Lateral Controllers using Neuro-Fuzzy Systems for Automated Vehicles:A Comparative Study

Sarouthan Sriranjan1, Ray Lattarulo2, Joshue Perez-Rastelli2, Javier Ibanez-Guzman1, Alberto Pena2

Abstract— Different implementations on automated vehiclesare being introduced by researchers and manufacturers, par-ticularly for longitudinal control. Some applications includetraffic jam assistance, emergency assisted braking, CruiseControl, among others. However, lateral control applicationsare less common due to the complexities of the dynamic.In this paper, an Artificial Intelligence approach to controlthe steering wheel of an automated vehicle is presented. Twonew lateral controllers are developed. One is based on humanexpertise (Fuzzy Logic), and the other is based on an AdaptiveNetwork based Fuzzy Inference System (ANFIS) using expertdriver data. Those controllers have been tested in a simulationenvironment, called Dynacar, and they were compared with aclassical PID controller, giving promising results.

I. INTRODUCTION

In recent years, the research and development in auto-mated driving is intensively increased in automotive industry.Indeed, automated vehicles are opening a new road-map tomany new applications and benefits for the society, i.e.: newmobility alternative, increasing safety and reducing parkingareas, assistance to drivers and intelligent and connectedinfrastructures. Moreover, this is topic where many researchgroups, universities and manufactures are working aroundthe world.

Based on most of the previous real automated vehicleimplementations in the literature, a general control architec-ture is divided in six main stages: acquisition, perception,communication, decision, control and actuation ([1]), wherethe perception, decision and control are the most critical.An automated vehicle uses sensors to get information onthe external environment, i.e.: for the ego positioning (GPS,radars) and the detection of others obstacles around (Lidarsand cameras). This information is processed in order to finda safe trajectory to be followed by the vehicle. This processis called the Global and local planner module, some authorscall it navigation. Then, this trajectory is sent to the controlmodule to maintain the vehicles on the road. Finally, theactuators receive and execute this command by the steeringwheel and pedals.

The Original Equipment Manufacturers (OEMs) have beenstarted to work in this field fifteen years ago with the firstuses of Advanced Driver Assistance Systems (ADAS), wherethe most known is the Anti-lock braking system (ABS). The

1(e-mail: sarouthan.sriranjan@u-psud.fr and javier.ibanez-guzman@renault.com)

2Tecnalia Research and Innovation, Derio, Vizcaya, Spain, 48160. (e-mail: {rayalejandro.lattarulo, joshue.perez, alberto.pena}@tecnalia.com).

* Authors wants to thank to the ECSEL project ENABLE-S3 for itssupport in the development of this work, and the Non-Disclosure Agreementbetween Tecnalia and Renault s.a.s

main goal of ADAS is to improve the safety of the passengersin the vehicles and the Vulnerable Road Users. Studies saythat ninety five percent of the road accidents are causedbecause of a human factor ([2]). Most of the accidents arecaused by a human limitation, as well as reaction time ordistractions. The next step is the implementation of moresafety and robust functionalities for automated vehicle.

So far, lateral control applications have special attention,where complex models have been used mainly in auto-mated longitudinal system [3] and [4]. Other researcheshave demonstrated that some Artificial intelligence (AI)techniques, as fuzzy logic, offers a good solutions to controlcomplex system, like automated vehicles [5]. Fuzzy sets donot need an exact mathematical model of the plan, as in[6]. These controllers can imitate the human driver behaviorwith a knowledge base (or rules). However, in most of thecases, there aren’t standard methodologies defined these rulesbases and the membership functions. Saifizul et al. [7] hassimulated an ANFIS controller for the lateral applications.However, this approach only considers the constant curvaturein the circuit (not path planning), with some significantovershoot and oscillation on the steering angle at the momentthe curvature changes [7].

