research article study of model predictive control for...

Research ArticleStudy of Model Predictive Control for Path-FollowingAutonomous Ground Vehicle Control under Crosswind Effect

Fitri Yakub1 Aminudin Abu1 Shamsul Sarip2 and Yasuchika Mori3

1Malaysia Japan International Institute of Technology Universiti Teknologi Malaysia Jalan Semarak 54100 Kuala Lumpur Malaysia2UTM Razak School of Engineering and Advanced Technology Universiti Teknologi Malaysia Jalan Semarak54100 Kuala Lumpur Malaysia3Graduate School of System Design Tokyo Metropolitan University 6-6 Asahigaoka Hino Tokyo 191-0065 Japan

Correspondence should be addressed to Fitri Yakub mfitriklutmmy

Received 4 November 2015 Revised 1 March 2016 Accepted 17 March 2016

Academic Editor Yongji Wang

Copyright copy 2016 Fitri Yakub et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We present a comparative study of model predictive control approaches of two-wheel steering four-wheel steering and a combi-nation of two-wheel steering with direct yaw moment control manoeuvres for path-following control in autonomous car vehicledynamics systems Single-track mode based on a linearized vehicle and tire model is used Based on a given trajectory we drovethe vehicle at low and high forward speeds and on low and high road friction surfaces for a double-lane change scenario in orderto follow the desired trajectory as close as possible while rejecting the effects of wind gusts We compared the controller based onboth simple and complex bicycle models without and with the roll vehicle dynamics for different types of model predictive controlmanoeuvres The simulation result showed that the model predictive control gave a better performance in terms of robustness forboth forward speeds and road surface variation in autonomous path-following control It also demonstrated that model predictivecontrol is useful to maintain vehicle stability along the desired path and has an ability to eliminate the crosswind effect

1 Introduction

Today model predictive control (MPC) is one of the morepopular optimal control techniqueswhich iswidely employedfor the control of constrained linear or nonlinear systemsMPC uses amathematical dynamics processmodel to predictthe future behaviour of the system and optimize the processcontrol performance over a prediction horizon [1] The MPCmodel can be used easily at different levels of the processcontrol structure such as multiple input and multiple outputdynamics systems that offer attractive solutions for regulationand tracking problems while guaranteeing stability [2] Sincethe end of the 1980s robust MPCs which explicitly takeaccount of model uncertainties constraints and faults in thecontrol actuator plant-model mismatch and disturbancesor noise have been studied for more practical applications[3] Numerous research studies have investigated the stabilityproperties of MPC for systems without uncertainty and foruncertain linear systems Several robust predictive formula-tions utilize the minndashmax approach where the manipulated

input trajectory is computed by solving an optimizationproblem that requires minimizing the objective function andsatisfying the input and state constraints over all possible real-izations of the uncertainty These have been applied mainlyto impulse response models and state-space approaches bysolving a finite horizon open-loop control optimization prob-lem [4] Due to its advantagesMPChas been implemented inseveral applications for automotive and other transportationactive safety systems such as active steering active tractionactive braking and active differentials or suspension systemsin order to coordinate and improve vehicle handling stabilityand ride comfort [5ndash8]

A vehicle capable of handling many things at oncewithout any human intervention can be termed as an auto-nomous vehicle Basic functions of autonomous brakingand steering however are insufficient the vehicle has tohave the ability to sense its surrounding plus being able todetermine desired location which can be achieved using avariety of instruments and pieces of equipment such as radarglobal positioning system on-board camera for vision and

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2016 Article ID 6752671 18 pageshttpdxdoiorg10115520166752671

2 Journal of Control Science and Engineering

an independent operating unit All sensory data are thencomputed for obstacle identification avoidance is then exe-cuted using advanced control system In this paper we limitautonomous vehicles to ground vehicles which are increas-ingly being studied by several researchers from academiaindustry and military Several control methods are beingused including fuzzy logic [9] hybrid control [10] H-infinitycontrol [11] and linear quadratic regulators [12] The bestcomparative studies on model predictive control strategiesfor autonomous guidance vehicles can be found in Park et al[13] Yoon et al [14] and Falcone et al [15] where a nonlineardynamics model of a vehicle is used for the controller designof an active front steeringmanoeuvre in a double-lane changescenario Keviczky et al [16] studied the effect of side wind viaan active front steeringmanoeuvre for an autonomous vehicleusing nonlinear MPC Since nonlinear MPC poses consid-erable challenges due to its real-time implementation algo-rithmmany researchers opted for linearMPC for their study

The assumption of this study are as follows vehicle trajec-tory is known as per Borrelli et alrsquos [17] study and the cross-wind effect will be assigned as a step response since thecrosswind effect disturbance on the vehicle can be approx-imated as a constant In this paper we extend the conceptof MPC for application in vehicle manoeuvring problemswhere a trajectory optimization is solved at each time stepThe trajectorywas designed to be a double-lane changing sce-nario The autonomous vehicle manoeuvring was simulatedin a variety of conditions low (10msminus1) and high (30msminus1)forward speed and low (icy) and high (concrete wet) roadfriction surface with the intention of following predeter-mined trajectory as close as possible while maintainingvehicle stability The control inputs were front steering anglerear steering angle and direct yawmoment control while theoutput controls were the yaw angle and lateral vehicle posi-tion Two different controllers were compared to evaluatethe performance of the six-degree-of-freedom (6DoF) vehi-cle model a simple (2DoF) controller without vehicle rolldynamic and a complex (3DoF) bicycle model controllerwith roll dynamics Other performance indexes evaluatedwere efficacy and robustness of the MPC for the autonomousvehicle in terms of control and stability

Themain objective of this paper is to evaluate the robust-ness of model predictive control approaches for autonomouspath-following car dynamics control with simple and com-plex models of the vehicle while rejecting the effects of windgusts to the systemThere are many studies to be consulted instabilization of the vehicle examples are two-wheel steering(2WS) [15 18] four-wheel steering (4WS) [19] and 2WS withdirect yaw moment control (DYC) [5 20 21] with differentcontrol strategies The first contribution of this paper is theeffect of vehicle roll dynamics motion consideration to thesystem whereas most previous papers only focused on a2DoF vehicle model (lateral and yaw motion) Moreoverbased on the authorsrsquo knowledge there is no comparativestudy for autonomous path-following vehicle control usingMPC techniques for three control signalmanoeuvres (includ-ing the three control signals here) the robustness evaluationdiscussed here becomes the main novelty of this paperFurthermore we would like to investigate the effectiveness

of model predictive control manoeuvres in the case of thecrosswind effect to the system in a variety of forward speedsand road adhesions The rest of the paper is organized asfollows Section 2 describes the linear vehicle model lineartire model and wind model Next a linear model predictivecontrol algorithm concept is explained in Section 3 Section 4examines and describes the effectiveness of the linear MPCfor a car dynamics system on a two-lane change scenarioLastly conclusions and future works are given in Section 5

2 Vehicle Model

21 Bicycle Model Figure 1 shows a well-known vehiclemodel which is a single-track model based on the simplifica-tion that the right and leftwheels are lumped in a single wheelat the front and rear axles The simplified vehicle model usedin this paper illustrates the motion movement and dynamicsconcerning the car vehicle subject to the longitudinal lateralyaw roll and rotational dynamics of the front and rear wheelmotion represented as 6DoF The longitudinal lateral andyaw dynamics effects are shown in Figure 1(b) as a top viewof the car vehicle and in Figure 1(a) the roll dynamics effectis explained with the nomenclature for a front view of thevehicle In this paper the nonlinear vehicle was linearizedbased on the assumption that sin 120579 = 0 and cos 120579 = 1 for bothsteering angles the vehicle side slip angle and the roll angleWe also assumed that thewhole vehiclemass is sprung whichis ignoring the suspension and wheel weights for unsprungmass This linearized model still behaves and represents theactual nonlinear vehicle model at certain operating points ofthe regionThe details of themathematical calculation for thevehiclemodel are presented inChen andPeng [22] for furtherknowledge

In this paper we use the following nomenclature 119865119909

and 119865119910

represent the longitudinal and lateral tire forcesrespectively 119865

119911

is the normal tire load 119865119908

and 119872119908

rep-resent the force and moment exerted by the side windrespectively 119909 119910 and 119911 correspond to the coordinates of thebody frame of a car position 119897 is the vehicle wheelbase 119879

119887

isthe wheel torque V

119909

and V119910

are the longitudinal and lateralwheels velocities respectively 120575

119891

and 120575119903

express the steeringangle of the front and rear wheels respectively 119872

119891

and119872119903

represent the reaction yaw moment appearing at the frontand rear wheels respectively119872

119911

is the total reaction of yawmoment of the wheels produced by the DYC 120583 acts as thetrack friction coefficient 120595 is the yawheading angle and isthe yaw rate120573 is the vehicle side slip angle and120601 and are theroll and roll rate angles respectively The variable at the frontand rear wheels is denoted by lower subscripts (sdot)

119891

and (sdot)119903

The motion of longitudinal lateral yaw roll and rota-

tional dynamics of the front and rear wheels using a 6DoFsystem based on a linear vehicle model is described throughthe following differential equations [23]

119898 = 119898 + 2119865119909119891

+ 2119865119909119903

minus 2ℎ119898 (1a)

119898 = minus119898 + 2119865119910119891

+ 2119865119910119903

+ ℎ119898 + 119865119908

(1b)

119868119911119911

= 2119897119891

119865119910119891

minus 2119897119903

119865119910119891

+ 119868119909119911

+ 119872119891

+119872119903

+119872119908

(1c)

Journal of Control Science and Engineering 3

z

h

y

120601

mg

Mw

b120601

Fzl Fzr

k120601

Fw

(a) Front view

x

Fyf

120575fxf

120572f f

Mf

yflf

x120573

FwMw

lr

120575r

Fyr

Mr

Fxr

120595y

(b) Top view

Figure 1 Simplified bicycle model

(119868119909119909

+ 119898ℎ2

) = 119898119892ℎ120601 minus 2119896120601

120601 minus 2119887120601

+ 119898ℎ ( + ) + 119868119909119911

(1d)

119869119887

119908119894

= minus119903119908

119865119909119894

minus 119879119887119894

minus 119887119908

120596119894

119894 = (119891 119903) (1e)

The motion equations for the vehicle in an inertial frame oron 119910-119909 axis under the assumption of a small yaw angle maybe given as

= cos120595 minus sin120595 = V119909

minus 120595

= sin120595 + cos120595 = V119909

120595 +

(2)

