Julia Bongiorno
email: julia.bongiorno@lpl-aix.fr

Sophie Herment
email: sophie.herment@univ-amu.fr

A qualitative analysis of rising tones in Dublin English

Keywords: Dublin English, rising contours, uptalk, interactional functions of intonation, phonetic form

), but we argue that some of these rising tones are occurrences of Uptalk and do not belong to the Urban Northern British Intonation (UNBI) that is found in Belfast. Indeed the analysis of extracts of conversations providing an ecological context makes it possible to perform a qualitative study of the interactional and pragmatic functions linked to Uptalk, and this is, as far as we know, the first study of the kind on Dublin English rising tones. We conclude that UNB rises take the form of rise-plateaus in DE. Continuation rises can be realized as rise-plateaus or low rises, while uptalk takes the form of full rises and high rises.

Introduction

This paper focuses on the variety of English spoken in the Republic of Ireland, namely Southern Hiberno English [START_REF] Harris | Phonological variation and change[END_REF], and more specifically in Dublin, which we will refer to as Dublin English (DE) hereafter. The segmental characteristics of Southern Irish English have been widely described (see amongst others [START_REF] Harris | Phonological variation and change[END_REF], [START_REF] Hickey | Irish English : phonology[END_REF], [START_REF] Ferragne | La République d'Irlande[END_REF]), and [START_REF] Hickey | Dublin English : current changes and their motivation[END_REF] studied DE more particularly. However, the prosodic characteristics are hardly ever mentioned. [START_REF] Dalton | Nuclear Accents in Four Irish (Gaelic) Dialects[END_REF] have studied the intonation of four dialects of Ireland, but have not analysed DE. [START_REF] Wells | Accents of English[END_REF] writes that "the intonation of (Southern) Irish English is not strikingly different from that of RP". This might explain why it has received so little attention. [START_REF] Kalaldeh | Tonal Alignment in Three Varieties of Hiberno-English[END_REF] have looked at tonal alignment in three dialects of Hiberno-English: Donegal, Drogheda and Dublin. They report that declaratives are mainly realised H*L in Dublin, with an alignment of H* fixed at VC boundary. In the framework of the IViE project, recordings were performed in Dublin and [START_REF] Grabe | Intonational variation in urban dialects of English spoken in the British Isles[END_REF] confirms that the intonation in Dublin is not much different from that of Cambridge and reports that "rising declaratives are possible, but not particularly common" (only 6% in Dublin). [START_REF] Kalaldeh | Tonal Alignment in Three Varieties of Hiberno-English[END_REF] and [START_REF] Grabe | Intonational variation in urban dialects of English spoken in the British Isles[END_REF]'s findings, however, are based on read speech. [START_REF] Grabe | Intonational variation in urban dialects of English spoken in the British Isles[END_REF] analysed 22 phonetically controlled sentences with a range of grammatical structures (declaratives, yes-no questions, wh-questions, and declarative questions).

In this paper, we propose to give a brief preliminary overview of the intonation system found in DE, and to focus on rising intonations, on the basis of a corpus recorded in Dublin by the first author in the framework of the PAC project [START_REF] Carr | The PAC Project : Principles and Methods[END_REF]. For the purpose of the study, we base our findings on the close analysis of a few sentences and the context in which they appear. Our analysis is therefore mainly qualitative.

Corpus and method

The PAC Project

The PAC Project (Phonologie de l'Anglais Contemporain, [START_REF] Carr | The PAC Project : Principles and Methods[END_REF]) was initiated in 2004. It aims at describing the English(es) spoken around the world from a systematic and comparative point of view. The main goal of this program is to create an interdisciplinary database of different varieties of spoken English in order to allow specialists of several disciplines to study and compare them. In 2016, around 40 researchers were part of the program, and 37 corpora had been collected (several cities in England, Australia, New-Zealand, Singapore, India…).

All the recordings in the PAC program follow a common protocol:

• 2 word lists (one for vowels, one for consonants);

• a text; • a formal conversation in two parts led by the researcher: the first part is a questionnaire about the origins and personal information of the speaker, and the second part is the LVTI questionnaire (Langue, Ville, Travail, Identité -Language, Urban life, Work, Identity- [START_REF] Przewozny | Language, Urban life, Work, Identity: Ways and Means[END_REF]), with questions about work and urban life, leading to a thematic conversation about their work life, some of their thoughts about the city they live in and their perception of the variety of English they speak. • a free informal conversation recorded by a third party in the absence of the researcher in order to avoid the paradox of the observer ( [START_REF] Labov | Sociolinguistic Patterns[END_REF]).

The PAC Dublin corpus

Recordings were performed in Dublin in 2016 ( [START_REF] Bongiorno | Etude du système phonologique de l'anglais parlé à Dublin dans le cadre du programme PAC[END_REF]): the corpus is composed of 10 native speakers of English between 24 and 78 who were born and have spent their whole life in Dublin. They all live south of the river Liffey (a part of Dublin also called Southside) and are either employed or retired (see Table 1). They all belong to the same social network: family or close friends who have known each other for decades. The recordings took place at the informants' places so that felt as comfortable as possible.

Method

For the pilot study presented here, only the thematic conversations were analysed (LVTI questionnaires on work and urban life, see 2.1). They were not recorded by the first author but by a relative or friend of the informant who is also a Dubliner and who asked the questions The corpus analysed amounts to more than 1h 15mns of recording (mean 7.30 mns per speaker).

Extraction of utterances

An auditory analysis was performed first, passages were selected by the authors as follows: for each speaker, 10 declaratives with a falling contour, 10 declaratives with a rising contour, 10 incomplete sentences with a falling contour, 10 incomplete sentences with a rising contour, emphatic segments and yes-no questions were extracted. For the last two categories, it was impossible to find 10 occurrences, so only a few were extracted. These segments of speech were analysed through PRAAT [START_REF] Boersma | PRAAT, a system for doing phonetics by computer[END_REF]. Due to the subjective mode of selection and the lack of data for some categories, no quantitative analysis could be performed.

Automatic annotation and detection errors

In order to automatically annotate the extracted utterances, we used SPPAS [START_REF] Bigi | SPPAS -Multi-lingual Approaches to the Automatic Annotation of Speech[END_REF], and Momel & Intsint [START_REF] Hirst | A Praat plugin for Momel and INTSINT with improved algorithms for modeling and coding intonation[END_REF].

The annotation, however, was not always reliable because of some background noises that could not be avoided due to the fact that we only studied conversations. Figure 1 below shows an example where detection errors are obvious: the second tier on the figure contains the Hertz values as extracted by Momel and the third tier shows the corresponding Intsint coding. B stands for Bottom and T for Top. The two T target points are obviously erroneous if we look at the F0 curve and the pitch settings. This is due to a background noise that is perceivable when listening to the sound file. The annotations were therefore all manually corrected.

Intonation system in Dublin: preliminary results

Our preliminary results, based on auditory impressions and PRAAT analysis, show that both falling and rising contours in DE sound like General British (GB) intonation ( [START_REF] Cruttenden | Gimson's Pronunciation of English[END_REF]). This confirms [START_REF] Kalaldeh | Tonal Alignment in Three Varieties of Hiberno-English[END_REF] and [START_REF] Grabe | Intonational variation in urban dialects of English spoken in the British Isles[END_REF]'s conclusions. We also found contours that are not present in GB intonation, such as rise-plateaus (that are present in Belfast English, see [START_REF] Turcsan | L'anglais du Nord de l'Irlande[END_REF]), rise-plateauslumps, and rise-falls.

Rise-plateaus

A rise-plateau is characterised by a rise on the nuclear syllable and the following syllables uttered on a relatively high plateau. When there are no post-nuclear syllables, the rise and the plateau occur on the nuclear syllable as in figure 2 below (rise and plateau on sea):

Rise-plateau-slumps

Rise-plateau-slumps are also present in DE. Like rise-plateaus, they typically show a rise on the nuclear syllable, a high plateau, but then a fall on the last syllable that does not go down to the bottom level (see figure 3, where the rise and the plateau are on should and the slump takes place on be). We conclude that the intonation system of DE is a hybrid one that mixes standard English contours and Northern Irish ones, like the UNB rises on declaratives. Hybrid intonational systems exist in other varieties of English: [START_REF] Cruttenden | Intonation[END_REF] mentions biintonational speakers who alternate between rises and falls in declarative sentences, the criteria for choosing between a rise and a fall being unknown to the best of our knowledge. This could be the final point of the analysis. However, in DE, some of the rises found on declaratives seem to have stylistic and interactional functions. Our hypothesis is therefore that in DE some of the rises on declaratives are occurrences of uptalk and not UNB rises. The next section focuses on rising tones.