In this paper, we will focus on the lateral control ofthe vehicle applying three different controllers. Differentmaneuvers have been tested, as urban intersections, lanekeeping and lane changes, based on a real time path planningpresented on [8]. The goal is to reduce the lateral error toreference given by the path planner. In this work, a studyof different control techniques is presented, where a PID, aFuzzy Logic and an ANFIS controllers are considered for thelateral dynamic of an automated vehicle. The modelled ve-hicle used to validate our approach is an automated RenaultTwizy.

The rest of the paper is organized as follow: a brief stateof the art of the control in the automotive field in Section 2.Next there is a description of the simulation environment,Dynacar, used for our validation. Then we will see thefunctioning of tree different controllers for the lateral control:a PID controller, the fuzzy logic and the Neuro-Fuzzy controlin Section 4. Finally, we will compare the performances ofthese three controllers in Section 5. We concluded on theperformances of these controllers and the future works.

II. WORK MOTIVATION

In automated driving field, the control of the vehicle isdivided in lateral and longitudinal. The first one concernsthe action on the steering wheel. There are different kinds

of controllers that can be used for the case of a lateral orlongitudinal actions ([9]).

The steering of a vehicle is considered as a nonlineardynamic system, especially at high speed. It is possible tocontrol this system through techniques that allows quick,smooth and high quality control ([5]). The action on thelateral control depends mainly of 2 modules of the globalarchitecture, the path planner (trajectory) and controller itself(tracking) ([1]).

Sei-Bum Choi has developed an adaptive control law forthe lateral control of automated vehicle using magnetic sen-sors in the vehicle?s front wheels. Another big change in thelow level steering wheel system has been the incorporationof electric-power-assisted steering (EPS) as a substitution forthe traditional hydraulic power steering (HPS) systems in thenew generation of vehicles ([10]).

However, the most classical lateral controller found isthe Proportional Integral Derivative (PID) controller ([11]).Indeed, this controller is present in many applications in theindustry because of the reduced number of parameters to betuned.

Methods using fuzzy logic, linear matrix inequality opti-mization and yaw rate control have been used in order tomake the vehicle following the reference trajectory ([12],[13]).

The main advantage of a fuzzy controller is that it isnot necessary to have an exact mathematical model of thesystem to control it. The control problem is reduced toestimate the input, set up a rule base and assign the outputvalues. Besides, this controller can emulate the behavior fromdrivers due to knowledge base, using the human experience,and if-then rules. Many contributions related with FuzzyLogic controller have been published ([6], [9]). However,the problem to tune and to estimate the rule bases for lateralapplications remains still an open issue.

Some automated methods to tune the Fuzzy controllerhave been developed for longitudinal controllers [14]. ThisNeuro-Fuzzy system combines the semantic rules and learn-ing capability of neural networks. Some applications haveused neuro-fuzzy systems to control nonlinear systems orto adjust controllers [15]. In the Intelligent TransportationSystem (ITS) field, neuro-fuzzy systems had been used in thetraffic modelling, as in [16]. However, this kind of controllerhas not been tested in lateral dynamic for automated vehicles.

Previous works on neuro-fuzzy controller ([14]) presents areal time implementation of a neuro-fuzzy controller for thelongitudinal control of a vehicle. This neuro-fuzzy systemimproves the performances of previous controller by includ-ing the experience of expert drivers. In light of the size of thedata base used, this controller gives good results. We are onthe next step, to study the use of fuzzy logic and neuro-fuzzycontroller for the lateral control of the vehicle.

III. SIMULATION PLATFORM

Dynacar (figure 1) is a simulation tool developed byTecnalia which provides a real-time vehicle model. It focuseson two main domains the dynamics of the vehicle and the

Fig. 1: Dynacar by Tecnalia

electronics architecture of the vehicle. It provides a completearchitecture to simulate and validate the automated capabili-ties of a vehicle [17]. This architecture is particularly adaptedfor urban scenarios. Different lateral control algorithms weretested with this platforme.