22 Tire Model Tire dynamics must be considered for thevehicle model since the tires are the only contact that thevehicle has with the road surface Besides the forces ofgravity and aerodynamics all the forces are induced by thetires which may affect the vehicle chassis handling andstabilityTheir complexity and nonlinear behaviourmust alsoreflect the operating condition of the controller over theirwhole region throughout varied manoeuvring range in long-itudinal lateral and roll directionsThemost frequently usedexisting nonlinear tire models of application and structureare determined through key parameters and analytical con-siderations based on tire measurement data They are calledsemiempirical tire models or Pacejka tire model [24]

On the other hand the nonlinear tire model can alsobe described linearly for some parts of the operating con-ditions therefore in this paper we will consider the linear

Fx

x

Fy

120572

Fz

Tb

Figure 2 Tire model

tire model Figure 2 illustrates the terminology used fordescribing the longitudinal lateral and vertical tire forcesand their orientation Thus the linear tire model is validunder constant normal load forces on the tires constantlongitudinal slip of tires and neglected aerodynamic dragThe relationship between the longitudinal force verticalforce and the longitudinal tire slip ratio is given by thefollowing equations

119865119909

= 120583119909

(119904) 119865119911

(3a)

119904 =119903119908

120596119908

V119909

minus 1 (3b)


119865119911119891

=119897119903

119898119892

2119897

119865119911119903

=119897119891

119898119892

2119897

(3c)

where 119903119908

is the tirersquos geometric radius120596119908

is the angular veloc-ity of the tires V

119909

in (3b) is the tirersquos forward velocity 119865119909

isproportional to the normal force 119865

119911

and 120583119909

(119904) represents thelongitudinal wheel slip friction coefficient of road adhesionsand is a function of slip ratio 119904

The lateral forces on the front and rear tires are char-acterized and modelled by a linear function with the frontand rear tire slip angles 120572

119891

and 120572119903

denoted by 119865119910119891

and119865119910119903

respectively The linear tire model yields the followingexpression for the front and rear tire forces

119865119910119891

= 119862119891

120572119891

119865119910119903

= 119862119903

120572119903

(4)

where 119862119891

and 119862119903

are the tire cornering stiffness parametersfor the front and rear tires respectively The slip angles forthe front and rear wheels with a small angle assumption aregiven such that

120572119891

=V119910

+ 119897119891

V119909

minus 120575119891

120572119903

=V119910

minus 119897119903

V119909

minus 120575119903

(5)

The details of mathematical equations for a linear tire modelcan be read through in [25] Assumptions and approxi-mations presented in this paper are representative of thenonlinear tire model at certain regional points this providesa good balance between capturing the important features andregions of laterally unstable behaviour [26]

23 Wind Model The effect of wind on the stability of thevehicle is an important and primary safety consideration ofthis paper A strong gust of wind from the inward or outwardside will generate force and torque that could be large enoughfor a vehicle to roll over or go outside of the laneThe resultingwind pressure forces and torques acting on the rigid body ingeneral can be represented by three axes longitudinal lateraland vertical A general expression of force and torque is givenby the following equations

119865119908

=119862119865

120588119860V2119903

2

119872119908

=119862119872

120588119860119871V2119903

2

(6)

In the above equations 119860 is the vehicle area 119871 is the vehiclelength 119871 = 119897

119891

+ 119897119903

120588 is the density of air V119903

is the relativewind speed and 119862

119865

and 119862119872

are the force and momentnondimensional coefficients respectively The wind speedor crosswind is represented by V

119908

as shown in Figure 3 In

w

r

x

120595

Figure 3 Vehicle wind speed in crosswind situation

general crosswind can be at various angles but for simplicityin this paper we will assume the crosswind to be at a 90-degree angle andwill focus on the windrsquos impact on the lateralforces and yaw torques [27]

The vehicle motion in ((1a) (1b) (1c) (1d) (1e))ndash(6) canbe described by the following compact differential equation

= 119860119909 + 1198611

119906 + 1198612

119908 + 1198613

119903

119910 = 119862119909 + 119863119906

(7)

with 119909 isin 119877119909 119906 isin 119877119906119908 isin 119877119908 119903 isin 119877119903 and 119910 isin 119877119910 representing

the state vectors control input vectors crosswind effects as adisturbance vector desired trajectory vectors and measuredoutput vectors respectively We define

119909 = [V119910

119884 120595 120601 120596119891

120596119903

]119879

119906 = [120575119891

120575119903

119872119911

]119879

119908 = [119865119908

119872119908

]119879

119903 = [119884des 120595des]119879

ℎ (120585) = [119884 120595]119879

(8)

The state vectors represent the states for lateral velocity lateralposition yaw rate yaw angle roll rate roll angle and frontand rear wheels angular speed respectively and the outputvectors represent lateral position and yaw angle

3 Linear Model Predictive Control

MPC has been used as a highly effective and very successfulcontrol scheme with the simple design framework provingto be a practical controller able to combine multivariablesystems and utilize online optimization process control Thestability guarantees of existing predictive control approachesfor nonlinear systems with uncertainty however remaincontingent upon the assumption of the initial feasibility ofthe optimization and the set of initial conditions startingfrom where feasibility of the optimization problem andtherefore stability of the closed-loop system is guaranteed isnot explicitly characterized [28] For example the occurrenceof faults in control actuators adds another layer of complexityto the problem of controller design for nonlinear uncertainsystems Note that the stability guarantees provided by acontroller may no longer hold in the presence of faults inthe control actuators that prevent the implementation ofthe control action prescribed by the control law and these


Modelpredictivecontrol

Linear tiremodel

Referencetracking

Dist

urba

nce Linear vehicle

model

x

Yref120575f

120575r

Fx Fy

Y

Mz120595ref

120595

Figure 4 Predictive control structure

faults can have substantial negative ramifications owing to theinterconnected nature of processes [29]

In order to implement MPC with a receding horizoncontrol strategy the following strategy method is adopted

(1) A dynamics process model is used to predict thebehaviour of the plant and future plant outputs ateach instant 119896 based on both previous and the latestobservations of the systemrsquos inputs and outputs

(2) The control signal inputs are calculated by minimiz-ing the error of tracking between the predicted outputand desired trajectory signal to keep the process asclose as possible to following the trajectory whileconsidering the objective functions and constraints

(3) Only the first control signal is implemented on theplant whilst others are rejected in anticipation of thenext sampling instant where the future output will beknown

(4) Step (1) is repeated with updated values and all ordersare updated

In this paper we use the linear model of predictive controlThe hierarchical control structure is adopted in MPC asshown in Figure 4 Figure 4 illustrates the control structurefor 2WS that uses front steering only 120575

119891

for 4WS that usesfront and rear steering 120575

119891

and 120575119903

and for 2WS with DYCthat produces external yaw moment (119872

119911

) at both front andrear wheels as a control input to the system These systemsare used to control the vehicle in order to follow a givenreference trajectory They include the vehicle speed desiredreference trajectory modelled predictive control and linearvehicle model with linear tire model

Using the equations from the vehicle and tire model asexplained and defined in (7) the basic equations of linearvehicle motion can be given as follows

119898V119910

=1

119868119909119909

V119909

[minus (120583119862119903

+ 119862119891

) 119869119909119902

V119910

+ (120583 (119862119903

119897119903

minus 119862119891

119897119891

) 119869119909119902

minus 119868119909119909

119898V2119909

) ]

minus1

119868119909119909

[(ℎ119887120601

) minus ℎ (119898119892ℎ minus 119896120601

) 120601 minus 120583119862119891

119869119909119902

120575119891

+ 120583119862119903

119869119909119902

120575119903

]

(9a)

119868119911119911

=1

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) V119910

minus 120583 (119862119891

119897119891

2

+ 119862119903

119897119903

2

) ] + 120583119862119891

119897119891

120575119891

minus 120583119862119903

119897119903

120575119903

+119872119911

(9b)

119868119909119909

=ℎ

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) minus 120583 (119862119891

+ 119862119903

) V119910

]

minus 119887120601

+ (119898119892ℎ minus 119896120601

) 120601 + 120583119862119891

ℎ120575119891

+ 120583119862119903

ℎ120575119903

(9c)

where 119869119909119902

= 119868119909119909

+ 119898ℎ2 A DYC that produces the reaction

moment occurring at the front and rear wheels due to thesteering angle effect (as an external yaw moments (119872

119911

)) canbe approximated with the following equations

119872119891

asymp 2119897119891

119862119891

119872119911

119872119903

asymp 2119897119903

119862119903

119872119911

(10)

We define front steering angle rear steering angle and directyaw moment control as the inputs to the system Thus thevehicle motion can be represented in a given discrete state-space structure as follows

119909119897

(119896 + 1 | 119896) = 119860119897

119909119897

(119896 | 119896) + 119861119897

119906119897

(119896 | 119896)

+ 119861119903

119903119897

(119896 | 119896)

119910119897

(119896 | 119896) = 119862119897

119909119897

(119896 | 119896) + 119863119897

119906119897

(119896 | 119896)

(11)

where 119909119897

(119896 | 119896) is the state vector at time step 119896 and 119909119897

(119896 +

1 | 119896) is the state vector at time step 119896 + 1 with 119909119897

(119896 | 119896) isin

119877119909119897(119896|119896) 119906

119897

(119896 | 119896) isin 119877119906119897(119896|119896) 119903

119897

(119896 | 119896) isin 119877119903119897(119896|119896) and 119910

119897

(119896 | 119896) isin

119877119910119897(119896|119896) representing the state vectors control input vectors

reference vectors and measured output vectors respectivelyWe define

119909119897

(119896) = [V119910

119884 120595 120601]119879

119903119897

(119896) = [119884des 120595des]119879

119910119897

(119896) = [119884 120595]119879

(12)

For 2WS 4WS and 2WS with DYC the control signal to thesystems with the same tuning control parameters is given asfollows

119906119897

(119896) = [120575119891

]

119906119897

(119896) = [120575119891

120575119903

]119879

119906119897

(119896) = [120575119891

119872119911

]119879

(13)

We formulate the optimization of the predictive controlsystem which takes the constraints imposed on the input andinput rate respectively as given in the following form

minus119906119897

le 119906119897

(119896) le +119906119897

minusΔ119906119897

le Δ119906119897

(119896) le +Δ119906119897

(14)