Focus on rising tones

Rises on declaratives are the default intonation in UNB varieties of English (see [START_REF] Cruttenden | Intonation[END_REF]) like Ulster English [START_REF] Jarman | Belfast intonation and the myth of the fall[END_REF] (and also amongst others Glasgow English [START_REF] Mayo | Prosodic transcription of Glasgow English: an evaluation study of GlaToBI[END_REF][START_REF] Cruttenden | Intonational diglossia: a case study of Glasgow[END_REF], Liverpool English [START_REF] Nance | Intonational variation in Liverpool English[END_REF] or Manchester English [START_REF] Cruttenden | Mancunian intonation and intonational representation[END_REF]): they have a systemic function. In DE, these types of rises on declaratives occur, along with rises that seem to be occurrences of uptalk.

The phenomenon of uptalk is acknowledged in Irish English as a recent innovation, but no scientific study was led on the subject [START_REF] Warren | Uptalk[END_REF]. We hypothesize that not all the rising contours are occurrences of uptalk and that three different types of rising contours exist in DE: uptalk, UNB rises, and continuation rises (similar to question rises). The first type has pragmatic functions, the second type is used on declaratives as a feature similar to Belfast English, and the last occurs on incomplete parts of speech (and yes-no questions). We deal in the rest of the paper with the interactional functions and the phonetic form of the rising contours in our corpus.

Interactional functions

Most authors agree that uptalk has interactional functions but disagree about those functions. To sum up, [23, p. 68] writes: "it [uptalk] is used for checking and for seeking feedback […]. It asks 'Are you following me?'. It shares rather than tells." In our corpus, some occurrences seem to be uptalk in that respect.

Some rises seem to be used for seeking feedback, and for asking confirmation to the interviewer:

And people from all over the country that have very soft accents, and I like to think that I am probably one of them (RCL1)

The speaker (RCL1, a 32 year-old woman artist and music teacher, see table 1) talks about the different accents she heard in Ireland. The contour on the underlined part is rising, probably because the speaker asks for confirmation and asks if her accent is as soft as she thinks it is. In this case, the rising tone is an occurrence of uptalk and its function is seeking confirmation.

Rising contours on declaratives are also largely used by the speakers in our corpus for checking if what they say is what the interviewer is expecting from them (see [START_REF] Eckert | The Whole Woman: Sex and Gender Differences in Variation[END_REF] and [START_REF] Lakoff | Language and Woman's Place[END_REF]). In our recordings, people talk about themselves and give information that the interviewer already knows (work life, personal life…), so the rising tone sounds as if the speaker apologised for that or as if they checked if what they say is what is expected.

So I work as a pediatric doctor in Tallaght hospital at the moment. (SK1) So I'm a guitar teacher. (MC1)

In both situations, the interviewer is a relative of the speaker, so they already have the piece of information.

Phonetic form

The phonetic form of uptalk varies according to the variety of English [START_REF] Liberman | The phonetics of uptalk[END_REF], and there is little agreement concerning its shape [START_REF] Warren | Uptalk[END_REF]. For instance, [START_REF] Ritchart | The form and use of uptalk in Southern Californian English[END_REF] report that the contour of Australian uptalk is L*H-H or H*H-H%, while for Glasgow it is L*H H-L%. [START_REF] Wilhelm | Quand les paroles s'envolent : réflexions sur les caractéristiques et la forme phonétique du High Rising Terminal en anglais contemporain[END_REF] distinguishes 5 different contours for uptalk: high rise, full rise, low rise, low flat, and fall-rise. According to [START_REF] Warren | Uptalk[END_REF] the only elements that are common to most forms of uptalk are the fact that the average pitch levels are lower, the rise starts later and from a lower level, thus resulting in a more dramatic rising pattern for uptalk than for questions.

Phonetic form of uptalk in DE

We analysed several occurrences that we classified as uptalk in our corpus because they had interactional functions, and found several full-rise tones, in which the starting point of the rise is lower than the preceding syllables (Figure 5):

-Do you feel like you're a true Dubliner? -Yes. Shall I expand on that? Er well I was born in Dublin, I've always lived in Dublin, er I don't know. (SK1)

In this example, the speaker (SK1) is asked whether she feels she is a true Dubliner or not. This is a good example of uptalk, because SK1 gives her opinion, and at the same time she asks the interviewer if being born in Dublin and having lived there her whole life is enough to be considered a 'True Dubliner'. We also found occurrences of high rises, where the starting point of the rise is rather high in the pitch range (Figure 6).

As you know I've just come back from India where I took 2000 odd photos (RF1)

Here, the speaker (RF1) is being interviewed by his partner's uncle (MC1), who already knows he went to India and took pictures but he probably doesn't know about the crazy number of pictures and the rising tone sounds as if RF1 was expressing something like "Can you believe this? I know it's crazy."

Phonetic form of continuation rise (and yes-no rise) in DE

Most studies dealing with uptalk compare the uptalk contour to that of yes-no questions (see [START_REF] Warren | Uptalk[END_REF] amongst others). It is also interesting to compare uptalk contours to rising contours found in incomplete sentences. In DE, as in Standard English, low rises are realised for both categories (Figures 7 and8) :

So if anything is in cyclable distance from the city center or where I need to go to work then that's a really big advantage (RCL1) For incomplete statements, a rise-plateau can also be heard, and for yes-no questions we found rise-plateau-slumps too, but the latter will not be taken into account since they are not strictly rising contours but rather rising-falling (even though slightly) contours.

Discussion

Our hypothesis was that in DE three different types of rising contours existed: uptalk, UNB rises, and continuation rises (similar to question rises). We analysed the phonetic form of those rising contours, and it turns out that in our DE data, four different forms can be distinguished:

• Rise-plateau

• Low rise • Full rise
• High rise Rise-plateau is found on declaratives in DE. Rise-plateau is also used in incomplete statements, along with low rise, showing non-finality, while full rise and high rise are used as uptalk contours to convey interactional/pragmatic functions as discussed in 4.1. However, it is sometimes difficult to say whether a rising contour corresponds to an uptalk contour or a continuation contour, as in the example below (Figure 9). Does the first rise (on West Meath) indicate non finality, or does the speaker (FS1) use an uptalk rise because the interviewer (her friend) already knows that she lived in West Meath (in this case, she could be using uptalk to apologise because she is giving a piece of information that is already known, see 4.1)?

I was out of Dublin for 6 years, I lived in West Meath uhm in the sixties so I don't know whether that had any influence on, you know the way that you would be. (FS1)

Figure 9: uptalk or continuation contour?

The contour on West Meath is a rise plateau. Our results would therefore tend to favour a continuation rise here.

On the contrary, the second rise, on sixties, is clearly a case of uptalk: it integrates the question which the speaker makes explicit just afterwards, wondering if the fact that she lived in West Meath can have any influence on the way she speaks and almost asking her co-speaker's opinion. The contour is a full rise. This is interesting because speaker FS1 is aged 74, which would tend to go against the idea that uptalk is a recent innovation in DE (unless FS1 has taken up uptalk contours recently, which seems rather improbable).

