An MPC approach to the design of motion cueing algorithms fordriving simulators

Mauro Baseggio, Alessandro Beghi, Mattia Bruschetta, Fabio Maran and Diego Minen

Abstract— Driving simulators play an important role in thedevelopment of new vehicles and advanced driver assistancedevices. In fact, on the one hand, having a human driver ona driving simulator allows automotive OEMs to bridge thegap between virtual prototyping and on-road testing duringthe vehicle development phase. On the other hand, noveldriver assistance systems (such as advanced accident avoidancesystems) can be safely tested by having the driver operatingthe vehicle in a virtual, highly realistic environment, whilebeing exposed to hazardous situations. In both applications,it is crucial to faithfully reproduce in the simulator the driversperception of forces acting on the vehicle and its acceleration.The strategy used to operate the simulator platform withinits limited working space to provide the driver with the mostrealistic perception goes under the name of motion cueing.In this paper we describe a novel approach to motion cueingdesign that is based on Model Predictive Control techniques.Two features characterize the algorithm, namely, the use of adetailed model of the human vestibular system and a predictivestrategy based on the availability of a virtual driver. Differentlyfrom classical schemes based on washout filters, such featuresallows a better implementation of tilt coordination and tohandle more efficiently the platform limits.

I. INTRODUCTION

In the automotive field, there is an increasing intereston the development of dynamic driving simulator systems.Applications of such systems are in fact becoming more andmore numerous and diverse, from driver’s training and virtualvehicle set-up in the racing context, to the development ofadvanced driver assistance and accident avoidance systems.Automotive OEMs exploit driving simulators to cut downthe costs for prototyping, by anticipating the on road vehiclebehavior. Furthermore, such systems allow to ease the devel-opment process of the various vehicle components, by testingdifferent hardware and software solutions, by resorting tosophisticated Hardware-In-the-Loop (HIL) tools, in a safeand realistic virtual environment. Given the wide range of ap-plications, there is an ever growing need of developing smallsize, low cost dynamic simulators. In a different perspective,realistic dynamic simulators are crucial to develop detaileddriver behavior models to devise accident avoidance strate-gies, for example by putting a standard driver in simulateddangerous condition and measuring his/her reactions. Also,assessment of driver performance under stress conditions(i.e., adverse weather conditions, endurance driving, etc.) can

This work was supported by VI-Grade ItalyMauro Baseggio, Alessandro Beghi, Mattia Bruschetta, Fabio Maran are

with University of Padova, Department of Information Engineering ViaGradenigo 6/b, 35131, Padova, , Italy name.lastname@unipd.it

Diego Minen is with VI-Grade Italy, Via l’Aquila 1c 33010, Tavagnacco,Udine, Italy diego.minen@vi-grade.com

be more effectively performed by using dynamic simulatorswith a high degree of immersion into virtual environments.To this regard, ever more effective Hazard Perception Testcan be devised and used as requirements for achievinga driver license. In this scenario, the role of the motioncueing (MC) strategy, i.e. the algorithm for transformingvehicle accelerations into admissible motion commands tothe platform, becomes more and more crucial to guarantee arealistic perception of the driving conditions. Motion cueingis a very complicated part of a dynamic simulator due tothe complex nature of the human perception systems. Infact, it is not clear yet, from a physiological point of view,the role and priorities of stimula of different nature to theoverall perception of accelerations and force. It is howeverwell established that a coordinated visual-motion action isfundamental for achieving satisfactory performance of a MCalgorithm. Given the above motivations the necessity of aperceptive model within the MC algorithm becomes evident.The “classical” approach to MC is based on high passfiltering the reference acceleration signal to keep platformexcursions within the operational limits. Such approach issimple and has been implemented in many different waysover the years. However, it has some shortcomings:

• it is a conservative approach, and as a consequence, theplatform operational space is not fully exploited;

• it cannot explicitly handle hard constraints on the plat-form movements and accelerations;

• being a non model-based approach, set-up vehicle vari-ations are hardly distinguishable from modification ofthe tuning of MC algorithm.

Recently, a novel approach to motion cueing has beenproposed in [1], [2], based on a strategy already consolidatedin the field of industrial process control, namely, ModelPredictive Control (MPC). MPC is a model-based controlmethodology that allows to handle limits on the workingspace and to exploit information on future reference signal.In this approach, a model of the human perception systemscan be included in the motion cueing strategy and predictionsof the future trajectory can be used to fully exploit theplatform working area and generate accurate cues. In thispaper we propose a MC algorithm for a small size dynamicsimulator that is based on a specific implementation of theMPC. In particular, a detailed model of the human vestibularsystem is employed, as well as and availability of predictionsof the future vehicle behavior as provided by a virtual driverdeveloped in a detailed virtual prototyping environment.Performance of the algorithm is evaluated by comparison

2011 14th International IEEE Conference onIntelligent Transportation SystemsWashington, DC, USA. October 5-7, 2011

978-1-4577-2197-7/11/$26.00 ©2011 IEEE 692

TABLE IPLATFORM PERFORMANCE.