One approach to maintain closed-loop stability would be touse all available control actuators (13) so that even if one ofthe control actuators fails the rest can maintain closed-loopstability which the reliable control approaches The use ofredundant control actuators however incurs possibly pre-ventable operation and maintenance costs These economicconsiderations dictate the use of only as many control loopsas is required at a time To achieve tolerance with respect tofaults control-loop reconfiguration can be carried out in theevent of failure of the primary control configuration based onthe assumption of a linear system

Based on the linear vehicle model in (11) and by definingthe outputs in (12) we consider the following cost functionsto the system

119869 (119909119897

(119896) 119880119897119896

) =

119867119901

sum

119894=1

1003817100381710038171003817119897 (119896 + 119894 | 119896) minus 119903 (119896 + 119894 | 119896)10038171003817100381710038172

119876119894

+

119867119888minus1

sum

119894=0

1003817100381710038171003817Δ119897 (119896 + 119894 | 119896)10038171003817100381710038172

119877119894

(15)

In (15) the first summation of the given cost functionreflects the reduction of trajectory tracking errors among thepredicted outputs

119897

(119896 + 119894 | 119896) (119894 = 0 119867119901

minus 1) and theoutput reference signals 119903(119896+119894 | 119896) (119894 = 0 119867

119901

minus1) and thesecond summation reflects on the penalization of the controlsignal effort Δ

119897

(119896 + 119894 | 119896) (119894 = 0 119867119888

minus 1) of the steeringcontrol manoeuvre The aim of the predictive control systemis to determine the optimal control input vector Δ

119897

(119896+ 119894 | 119896)

so that the error function between the reference signal andthe predicted output is reduced

The difference in the steering angle Δ119897

(119896 + 119894 | 119896) is givenin the case that the cost function is at a minimum valueThe weight matrices 119876(119894) and 119877(119894) are semipositive definiteand positive definite respectively and can be tuned for anydesired closed-loop performance 119876(119894) is defined as the statetracking weight since the error

119897

(119896 + 119894 | 119896) minus 119903(119896 + 119894 | 119896) canbecome as small as possible by increasing 119876(119894) In a similarfashion 119877(119894) represents the input tracking weight and thevariation of the input is decreased to slow down the responseof the system by increasing 119877(119894) The predictive and controlhorizon are typically considered to be 119867

119901

ge 119867119888

while thecontrol signal is considered constant for 119867

119888

le 119894 le 119867119901

Matrices 119876(119894) and 119877(119894) represent the matrix weight of theirappropriate dimensions for outputs and inputs respectivelygiving the state feedback control law as follows

119906119897

(119896 119910119897

(119896)) = 119906119897

(119896 minus 1) + Δ119906119897

(119910119897

(119896)) (16)

An optimal input was computed for the following time steprather than being calculated for the immediate time step byaddressing convex optimization problems during each timestep After that the first input is applied on the plant in (11)and the others are rejected which yield the optimal controlsequence as (16) The optimization problem in (15) is iteratedwith the new value at a time 119896 + 1 via new state 119909(119896 + 1) andall orders are then updated

The required direct yaw moment control119872119911

is obtainedfrom the variation between the two sides of the vehicle torque

as in (1e) In this research the braking torque is only usedbased on the yaw rate in otherwords it is only activated in thecase that the vehiclemoves toward instability or in emergencymanoeuvres since it impacts the longitudinal motion whilethe rear steering angle is assumed for the total manoeuvre tobe in control or in standard drivingmanoeuvresWe take intoaccount three control inputs that is front and rear steeringangles as well as differential braking at rear right and left tirebut only one control input is used at a time [30]

4 Simulation Results

41 Scenario Description The linear model predictive con-troller explained andpresentedwas implemented for a vehiclepath following a double-lane change scenario with a cross-wind effect present throughout the simulation A double-lanechange manoeuvre approximates as an emergency manoeu-vre case and generally demonstrates the agility and capabili-ties of the vehicle in lateral and roll dynamics During such amanoeuvre an understeering or oversteering or even a roll-over situation may occur In this scenario the vehicle is con-sidered travelling horizontally or straightforward followingthe path with a constant velocity of 10msminus1 and 30msminus1without braking or accelerating The drag force and torquegiven by (6) in the initial driving conditions are assumed toact in the direction of the path at time 119905 = 1 sec with a windvelocity of V

119908

= 10msminus1 The forces and torques arising fromthis sidewise acting wind gust are assumed to be persistentand are applied as step functions throughout the simulationtime as shown in Figure 5 Table 1 shows the sport utilitypassenger car model parameters and their definitions used inthis paper based on Solmaz et al [31]

For stability analysis we simulated the system with onlyone inputmdashin particular the front steering angle 120575

119891

or 2WSWe set the vehicle velocity to be constant at V

119909

= 15msminus1the road adhesion coefficient 120583 = 1 and wind velocity V

119908

=

10msminus1 Figure 6(a) shows a stability analysis based on theroot locus of the open-loop system in (7) showing matrix 119860without the crosswind effect (119861

2

= 0) and references signal(1198613

= 0) Those settings contribute to a stable region for bothoutputs (vehicle side slip and yaw rate responses) Matrix 119860is given in (8) with input signal being front steering angle(1198611

= 120575119891

) Since the root locus command inMATLAB is onlyworking on the single-input single-output therefore we eval-uate separately the output response with single input signal

Figure 6(b) illustrates the effect of these factors a cross-wind effect (119861

2

= 0) references signal (1198613

= 0) and con-trol signal (119861

1

= 0) with the same matrix 119860 as in (8) thatyields unstable responses for both vehicle side slip and yawrate We can also notice that the poles are different for bothcases due to 119861

2

matrices that are based on the crosswindeffect Furthermore Figure 6(b) shows that within a windvelocity V

119908

= 10msminus1 the system is stable with the appropri-ate matrices of 119860 119861

1

and 1198612

Figure 6(a) also illustrates thatpaired 119860 and 119861

1

are controllable based on the model para-meters listed in Table 1

In this paper the predictive controller was implementedby minimizing vehicle deviation from the target path to


0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)

Figure 5 Force and torque for crosswind speed of 10msminus1

Table 1 Car vehicle parameters

Parameter ValueCar mass [kg] 1300Inertia around the roll 119909-axis [kgm2] 370Inertia around 119911-axis [kgm2] 216756Distance of front and rear wheels from centre of gravity (CoG) [m] 145 107Distance between the vehicle CoG and the assumed roll axis [m] 045Equivalent suspension roll damping coefficient [Nms] 4200Equivalent suspension roll stiffness coefficient [Nm] 40000Linear approximation of tire stiffness for front and rear tire [Nrad] 133000 121000Gravitational constant [ms2] 98

achieve the main aim which is to follow the desired or refer-ence trajectory as close as possible The controllers are com-pared against each other for 2DoF and 3DoF bicycle modelswhich excludes vehicle roll dynamics at various speedsspecifically low (10msminus1) and high (30msminus1) and also underwet concrete (120583 = 07) and icy (120583 = 01) road surfaces

Since our study focused on an autonomous vehicle it isreasonable to assume that the controllers will adapt to theroad or environment such as in the case of road adhesionsadverse weather visual cues traffic and overall relevantdriving conditions Therefore both controllers (2DoF and3DoF) were designed and implemented with the parametersand conditions given in Tables 2 3 and 4 for different vehicleforward speeds and road adhesion coefficients The path-following tracking error is a measurement of how closelythe output responses follow the reference trajectory whichis a measure of the deviation from the benchmark In this

paper we use the standard deviation of the root-mean squareformula to calculate the tracking error given by the followingequation

119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905

is the tracking error 119899 represents the number oftime periods and 119910

119900

and 119910119903

express the measured output andreference

42 Results and Discussions Prior to proposed simulationswe carried out standard vehicle manoeuvres tests to validateour model in the open-loop simulation scenario Standardtests available are the J-turn fishhook and double-lanechange [32] which are representative of on-roadmanoeuvreswithout tripping (caused by external force from road curb or


0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40

minus50minus50minus100minus150minus200minus250minus300

Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8

minus10minus20minus40minus60minus80minus100minus120minus140

Real axis (sminus1)

120573

(a) Without crosswind effect

0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400

minus20minus40minus60minus800 20

0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573


(b) With crosswind effect

Figure 6 Open-loop system in (7)

collisionwith other vehicles)We performed only the double-lane change and roll rate feedback fishhook test for vehiclevalidation purposes in the open-loop simulation as shown inFigures 7 and 8 The vehicle speed was set at 30msminus1 whichis suitable for both tests with a road surface coefficient of 01As illustrated in Figures 7 and 8 the vehicle response in terms

of yaw rate roll rate and lateral acceleration has been provento be validated thus being suitable for other simulations

For easier comparison between controllersrsquo perfor-mances in achieving vehicle stabilization when subjectedto various conditions controllers tuning parameters fromTables 3 and 4 were selected as suitable The weighting gains


0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595

Figure 7 Vehicle manoeuvre test of single-lane change at 30msminus1 with 120583 = 01

Table 2 Model predictive control parameters

Parameter ValuePredictive horizon 20Control horizon 9Sampling time [s] 005Constraints on max and min steering angles [deg] plusmn20Constraints on max and min changes in steering angles [degs] plusmn10Constraints on max and min changes in moment torque [Nmrad] plusmn2000Constraints on max and min moment torque [Nmrads] plusmn1500Simulation time [s] 15

for controllers input and output were selected using trial-and-error method where selection criteria were based on thebest response output for both input and output for weightinggains

The first simulation revolves around various road surfacefriction coefficients from wet concrete (120583 = 07) to icy sur-face condition (120583 = 01) with a constant forward speed of10msminus1 The MPC weighting tuning parameters are listedin Table 3 We evaluated the controllerrsquos robustness for theoutput responses by comparing the performance of 2WS4WS and 2WS with DYC manoeuvres at a forward speed of

10msminus1 as shown in Figures 9ndash11 The controller trackingerrors based on (17) for lateral position and yaw angleresponses are summarized in Table 5 From Figure 9 thereare not many differences between both controllers underthe conditions of lowest speed and high road adhesioncoefficient both controllers yielded perfect response whenfollowing a given trajectory while maintaining vehicle stabil-ity and rejecting external crosswind effect It can be seen thatfor 4WS and 2WS with DYC manoeuvres the rear steeringangle and the direct yaw moment are almost unused sincethe front steering can provide sufficient control ability This


0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595

Figure 8 Vehicle manoeuvre test of roll rate feedback at 30msminus1 with 120583 = 01