Conclusion & perspectives

To the best of our knowledge, our study is the first to analyse DE rising contours in conversations. It is also the first to try and describe the variation present in DE intonational system. The present analysis, although a pilot study, shows that the intonational system of DE is a hybrid one, mixing Northern Irish contours like rise-falls and UNB contours like riseplateaus and rise-plateau-slumps on declaratives, with more standard contours like low falls and low rises. Our results tend to show that UNB rises take the form of rise-plateaus in DE and that continuation rises can be realized as rise-plateaus too or low rises. Our study also attests that uptalk is present in DE, that it is probably not a recent innovation, and that it takes the form of full rises and high rises, which correlates [START_REF] Wilhelm | Quand les paroles s'envolent : réflexions sur les caractéristiques et la forme phonétique du High Rising Terminal en anglais contemporain[END_REF]'s findings on uptalk contours by a Derry speaker. Uptalk in DE would have the same phonetic forms as in Ulster English. Our study also confirms [START_REF] Wilhelm | Towards a typological classification and description of HRTs in a multidialectal corpus of contemporary English[END_REF]'s conclusions that uptalk contours are not restricted to high rise. This needs further analysis and our aim in the near future is to extend the PAC Dublin corpus, analyse extracts from both the formal and informal conversations and elaborate a robust method of extraction and annotation so as to be able to provide a detailed description of the intonation system of Dublin English and perform a quantitative analysis of rising contours. Our present data show considerable inter-speaker variation: different speakers are likely to use different intonation patterns for the same purpose. It would be interesting to see whether intonational variation is correlated to a speaker's profile taking into consideration factors like age, social origins, areas of the city where the speaker lives (see [START_REF] Hickey | Dublin English : current changes and their motivation[END_REF]'s local vs. non-local varieties), but also factors linked to the identification of the speaker with their city (see [START_REF] Hickey | Dublin English : current changes and their motivation[END_REF]'s profiles of mainstream and fashionable Dubliners).

Figure 1 :

 1 Figure 1: Detection errors

Figure 2 :

 2 Figure 2: Rise-plateau (speaker CC1)

Figure 3 :

 3 Figure 3: Rise-plateau-slump (speaker FS1)3.1.3. Rise-fallsRise-falls are also found in DE, in emphatic contexts mostly, where GB speakers are likely to realise a fall-rise. In rise-falls (Figure4), the starting point of the rise and the end of the fall are at the same level and the rise is sharper than in the riseplateau-slump.

Figure 4 :

 4 Figure 4: Rise-fall (speaker FK1) 3.1.4. Partial conclusion Dubliners, like speakers of Mid-Ulster English, use riseplateaus and rise-plateau-slumps on declaratives and rise-falls

Figure 5 :

 5 Figure 5: Full rise

Figure 6 :

 6 Figure 6: High rise

Figure 7 :Figure 8 :

 78 Figure 7: Low rise in an incomplete sentence Is there anything you'd like to talk about?(MC1)

Table 1 :

 1 Informants

	Activity	Speaker Age Sex	Job/studies
	Young	BB1	24	M	Retail
	workers	SK1	27	F	Doctor
	First job	RCL1	32	F	Music teacher/art
	People who	RF1	43	M	IT engineer
	have been	TC1	58	F	Costume designer


Moad Kissai

Xavier Mouton

Bruno Monsuez

Didier Martinez

Adriana Tapus

Optimizing Vehicle Motion Control for Generating Multiple Sensations

Keywords: Autonomous Vehicles, Vehicle Motion Control, Chassis Systems, Control Allocation, Optimization, Cosimulation

Most of automotive researches focus on autonomous vehicles. Studies regarding trajectory planning and trajectory tracking became preponderant. As in case of commercial ground vehicles there is a driver in the loop, one should raise the important question of how the trajectory should be tracked. In this paper, we investigate the influence of controlling integrated chassis systems on the vehicle's behavior. A fixed Model Predictive Control is used to track the trajectory. Tunable vehicle motion control is however used to provide different motion feelings. Results show that a specific trajectory could be followed in different manners. Therefore, vehicle dynamics can be and should be controlled in such a way to generate adaptive trust feelings to passengers in case of autonomous driving.

I. INTRODUCTION

Advanced Driver Assistance Systems (ADAS) are one of the most important features in ground vehicles. Normal drivers are usually trained to handle a vehicle in normal situations. In hazardous situations, vehicle dynamics become less obvious to predict. Assistance systems provide then the necessary control to help drivers continue their maneuvers with less damages. Both car manufacturers and equipment suppliers are actively working on developing new technologies to enhance the vehicle's safety. It started with the Anti-lock Braking System (ABS) in 1978 [START_REF] Gerard | Global Chassis Control and Braking Control using Tyre Forces Measurement[END_REF]. This system consists of relaxing the brakes to regain adherence and then braking again to decelerate the vehicle. The major goal of ABS was to reduce the distance of braking for better longitudinal control. A significant progress was provided by the Electronic Stability Program (ESP) in 1992 [START_REF] Gerard | Global Chassis Control and Braking Control using Tyre Forces Measurement[END_REF]. This system consists of a differential braking between right and left tires to provide a yaw moment and control the yaw rate. This is particularly beneficial for obstacle avoidance for example. The ESP brought then a lateral control to help drivers stabilize their vehicles. A natural evolution would be a global control or fully autonomous vehicles. In this case, longitudinal, lateral, and eventually vertical control logics should be coordinated to handle vehicle and tire dynamic couplings [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. Moreover, with the addition of new technologies, vehicles become over-actuated [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]. Control Palaiseau Cedex, France {moad.kissai, bruno.monsuez, adriana.tapus}@ensta-paristech.fr {xavier.mouton, didier.d.martinez}@renault.com should be allocated to the right actuators and effectors no matter what the situation is.

In this context, different strategies have been adopted in the literature. Two major control approaches have been distinguished in [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]: the Downstream Approach and the Upstream Approach. In the first approach, data-based and techniques such as Artificial Neural Network [START_REF] Nwagboso | Development of neuralnetwork control of steer-by-wire system for intelligent vehicles[END_REF], or rulebased techniques such as Fuzzy Logic Control [START_REF] Wang | Agent-based coordination framework for integrated vehicle chassis control[END_REF] are used downstream systems' standalone controllers. These techniques handle specific use-cases and depend on designers' expertise. As no customer feedback about autonomous vehicles is available, coordination should rather be more general independent from any use-case. This can only be done by describing mathematically the dynamic couplings and use optimization-based techniques. A sufficient amount of information is then required to distribute the commands and allocation is done upstream the systems' standalone controllers [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. Optimization-based control allocation techniques offer additional attractive features. In fact, optimization is carried out by taking into account multi-objectives. In [START_REF] Shyrokau | Control allocation with dynamic weight scheduling for two-task integrated vehicle control[END_REF], [START_REF] Chen | Energy-efficient control allocation with applications on planar motion control of electric ground vehicles[END_REF], [START_REF] Jing | Multi-objective optimal control allocation for a four-wheel-independent-drive electric vehicle[END_REF] for example, energy consumption has been used as a criterion to allocation precision and stability. This is particularly beneficial for electric vehicles [START_REF] Shyrokau | Analysis of subsystems coordination for electric vehicle during straight-line braking and brake-in-turn[END_REF]. Having multiple ADAS or chassis systems can then offer supplementary possibilities. Vehicle motion can be then modified in a way to fulfill multiple objectives.

For autonomous vehicles however, qualitative objectives could be required. When a driver has its hands off the steering wheel, if an unexpected motion is generated, he could be tempted to regain control of the vehicle. In case of a vehicle equipped with an Electric Power-Assisted Steering (EPAS) system, this may present few risks for drivers' hands due to the important amount of steering wheel torque [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]. One way to prevent this, is to tune the vehicle motion in a way to generate expected motions like a human being would do. To the best of our knowledge, there exist two method to tune the vehicle behavior. Either we act on motion references to be followed by the vehicle so the controllers impose different commands to actuators, or we modify the control allocation strategy so the commands are distributed differently.

The purpose of this paper is to compare both approaches to highlight the advantages and drawbacks of each one. The goal is to give few insights about the ability of modern control techniques to provide additional degrees of freedom regarding motion feelings control. Investigations aiming to adapt these techniques to drivers' profiles are still needed with the help of experiments. Here, a Model Predictive Control (MPC) provided by LMS Imagine.Lab AMESim R is used for trajectory tracking. Focus has been put more on vehicle motion control tuning. A Gain-Scheduled H ∞ controller has been selected as the high-level controller for its robustness and dynamic couplings management. Optimizationbased Control Allocation methods are then used to distribute the commands into the different actuators taking into account tire potential. Results by co-simulation of AMESim R and Matlab/Simulink R showed attractive improvements brought by these control methods to handle on one hand complex coupled situations, and on the other hand, to provide different motions while tracking the same trajectory.