It provides a high-fidelity vehicle physics simulation. Thisis combined with a Pacejka tire model, and submodelsfor elements like the engine, transmission, steering system,braking system, aerodynamics, etc ([18]). For this work, weuse the equations of the lateral dynamic of the bicycle modelas shown in (1) and (2), as are explained in [19]:

y = −2Cαf + 2CαrmVx

y+

(−2αCαf − 2bCαr

mVx−Vx

)ψ+

2αCαfm

δ

(1)

ψ = −2αCαf + 2CαrIzVx

y +

(− 2a2Cαf − 2b2Cαr

IzVx

)+

2αCαrIz

δ,

(2)

where m is the vehicle mass, Vx is the longitudinal speed,Iz is the yaw inertia, a and b are the distance between thefront/rear wheels and the center of gravity, respectively, andδ represents the front wheel steering angle (which is thecontrol signal in the automated control approach).

The values used in model for the twizy described beforeare resumed in table I:

TABLE I

Parameter Value Unitm 582.5 [kg]Iz 314.28 [kg.m2]

Wheelbase 1.686 mDist. to COG (b) 0.4231 m

Cαf 5.784 [1/rad]Cαr 17.163 [1/rad]

The real-time capability is very valuable, as, combinedwith its notable modularity and interfacing options, it permitsto execute tests with driver-in-the-loop (DiL) and hardware-in-the-loop (HiL) setups, for instance for ECU (ElectronicControl Unit) development or also motor test bench testing([20]).

For this application, a reference trajectory is generatedusing parametric curves as in [8]. This path planner is used

Fig. 2: Membership function for the Lateral Error.

Fig. 3: Membership function for the Angular Error.

as the reference for the lateral control module, using differentcontrollers.

IV. LATERAL CONTROL

On the current section, three control techniques will beexplain to gather some concepts related to these ones, in-cluding the designing process. These ones were tested on anautomated driving simulator to verify the differences betweenthem and, advantages and disadvantages that each presents.

A. PID controller

The first controller implemented on the current approachwas a PID controller associated to the lateral error (this iscalculated as a reference of the frontal point of the vehicleand the path). The equation associated to the steering is:

Cv = Kpelat +Ki

∫t

elatdt+Kdd

dtelat (3)

Kp, Ki and Kd are the gains fixed manually on the vehicleusing classic techniques of tuning.

B. Fuzzy logic controller

For the fuzzy controller, two input variables were used:the lateral and the angular error. Each variable is defined bya membership function affecting its corresponding linguisticlabels, which is represented in the rule base. For the cur-rent approach, a triangular shape membership function wasimplemented.

The lateral and angular errors use three labels in eachcase: Left, Middle and Right. The membership functions aresymmetric considering the ideal symmetry of the steeringwheel. The range used for the lateral error is [-0.6; 0.6] (m)as it is illustrated on figure 2 and the one for the angularerror is [-20; 20] (degrees) as it is illustrated on figure 3.

The defuzzification operation uses a method called“center-of-area” [5]. This is one of the most prevalent and

physically appealing of all defuzzification methods. Here, Wi

are the weights of the linguistic label i for each membershipfunction. Oi are the assigned values of the singleton outputfor the label i. Finally, Xi is the crisp value of each rulecondition. Each crisp value is calculated by the Mamdaniinference method:

Xi =∑ WiOi

Wi(4)

To define the output, nine singletons were established withvarious weights: RightP4, RightP3, RightP2, RightP1,Middle, LeftP1, LeftP2, LeftP3, LeftP4, which weredefined between [-1 and 1] and spaced each 0.25.