Range Position Velocity Accelerationx 1m 1.3m/s 3.3m/s2

y 1m 1.3m/s 3.6m/s2

z 0.3m 0.9m/s 4.9m/s2

Roll 30deg 112deg/s 600deg/s2

Pitch 24deg 61deg/s 600deg/s2

Yaw 50deg 61deg/s 240deg/s2

with classical MC strategies, showing the effectiveness ofthe proposed approach.

II. PROBLEM STATEMENT

In Fig. 1 the platform considered in this study is repre-sented. Its peculiarity is in the mechanical structure. By usinglinear actuators instead of the classic hexapodal structure,it is possible to achieve satisfactory results in physicalsimulation with a relatively small size hardware, that can fitstandard laboratories environments, whereas traditional, largedimensional, hexapodal platform require dedicated hangars.

Fig. 1. Platform sketch.

The architecture is based on three completely decoupleddegrees of freedom (DOFs, longitudinal and lateral axis,and yaw), and three partially coupled DOFs. The simulatorkernel, i.e. the vehicle dynamics physical engine, has beendeveloped and extensively tested on the field and providesa highly reliable representation of the real vehicle behav-ior. The screen covers more than 180 deg and moves inagreement with the platform to guarantee full immersion ofthe driver in the virtual environment. Finally, force feedbackon the steering wheel and the braking system enhances the“driver’s feeling” of the vehicle behaviour.

The platform dynamic performance reported in Tab. Ihighlights the limitations of the operational space, withmaximal linear excursions of 1 m. This fact makes the roleof the MC algorithm crucial. The MC strategy has to providethe displacement references to the control system of theplatform, which is assumed to be able to perfectly track thereference signals, with a fixed time delay. The conceptualscheme of the MC procedure is shown in Fig. 2, and iscomposed by the following steps:

1) obtain the actual vehicle accelerations a from thesimulation software;

2) obtain the perceived acceleration r by filtering a via thevestibular system model, thus generating the reference

Fig. 2. Scheme of motion cueing strategy.

Fig. 3. Representation of MPC principle.

signal for the MPC algorithm;3) compute via MPC the displacement signal d passed to

the platform control system.

III. MODEL PREDICTIVE CONTROL

Model Predictive Control (MPC) is an advanced controltechnique widely used in industrial applications [3], [4] sincethe 1980s. In recent years, robust and efficient implemen-tations have been developed, as well as software tools instandard computational environments that ease the designof MPC algorithms. The main advantages of MPC can besummarized as follows:

• its underlying idea is simple and intuitive to understand;• it’s the only generic control technique that efficiently

deals with constraints;• it can handle Multi-Input Multi-Output (MIMO) sys-

tems without formally increasing the complexity of theproblem;

• it can handle non linearities in both the model and theconstraints.

A. MPC basics

Assume (discrete-time problem) that at time k a referencetrajectory r(t|k), t ≥ k and a current measure of the outputy(k), are available. Note that the current input is not yetcomputed. Now, suppose to have a model of the process tobe controlled and that the state of the system (or its estimate)is available. We can therefore predict the future output y(k+i|k), i = 1, . . . , Np corresponding to the input sequenceu(k + i|k), i = 0, . . . , Np − 1 in a time-window of lengthNp, where Np is the prediction horizon length (Fig. 3).

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The idea is to compute the input sequence u(k+ i|k) thatminimizes a cost function, e.g. a function of the trackingerror

ε(k + i|k) = r(k + i|k)− y(k + i|k),

while respecting a set of constraints. The input to be appliedat time k is chosen as

u(k) = u(k|k);

at time k + 1 a new output y(k + 1) is measured and thealgorithm is iterated applying only the first element of thecomputed optimal input sequence.

B. Process model

In the literature, different implementations of the MPCprinciple have been proposed, with different model struc-tures. In the application we are considering, the real-timeconstraints and the MIMO structure of the model are welldescribed by a linear discrete state space model (sampledversion of the continuous process) of the form

xm(k + 1) = Amxm(k) +Bmu(k)

y(k) = Cmxm(k).

We assume that the input does not have a direct effect onthe output (strictly proper system). State-space models areparticularly well suited to design state estimators by usingwell-established tools of statistical filtering theory.