Table 3 Model predictive control weighting matrices parameters for V119909

= 10msminus1

Control manoeuvres 2DoF 3DoF

2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)

Figure 9 2DoF controller at 10msminus1 and 120583 = 07 by 2WS 4WS and 2WS + DYC

may be partly due to the fact that the rear steering and DYCwere not used in lower speed manoeuvres

Moreover when the road surface friction was set to icythe output responses from both controllers and all controlmanoeuvre techniques did not perfectly follow the desiredtrajectory as shown in Figures 10 and 11 2WS with DYCyielded the best performance output compared to the othersespecially in yaw rate response 4WSwas the next best follow-ing 2WS where the lateral position and yaw angle lookalmost identical It seems that the rear steering and direct yawmoment controls were used in conjunction with front steer-ing for vehicle stabilization along the trajectory Howeverfrom Table 5 the controller with 3DoF gives slightly bettertracking error performance manoeuvres compared to con-troller 2DoF due to the fact that roll dynamics will not havemuch influence during low speed manoeuvres Another factis that at low vehicle speed all control inputs (front steeringangle rear steering angle and direct yawmoment control) areunder constraints

Next we tested the vehicle at various road friction coef-ficients again however this time the vehicle was tested undera high forward speed of 30msminus1 The same MPC design wasused of which the parameter controls are listed in Table 4Wecompared the simulation results for 2WS 4WS and 2WSwithDYC control manoeuvres for both controllers and presentthe comparison in Figures 12ndash15The simulation results show

that for 2DoF controller at 30msminus1 and on wet concrete(120583 = 07) all control manoeuvres give slightly similar out-puts performances Better responses were achieved in lateralpositioning and although the tracking performance of yawangle and yaw rate deteriorated the system still allowedthe vehicle to track and follow the trajectory successfullyrejecting the effects of wind gust that impact the vehicle

As tabulated in Table 6 4WS and 2WS with DYC showslightly better tracking performance compared to 2WS onlyHowever in the case of the 3DoF controller it can be clearlyseen that 2WS with DYC and 4WS control manoeuvresoffered amuch higher performing response especially in yawangle and yaw rate response than 2WS This is shown inFigure 13 In this scenario the rear steering and direct yawmoment control was fully utilized to control and enhancevehicle stability It is therefore very important to consider rolldynamics in order to enhance vehicle stability and to followthe path trajectory From Figures 12 and 13 there are somestrong frequency oscillations in front of some responsesthat is front lateral force vehicle side slip angle and lateralacceleration trace based on authorsrsquo knowledge come fromthe numerical calculation or associated glitches and initialcondition of the system

Furthermore when we simulated vehicle manoeuvre forhigh speed (30msminus1) and icy road condition (120583 = 01) for2DoF controller it can be seen that all manoeuvres control


Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25

simulation the tracking responses become unstable andimpossible to control especially under the crosswind effectas shown in Figure 14 The most probable cause is the rolldynamic motion neglect in the 2DoF controller design whenthe vehicle itself was modelled by including roll dynamicfactor It can be said that the inclusion of roll dynamic factor

is important for vehicle manoeuvre in terms of stability andcontrollability at high speed and icy road condition Sincehigh speed coupled with icy road condition will render theequation to become highly nonlinear it is impossible fora linear tire model to react positively since the handlingpropertiesmay be significantly different from those generated


0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)


Table 5 Path following tracking errors with road friction surface 120583 = 07

Vehicle speed Manoeuvre control Controller 2DoF Controller 3DoF119884 [m] Ψ [rad] 119884 [m] Ψ [rad]

102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254

by the linear tire model These results show that linear tiremodel is only suitable for analyzing a stable vehicle behaviourunder the assumption of small steering and acceleration

Next for the 3DoF controller simulation 2WS with DYCmanoeuvres provides a much better tracking response incomparison to 4WS particularly in the case of lateral outputOn the contrary 4WS manoeuvre demonstrates a much bet-ter tracking response in the yaw angle and yaw rate responsesas tabulated in Table 6 With appropriate weight tuning gainthe rear steering angle and direct yaw moment control arefully optimized in order to become stable along the given tra-jectory However for the 2WS manoeuvre the vehicleresponses become unstable despite several instances wherethe weighting tuning gains are adjusted for output and inputgains With the inclusion of another input control to the con-troller design we can enhance the vehicle responses for both

2WS with DYC and 4WS control manoeuvres show Thismeans that for 2WS controller design it may have to usemore than just front steering to stabilize the vehicle under theeffects of wind gusts Figure 15 shows that rear steering angleand direct yaw moment are fully utilized in order to stabilizethe vehicle for 2WS with DYC and 4WSmanoeuvres control

In contrast to the 2DoF controller as shown in Figure 14in the 3DoF controllers the 2WS control manoeuvre canstill be used to track a given trajectory despite not perfectlyfollowing the trajectory in a satisfactory manner especiallyunder crosswind effects In Figure 15 we can see some oscil-lations in few traces responses at the end of the responsesBased on the authorsrsquo knowledge these oscillationsmay comefrom the vehicle model and some initial conditions of thesystem with imperfect controllers tuning weighting gains Inthese conditions neither 2WS nor 4WS control manoeuvres


0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)


for lateral response and neither 2WS nor 2WS with DYCcontrol manoeuvres for yaw angle or yaw rate responseperformed well causing an increase in vehicle instabilityincreased vibration and tracking responses deteriorationWewill next focus on how to enhance the controller in order tostabilize vehicle manoeuvrability and handling stability

We can therefore conclude that for 4WS the rear wheelswere helping the car to steer by improving the vehiclehandling at high speed while decreasing the turning radiusat low speed as shown by the control signal in Figures 12 and13 Meanwhile for 2WS with DYC active front steering wasused in low speed manoeuvres for lateral acceleration whileinclusion of DYC was adopted for high lateral accelerationwhen the tires were saturated and could not produce enoughlateral force for vehicle control and stability as intendedIn 2WS vehicles the rear set of wheels do not play an

active role in controlling the steering From Table 5 it canbe seen that among the three controllers 4WS gave the bestperformance by reducing the tracking error for lateral andyaw angle responses when compared with 2WS with DYCand 2WS only Tables 5 and 6 tabulated the MPC robustnessand the tracking errors in (17) for all types of manoeuvre at10msminus1 and 30msminus1 vehicle speeds and under various roadsurfaces Furthermore all controlmanoeuvre signals for bothcontrollers were within the input constraints We would liketo highlight that in MPC approaches although there was anadvantage in multivariable systems in this study there was atrade-off between theweighting tuning parameter to focus oneither lateral position or yaw angle trajectory In this paper wehave chosen lateral position as the weighting tuning priorityso we may get a better response on yaw angle and yaw rateresponse by sacrificing lateral position precision


0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083

302WS Uncontrolled Uncontrolled 21352 052644WS Uncontrolled Uncontrolled 08824 02982

2WS + DYC Uncontrolled Uncontrolled 09964 04580


0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion

This paper presents the robustness of model predictive con-trol for an autonomous ground vehicle on a path-followingcontrol with consideration of wind gust effects subjectedto the variation of forward speeds and road surfaces condi-tion in a double-lane change scenario The predictive con-trollers were designed based on two- (lateral-yaw model)and three- (lateral-roll model) degree-of-freedom vehiclemodels The only difference between the models is the rolldynamics factor which is taken into consideration andboth controllers were implemented into a six-degree-of-free-dom vehicle model Based on linear vehicle and tire modelapproximations of a known trajectory we evaluated the effectand impact of roll dynamics at low and high forward vehicle

speeds and at various road frictions (wet concrete to icyroads) in order to follow a desired trajectory as close as pos-sible while rejecting the crosswind effects and maintainingvehicle stability We also evaluated and compared the effi-ciency of the different manoeuvres via two-wheel steeringfour-wheel steering and two-wheel steering with direct yawmoment control

The simulation results showed that with the inclusion ofroll dynamics in the linear vehicle model the vehicle stabilityand adherence to trajectory was considerably improved forthe case of high speed manoeuvres on a higher road surfacefriction coefficient (120583 = 07) and improved even more for thecase of a lower road surface coefficient (120583 = 01) Further-more the obtained results showed and proved that the rearwheels and direct yaw moment are beneficial to help steering


0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)


the car by improving the vehicle handling at high speeddecreasing the turning radius at low speeds and reducing thetracking error for lateral position and yaw angle response

The simulation also demonstrated that model predictivecontrol has an ability to reject the side wind effect as adisturbance to the system which is particularly effective at10msminus1 for all cases except for the 2DoF controller duringsimulation of higher speeds on lower road surface adhesionHowever both controllers were not able to provide a betterresponse when the vehicle performed at a high forwardspeedwith a low road adhesion coefficient particularly when2DoF controller was simulated all results showed unstablevehicle response Thus for this scenario we are currentlyinvestigating new approaches with a real-time implementable

control scheme Further improvement for future works oncontrol methodology will also be considered to minimizetracking error and to enhance vehicle stability

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors would like to thank Professor Zidong Wangand Professor Manfred Ploechl for their comments andadvice Special thanks are also extended to Dr A Zahran MKhudzari for his help preparing this paper


References

[1] E F Camacho and C Bordons Model Predictive ControlSpringer London UK 2nd edition 2007

[2] C E Garcıa DM Prett andMMorari ldquoModel predictive con-trol theory and practicemdasha surveyrdquo Automatica vol 25 no 3pp 335ndash348 1989

[3] P Mhaskar ldquoRobust model predictive control design for fault-tolerant control of process systemsrdquo Industrial amp EngineeringChemistry Research vol 45 no 25 pp 8565ndash8574 2006

[4] V Vesely and D Rosinova ldquoRobust model predictive controldesignrdquo in Model Predictive Control T Zheng Ed pp 1ndash24InTech Rijeka Croatia 2010

[5] M Nagai M Shino and F Gao ldquoStudy on integrated control ofactive front steer angle and direct yaw momentrdquo JSAE Reviewvol 23 no 3 pp 309ndash315 2002

[6] F Yakub and Y Mori ldquoComparative study of autonomous path-following vehicle control viamodel predictive control and linearquadratic controlrdquo Proceedings of the Institution of MechanicalEngineers Part D vol 229 no 12 pp 1695ndash1714 2015

[7] C March and T Shim ldquoIntegrated control of suspension andfront steering to enhance vehicle handlingrdquo Proceedings of theInstitution of Mechanical Engineers Part D Journal of Auto-mobile Engineering vol 221 no 4 pp 377ndash391 2007