The rule base interprets the input variables, based on theIF . . . THEN form. The target output is given by the steeringposition. The rules are shown as follows:

IF LateralError Right AND AngularError Right THENSteering RightP4

IF LateralError Right AND AngularError Middle THENSteering RightP3

IF LateralError Right AND AngularError Left THENSteering RightP2

IF LateralError Middle AND AngularError Right THENSteering RightP1

IF LateralError Middle AND AngularError MiddleTHEN Steering MiddleIF LateralError Middle AND AngularError Left THENSteering LeftP1

IF LateralError Left AND AngularError Right THENSteering LeftP2

IF LateralError Left AND AngularError Middle THENSteering LeftP3

IF LateralError Left AND AngularError Left THENSteering LeftP4

C. Neuro-Fuzzy Controller

Pursuing the development of fuzzy-logic-based controller,many industrial processes are now controlled using theknowledge of expert operators. Thus, the fusion of ArtificialNeural Networks and Fuzzy Inference Systems has growninterest among researchers. There are some limitations inthe IF ... THEN systems. There are not standard methods fortransforming experience from the driver into the rule base.

The learning process of the Neural Networks is based onthe adjustment of the weight of the connections between thenodes net. Neuro-Fuzzy systems combine the easy handlingof the IF ... THEN rules of the fuzzy logic with the learningcapacity of neural networks.

The Adaptive-Network-Based-Fuzzy Inference System(ANFIS) was one of the first neuro-fuzzy systems developed.The principle is to extract fuzzy rules at each level of a neuralnetwork. When the rules have been obtained, they provide theinformation on the overall behavior of the process. ANFISimplements the Takagi-Sugeno model for the IF ... THENrules of the fuzzy logic.

Fig. 4: Membership function for the Lateral Error of theANFIS.

Fig. 5: Membership function for the Angular Error of theANFIS.

Neuro Fuzzy is based on the creation of a controller byusing a learning process from a data base. We want to trainour ANFIS system using as reference the expert knowledgeof a driver and for this purposes, it was recorded the behaviorof this driver trying to follow the road. The steering position,the lateral and the angular error were recorded during therolling session.

The parameters chosen for the learning process of theANFIS systems were:

Algorithm ANFISSystem 2 Inputs and 1 Output

Membership function shape TriangularNumber of membership func. 3

Inference system Takagi-SugenoNumber of rules 9

Training algorithm Back propagationTraining data set 25000

Validation data set 25000

The proposed neuro-fuzzy controller has two input vari-able like the previous fuzzy controller studied (the lateral andthe angular error) and one output variable (the steering posi-tion). Each input has three membership functions, bringingto nine rules.

The two inputs have still the same membership functionshape: three triangular shapes. The range used for the lateralerror is [-1; 1] meters (figure 4) and the one for the angularerror is [-20; 20] degrees (figure 5). These ranges dependon the date base used for the learning process and, ofcourse, a human driver has a driving way that contains moreimprecision than a driving from a controller which is tunedto have the lowest error.

Fig. 6: Circuit of the driving session for the Simulation onDynacar.

The nine singletons of the ANFIS system are:

Singleton ValueRight P4 -0.9535Right P3 -0.538Right P2 -0.485Right P1 -0.235Middle 0.02Left P1 0.24Left P2 0.46Left P3 0.67Left P4 0.95

In previous works [7], the dataset was tuned by a FuzzyLogic model. In our approach with ANFIS, the controlleris trained by human knowledge. The fuzzy controller has aclose behavior to the human driver.

V. TESTS AND RESULTS

In order to compare the performances of these three con-trollers, they have been tested in simulation using a predefinecircuit. It contains six intersections as it is illustrated onfigure 6.

Additionally, the use cases defined to verify the behaviorof the controllers were four. A segment of the circuit withthree consecutive intersections and a lane change, both atlow speed, are the first and the second scenario. In the caseof the third and fourth use cases are considered the sameintersections and lane changing but at high speed.

For the purposes of the current work, low speed is consid-ered as a constant speed of 20 km/h and high speed is basedon a speed profile given by comfort and curvature constrainswith a maximum value of 50 km/h. And the controllers willbe compared using the lateral error and steering responses.

(a) Intersections (lateral error)

(b) Intersections (steering)

(c) Lane change (lateral error)

(d) Lane change (steering)

Fig. 7: Lateral error and Steering at low speed.