In our case, as proposed by Wang [3], we consider as theelement to be optimized the input difference ∆u(k) = u(k)−u(k − 1): considering also the state difference ∆xm(k), wecan write a new state equation

∆xm(k + 1) = Am∆xm(k) +Bm∆u(k).

Considering the output difference

y(k + 1)− y(k) = CmAm∆xm(k) + CmBm∆u(k)

and defining a new, augmented state x(k) :=[∆xm(k)T y(k)T ]T , we obtain a new model

x(k + 1) =

[Am 0

CmAm I

]x(k) +

[Bm

CmBm

]∆u(k)

y(k) =[0 I

]x(k)

where the control input is ∆u(k).

C. Cost function and state estimation

The optimal input sequence ∆u(k+i|k), i = 0, . . . , Np−1is computed by minimizing a cost function of the form [3]

J(∆U) = (Rs − Y )TQ(Rs − Y ) + UTSU + ∆UTR∆U

where the tracking error, the input variations and the controlinputs are weighted by matrices Q, R and S respectively. Rs,Y , U , and ∆U are matrices of appropriate sizes obtainedfrom the vectorization of the reference signal rs(k + i),the output prediction y(k + i|k), the input u(k + i) andits difference ∆u(k + i), all considered on a horizon ofNp samples. The cost function can be rewritten in order todepend only on the input difference matrix ∆U , obtaining

the classic formulation of a quadratic problem (QP) [3], thatis,

J =1

2∆UTH∆U + ∆UTF.

Note that the length of the prediction horizon Np candiffer from the control horizon Nc: for the sake of simplicity,we will consider Np = Nc. Np is a fundamental parameterboth in terms of computational complexity of the problemand stabilizing properties of the resulting control law. Theweights Q and R, on the tracking error and on the inputrespectively, allow to tune the control law to obtain thedesired behavior.

To deal with constraints, limitations on the system inputsU and outputs Y can be written in terms of constraints onthe input variations ∆U [3]

A ·∆U ≤ b .

As a consequence, the QP becomes a constrained QP, forwhich a variety of solving algorithms are available in liter-ature. This is a key step to ensure that the control problem,and consequently the MC algorithm, can be solved in realtime.

State estimation is also an important element of the MPCscheme since it represents the key to actually close thecontrol loop. In the considered setup, since the platform hasits own position controller, state estimation is not necessary.Nevertheless, it can be used to close a second control loopin case the platform control system is linear.

IV. THE VESTIBULAR SYSTEM

The vestibular system is located in the inner ear and iscomposed by the semicircular canals and the otolith organs.The former sense the angular rotation and the latter linearmotion. Accurate mathematical models of the two systemshave been derived starting from the ’70s for application toMC of flight simulators. Zacharias [5], in a survey writtenin the 1979, reported most of the results nowadays available.Telban and Cardullo in 2005 [6], [7] published a simplifiedtransfer function model with estimates of the correspondingparameter values. For the semicircular canal, the transferfunction that can best relate the sensed angular velocity tothe acceleration stimulus in a MC control problem is thefollowing:

WSCC(s) =ω (s)

α(s)= 5.73

80s2

(1 + 80s)(1 + 5.73s)(1)

The otoliths are described in terms of the following transferfunction that relates the sensed response to the specific forcestimulus:

WOTH(s) =f(s)

f(s)= 0.4

1 + 10s

(1 + 5s)(1 + 0.016s)(2)

A. Tilt coordination

An important component of perception in a dynamicsimulator is given by tilt coordination. Otoliths are notcapable to discriminate between gravitational and longitu-dinal forces. Hence, by using a non-zero pitch angle and

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without any other visual reference, it is possible to pro-vide the driver in the simulator with a ”fake” longitudinalacceleration sensation. The same holds true for roll andlateral acceleration. Such approach goes under the name oftilt coordination. Taking into account this effect is crucialto reproduce low frequency behavior with a reduced rangeworking area. Tilt coordination is particularly relevant whenpredictions of the future vehicle trajectories are available,since, differently from classical cueing strategies, it can yieldto less conservative strategies and thus to better exploitationof the platform working space. In the perception model,because of linearization, tilt coordination is nothing but afurther contribution in the otoliths model WOTH(s) due tothe pitch angle in the longitudinal direction and to the rollangle in the lateral direction.