[8] J Wang D A Wilson W Xu and D A Crolla ldquoIntegratedvehicle ride and steady-state handling control via active suspen-sionsrdquo International Journal of Vehicle Design vol 42 no 3-4pp 306ndash327 2006

[9] M J L Boada B L Boada A Munoz and V Dıaz ldquoIntegratedcontrol of front-wheel steering and front braking forces on thebasis of fuzzy logicrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 220no 3 pp 253ndash267 2006

[10] A Balluchi A Bicchi and P Soueres ldquoPath-following with abounded-curvature vehicle a hybrid control approachrdquo Inter-national Journal of Control vol 78 no 15 pp 1228ndash1247 2005

[11] KMoriwaki ldquoAutonomous steering control for electric vehiclesusing nonlinear state feedback119867

infin

controlrdquoNonlinear AnalysisTheory Methods and Applications vol 63 no 5ndash7 pp e2257ndashe2268 2005

[12] B Mashadi P Ahmadizadeh and M Majidi ldquoIntegrated con-troller design for path following in autonomous vehiclesrdquo SAETechnical Paper 2011-01-1032 SAE International 2011

[13] J-M Park D-W Kim Y-S Yoon H J Kim and K-S YildquoObstacle avoidance of autonomous vehicles based on modelpredictive controlrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 223no 12 pp 1499ndash1516 2009

[14] Y Yoon J Shin H J Kim Y Park and S Sastry ldquoModel-pre-dictive active steering and obstacle avoidance for autonomousground vehiclesrdquo Control Engineering Practice vol 17 no 7 pp741ndash750 2009

[15] P Falcone F Borrelli J Asgari H E Tseng andDHrovat ldquoPre-dictive active steering control for autonomous vehicle systemsrdquoIEEE Transactions on Control Systems Technology vol 15 no 3pp 566ndash580 2007

[16] T Keviczky P Falcone F Borrelli J Asgari and D HrovatldquoPredictive control approach to autonomous vehicle steeringrdquoin Proceedings of the American Control Conference pp 4670ndash4675 IEEE Minneapolis Minn USA June 2006

[17] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomous

vehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[18] K Nam S Oh H Fujimoto and Y Hori ldquoRobust yaw stabilitycontrol for electric vehicles based on active front steering con-trol through a steer-by-wire systemrdquo International Journal ofAutomotive Technology vol 13 no 7 pp 1169ndash1176 2012

[19] H Yoshida S Shinohara and M Nagai ldquoLane change steeringmanoeuvre using model predictive control theoryrdquo VehicleSystem Dynamics vol 46 no 1 pp 669ndash681 2008

[20] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

[21] W Kim D Kim K Yi and H J Kim ldquoDevelopment of apath-tracking control system based onmodel predictive controlusing infrastructure sensorsrdquo Vehicle System Dynamics vol 50no 6 pp 1001ndash1023 2012

[22] B-C Chen and H Peng ldquoDifferential-braking-based rolloverprevention for sport utility vehicles with human-in-the-loopevaluationsrdquo Vehicle System Dynamics vol 36 no 4-5 pp 359ndash389 2001

[23] G Palmieri P Falcone H E Tseng and L Glielmo ldquoA prelim-inary study on the effects of roll dynamics in predictive vehiclestability controlrdquo in Proceedings of the 47th IEEE Conference onDecision and Control (CDC rsquo08) pp 5354ndash5359 IEEE CancunMexico December 2008

[24] H PacejkaTire andVehicleDynamics ElsevierOxfordUK 3rdedition 2012

[25] R N Jazar Vehicle Dynamics Theory and Application SpringerNew York NY USA 3rd edition 2009

[26] C R Carlson and J C Gerdes ldquoOptimal rollover preventionwith steer by wire and differential brakingrdquo in Proceedings of theASME InternationalMechanical Engineering Congress vol 1 no1 pp 345ndash354 Washington Wash USA November 2003

[27] C J Baker ldquoMeasures to control vehicle movement at exposedsites during windy periodsrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 25 no 2 pp 151ndash161 1987

[28] M Mahmood and P Mhaskar ldquoOn constructing constrainedcontrol Lyapunov functions for linear systemsrdquo IEEE Transac-tions on Automatic Control vol 56 no 5 pp 1136ndash1140 2011

[29] M Mahmood and P Mhaskar ldquoEnhanced stability regions formodel predictive control of nonlinear process systemsrdquo AIChEJournal vol 54 no 6 pp 1487ndash1498 2008

[30] F Yakub and Y Mori ldquoHeavy vehicle stability and rollover pre-vention via switching model predictive controlrdquo InternationalJournal of Innovative Computing Information and Control vol11 no 5 pp 1751ndash1764 2015

[31] S Solmaz M Corless and R Shorten ldquoA methodology for thedesign of robust rollover prevention controllers for automotivevehicles with active steeringrdquo International Journal of Controlvol 80 no 11 pp 1763ndash1779 2007

[32] D C Viano and C Parenteau ldquoCase study of vehicle maneuversleading to rollovers need for a vehicle test simulating off roadexcursions recovery and handlingrdquo SAE Technical Paper 2003-01-0169 SAE International 2003

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



an independent operating unit All sensory data are thencomputed for obstacle identification avoidance is then exe-cuted using advanced control system In this paper we limitautonomous vehicles to ground vehicles which are increas-ingly being studied by several researchers from academiaindustry and military Several control methods are beingused including fuzzy logic [9] hybrid control [10] H-infinitycontrol [11] and linear quadratic regulators [12] The bestcomparative studies on model predictive control strategiesfor autonomous guidance vehicles can be found in Park et al[13] Yoon et al [14] and Falcone et al [15] where a nonlineardynamics model of a vehicle is used for the controller designof an active front steeringmanoeuvre in a double-lane changescenario Keviczky et al [16] studied the effect of side wind viaan active front steeringmanoeuvre for an autonomous vehicleusing nonlinear MPC Since nonlinear MPC poses consid-erable challenges due to its real-time implementation algo-rithmmany researchers opted for linearMPC for their study

The assumption of this study are as follows vehicle trajec-tory is known as per Borrelli et alrsquos [17] study and the cross-wind effect will be assigned as a step response since thecrosswind effect disturbance on the vehicle can be approx-imated as a constant In this paper we extend the conceptof MPC for application in vehicle manoeuvring problemswhere a trajectory optimization is solved at each time stepThe trajectorywas designed to be a double-lane changing sce-nario The autonomous vehicle manoeuvring was simulatedin a variety of conditions low (10msminus1) and high (30msminus1)forward speed and low (icy) and high (concrete wet) roadfriction surface with the intention of following predeter-mined trajectory as close as possible while maintainingvehicle stability The control inputs were front steering anglerear steering angle and direct yawmoment control while theoutput controls were the yaw angle and lateral vehicle posi-tion Two different controllers were compared to evaluatethe performance of the six-degree-of-freedom (6DoF) vehi-cle model a simple (2DoF) controller without vehicle rolldynamic and a complex (3DoF) bicycle model controllerwith roll dynamics Other performance indexes evaluatedwere efficacy and robustness of the MPC for the autonomousvehicle in terms of control and stability

Themain objective of this paper is to evaluate the robust-ness of model predictive control approaches for autonomouspath-following car dynamics control with simple and com-plex models of the vehicle while rejecting the effects of windgusts to the systemThere are many studies to be consulted instabilization of the vehicle examples are two-wheel steering(2WS) [15 18] four-wheel steering (4WS) [19] and 2WS withdirect yaw moment control (DYC) [5 20 21] with differentcontrol strategies The first contribution of this paper is theeffect of vehicle roll dynamics motion consideration to thesystem whereas most previous papers only focused on a2DoF vehicle model (lateral and yaw motion) Moreoverbased on the authorsrsquo knowledge there is no comparativestudy for autonomous path-following vehicle control usingMPC techniques for three control signalmanoeuvres (includ-ing the three control signals here) the robustness evaluationdiscussed here becomes the main novelty of this paperFurthermore we would like to investigate the effectiveness

of model predictive control manoeuvres in the case of thecrosswind effect to the system in a variety of forward speedsand road adhesions The rest of the paper is organized asfollows Section 2 describes the linear vehicle model lineartire model and wind model Next a linear model predictivecontrol algorithm concept is explained in Section 3 Section 4examines and describes the effectiveness of the linear MPCfor a car dynamics system on a two-lane change scenarioLastly conclusions and future works are given in Section 5

2 Vehicle Model

21 Bicycle Model Figure 1 shows a well-known vehiclemodel which is a single-track model based on the simplifica-tion that the right and leftwheels are lumped in a single wheelat the front and rear axles The simplified vehicle model usedin this paper illustrates the motion movement and dynamicsconcerning the car vehicle subject to the longitudinal lateralyaw roll and rotational dynamics of the front and rear wheelmotion represented as 6DoF The longitudinal lateral andyaw dynamics effects are shown in Figure 1(b) as a top viewof the car vehicle and in Figure 1(a) the roll dynamics effectis explained with the nomenclature for a front view of thevehicle In this paper the nonlinear vehicle was linearizedbased on the assumption that sin 120579 = 0 and cos 120579 = 1 for bothsteering angles the vehicle side slip angle and the roll angleWe also assumed that thewhole vehiclemass is sprung whichis ignoring the suspension and wheel weights for unsprungmass This linearized model still behaves and represents theactual nonlinear vehicle model at certain operating points ofthe regionThe details of themathematical calculation for thevehiclemodel are presented inChen andPeng [22] for furtherknowledge

In this paper we use the following nomenclature 119865119909

and 119865119910

represent the longitudinal and lateral tire forcesrespectively 119865

119911

is the normal tire load 119865119908

and 119872119908

rep-resent the force and moment exerted by the side windrespectively 119909 119910 and 119911 correspond to the coordinates of thebody frame of a car position 119897 is the vehicle wheelbase 119879

119887

isthe wheel torque V

119909

and V119910

are the longitudinal and lateralwheels velocities respectively 120575

119891

and 120575119903

express the steeringangle of the front and rear wheels respectively 119872

119891

and119872119903

represent the reaction yaw moment appearing at the frontand rear wheels respectively119872

119911

is the total reaction of yawmoment of the wheels produced by the DYC 120583 acts as thetrack friction coefficient 120595 is the yawheading angle and isthe yaw rate120573 is the vehicle side slip angle and120601 and are theroll and roll rate angles respectively The variable at the frontand rear wheels is denoted by lower subscripts (sdot)