The rest of the paper is structured as follows: We start in Section II by presenting the different modelings required for the problem definition. In Section III, the different control methods adopted are described. The two approaches enabling the motion behavior tuning are both presented in Section IV. Section V presents results obtained by co-simulation of Matlab/Simulink R and AMESim R . A discussion about future cars challenges and the relevance of this work is provided in Section VI. Conclusions and future works are outlined in Section VII.

II. SYSTEM MODELING

The vehicle considered in this paper is equipped with an Electric Power-Assisted Steering (EPAS) system, an Electronic Stability Program (ESP), and a Torque Vectoring (TV) system. This latter is realized by means of four motor-wheels. The EPAS is mainly controlled by the MPC. The goal is to study interactions between systems and what a better coordination can bring to the vehicle motion control.

As no active suspensions are considered, a planar vehicle model can be adopted. Nevertheless, as the ESP and TV are based on differential forces between right and left wheels, a four-wheeled vehicle model is necessary [START_REF] Yim | Fault-Tolerant Yaw Moment Control with Steer and Brakeby-Wire Devices[END_REF]. Using Newton's laws of motion, one can find easily the following staterepresentation [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]:

                         Vx ψ = 0 V y 0 0 V x ψ +    1 M 0 0 1 I zz    F xtot M ztot V x ψ = 1 0 0 1 V x ψ (1) (2)
With:

• V x : longitudinal velocity of the vehicle, Where:

               F xtot = F x f l + F x f r cos (δ f ) + F x rl + F xrr M ztot = F x f l + F x f r l f sin (δ f ) + F x f r -F x f l t r 2 cos (δ f ) + (F xrr -F x rl ) t r 2 (3) (4)
With:

• F x f,r : front-right longitudinal force,

• F x f,l : front-left longitudinal force,

• F xr,r : rear-right longitudinal force,

• F x r,l : rear-left longitudinal force,

• δ f : front steering angle, • l f : distance between the front axle and the vehicle's CoG, • t r : vehicle's track. Note that we have considered only controllable forces to distribute by the control allocation algorithm. In fact, the lateral force induced by the front steering is controlled by the MPC. Introducing this force also in the vehicle motion control induces request conflicts 1 .

Regarding tire forces, a linear tire model with varying parameters developed in [START_REF] Kissai | A new linear tire model with varying parameters[END_REF] is used to take into account the couplings at the tire level. The forces are expressed as following:

F x = C * s (α, µ, F z ) κ F y = C * α (κ, µ, F z ) α (5) (6)
where:

• κ : the longitudinal slip, • α

: the side-slip, • µ : the friction coefficient, • F z : the vertical load, • C * s (α, µ, F z ) : the tire varying longitudinal stiffness with respect to the side-slip α, µ, and F z , • C * α (κ, µ, F z ) : the tire varying cornering stiffness with respect to the longitudinal slip κ, µ, and F z . Detailed expressions of C * s (α, µ, F z ) and C * α (κ, µ, F z ) can be found in [START_REF] Kissai | A new linear tire model with varying parameters[END_REF].

In order to respect the friction ellipse concept [START_REF] Pacejka | Tyre and Vehicle Dynamics[END_REF], dynamic constraints are added [START_REF] Kissai | A new linear tire model with varying parameters[END_REF]:

     F x ≤ (µF z ) 2 -F 2 y F y ≤ (µF z ) 2 -F 2 x (7) (8)

III. VEHICLE MOTION CONTROL

Today's vehicles are over-actuated [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]. Integrated systems are expected to grow in number in the upcoming years due to the road-map towards autonomous vehicles. A discussion about control architectures to be adopted in order to face the growing number of integrated systems is provided in [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. A multi-layered architecture is claimed to present several advantages, especially when systems coordination is located upstream the systems themselves. The same approach is adopted here. The control architecture is divided in a highlevel control to generate the required sum of forces and moments necessary to move the vehicle, a middle-level control is used to distribute optimally the commands into the four wheels, and a low-level control is used to transform the forces into torques to be generated by the different actuators.

A. High-Level Control

The objective of this layer is to generate the generalized forces and moments to be applied at the vehicle's CoG. Equations (1) and (2) are considered. The model can be then considered as linear with the varying parameter V y . To take into account this variation, a gain scheduled controller is chosen with V y as the scheduling variable. In fact, today's vehicles are equipped with an inertial measurement unit and a yaw rate sensor 2 . Therefore, V y can be estimated using a simplified vehicle model as in [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF].

Moreover, as stated in [START_REF] Chebly | Coupled Longitudinal and Lateral Control for an Autonomous Vehicle Dynamics Modeled Using a Robotics Formalism[END_REF], vehicle motion control faces several problems related to parameter uncertainties. The control should valid whether there is only the driver in the vehicle or with other passengers, whether tires are brand new or not and so on. A robust controller is then needed. The H ∞ synthesis has been selected to be able to optimize the controller parameters. As this synthesis usually generate high order controllers [START_REF] Skogestad | Multivariable Feedback Control: Analysis and Design[END_REF], a common practice consists on reducing the controller in the frequency domain while keeping an acceptable level of robustness [START_REF] Pita-Gil | Application de techniques de commande avancées dans le domaine automobile[END_REF]. Here, a different methodology is adopted. As most industrials prefer PID controllers for implementation issues, we add the controller structure as a requirement in the H ∞ synthesis. To choose the suitable structure to be adopted, a pre-study of the plant is required. We suppose that in stable maneuvers V y has a very low value. Therefore, a decoupled controller can be chosen. Moreover, due to the integral characteristic of each control axis, a PI controller can be chosen at each axis. Four tunable parameters are then chosen in the optimization H ∞ problem. More details about this methodology can be found in [START_REF] Apkarian | Nonsmooth H-infinity Synthesis[END_REF].

Regarding performance weighting functions, closed loop shaping is used for defining control design requirements as in [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]. We choose here a steady-state offset less than 1%, a closed-loop bandwidth higher than 1Hz 3 , and an amplification of high-frequency noise less than a factor 3. The H ∞ synthesis is iterated for different values V y . A gain-scheduled H ∞ controller is finally synthesized, which depends on V y estimations.

One major difference with respect to [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF] investigations is the scheduling parameter. In our case, the gain-scheduling is only used for the high-level control. In [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF] gain-scheduling is used to coordinate subsystems depending on a stability index. In this paper, optimization-based control allocation techniques are selected to handle subsystems coordination. 2 According to the co-authors working in the Group Renault. 3 To prevent the control allocation algorithm from operating at 100Hz frequencies for example.

B. Middle-Level Control

The goal of middle-level control is to optimally distribute the generalized forces generated by the high-level control to ensure the execution of these forces. As long as an overactuated system is concerned, multiple objectives can be fulfilled. This is very important for this study as several problems are aimed to be addressed regarding autonomous vehicles. Optimization-based control allocation techniques are then selected to handle the forces distribution problem.

The control allocation problem is defined as follows [START_REF] Johansen | Control Allocation -A survey[END_REF]: find the control vector, u ∈ R n such that

B eff u = v des (9)
subject to

u min ≤ u ≤ u max ˙ u ≤ ˙ u max (10) (11)
where B eff ∈ R m×n is a control effectiveness matrix, u min ∈ R n and u max ∈ R n are the lower and upper position limits, respectively, ˙ u ∈ R n is the control rate, ˙ u max ∈ R n is the maximum control rate, v des ∈ R m are the desired accelerations, n is the number of control effectors, and m is the number of axes to control.