B. The complete model

In order to use the perception models in the MPC ap-proach, state space realization of WOTH(s) and WSCC(s)are obtained and coupled with the tilt coordination contribu-tion for all the 6 DOFs. The resulting system can be writtenas

x =AV ESTx+BV ESTu

y =CV ESTx+DV ESTu

where the input u is composed by the three applied lon-gitudinal accelerations and the three angular velocities, i.eu = [ax, ay, az, βx, βy, βz]T . The overall state vector x is

x =[xSCC xOTH vx px vy py vz pz θ φ ψ

]T(3)

where the actual angles, positions and velocities are ob-tained by integration from the inputs u and xOTH andxSCC are the state variable for the dynamical systemsassociated with the otoliths and semicircular canals. Toimpose a set of constraints in a simple manner we choosey = [v, f , vx, px, vy, py, vz, pz, θ, φ, ψ]T , where v and f arethe vectors of perceived angular velocities and longitudinalacceleration along all the DOFs.

V. RESULTS

We report here some results obtained by using data forma non professional driver training session on the Silverstonetrack with a GP2-class car. Since the platform is almost de-coupled for all the 6 DOFs, we consider here the longitudinaldynamics only, hence the longitudinal acceleration, that hasto be reproduced as faithfully as possible (in terms of driversensations) by operating the platform with longitudinal andpitch motions. With reference to the algorithm structure asdescribed in Section III, Fig. 2, we introduce an intermediatestep, that is, longitudinal accelerations from the simulatorare appropriately scaled to obtain a feasible profile for theplatform.

0 5 10 15 20 25

−1

−0.5

0

0.5

time [s]

m /

s2

Ref: Perceived long. acc. x axisPerceived longit. acc.

Fig. 4. Perceived acceleration tracking based on MPC approach withoutlook ahead

A. Comparison with classical Motion Cueing Algorithm

To better understand the potential of MPC for designingMC algorithms, in this Subsection we show that it is possibleto reproduce the behavior of classical MC algorithms, basedon the combination of filters with a washout strategy, byappropriately tuning the MPC parameters. To this aim, weset up a simulation based on experimental telemetry data. Tobetter highlight the properties of the algorithms, we concen-trate on the pure longitudinal dynamic with no pitch action,hence with no tilt coordination. This is a reasonable conditionsince in the classical approach prediction is not exploited andtilt coordination cannot be effectively performed. To mimicwhat happens in the classical approach, telemetry data arehigh pass filtered after linear scaling, and used to computethe reference signal for the MPC. The wash-out action isperformed by the MPC strategy by weighting the positionof the platform in the cost function. In agreement with theclassical approach, no look ahead is used. Tuning of theweights is performed so as to reproduce a similar behavior ofthe classical and MPC algorithms. In Fig. 4 tracking of theperceived accelerations obtained by using the MPC approachis shown. Tracking is not fully satisfactory because of thewash-out action. In Fig. 5 and Fig. 6 the comparison of thereal platform acceleration (classical MC) and the MPC basedone is presented, both in terms of accelerations and positions.The reference trajectory for for the MPC algorithm is alsoreported. In this segment of the circuit the two strategiesappear to be almost equivalent, in terms of both accelerationand position signals. It is interesting to note that the wash-out action can be clearly identified as a deviation from thereference trajectory in both strategies (after time t = 15 sin Fig. 5), and it can be interpreted as generating a lowfrequency tracking error.

B. Using the look ahead

In the look ahead approach, we make use of a virtualdriver to predict the future telemetry and feed such signal as areference to the MPC based MC algorithm, also consideringthe hard constraints provided by the platform operationalspace. In Fig. 7 a look ahead prediction over a time intervalof 2 s is used. The comparison with the classical approachis reported in Figs. 8 and 9 in terms of accelerations andposition signals, respectively. The MPC based algorithm with

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0 5 10 15 20 25 30

−1

−0.5

0

0.5

1

time [s]

m /

s2

Ref. longit. acc. x axis (scaled)Applied longit. acc. MPCApplied longit. acc. classical MC

Fig. 5. Comparison of applied acceleration tracking without look ahead:MPC based and classical motion cueing

0 10 20 30 40 50 60 70−0.3

−0.2

−0.1

0

0.1

0.2

0.3

time [s]

m

Longit. displ. x axis with MPCLongit. displ. x axis with classical MC

Fig. 6. Comparison of actual position without look ahead: MPC based andclassical motion cueing

look ahead allows to achieve better tracking performancewithout low frequency error. The platform working area isalso fully exploited. Observe that the main difficulties inthe replication of perceived accelerations is associated withthe necessity of reproducing constant accelerations over longperiods of time, that is, to velocity peaks.