119891

and (sdot)119903

The motion of longitudinal lateral yaw roll and rota-

tional dynamics of the front and rear wheels using a 6DoFsystem based on a linear vehicle model is described throughthe following differential equations [23]

119898 = 119898 + 2119865119909119891

+ 2119865119909119903

minus 2ℎ119898 (1a)

119898 = minus119898 + 2119865119910119891

+ 2119865119910119903

+ ℎ119898 + 119865119908

(1b)

119868119911119911

= 2119897119891

119865119910119891

minus 2119897119903

119865119910119891

+ 119868119909119911

+ 119872119891

+119872119903

+119872119908

(1c)


z

h

y

120601

mg

Mw

b120601

Fzl Fzr

k120601

Fw

(a) Front view

x

Fyf

120575fxf

120572f f

Mf

yflf

x120573

FwMw

lr

120575r

Fyr

Mr

Fxr

120595y

(b) Top view


(119868119909119909

+ 119898ℎ2

) = 119898119892ℎ120601 minus 2119896120601

120601 minus 2119887120601

+ 119898ℎ ( + ) + 119868119909119911

(1d)

119869119887

119908119894

= minus119903119908

119865119909119894

minus 119879119887119894

minus 119887119908

120596119894

119894 = (119891 119903) (1e)


= cos120595 minus sin120595 = V119909

minus 120595

= sin120595 + cos120595 = V119909

120595 +

(2)



Fx

x

Fy

120572

Fz

Tb

Figure 2 Tire model


119865119909

= 120583119909

(119904) 119865119911

(3a)

119904 =119903119908

120596119908

V119909

minus 1 (3b)


119865119911119891

=119897119903

119898119892

2119897

119865119911119903

=119897119891

119898119892

2119897

(3c)

where 119903119908



119909



119911

and 120583119909



119891

and 120572119903

denoted by 119865119910119891

and119865119910119903


119865119910119891

= 119862119891

120572119891

119865119910119903

= 119862119903

120572119903

(4)

where 119862119891

and 119862119903


120572119891

=V119910

+ 119897119891

V119909

minus 120575119891

120572119903

=V119910

minus 119897119903

V119909

minus 120575119903

(5)



119865119908

=119862119865

120588119860V2119903

2

119872119908

=119862119872

120588119860119871V2119903

2

(6)


119891

+ 119897119903



119865

and 119862119872


119908


w

r

x

120595




= 119860119909 + 1198611

119906 + 1198612

119908 + 1198613

119903

119910 = 119862119909 + 119863119906

(7)



119909 = [V119910

119884 120595 120601 120596119891

120596119903

]119879

119906 = [120575119891

120575119903

119872119911

]119879

119908 = [119865119908

119872119908

]119879

119903 = [119884des 120595des]119879

ℎ (120585) = [119884 120595]119879

(8)






Linear tiremodel

Referencetracking

Dist

urba

nce Linear vehicle

model

x

Yref120575f

120575r

Fx Fy

Y

Mz120595ref

120595









119891


119891

and 120575119903


119911



119898V119910

=1

119868119909119909

V119909

[minus (120583119862119903

+ 119862119891

) 119869119909119902

V119910

+ (120583 (119862119903

119897119903

minus 119862119891

119897119891

) 119869119909119902

minus 119868119909119909

119898V2119909

) ]

minus1

119868119909119909

[(ℎ119887120601

) minus ℎ (119898119892ℎ minus 119896120601

) 120601 minus 120583119862119891

119869119909119902

120575119891

+ 120583119862119903

119869119909119902

120575119903

]

(9a)

119868119911119911

=1

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) V119910

minus 120583 (119862119891

119897119891

2

+ 119862119903

119897119903

2

) ] + 120583119862119891

119897119891

120575119891

minus 120583119862119903

119897119903

120575119903

+119872119911

(9b)

119868119909119909

=ℎ

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) minus 120583 (119862119891

+ 119862119903

) V119910

]

minus 119887120601

+ (119898119892ℎ minus 119896120601

) 120601 + 120583119862119891

ℎ120575119891

+ 120583119862119903

ℎ120575119903

(9c)

where 119869119909119902

= 119868119909119909



119911


119872119891

asymp 2119897119891

119862119891

119872119911

119872119903

asymp 2119897119903

119862119903

119872119911

(10)


119909119897

(119896 + 1 | 119896) = 119860119897

119909119897

(119896 | 119896) + 119861119897

119906119897

(119896 | 119896)

+ 119861119903

119903119897

(119896 | 119896)

119910119897

(119896 | 119896) = 119862119897

119909119897

(119896 | 119896) + 119863119897

119906119897

(119896 | 119896)

(11)

where 119909119897


(119896 +


(119896 | 119896) isin

119877119909119897(119896|119896) 119906

119897

(119896 | 119896) isin 119877119906119897(119896|119896) 119903

119897

(119896 | 119896) isin 119877119903119897(119896|119896) and 119910

119897

(119896 | 119896) isin



119909119897

(119896) = [V119910

119884 120595 120601]119879

119903119897

(119896) = [119884des 120595des]119879

119910119897

(119896) = [119884 120595]119879

(12)


119906119897

(119896) = [120575119891

]

119906119897

(119896) = [120575119891

120575119903

]119879

119906119897

(119896) = [120575119891

119872119911

]119879

(13)


minus119906119897

le 119906119897

(119896) le +119906119897

minusΔ119906119897

le Δ119906119897

(119896) le +Δ119906119897

(14)




119869 (119909119897

(119896) 119880119897119896

) =

119867119901

sum

119894=1

1003817100381710038171003817119897 (119896 + 119894 | 119896) minus 119903 (119896 + 119894 | 119896)10038171003817100381710038172

119876119894

+

119867119888minus1

sum

119894=0

1003817100381710038171003817Δ119897 (119896 + 119894 | 119896)10038171003817100381710038172

119877119894

(15)


119897

(119896 + 119894 | 119896) (119894 = 0 119867119901


119901


119897

(119896 + 119894 | 119896) (119894 = 0 119867119888


119897

(119896+ 119894 | 119896)




119897


119901

ge 119867119888


119888

le 119894 le 119867119901


119906119897

(119896 119910119897

(119896)) = 119906119897

(119896 minus 1) + Δ119906119897

(119910119897

(119896)) (16)







119908



119891


119909


119908

=


2



= 120575119891



2



1


2


119908


1

and 1198612


1




0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)







119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905


119900

and 119910119903




0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










z

h

y

120601

mg

Mw

b120601

Fzl Fzr

k120601

Fw

(a) Front view

x

Fyf

120575fxf

120572f f

Mf

yflf

x120573

FwMw

lr

120575r

Fyr

Mr

Fxr

120595y

(b) Top view


(119868119909119909

+ 119898ℎ2

) = 119898119892ℎ120601 minus 2119896120601

120601 minus 2119887120601

+ 119898ℎ ( + ) + 119868119909119911

(1d)

119869119887

119908119894

= minus119903119908

119865119909119894

minus 119879119887119894

minus 119887119908

120596119894

119894 = (119891 119903) (1e)


= cos120595 minus sin120595 = V119909

minus 120595

= sin120595 + cos120595 = V119909

120595 +

(2)



Fx

x

Fy

120572

Fz

Tb

Figure 2 Tire model


119865119909

= 120583119909

(119904) 119865119911

(3a)

119904 =119903119908

120596119908

V119909

minus 1 (3b)


119865119911119891

=119897119903

119898119892

2119897

119865119911119903

=119897119891

119898119892

2119897

(3c)

where 119903119908



119909



119911

and 120583119909



119891

and 120572119903

denoted by 119865119910119891

and119865119910119903


119865119910119891

= 119862119891

120572119891

119865119910119903

= 119862119903

120572119903

(4)

where 119862119891

and 119862119903


120572119891

=V119910

+ 119897119891

V119909

minus 120575119891

120572119903

=V119910

minus 119897119903

V119909

minus 120575119903

(5)



119865119908

=119862119865

120588119860V2119903

2

119872119908

=119862119872

120588119860119871V2119903

2

(6)


119891

+ 119897119903



119865

and 119862119872


119908


w

r

x

120595




= 119860119909 + 1198611

119906 + 1198612

119908 + 1198613

119903

119910 = 119862119909 + 119863119906

(7)



119909 = [V119910

119884 120595 120601 120596119891

120596119903

]119879

119906 = [120575119891

120575119903

119872119911

]119879

119908 = [119865119908

119872119908

]119879

119903 = [119884des 120595des]119879

ℎ (120585) = [119884 120595]119879

(8)






Linear tiremodel

Referencetracking

Dist

urba

nce Linear vehicle

model

x

Yref120575f

120575r

Fx Fy

Y

Mz120595ref

120595









119891


119891

and 120575119903


119911



119898V119910

=1

119868119909119909

V119909

[minus (120583119862119903

+ 119862119891

) 119869119909119902

V119910

+ (120583 (119862119903

119897119903

minus 119862119891

119897119891

) 119869119909119902

minus 119868119909119909

119898V2119909

) ]

minus1

119868119909119909

[(ℎ119887120601

) minus ℎ (119898119892ℎ minus 119896120601

) 120601 minus 120583119862119891

119869119909119902

120575119891

+ 120583119862119903

119869119909119902

120575119903

]

(9a)

119868119911119911

=1

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) V119910

minus 120583 (119862119891

119897119891

2

+ 119862119903

119897119903

2

) ] + 120583119862119891

119897119891

120575119891

minus 120583119862119903

119897119903

120575119903

+119872119911

(9b)

119868119909119909

=ℎ

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) minus 120583 (119862119891

+ 119862119903

) V119910

]

minus 119887120601

+ (119898119892ℎ minus 119896120601

) 120601 + 120583119862119891

ℎ120575119891

+ 120583119862119903

ℎ120575119903

(9c)

where 119869119909119902

= 119868119909119909



119911


119872119891

asymp 2119897119891

119862119891

119872119911

119872119903

asymp 2119897119903

119862119903

119872119911

(10)


119909119897

(119896 + 1 | 119896) = 119860119897

119909119897

(119896 | 119896) + 119861119897

119906119897

(119896 | 119896)

+ 119861119903

119903119897

(119896 | 119896)

119910119897

(119896 | 119896) = 119862119897

119909119897

(119896 | 119896) + 119863119897

119906119897

(119896 | 119896)

