���

battery

L 3f L f

φ 43

: rear wheel basis

φ 2 : front wheel basis

--

Fig. 5 Outline of constructed rear wheel steer vehicle

Table 1 Parameter of robotic vehicle

ma 0.777 kg mb 0.999 kg

Ia 0.0007 kgm2 Ib 0.0041 kgm2

lf 0.0525 m lr 0.1575 m

lf f 0.02625 m lrr 0.07875 m

L 0.210 m m 1.776 kg

Wf 9.97 N Wr 7.38 N

kd 40.0 Nm/rad cd 0.8 Nm s/rad

Kf 1.269 N/deg Kr 1.012 N/deg

Table 2 Estimated friction parameter

case 1

μf 1

μk 0

Td -

case 2

drift slip

0.0135 0.414

0.009 0.46

0.0025 sec -

[4] Shladover, S.E., et al., Steering Controller Design For AutomatedGuideway Transit Vehicles, Transactions of the American Society ofMechanical Engineers, Vol. 100, pp.1-8, 1978.

[5] Tsunashima, H., A Simulation Study on Performance of Lateral

Proceedings of the World Congress on Engineering and Computer Science 2012 Vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

ISBN: 978-988-19251-6-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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guideway

joint

(a) loci

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2.4

2.6

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ocity

(m

/s)

Time (s)

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joint

(b) velocity

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Art

icul

atio

n an

gle

(deg

)

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target

controlled angle

(c) articulation angle

-20

-15

-10

-5

0

5

0 0.5 1 1.5 2 2.5 3 3.5

Slip

ang

le (

deg)

Time (s)

rear

front

(d) slip angle

Fig. 6 Simulated data by rear wheel basis SSM at high-speed

Guidance System for Dual Mode Truck, Transactions of the JapanSociety of Mechanical Engineers C, Vol.65, No.634, pp.2279-2286,1999.

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(a) loci

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2.4

2.6

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/s)

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101520253035

0 0.5 1 1.5 2 2.5 3 3.5

Art

icul

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gle

(deg

)

Time (s)

target

controlled angle

(c) articulation angle

-20

-15

-10

-5

0

5

0 0.5 1 1.5 2 2.5 3 3.5

Slip

ang

le (

deg)

Time (s)

rear

front

(d) slip angle

Fig. 7 Experimental data by rear wheel basis SSM at high-speed

mining Vehicle, Proceedings of the 2001 Australian Conference onRobotics and Automation, pp. 26-31, 2001.

[10]Marshall, J., Barfoot, T. and Larsson, J., Autonomous UndergroundTramming for Center-Articulated Vehicles, Journal of Field Robotics,Vol. 25, No. 6-7, pp. 400-421, 2008.

[11]Ishimoto, H., Tsubouchi, T., Sarata, S. and Yuta, S., A PracticalTrajectory Following of an Articulated Steering Type Vehicle,International Conference on Field and Service Robotics, pp.412-419,1997.

[12]Koyachi, N. Sarata, S. and Sugawara, K., Scoop and Loading Execution

by the Autonomous Wheel Loader "Yamazumi-4" -Task Control andPath Following Control -, Journal of the Robotics Society of Japan,Vol. 26, No. 6, pp.514-521, 2008.

[13]Takita, Y., High-speed Driving of a Lateral Guided Vehicle with Sensor

Proceedings of the World Congress on Engineering and Computer Science 2012 Vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

ISBN: 978-988-19251-6-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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0

5

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ang

le (

deg)

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front

(d) slip angle

Fig. 8 Simulated data by front wheel basis SSM at high-speed

Steering Mechanism, Transactions of the Japan Society of MechanicalEngineers C, Vol.65, No.630, pp.622-629, 1999.

[14]Takita, Y., et al., High-speed Cornering of Lateral Guided Vehicle withSensor Steering Mechanism, Transactions of the Japan Society ofMechanical Engineers C, Vol.66, No.652, pp.3888-3896, 2000.

[15]Takita, Y., Drift Turning of Lateral Guided Vehicle with Sensor SteeringMechanism(Application of a Variable Kinetic Friction Model),Transactions of the Japan Society of Mechanical Engineers C, Vol.68,No.675, pp.3170-3177, 2002.

[16]Takita, Y., Mukouzaka, N. and Date, H., Control of Lateral GuidedVehicle with Sensor Steering Mechanism Using Miniaturized 1kHzSmart Camera(Stabilization by Dynamic Damper), Transactions of theJapan Society of Mechanical Engineers C, Vol.71, No.701, pp.193-199,2005.

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-5

0

5

0 0.5 1 1.5 2 2.5 3 3.5

Slip

ang

le (

deg)

Time (s)

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front

(d) slip angle

Fig. 9 Experimental data by front wheel basis SSM at high-speed

[17] Takita, Y., Sakai, Y., Takahashi, T., Date, H. and Mukouzaka, N.,Increasing the Speed of a Lateral Guided Vehicle with a Sensor SteeringMechanism Using 1kHz Intelligent Camera (Drift Control by Changingof Steering and Arm Length Ratio), Transactions of the Japan Society ofMechanical Engineers C, Vol.72, No.717, pp.1558-1565, 2006.

[18] Takita, Y. and Date, H., Dynamical Characteristics of Lateral GuidedRobotic Vehicle with a Rear Wheel Steer Mechanism Controlled bySensor Steering Mechanism, Transactions of the Japan Society ofMechanical Engineers, Series C, Vol.75, No.753, pp.1346-1353, 2009

[19] Takita, Y., Kasai, K. and Date, H., Proposition of SSM for Lateral

Guided Vehicle with Articlated Body, Transactions of the Japan Societyof Mechanical Engineers C, Vol. 76, No. 765, pp. 1130-1138, 2010.

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