C. Longitudinal-Pitch coupling

By coupling the longitudinal and pitch DOFs we can testthe proposed strategy in a more complex and interestingoperating condition. We expect to observe the effect of tiltcoordination that allows to reproduce the low frequencycomponent. The MPC is now tuned by taking the physicallimits of the platform as constraints and by choosing theweights in the cost function to exploit at best the platformworking space. The reference signal is still supposed to be

0 5 10 15 20 25−1.5

−1

−0.5

0

0.5

1

time [s]

m /

s2

Reference: long. acc. x axisPerceived longit. acc.

Fig. 7. Perceived acceleration tracking based on MPC approach with lookahead.

0 5 10 15 20 25−1.5

−1

−0.5

0

0.5

1

time [s]

m /

s2

Ref. longit. acc. x axis (scaled)Applied longit. acc. MPCApplied longit. acc. classical MC

Fig. 8. Comparison of applied acceleration tracking with look ahead: MPCbased and classical motion cueing.

0 5 10 15 20 25 30 35 40 45 50−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

time [s]

[m]

Fig. 9. Actual position with look ahead.

known in advance, to introduce tilt coordination, and no pre-filtering of the telemetry data is performed. In Fig. 10 thereference signal, that is, the driver perceived longitudinalacceleration, is compared with that perceived in the platform,showing that an almost perfect tracking is achieved. InFig. 11 and Fig. 12 the pitch angle and the longitudinalposition of the platform are shown. Tilt coordination isclear when analyzing the platform behavior during the twobraking events. The pitch angle gives the low frequencycomponent of the longitudinal acceleration. The effect of tiltcoordination is even more evident in Fig. 13 by comparingthe scaled version of the original longitudinal accelerationsignal with the only actual longitudinal acceleration ofthe platform. The platform acceleration produces the highfrequency contribution only. In Fig. 14 the virtual vehiclejerk signal along the longitudinal axis is compared with theplatform one, to underline the quality of the result. Finallyin Fig. 15 the frequency contributions due to pitch and purelongitudinal dynamic are shown. As we expected the pitch,in a natural way, is used to cover the low frequencies of theperceived acceleration.

VI. CONCLUSIONS

In this paper we describ the design of a MC algorithmfor a small size dynamic driver simulator, that is based onMPC techniques. The most relevant features of the developedalgorithm are the possibility of implementing look-aheadstrategies by generating reference trajectories by means of anadvanced virtual driver and the use of a detailed model of thehuman vestibular system to accurately reproduce the driver’s

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Fig. 10. Perceived acceleration tracking in combined longitudinal and pitchsimulation.

Fig. 11. Longitudinal displacement in combined longitudinal and pitchsimulation.

Fig. 12. Angular displacement in combined longitudinal and pitchsimulation.

Fig. 13. Actual longitudinal acceleration comparison in combined longi-tudinal and pitch simulation.

Fig. 14. Longitudinal jerk in combined longitudinal and pitch simulation.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

200

400

600

800

1000

1200

1400

Frequency [Hz]

Overall perception Longitudinal ContributionPitch Contribution

Fig. 15. Frequency contribution of Longitudinal and Pitch DOF.

perception. Results show that the proposed algorithm exhibitsbetter performance with respect to standard algorithms basedon wash-out filters both in avoiding platforms movementsthat induce misleading cues to the driver and in exploitingthe platform operational space. The implementation of thedeveloped algorithm on a real device is undergoing. Thiswill allow to assess the algorithm performance by analyzingalso real drivers’ response. Results of such analysis will bereported in future publications.

REFERENCES

[1] M. Dagdelen, G. Reymond, A. Kemeny, M. Bordier, and N. Maızi,“Model-based predictive motion cueing strategy for vehicle drivingsimulators,” Control Engineering Practice, vol. 17, no. 9, pp. 995–1003,2009.

[2] B. Augusto and Loureiro, “Motion cueing in the chalmers drivingsimulator: A model predictive control approach.”

[3] L. Wang, Model predictive control system design and implementationusing MATLAB. Springer Verlag, 2009.

[4] J. Maciejowski, Predictive control: with constraints. Pearson educa-tion, 2002.

[5] G. Zacharias, “Motion cue models for pilot-vehicle analysis,” boltberanek and newman inc Cambridge ma control systems dept, Tech.Rep., 1978.

[6] J. A. Houck, R. J. Telban, and F. M. Cardullo, “Motioncueing algorithm development: Human-centered linear and nonlinearapproaches,” NASACR, vol. 213747, no. May, 2005. [Online].Available: http://hdl.handle.net/2060/20050180246

[7] R. Telban, W. Wu, F. Cardullo, and L. R. Center, Motion CueingAlgorithm Development: Initial Investigation and Redesign of theAlgorithms. National Aeronautics and Space Administration, LangleyResearch Center, 2000.

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