(11)

where 119909119897


(119896 +


(119896 | 119896) isin

119877119909119897(119896|119896) 119906

119897

(119896 | 119896) isin 119877119906119897(119896|119896) 119903

119897

(119896 | 119896) isin 119877119903119897(119896|119896) and 119910

119897

(119896 | 119896) isin



119909119897

(119896) = [V119910

119884 120595 120601]119879

119903119897

(119896) = [119884des 120595des]119879

119910119897

(119896) = [119884 120595]119879

(12)


119906119897

(119896) = [120575119891

]

119906119897

(119896) = [120575119891

120575119903

]119879

119906119897

(119896) = [120575119891

119872119911

]119879

(13)


minus119906119897

le 119906119897

(119896) le +119906119897

minusΔ119906119897

le Δ119906119897

(119896) le +Δ119906119897

(14)




119869 (119909119897

(119896) 119880119897119896

) =

119867119901

sum

119894=1

1003817100381710038171003817119897 (119896 + 119894 | 119896) minus 119903 (119896 + 119894 | 119896)10038171003817100381710038172

119876119894

+

119867119888minus1

sum

119894=0

1003817100381710038171003817Δ119897 (119896 + 119894 | 119896)10038171003817100381710038172

119877119894

(15)


119897

(119896 + 119894 | 119896) (119894 = 0 119867119901


119901


119897

(119896 + 119894 | 119896) (119894 = 0 119867119888


119897

(119896+ 119894 | 119896)




119897


119901

ge 119867119888


119888

le 119894 le 119867119901


119906119897

(119896 119910119897

(119896)) = 119906119897

(119896 minus 1) + Δ119906119897

(119910119897

(119896)) (16)







119908



119891


119909


119908

=


2



= 120575119891



2



1


2


119908


1

and 1198612


1




0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)







119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905


119900

and 119910119903




0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119865119911119891

=119897119903

119898119892

2119897

119865119911119903

=119897119891

119898119892

2119897

(3c)

where 119903119908



119909



119911

and 120583119909



119891

and 120572119903

denoted by 119865119910119891

and119865119910119903


119865119910119891

= 119862119891

120572119891

119865119910119903

= 119862119903

120572119903

(4)

where 119862119891

and 119862119903


120572119891

=V119910

+ 119897119891

V119909

minus 120575119891

120572119903

=V119910

minus 119897119903

V119909

minus 120575119903

(5)



119865119908

=119862119865

120588119860V2119903

2

119872119908

=119862119872

120588119860119871V2119903

2

(6)


119891

+ 119897119903



119865

and 119862119872


119908


w

r

x

120595




= 119860119909 + 1198611

119906 + 1198612

119908 + 1198613

119903

119910 = 119862119909 + 119863119906

(7)



119909 = [V119910

119884 120595 120601 120596119891

120596119903

]119879

119906 = [120575119891

120575119903

119872119911

]119879

119908 = [119865119908

119872119908

]119879

119903 = [119884des 120595des]119879

ℎ (120585) = [119884 120595]119879

(8)






Linear tiremodel

Referencetracking

Dist

urba

nce Linear vehicle

model

x

Yref120575f

120575r

Fx Fy

Y

Mz120595ref

120595









119891


119891

and 120575119903


119911



119898V119910

=1

119868119909119909

V119909

[minus (120583119862119903

+ 119862119891

) 119869119909119902

V119910

+ (120583 (119862119903

119897119903

minus 119862119891

119897119891

) 119869119909119902

minus 119868119909119909

119898V2119909

) ]

minus1

119868119909119909

[(ℎ119887120601

) minus ℎ (119898119892ℎ minus 119896120601

) 120601 minus 120583119862119891

119869119909119902

120575119891

+ 120583119862119903

119869119909119902

120575119903

]

(9a)

119868119911119911

=1

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) V119910

minus 120583 (119862119891

119897119891

2

+ 119862119903

119897119903

2

) ] + 120583119862119891

119897119891

120575119891

minus 120583119862119903

119897119903

120575119903

+119872119911

(9b)

119868119909119909

=ℎ

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) minus 120583 (119862119891

+ 119862119903

) V119910

]

minus 119887120601

+ (119898119892ℎ minus 119896120601

) 120601 + 120583119862119891

ℎ120575119891

+ 120583119862119903

ℎ120575119903

(9c)

where 119869119909119902

= 119868119909119909



119911


119872119891

asymp 2119897119891

119862119891

119872119911

119872119903

asymp 2119897119903

119862119903

119872119911

(10)


119909119897

(119896 + 1 | 119896) = 119860119897

119909119897

(119896 | 119896) + 119861119897

119906119897

(119896 | 119896)

+ 119861119903

119903119897

(119896 | 119896)

119910119897

(119896 | 119896) = 119862119897

119909119897

(119896 | 119896) + 119863119897

119906119897

(119896 | 119896)

(11)

where 119909119897


(119896 +


(119896 | 119896) isin

119877119909119897(119896|119896) 119906

119897

(119896 | 119896) isin 119877119906119897(119896|119896) 119903

119897

(119896 | 119896) isin 119877119903119897(119896|119896) and 119910

119897

(119896 | 119896) isin



119909119897

(119896) = [V119910

119884 120595 120601]119879

119903119897

(119896) = [119884des 120595des]119879

119910119897

(119896) = [119884 120595]119879

(12)


119906119897

(119896) = [120575119891

]

119906119897

(119896) = [120575119891

120575119903

]119879

119906119897

(119896) = [120575119891

119872119911

]119879

(13)


minus119906119897

le 119906119897

(119896) le +119906119897

minusΔ119906119897

le Δ119906119897

(119896) le +Δ119906119897

(14)




119869 (119909119897

(119896) 119880119897119896

) =

119867119901

sum

119894=1

1003817100381710038171003817119897 (119896 + 119894 | 119896) minus 119903 (119896 + 119894 | 119896)10038171003817100381710038172

119876119894

+

119867119888minus1

sum

119894=0

1003817100381710038171003817Δ119897 (119896 + 119894 | 119896)10038171003817100381710038172

119877119894

(15)


119897

(119896 + 119894 | 119896) (119894 = 0 119867119901


119901


119897

(119896 + 119894 | 119896) (119894 = 0 119867119888


119897

(119896+ 119894 | 119896)




119897


119901

ge 119867119888


119888

le 119894 le 119867119901


119906119897

(119896 119910119897

(119896)) = 119906119897

(119896 minus 1) + Δ119906119897

(119910119897

(119896)) (16)







119908



119891


119909


119908

=


2



= 120575119891



2



1


2


119908


1

and 1198612


1




0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)







119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905


119900

and 119910119903




0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Linear tiremodel

Referencetracking

Dist

urba

nce Linear vehicle

model

x

Yref120575f

120575r

Fx Fy

Y

Mz120595ref

120595









119891


119891

and 120575119903


119911



119898V119910

=1

119868119909119909

V119909

[minus (120583119862119903

+ 119862119891

) 119869119909119902

V119910

+ (120583 (119862119903

119897119903

minus 119862119891

119897119891

) 119869119909119902

minus 119868119909119909

119898V2119909

) ]

minus1

119868119909119909

[(ℎ119887120601

) minus ℎ (119898119892ℎ minus 119896120601

) 120601 minus 120583119862119891

119869119909119902

120575119891

+ 120583119862119903

119869119909119902

120575119903

]

(9a)

119868119911119911

=1

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) V119910

minus 120583 (119862119891

119897119891

2

+ 119862119903

119897119903

2

) ] + 120583119862119891

119897119891

120575119891

minus 120583119862119903

119897119903

120575119903

+119872119911

(9b)

119868119909119909

=ℎ

V119909

[120583 (119862119903

119897119903

minus 119862119891

119897119891

) minus 120583 (119862119891

+ 119862119903

) V119910

]

minus 119887120601

+ (119898119892ℎ minus 119896120601

) 120601 + 120583119862119891

ℎ120575119891

+ 120583119862119903

ℎ120575119903

(9c)

where 119869119909119902

= 119868119909119909



119911


119872119891

asymp 2119897119891

119862119891

119872119911

119872119903

asymp 2119897119903

119862119903

119872119911

(10)


119909119897

(119896 + 1 | 119896) = 119860119897

119909119897

(119896 | 119896) + 119861119897

119906119897

(119896 | 119896)

+ 119861119903

119903119897

(119896 | 119896)

119910119897

(119896 | 119896) = 119862119897

119909119897

(119896 | 119896) + 119863119897

119906119897

(119896 | 119896)

(11)

where 119909119897


(119896 +


(119896 | 119896) isin

119877119909119897(119896|119896) 119906

119897

(119896 | 119896) isin 119877119906119897(119896|119896) 119903

119897

(119896 | 119896) isin 119877119903119897(119896|119896) and 119910

119897

(119896 | 119896) isin



119909119897

(119896) = [V119910

119884 120595 120601]119879

119903119897

(119896) = [119884des 120595des]119879

119910119897

(119896) = [119884 120595]119879

(12)


119906119897

(119896) = [120575119891

]

119906119897

(119896) = [120575119891

120575119903

]119879

119906119897

(119896) = [120575119891

119872119911

]119879

(13)


minus119906119897

le 119906119897

(119896) le +119906119897

minusΔ119906119897

le Δ119906119897

(119896) le +Δ119906119897

(14)




119869 (119909119897

(119896) 119880119897119896

) =

119867119901

sum

119894=1

1003817100381710038171003817119897 (119896 + 119894 | 119896) minus 119903 (119896 + 119894 | 119896)10038171003817100381710038172

119876119894

+

119867119888minus1

sum

119894=0

1003817100381710038171003817Δ119897 (119896 + 119894 | 119896)10038171003817100381710038172

119877119894

(15)


119897

(119896 + 119894 | 119896) (119894 = 0 119867119901


119901


119897

(119896 + 119894 | 119896) (119894 = 0 119867119888


119897

(119896+ 119894 | 119896)




119897


119901

ge 119867119888


119888

le 119894 le 119867119901


119906119897

(119896 119910119897

(119896)) = 119906119897

(119896 minus 1) + Δ119906119897

(119910119897

(119896)) (16)







119908



119891


119909


119908

=


2



= 120575119891



2



1


2


119908


1

and 1198612


1




0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)







119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905


119900

and 119910119903




0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119869 (119909119897

(119896) 119880119897119896

) =

119867119901

sum

119894=1

1003817100381710038171003817119897 (119896 + 119894 | 119896) minus 119903 (119896 + 119894 | 119896)10038171003817100381710038172