Several solvers can be used to solve a multi-objective problem. Sequential Least Squares (SLS) uses a two stage Active Set Algorithm (ASA) to handle two optimization problems [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. The Weighted Least Squares (WLS) solves the bounded least squares problem using one stage ASA after few matrix transformations by means of different weights [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. Other techniques not based on ASA that can be cited are Cascading Generalized Inverses (CGI) [START_REF] Bordignon | Constrained Control Allocation for Systems with Redundant Control Effectors[END_REF] and the Fixed-Point Iteration (FPI) [START_REF] Burken | Two Reconfigurable Flight-Control Design Methods: Robust Servomechanism and Control Allocation[END_REF]. We choose here the WLS based on ASA for its flexibility to express multiple objectives, and for its relative rapidity due to its one stage formulation. The optimal solution is then:

u opt = arg min umin≤ u≤ umax l γ i W i (B i u -v i ) 2 (12)
• u opt : optimal control vector,

• l : number of objectives, • γ i : weight of the i th objective, • W i : non-singular weighting matrices defining preferences of each axis, • v i : desired vector of the i th objective, • B i : effectiveness matrix relating the control vector to the desired i th objective.

Regarding the EPAS-ESP-TV coordination case:

u =     F x f l F x f r F x rl F xrr     (13)
u min and u max reflect tire limits with respect to the friction ellipse concept [START_REF] Chen | Energy-efficient control allocation with applications on planar motion control of electric ground vehicles[END_REF] and [START_REF] Jing | Multi-objective optimal control allocation for a four-wheel-independent-drive electric vehicle[END_REF]. Regarding vertical forces, we have [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]:

                         F z f l = 1 2 M g l r L - 1 2 M a x h L - 1 2 M a y h t r F z f r = 1 2 M g l r L - 1 2 M a x h L + 1 2 M a y h t r F z rl = 1 2 M g l f L + 1 2 M a x h L - 1 2 M a y h t r F zrr = 1 2 M g l f L + 1 2 M a x h L + 1 2 M a y h t r (14) (15) (16) (17)
where:

• g : gravitational acceleration,

• a x : vehicle's longitudinal acceleration,

• a y : vehicle's lateral acceleration,

• l r : distance between the rear axle and the vehicle's CoG, • L : vehicle's wheelbase,

• h : height of vehicle's centre of gravity. For the friction coefficient, the problem is more complex. In fact, tires are the only effectors for ground vehicles. Their behavior changes with friction. Control logic would not be as effective as in the normal situation. The changes in friction should then be predicted to reconfigure the control algorithm and act differently on tire, and on the reference in order to follow feasible targets. The difficulty is that this coefficient can only be estimated when exceeding it when using effect-based estimation methods [START_REF] Villagra | A diagnosisbased approach for tire/road forces and maximum friction estimation[END_REF]. It could be then too late to control the vehicle afterwards. Data-based techniques could provide better solutions [START_REF] Liu | Estimation of tireroad friction coefficient based on combined APF-IEKF and iteration algorithm[END_REF]. Experimental tests showed promising results. These techniques should be further investigated. This however goes beyond the scope of this work. In this paper, we suppose that the friction coefficient can be estimated as in [START_REF] Svendenius | Tire Modeling and Friction Estimation Department of Automatic Control[END_REF]. H ∞ synthesis has been chosen in order the generate a high-level robust controller and reduce the negative effects of this hypothesis.

The desired acceleration v des in this case is:

v des = F xtot M ztot (18)
The effectiveness matrix related to control allocation precision B eff is:

B eff = cos (δ f ) cos (δ f ) 1 1 b 2,1 b 2,2 - t r 2 t r 2 (19)
where:

• b 2,1 = l f sin (δ f ) - t r 2 cos (δ f ) , • b 2,2 = l f sin (δ f ) + t r 2 cos (δ f ) .

C. Low-Level Control

The low-level control corresponds to the most intern loop. Adopting a closed loop here leads to very high crossover frequencies. Moreover, the control allocation algorithm generates tire forces. Therefore, for a closed-loop low-level control, either we should be able to measure online tire forces, which is not the case in commercial vehicles, or we can use the inverse of the linear tire model with varying parameters as an interface between the two layers, and control the wheels' speed. For simplicity, and as this part goes beyond the scope of this paper, only a direct calculation is adopted:

T bij = -R i F xij (20)
Where:

• T bi,j : brake torque at the i -j 4 wheel,

• R i : wheels' effective radius of axle "i".

IV. TUNABLE MOTION BEHAVIOR

Several challenges need to be overcome regarding autonomous vehicles. Most researches focus on trajectory planning and tracking problems. However, this needs to be designed by taking into account the human in the loop. The vehicle behavior should be more similar to a human driving than a robot driving. Drivers have different profiles and different driving styles. Motions generating excitement feelings among certain people could generate in contrast fear feelings among others. The goal of this paper is to prove the ability of modern control techniques to provide different motion behaviors, and therefore different motion feelings to passengers.

Two different approaches to tune the vehicle motion behavior are exposed here. The first approach consists of modifying the motion targets to follow. The high-level control should in this case generate different generalized forces in order to amplify or reduce the vehicle response, or change its dynamics. The second approach consists of allocating differently the commands into the subsystems to generate different accelerations.

A. Reference Tuning

It should be noted that the MPC algorithm provided by LMS Imagine.Lab AMESim R can generate a steering wheel angle and a velocity profile. The MPC here can represent a driver model or a virtual driver. This paper focuses more on the vehicle motion control in general after receiving the signals generated by the MPC without differentiating between a real or virtual driver.

The yaw rate reference needs to be generated using only the steering wheel angle value and the vehicle's speed value. The bicycle model can then be used to generate the yaw rate target [START_REF] Selby | Intelligent Vehicle Motion Control[END_REF]. This simplified vehicle model represents the nominal lateral behavior of the car and is characterized by its fast computation to generate a reference, especially the static version of the model. Nevertheless, the dynamic bicycle model is used here to be able to not only generate and amplified yaw rate, but also to be able to control the transient behavior of the vehicle. The yaw rate reference is then:

ψref = K tun 1 + τ tun s V x L + M V 2 x LC α f C αr C αr l r -C α f l f δ f (21)
4 i = f for "front" or r for "rear", and j = l for "left" or r for "right".

where:

• K tun : tuning gain,

• τ tun : tuning lag,

• C α f : initial cornering stiffness of front axle when no longitudinal slip is considered, • C αr : initial cornering stiffness of rear axle when no longitudinal slip is considered. K tun and τ tun can be then manually varied to see the influence on the vehicle behavior.

B. Tuned Control Allocation

It is claimed that motion sickness and discomfort are related to the vehicle's accelerations [START_REF] Raimondi | Fuzzy motion control strategy for cooperation of multiple automated vehicles with passengers comfort[END_REF]. One could think of adding an additional objective to the control allocation problem to distribute differently the commands, and try to fulfill different objectives when it is possible. However, in equation ( 9), as we express tire forces with respect to generalized forces at the vehicle's center of gravity, we already link tire forces to accelerations. Adding another objective with almost the same effectiveness matrix leads to a rank deficiency. The optimization algorithm cannot then find a solution. This would not have been the case, if for example we want to penalize the lateral acceleration with another subsystem as the 4-Wheel Steering System. The idea is then to amplify or reduce the accelerations directly by generating amplified or reduced generalized forces. Equation (9) becomes then:

B eff u = T v des ( 22
)
Where T is a diagonal matrix with tuning parameters to amplify or reduce components of v des . This actually prevents from several difficulties. In this way, desired accelerations are not be predefined. And there is no need to add an additional objective, which can slow down the computation. However, this can lead to control imprecision. The tuning parameters should not reach large values. Again, this may need additional experimental tests. The optimal control vector is then:

u opt = arg min umin≤ u≤ umax W ca (B eff u -T v des ) 2 (23)
The Active Set Algorithm (ASA) is then used [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. The cost function is rewritten following the ASA formulation:

u opt = arg min umin≤ u≤ umax A u -b (24)
V. CO-SIMULATION RESULTS

As optimization-based control allocation algorithms are involved, the solver has been written in Matlab R2015a R for its strong numerical computation. Regarding LMS Imagine.Lab AMESim R , it proposes a wide vehicle dynamics library for high-fidelity modeling. To take advantage from each software, both are co-simulated using Simulink R as an interface. The high, middle, and low level control logic is implemented in Simulink, while a high-fidelity car model with 15 degrees of freedom is selected in AMESim. The maneuver consists on a trajectory race tracking with highspeed values. The approved Magny-Cours area 5 has been reproduced in 3D by AMESim developers using softwares Open Street Map and JOSM. We use then this severe maneuver to see the motion feelings generated while keeping the same trajectory.