A. Test at low speed

Figure 7 shows the lateral error (figures 7a and 7c) andsteering (figures 7b and 7d) at constant speed of 20 km/h. Insuch a way, the figure 7a depicts how the fuzzy controllerhas a better response reducing the lateral error on theintersections scenario. In the case of the fuzzy trained withANFIS has a better response reducing the lateral error, butin the other direction is less effective that the PID controller(directly related with the data used for training). In otherhand, the figure 7b illustrates the steering for these threecontrollers and they depict a similar response (in some cases

the fuzzy controllers is a little less noisy).On figures 7c and 7d are illustrated the lateral error

and steering (respectively) on the lane change scenario (atlow speed) but there are not big differences between thecontrollers. However, the fuzzy and ANFIS controllers aremore effective to correct the lateral error (faster than thePID).

B. Test at high speed (using speed profile)

Figure 8 shows the lateral error (figures 8a and 8c) andsteering (figures 8b and 8d) using a speed profile associ-ated with the curvature of the path and lateral accelerationconcepts (related with comfort on driving) with a maximumspeed of 50 km/h. The figures 8a and 8b depict the samebehavior that in the case of lateral error behavior associatedto the intersections scenario at low speed.

Figures 7c and 7d are illustrated the lateral error andsteering (respectively) on the lane change maneuver. Inthis case, the behaviors of the controllers have changedconsiderably, compared to the low speed scenario. The lateralerror has less overshoots in the case of the fuzzy controllertrained with ANFIS and it has less abrupt changes on thesteering and less overshoots.

VI. CONCLUSION

On the current approach, three controller techniques weretested for the lateral control of a automated vehicle to verifythe advantages and disadvantages that each presents.

The PID controller illustrates a good response at lowspeed. However, PID controller are difficult to be tuned andthe gains are not adapted to the speed. Fuzzy logic is usefulcompared to PID controller because a complex mathematicmodel is not needed. Fuzzy Logic is intuitive by thanks tousing Labels and semantic rules, as humans do.

Besides, using neural methods are powerful because wejust need Driver experience to train the system (no mathemat-ical model or label based model). Our controller is generatedby the data set from human drivers’ experiences, giving abetter result.

In the case of the fuzzy controller, it shows a good re-sponse with some overshoots on the cases of abrupt changesas on lane change. For the current approach the fuzzycontroller was designed just using lateral parameters (lateralerror and angular error) but in future works will considervariables of the longitudinal domain as speed (MISO system)to improve the response of the controller (the PID is justpresented for SISO systems).

The ANFIS techniques used to train a fuzzy controllercould be considered as the best alternative. Admittedly, someresults are a bit less effective than the fuzzy controller inour tests. But these performances can be improved due tothey used the data gather from an expert driver to emulatethe driving behaviors. The time used to develop and tunethis controller is really short compared to the time for theother controllers thanks to the use of learning process. Infuture works, this controller can be improved with a greatamount of data. This lateral longitudinal control can also be

(a) Intersections (lateral error)

(b) Intersections (steering)

(c) Lane change (lateral error)

(d) Lane change (steering)

Fig. 8: Lateral error and Steering at high speed.

improved if other variables are taking into account. Finally,a multi-variable system, considering longitudinal variables,and more driving situations may improve our approach.

REFERENCES

[1] D. Gonzalez and J. Perez, “Control architecture for cybernetic trans-portation systems in urban environments,” IEEE Intelligent VehiclesSymposium Proceedings (IV), 2013.

[2] L. Li and X. Zhu, “Desgin concept and method of advanced driverassistance systems,” Fifth conference on measuring technology andmechatronics automation, pp. 434 – 437, 2013.

[3] A. Katriniok, J. P. Maschuw, F. Christen, L. Eckstein, and D. Abel,“Optimal vehicle dynamics control for combined longitudinal andlateral autonomous vehicle guidance,” in Control Conference (ECC),2013 European, pp. 974–979, July 2013.