119876119894

+

119867119888minus1

sum

119894=0

1003817100381710038171003817Δ119897 (119896 + 119894 | 119896)10038171003817100381710038172

119877119894

(15)


119897

(119896 + 119894 | 119896) (119894 = 0 119867119901


119901


119897

(119896 + 119894 | 119896) (119894 = 0 119867119888


119897

(119896+ 119894 | 119896)




119897


119901

ge 119867119888


119888

le 119894 le 119867119901


119906119897

(119896 119910119897

(119896)) = 119906119897

(119896 minus 1) + Δ119906119897

(119910119897

(119896)) (16)







119908



119891


119909


119908

=


2



= 120575119891



2



1


2


119908


1

and 1198612


1




0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)







119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905


119900

and 119910119903




0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 150

5

10

Time (s)

Cros

swin

d sp

eed

w(m

s)

Time (s)0 5 10 15

0

100

200

300

400

Win

d fo

rce

Fw

(N)

Time (s)0 5 10 15

0

minus500

minus1000

Win

d to

rque

Mw

(Nm

)







119890119905

= radicVar (119910119900

minus 119910119903

) = radic1

(119899 minus 1)sum (119910119900

minus 119910119903

)2

(17)

where 119890119905


119900

and 119910119903




0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50

0

10

20

30

40

50Root locus

Imag

inar

y ax

is (sminus1)

minus10

minus20

minus30

minus40


Real axis (sminus1)

120595998400

0 20

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

minus2

minus4

minus6

minus8


Real axis (sminus1)

120573


0 20 40 60

0

2

4

6

8

10Root locus

Imag

inar

y ax

is (sminus1)

Real axis (sminus1)

minus2

minus4

minus6

minus8

minus10

120595998400


0

5

10

15

20

25Root locus

Imag

inar

y ax

is (sminus1)

minus5

minus10

minus15

minus20

minus25

Real axis (sminus1)

120573








0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15

0

05

1

Time (s)

minus05

minus10 5 10 15

0

01

02

Time (s)

minus01

minus02

minus030 5 10 15

0

05

1

Time (s)

minus1

minus05

Tire

slip

angl

e120572f

(rad

)

0 5 10 15

0

05

1

Time (s)

minus05Yaw

angl

e res

pons

e120595

(rad

)

0 5 10 15

0

5

10

Time (s)

minus5

minus10

Fron

t ste

erin

g an

gle120575f

(deg

)

5 10 15

0

01

02

Time (s)

minus01

minus02

minus03Roll

angl

e res

pons

e120601

(rad

)

Time (s)0 5 10 15

0

10

20

30

40

50

Late

ral p

ositi

onY

(m)

0 5 10 15

0

2000

4000

Time (s)

minus2000

minus4000

Late

ral f

orce

Fyf

(N)

0 5 10 15Time (s)

10

5

0

minus5

minus10

Late

ral a

ccel

erat

ion

a y(m

s2)

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595








0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15

0

50

100

Time (s)

minus50

minus100

Late

ral a

ccel

erat

ion

a y(m

s2)

Time (s)0 5 10 15

0

1000

2000

3000

minus1000Late

ral p

ositi

onY

(m)

0 5 10 15

0

2

4

Time (s)

minus2

minus4

times104

Late

ral f

orce

Fyf

(N)

0 5 10 15

0

200

400

Time (s)

minus200

minus400

Fron

t ste

erin

g an

gle120575f

(deg

)

0 5 10 15

0

50

100

150

200

Time (s)

minus50

Yaw

angl

e res

pons

e120595

(rad

)

5 10 15

0

1

2

3

Time (s)

minus1

minus2Roll

angl

e res

pons

e120601

(rad

)

0 5 10 15

0

1

2

Time (s)

minus1

minus2Vehi

cle sl

ip an

gle120573

(rad

)

0 5 10 15

0

20

40

60

Time (s)

minus200 5 10 15

0

5

10

Time (s)

minus5

(rad

s)

Roll

rate

resp

onse

120601(rad

s)

Yaw

rate

resp

onse

120595



= 10msminus1


2WSV119909

= 10msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 195 11987622

= 05 11987611

= 525 11987622

= 05

V119909

= 10msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 152 11987622

= 05 11987611

= 395 11987622

= 05

4WS

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 195 11987622

= 05 11987611

= 45 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 153 11987622

= 05 11987611

= 35 11987622

= 05

2WS + DYC

V119909

= 10msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 193 11987622

= 05 11987611

= 37 11987622

= 05

V119909

= 10msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 152 11987622

= 05 11987611

= 35 11987622

= 05


Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Time (s)0 5 10 15

0

05

1

4WS

minus05

minus1

minus15

times10minus5Re

ar st

eerin

g an

gle120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

1

2

3

Time (s)

2WS + DYC

minus1

minus2

minus3

times10minus3

Dire

ct y

aw m

omen

tM

z(N

m)

0 5 10 15

0

02

0 5 10 15

0

02

04

Time (s)Time (s)

Ref2WS

4WS2WS + DYC

Ref2WS

4WS2WS + DYC

minus02

minus04

minus02

minus04

Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

Yaw

angl

e120595

(rad

)

Yaw

rate

120595998400

(rad

sminus1)









Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Time (s)0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

Time (s)0 5 10 15

0

01

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

Time (s)

2WS + DYC

minus01

minus02Dire

ct y

aw m

omen

tM

z(N

m)



= 30msminus1


2WSV119909

= 30msminus1 120583 = 07 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 565 11987622

= 05 11987611

= 355 11987622

= 05

V119909

= 30msminus1 120583 = 01 1198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 00311987611

= 0083 11987622

= 0042 11987611

= 003 11987622

= 045

4WS

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 155 11987622

= 25 11987611

= 135 11987622

= 35

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0005 11987622

= 0001 11987611

= 004 11987622

= 05

2WS + DYC

V119909

= 30msminus1 120583 = 071198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 505 11987622

= 05 11987611

= 35 11987622

= 05

V119909

= 30msminus1 120583 = 011198771

= 01 Δ1198771

= 003 1198771

= 01 Δ1198771

= 0031198772

= 01 Δ1198772

= 003 1198772

= 01 Δ1198772

= 00311987611

= 0092 11987622

= 004 11987611

= 05 11987622

= 25




0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

01

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

Time (s)

2WS4WS2WS + DYC

minus005

minus01

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

002

004

Time (s)

2WS + DYC

minus002

minus004

minus006Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00637 00085 00623 000744WS 00548 00054 00526 00051

2WS + DYC 00542 00051 00527 00051

302WS 00639 05348 00616 052154WS 00558 05239 00528 00023

2WS + DYC 00549 05226 00524 00254






0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15

0

2

4

Time (s)

Ref2WS

4WS2WS + DYC

minus2Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

Time (s)

2WS4WS2WS + DYC

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

001

002

Time (s)

2WS4WS2WS + DYC

minus001Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

1

2

Time (s)

2WS4WS2WS + DYC

minus1

minus2

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

001

002

003

Time (s)

2WS4WS2WS + DYC

minus001

minus002

Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

00005

0001

4WS

Time (s)

minus00005

minus0001

minus00015

Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

001

002

Time (s)

2WS + DYC

minus001

minus002

Dire

ct y

aw m

omen

tM

z(N

m)






0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15

0

2

4

Ref2WS

4WS2WS + DYC

Time (s)

minus2

Late

ral p

ositi

onY

(m)

0 5 10 15

0

02

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

angl

e120595

(rad

)

0 5 10 15

0

02

04

Ref2WS

4WS2WS + DYC

Time (s)

minus02

minus04

Yaw

rate

120595998400

(rad

sminus1)

0 5 10 15

0

1000

2000

2WS4WS2WS + DYC

Time (s)

minus1000

minus2000Fron

t lat

eral

forc

eFyf

(Nm

)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02

Vehi

cle si

de sl

ip120573

(rad

)

0 5 10 15

0

5

10

2WS4WS2WS + DYC

Time (s)

minus5

minus10Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 5 10 15

0

01

02

03

2WS4WS2WS + DYC

Time (s)

minus01

minus02Fron

t ste

erin

g an

gle120575f

(rad

)

0 5 10 15

0

01

02

03

4WS

Time (s)

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 5 10 15

0

005

01

2WS + DYC

Time (s)

minus005

minus01

Dire

ct y

aw m

omen

tM

z(N

m)




102WS 00874 00115 00841 001044WS 00838 00109 00832 00094

2WS + DYC 00838 00110 00835 00083




0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30

02468

10

Time (s)

Ref2WS

4WS2WS + DYC

minus2

minus4Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

04

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0020406

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

minus06

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15

Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

0020406

Time (s)

2WS4WS2WS + DYC

minus02

minus04

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

02

04

06

Time (s)

4WS

minus02

Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

005

01

Time (s)

2WS + DYC

minus005

Dire

ct y

aw m

omen

tM

z(N

m)

0 10 20 30

005

115

Time (s)

2WS4WS2WS + DYC

minus05

minus1

minus15Fron

t lat

eral

forc

eFyf

(Nm

) times104


5 Conclusion





0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30

0

5

Time (s)

Ref2WS

4WS2WS + DYC

minus10

minus5

minus15Late

ral p

ositi

onY

(m)

0 10 20 30

0

02

Time (s)

Ref2WS

4WS2WS + DYC

minus02

minus04

Yaw

angl

e120595

(rad

)

0 10 20 30

0

025

05

Time (s)

Ref2WS

4WS2WS + DYC

minus025

minus05

Yaw

rate

120595998400

(rad

sminus1)

0 10 20 30

0

500

1000

Time (s)

2WS4WS2WS + DYC

minus500

minus1000

minus1500Fron

t lat

eral

forc

eFyf

(Nm

)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02Vehi

cle si

de sl

ip120573

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS4WS2WS + DYC

minus2

minus4

Late

ral a

ccel

erat

ion

a y(m

sminus2)

0 10 20 30

001020304

Time (s)

2WS4WS2WS + DYC

minus01

minus02

Fron

t ste

erin

g an

gle120575f

(rad

)

0 10 20 30

0

01

02

03

Time (s)

4WS

minus01

minus02Rear

stee

ring

angl

e120575r

(rad

)

0 10 20 30

0

2

4

Time (s)

2WS + DYC

minus2

minus4

times10minus4

Dire

ct y

aw m

omen

tM

z(N

m)





Competing Interests


Acknowledgments



References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References












infin


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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