It is important to keep the same trajectory in all simulations because we want to separate the effect of generating different trajectories for different feelings from achieving this with different accelerations (Fig. 1). We notice that there is not much effect on the yaw rate response. In fact, when tracking the exact same trajectory with the same velocity, the yaw rate will always be the same. So when amplifying for example K tun , to keep the same yaw rate, the MPC computes less front steering angle so the reference stay the same as Fig. 3 shows.

In Fig. 4 we can see that it is the difference between right and left tire forces that complements the influence of the front steering to turn the vehicle.

Therefore, this approach is not efficient regarding tuning accelerations for different feelings when there is a strict trajectory tracking along with a vehicle motion control (Fig. 5). However, this can be relevant when there is a human driver as only few effort is needed to turn the vehicle. The torque vectoring and ESP act as assistance systems. This might also be even more beneficial for automated emergency steering for obstacle avoidance for example, as even if the driver want to take back the control, the steering wheel does not turn too much to hurt the driver's hands.

B. Second Approach: Tuned Control Allocation

Here, we penalize the forces allocation to influence directly the generated accelerations. As we can see in Fig. 6, we can obtain different lateral accelerations.

Which gives then different yaw rate responses while keeping the same trajectory (Fig. 7).

Regarding the front steering angle, this have little impact regarding the amplitude, only the transient behavior is different as Fig. 8 shows.

So to benefit from advantages of both approaches, a mixed approach is presented in the next paragraph.

C. Mixed Approach

Here, both the reference and the control allocation are tuned. This allows us the have different accelerations responses as Fig. 9 shows Along with different steering wheel effort at the same time.

And all of that while keeping the same trajectory. In this way, trajectory tracking can be decoupled from motion control, and both security and comfort can be ensured. But of course, with additional chassis systems, e.g. the 4-Wheel Steering system, we can even allow different trajectory generation to have even more motion feelings. This corresponds to one of our future works.

VI. FUTURE CARS MOTION-RELATED CHALLENGES

This paper aims to prove the potential of modern control technique to provide different motion feelings. This could be used to tune the vehicle behavior in order to make autonomous vehicles motions predictable and then trustful [START_REF] Hengstler | Applied artificial intelligence and trust -The case of autonomous vehicles and medical assistance devices[END_REF]. This can facilitate the acceptance of such robots/autonomous vehicles in the society and then accelerate their development. However, each driver has its own perception of what a trustful motion means. The same vehicle motion behavior can therefore generate different feelings in humans, depending on their past experience with non-autonomous vehicles. Two approaches to tune the vehicle motion behavior have been presented in this paper. The first approach consists of changing the motion reference, while the second one is based on a tuning of control allocation algorithms.

A. Importance of Motion References

In the first approach, an addition tuning gain and tuning lag have been added in order to change the response amplitude but also the transient behavior. This enables to parametrize the vehicle response to commands generated by either a human driver or a virtual driver. In fact, in case of a human drive, starting from a steering wheel angle input, the generated yaw rate by the vehicle can be amplified, reduced, delayed and so on, thanks to activation of the other subsystems. This provides different sensations to the driver itself and additional possibilities. The same logic can be applied for a virtual driver. If the MPC generates only a front steering angle to track a trajectory, the remaining systems can be used to change the dynamic responses of the vehicle. The driver can then choose among a sportive virtual driver, or a more careful virtual driver.

More complex reference models can be used to provide additional degrees of freedom. However, this additional parameters should be linked to motion feelings. Each parameter influence should be identified by experimental tests on humans. But these tests could be hard to interpret if results vary from a driver to another. A preliminary study could be necessary to classify first human drivers in order to be able to identify the influence of each parameter on generated sensations.

B. Control Allocation Challenges

Here, a simple approach has been adopted for tuning control allocation algorithms. Accelerations have been directly amplified or reduced as these variables are directly related to motion feelings. However, this approach faces the same problem as the first one. The amount of accelerations to add or reduce should be controllable and adapted to each driver. Only experimental tests involving humans could give insights about the influence of tuning control allocation objectives. Moreover, qualitative objectives as trust feelings, comfort and so one could be more sophisticated than only accelerations tuning. The control allocation problem could become a multi-objective problem with variable priorities depending on the situation. In this context, authors in [START_REF] Funke | Collision Avoidance and Stabilization for Autonomous Vehicles in Emergency Scenarios[END_REF] proposed an interesting approach regarding objectives priority variance. Their approach consists on defining stabilization and trajectory tracking envelopes in the MPC algorithm where the considered states should remain. But when an obstacle has to be avoided, these envelopes can be violated in a short amount of time to ensure passenger security, then stabilize the vehicle. These adaptability should be also permitted in control allocation optimization algorithms. But again, the considered qualitative objectives should be first identified and then formalized. Moreover, adaptability could also be needed not only to take account of the environment changes, but also depending on the driving styles. As authors of [START_REF] Frison | Driving Hotzenplotz: A Hybrid Interface for Vehicle Control Aiming to Maximize Pleasure in Highway Driving[END_REF] have reported, passengers have different expectations from autonomous driving than manual driving, as in the first case, passengers get easily bored.

Also, more chassis systems should be integrated and studied. 4-Wheels Steering (4WS) system for example could provide more comfortable and pleasant cornering maneuvers without influencing the vehicle's longitudinal speed as the brakes do [START_REF] Harada | Stability Criteria and Evaluation of Steering Maneuver in "Driver-Vehicle System[END_REF]. This shows the lack of researches in the literature about vehicle motion control and motion feelings. More support and corporation are expected from car manufacturer for deeper investigations.

VII. CONCLUSIONS

In this paper, two approaches for tuning vehicle behavior have been compared. While the first one consists of changing motion references dynamics, the second one consists of distributing differently the commands subsystems by means of a tuning matrix to amplify or reduce accelerations. Results showed that in the first approach, the use of TV and ESP is amplified to realize maneuvers with less front steering angle, and in the second approach, accelerations have directly been tuned to enable different motion feelings. Therefore, a mixed approach have been proposed to benefit from both advantages.

This demonstrates the need of implementing this kind of modern control algorithms in future cars. The more autonomous the vehicle will become, the more authority the driver should delegate, and the more the vehicle behavior should stay predictable to prevent drivers from taking back suddenly the control.

The goal of this paper is to prove that with a multilayered architecture, control problems are separated from distribution problems. Therefore, by means of modern control techniques, additional objectives can be satisfied. For future autonomous vehicles where human acceptance is not ensured yet, this represent an opportunity to exploit more the vehicle's potential in a way to adapt its behavior to humans expectations.

The authors recognize that more evidence should be provided by means of real experiments before proposing any standards. For this reason, future works will focus on taking care of implementation issues on one hand, and study the option of generating different trajectories for more motion feelings on the other hand. We expect more collaboration from car manufacturers in order to prove our claims and participate in autonomous vehicles development.

Fig. 1 .

 1 Fig. 1. Trajectories in all simulations.

Fig. 2 .

 2 Fig. 2. Yaw rate responses in case of reference tuning.

Fig. 3 .

 3 Fig. 3. Steering wheel angle in case of reference tuning.

Fig. 4 .

 4 Fig. 4. Engine torques in case of reference tuning.

Fig. 5 .

 5 Fig. 5. Lateral acceleration in case of reference tuning.

Fig. 6 .

 6 Fig. 6. Lateral acceleration in case of control allocation tuning.

Fig. 7 .

 7 Fig. 7. Yaw rate responses in case of control allocation tuning.

Fig. 8 .

 8 Fig. 8. Steering wheel angle in case of control allocation tuning.

Fig. 9 .

 9 Fig. 9. Lateral acceleration in case of mixed tuning.

Fig. 10 .

 10 Fig. 10. Steering wheel angle in case of mixed tuning.

Moad Kissai, Bruno Monsuez, and Adriana Tapus are with EN-STA ParisTech, Autonomous Systems and Robotics Lab, Department of Computer and System Engineering, 828 Boulevard des Marchaux, 91762

This case has been verified by simulation.