[4] P. Song, C. Zong, and M. Tomizuka, “Combined longitudinal andlateral control for automated lane guidance of full drive-by-wirevehicles,” SAE Int. J. Passeng. Cars Electron. Electr. Syst., vol. 8,pp. 419–424, 04 2015.

[5] M. Sugeno and M. Nishida, “Fuzzy control of model car,” Fuzzy SetsSystems, vol. 16, no. 2, pp. 103 – 113, 1985.

[6] J. Perez, V. Milanes, and E. Onieva, “Cascade architecture for lateralcontrol in autonomous vehicles,” IEEE Transactions on IntelligentTransportation Systems, vol. 12, no. 1, pp. 73 – 82, 2011.

[7] A. A. Saifizul, M. Z. Zainon, and N. A. A. Osman, “An anfiscontroller for vision-based lateral vehicle control system,” in 20069th International Conference on Control, Automation, Robotics andVision, pp. 1–4, Dec 2006.

[8] J. Perez, R. Lattarulo, and F. Nashashibi, “Dynamic trajectory genera-tion using continuous-curvature algorithms for door to door assistancevehicles,” IEEE Intelligent Vehicles Symposium Proceedings (IV),2014.

[9] V. Milanes, J. Villagra, J. Perez, and C. Gonzalez, “Low-speedlongitudinal controllers for mass-produced cars: A comparative study,”IEEE Transactions on Industrial Electronics, vol. 59, no. 1, pp. 620– 628, 2012.

[10] S. B. Choi, “The design of a look-down feedback adaptive controllerfor the lateral control of front-wheel-steering autonomous highwayvehicles,” IEEE Transactions On Vehicular Technology, vol. 49, no. 6,pp. 2257 – 2269, 2000.

[11] S. Bennett, “The past of pid controllers,” IFAC Workshop on DigitalControl: Past, Present and Future of PID Control, pp. 1 – 11, 2000.

[12] H.-S. Tan, F. Bu, and B. Bougler, “A real-world application oflaneguidance technologiesautomated snowblower,” IEEE Transactionson Intelligent Transportation Systems, vol. 8, no. 3, pp. 538 – 548,2007.

[13] R. White and M. Tomizuka, “Autonomous following lateral controlof heavy vehicles using laser scanning radar,” Proceedings of theAmerican Control Conference, vol. 3, pp. 2333 – 2338, 2001.

[14] J. Perez, A. Gajate, V. Milanes, E. Onieva, and M. Santos, “Designand implementation of a neuro-fuzzy system for longitudinal controlof autonomous vehicles,” IEEE International Conference on FuzzySystems, 2010.

[15] C. Quek, M. Pasquier, and B. Lim, “A novel self-organizing fuzzy rule-based system for modelling traffic flow behaviour,” Expert Systemswith Applications, vol. 36, no. 10, pp. 12167 – 12178, 2009.

[16] K. M. Udofia and J. O. Emagbetere, “Development of multi-agentanfis-based model for urban traffic signal control,” in 2013 Interna-tional Conference on Connected Vehicles and Expo (ICCVE), pp. 662–669, Dec 2013.

[17] R. Lattarulo, J. Perez, and M. Dendaluce, “A complete framework fordeveloping and testing automated driving controllers,” Preprints ofthe 20th World Congress The International Federation of AutomaticControl, 2017.

[18] I. Iglesias, “Herramienta para acelerar el desarrollo de nuevos sistemasy controles para automocin,” Revista Automtica e Intrumentacin,vol. 478, pp. 45 – 49, 2015.

[19] R. Rajamani., Vehicle Dynamics and Control. 2012.[20] I. I. Aguinaga, A. M. Sandi, and A. P. Rodriguez, “Vehicle modelling

for real time systems application. the virtual rolling chassis,” RevistaDyna, vol. 88, pp. 206 – 215, 2013.