Magny-Cours, Nevers, Niévre, Bourgogne, 58470, France.


Moad Kissai
email: moad.kissai@ensta-paristech.fr

Bruno Monsuez

Adriana A Tapus

Didier Xavier Mouton

Didier Martinez

Martinez Multi-Behavioural

Multi-Behavioural Control Allocation for Over-Actuated Vehicles

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Ground vehicles have always been identified as a way of providing pleasure when they are driven in contrast with other means of transport. Car manufacturers and equipment suppliers are constantly trying to propose new advanced technologies to improve the driver experience by making the vehicle more easily controllable. In the past few years, active chassis systems have realized a huge impact in this context. We recall for example the big success of the Anti-lock Braking System (ABS) in 1978 [START_REF] Gerard | Global Chassis Control and Braking Control using Tyre Forces Measurement[END_REF]. Since then, various systems have been added gradually to commercial vehicles. Some of these systems often influence the same physical variable making vehicles over-actuated. For example, the 4-Wheel Steering (4WS) system and the Electronic Stability Program (ESP) both influence the vehicle's yaw rate. This raises several questions about system's coordination especially if the ESP is activated while the rear wheels are steered.

The simpler solution consists in prioritizing one system over the other. The choice of prioritization is based on an off-line study of the most effective system in each situation. The simplicity of this method led car manufacturers to adopt it as long as two conflicted systems are concerned. However, the more numerous chassis systems are integrated, the more complex and unpredictable the car behavior becomes [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. Optimization-based methods should be then preferred for the upcoming advanced cars and future autonomous vehicles. Moreover, control allocation methods are specially developed for over-actuated systems in general [START_REF] Bodson | Evaluation of Optimization Methods for Control Allocation[END_REF]. In this context, daisy-chain method has been put along with the weighted pseudo-inverse (WPI) in [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF] to deal with ESP coordination with the Electric Power-Assisted Steering (EPAS) system. This gives a straightforward algebraic calculation of forces distribution using the inverse of maximum tire efforts as weights for the WPI. This can be sufficient if the only objective is allocation respecting tire maximum efforts or actuators constraints. For multi-objectives optimization problems, no general algebraic formulation exists. On-line optimization algorithms should be then preferred. Solvers based on Active Set Algorithms (ASA) showed good results to find optimal solutions in a finite number of iterations, which is essential for real-time operations [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. Various techniques have been derived from ASA. Sequential Least Squares (SLS) uses a two stage ASA to handle two optimization problems [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. The Weighted Least Squares (WLS) solves the bounded least squares problem using an one stage ASA after few matrix transformations by means of different weights [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. Other techniques not based on ASA that can be cited are Cascading Generalized Inverses (CGI) [START_REF] Bordignon | Constrained Control Allocation for Systems with Redundant Control Effectors[END_REF] and the Fixed-Point Iteration (FPI) [START_REF] Burken | Two Reconfigurable Flight-Control Design Methods -Robust Servomechanism and Control Allocation[END_REF].

These techniques have been tested to handle various multiobjectives problems. In [START_REF] Shyrokau | Control allocation with dynamic weight scheduling for two-task integrated vehicle control[END_REF], the Fixed-Point Iteration (FPI) has been used to handle the control allocation problem and tested in a Hardware-In-the-Loop procedure. In fact, the FPI is suitable for real-time applications [START_REF] Wang | Coordinated and Reconfigurable Vehicle Dynamics Control[END_REF]. Energy consumption and energy losses have been selected as performance criteria. However, these criteria were not formulated as additional cost functions to reduce the computational effort, but rather the objectives' weights have been tuned to meet the different performance requirements. The drawback is then the off-line pre-design of restriction weights, which approaches the industrial common practice. Authors of [START_REF] Chen | Energy-efficient control allocation with applications on planar motion control of electric ground vehicles[END_REF] have also focused on energy-efficient control allocation in the context of electric vehicles by adding a cost function. Stability has been added to energy optimization in [START_REF] Jing | Multi-objective optimal control allocation for a four-wheel-independent-drive electric vehicle[END_REF]. A two-step optimal control allocation has been developed: a preallocation for energy efficiency optimization assuming that the vehicle is stable, then a reallocation in case of wheels skidding or locking using Model Predictive Control. Generally, the literature has been more interested in power consumption and tire energy dissipation [START_REF] Shyrokau | Vehicle motion control with subsystem prioritization[END_REF]. The driving pleasure and comfort have always been ensured by the driver itself. Each driver corrects the vehicle behavior gradually until it fits its comfort and confidence requirements. But what about autonomous vehicles? To the best of our knowledge, chassis systems coordination taking into account the feelings generated has been ignored in the literature. In an autonomous driving context, coordination should be made in such a way so as to avoid generation of unexpected car behavior.

This paper raises the question of the ability of control allocation algorithms to influence car behavior. The Weighted Least Squares method based on Active Set Algorithm solver is used for its suitability by taking into account rapidly new objectives once formulated. Results showed that with the same reference, we can induce different responses when changing the weight of comfort requirements.

The rest of the paper is structured as follows. We start in Section Section 2 by detailing the method used for the multiobjectives control allocation. Section 3 presents results obtained by co-simulation of Matlab/Simulink R and AMESim R . The control allocation algorithm is developed in Matlab/Simulink R while AMESim R is used for its high-fidelity vehicle models. A discussion about the new challenges of future cars and motion feelings requirements is provided in Section 4. Conclusions and future works are outlined in Section 5.

WEIGHTED LEAST SQUARES METHOD

Here, we remind the basics of the Weighted Least Squares method that enables taking into account multi-objectives requirements in a simple formulation. To provide a more comprehensive explanation, we apply the method to a simple case study of a car equipped with the Active Rear Steering (ARS) system and the brake-based Vehicle Dynamics Control (VDC) system at the same time. This choice is motivated by the fact that on one hand both systems act on the yaw rate making the vehicle over-actuated, and on the other hand, it concerns a real vehicle developed by our collaborators in the Group Renault 1 .

Case Study

The considered car is equipped with two conflicting chassis systems. The ARS system generates a rear steering angle to facilitate turning maneuvers. The VDC systems generates a yaw moment by means of differential braking, which functionality is similar to the ESP's. Both systems influence the yaw rate. To determine how both systems should be coordinated, other requirements should be taken into account. In fact, the two systems act differently on the vehicle's longitudinal velocity, and both longitudinal and lateral acceleration. As it would be seen in the following equations, these systems don't generate the same amount of acceleration. As comfort requirements are closely related to the overall acceleration [START_REF] Raimondi | Fuzzy motion control strategy for cooperation of multiple automated vehicles with passengers comfort[END_REF], each system can induce different motion feelings. The control allocation method should give the passenger the possibility to tune the car behavior by acting on the systems' coordination.

System modeling

To be able TO study the influence of both ARS and VDC systems on the same vehicle, a four-wheeled vehicle model should be considered. Moreover, the ARS system generates lateral tire forces, while the VDC system is based on longitudinal tire forces. Interactions between the different tire forces should be taken into account by respecting the friction ellipse concept [START_REF] Pacejka | Tyre and Vehicle Dynamics, Second Edition[END_REF].

In this case, a planar vehicle model can be considered as long as vertical forces (suspensions) are not controllable. Nevertheless, these latter influence the tire behavior and should be taken into account in the control allocation constraints. Using Newton's laws of motion, we find the following state-space representation:

                                 Vx ψ = 0 V y 0 0 V x ψ +    1 M 0 0 1 I zz    F xtot M ztot V x ψ = 1 0 0 1 V x ψ (1)
(2)

1 More specifically, the Renault Talisman equipped with the two systems.

With:

                             F xtot = F x f l + F x f r cos (δ f ) + F x rl + F xrr M ztot = F x f l + F x f r l f sin (δ f ) + F x f r -F x f l E 2 cos (δ f ) + (F xrr -F x rl ) E 2 -F yr l r (3) (4)
Where:

• V x : longitudinal velocity of the vehicle,

• V y : lateral velocity of the vehicle,

• ψ : yaw rate of the vehicle,

• M : vehicle's mass,

• J z : vehicle's yaw moment of inertia,

• F xi,j : i -j braking force, where "i" is front or rear, and "j" is right or left,

• F yr = F y rl + F yrr lateral rear force,

• δ f : front steering angle,

• l i : distance between the front or rear axle and the vehicle's center of gravity (CoG),

• E : vehicle's track.

In order to optimally distribute the efforts into tires, we need also a tire model. This tire model should be simple enough for controllability requirements, depicts the combined slip as longitudinal and lateral forces are concerned, and depends on varying parameters that could be estimated on-line. We use then the Linear Varying-Parameter (LPV) model described in [START_REF] Kissai | A new linear tire model with varying parameters[END_REF].

High-level control

Before getting into the control allocation method, we should establish a high-level control that transforms target motion quantities into the generalized force and moment to distribute: F xtot and M ztot . According to equations (1) and (2), the problem is Multi-Inputs Multi-Outputs with a varying parameter V y with several parametric2 and dynamic3 uncertainties. Moreover, according to the structure of the matrix B, transfer function for each diagonal term can be approximated by an integrator. For all these reasons, a diagonal PI-structured gain scheduled H ∞ controller has been developed. Due to space limits and the scope of this paper, details of the high-level controller are not provided.

Control Allocation Method

The control allocation problem can be defined as follows [START_REF] Tor | Control allocation -A survey[END_REF]: find the control vector, u ∈ R n such that

B eff u = v des (5) subject to    u min ≤ u ≤ u max ˙ u ≤ ˙ u max (6) (7)
where B eff ∈ R m×n is a control effectiveness matrix, u min ∈ R n and u max ∈ R n are the lower and upper position limits, respectively, ˙ u ∈ R n is the control rate, ˙ u max ∈ R n is the maximum control rate, v des ∈ R m are the desired accelerations, n is the number of control effectors, and m is the number of axes to control.

As n > m, several solutions can be found. The control allocation algorithm should be able to pick the best solution by defining optimization objectives or cost functions. The algorithm can try to fulfill these objectives separately in a sequential way [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. The objectives order in the algorithm determines the priority of each objective. However, we want this priority to be tunable. Another way to express a multi-objectives problem is to merge optimization criteria into one by summation [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. This is called the Weighted Least Squares problem:

u opt = arg min umin≤ u≤ umax l γ i W i (B i u -v i ) 2 (8)
• u opt : optimal control vector,

• l : number of objectives,

• γ i : weight of the i th objective,

• W i : non-singular weighting matrices,

• v i : desired vector of the i th objective,

• B i : effectiveness matrix of the desired i th objective.

Problem definition

For the ARS-VDC coordination case, the control vector contains controllable tire forces:

u =      F x f l F x f r F x rl F xrr F yr      (9)
u min and u max reflect tire limits with respect to the friction ellipse concept [START_REF] Kissai | A new linear tire model with varying parameters[END_REF]. The desired acceleration v des contains:

v des = F xtot M ztot (10)
To complete the problem definition described in (5), B eff is filled by geometric relations between the vehicle and its tires using equations (3) and (4):

B eff = cos (δ f ) cos (δ f ) 1 1 0 b 2,1 b 2,2 - E 2 E 2 -l r (11)
where:

• b 2,1 = l f sin (δ f ) - E 2 cos (δ f ) , • b 2,2 = l f sin (δ f ) + E 2 cos (δ f ) .

Objectives formalization

Stability and robustness of the global control have been moved to the high-level control. If the combination of tire forces achieve the generalized forces required to stabilize the vehicle, then the stability is ensured. One can speculate that the prior objective of the weighted least squares algorithm should be then the control allocation precision. This prioritization is ensured by setting the control allocation precision corresponding weight to the highest value. However, when following this procedure, no effect could be obtained in terms of accelerations to change the vehicle's behavior as the algorithm prioritizes forces tracking generated by the high level control. Here, a penalization of precision is permitted in order to fulfill a secondary objective. The control effectiveness matrix and the desired acceleration vector have been defined in the previous paragraph. Regarding the corresponding weighting matrix; it enables us to favor one control axis instead of another. We remind that our first objective is to control the yaw rate by means of two chassis systems, but we also want to minimize the effect on the longitudinal speed. The weighting matrix, that we note W ca , is then chosen to be diagonal with higher value of the weight corresponding to the yaw moment. The originality of this work lies rather in the motion feelings objective. Motion sickness and discomfort are tightly related to the vehicle's accelerations [START_REF] Raimondi | Fuzzy motion control strategy for cooperation of multiple automated vehicles with passengers comfort[END_REF]. The major problem is how to fit the desired accelerations to each driver perception. The goal of this paper however is to show the ability of the control allocation algorithm proposed to change the vehicle's behavior. No standardizations are intended to be given for now as more experimental tests are needed. We chose then in this work to let the user set its preferences manually. In other words, as drivers have the option to select their preferred driving modes in recent cars, those modes are linked here to the second objective criteria. Let us first determine the relations between the control vector and accelerations. Equation (1) can be used for the longitudinal acceleration. In the same way, we can use Newton's laws of motion to express the lateral acceleration. The effectiveness matrix is therefore expressed as:

B mf =    cos (δ f ) M cos (δ f ) M 1 M 1 M 0 sin (δ f ) M sin (δ f ) M 0 0 1 M    (12)
The weighting matrix here, noted W mf , will favor the longitudinal acceleration to the lateral one or the opposite. As we are more interested in the overall acceleration, this matrix is set to the identity matrix. Desired tunable accelerations are contained in the desired vector noted v mf . This vector should not contains predefined values as this could lead to accelerations demand while the driver does not ask for them. This vector should rather be expressed according to the control vector. The objective is then:

W mf (B mf u -[B mf u + ε]) ( 13
)
where ε is the tunable weight that varies with the driver's preferences. One could think of the risk of divergence of the commands as the difference (B mf u -[B mf u + ε]) is never null for ε = 0. However, the first objective prevent the control vector from increasing too much to keep minimal the control allocation error. A null ε corresponds then to a neutral behavior, a non-null ε with the same sign of the current acceleration would give a higher acceleration than expected and corresponds then to a more sportive mode, and a non-null ε with an opposite sign would give a lower acceleration than expected and corresponds then to a more comfortable mode. The optimal control vector is then:

u opt = arg min umin≤ u≤ umax γ ca W ca (B eff u -v des ) 2 + γ mf W mf (B mf u -[B mf u + ε]) 2 (14)

Solver algorithm

The solver is based on Active Set Algorithm (ASA). For details regarding this algorithm, refer to [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. In this paper, we are more interested in how we can make use of the ASA to solve online the control allocation problem. To do so, we simply have to rewrite the cost function following the ASA formulation:

u opt = arg min umin≤ u≤ umax A u -b (15)
Which means rewrite the cost function in [START_REF] Pacejka | Tyre and Vehicle Dynamics, Second Edition[END_REF] as:

√ γ ca W ca B eff √ γ mf W mf B mf u - √ γ ca W ca v des √ γ mf W mf [B mf u + ε] 2 (16)
The algorithm tries to satisfy both objectives at the same time when possible. If it is not possible, then the cost function is at least minimized by favoring the objective with the highest weight. For real-time maneuvers, number of iterations are limited to a finite value. A sub-optimal solution could then be generated rather than an optimal one.

Low-level commands

The control allocation algorithm generates tire forces commands. These commands cannot be fed directly to the different actuators. As the relations between efforts and actuators inputs are dynamic, a proper way to interpret the tire forces commands would be to add additional low-level controllers. However, this will add additional time lags to the global control logic, and for good precision and robustness, a closed-loop will be needed while tire forces are not measurable in commercial vehicles. Therefore, here only an algebraic transformation is added to transform forces into torques or angles. Due to space limits, no further details are provided.

CO-SIMULATION RESULTS

To validate our control logic, a high-fidelity vehicle model equipped with a differential braking and a rear steering actuator has been validated in AMESim R . However, AMESim R does not contain enough features to test directly sophisticated control algorithms as the one presented in Section 2. AMESim R is rather used for vehicle dynamics validation for its high fidelity components. The algorithm is then written in Matlab R , called in Simulink R , and a co-simulation is carried out between AMESim R and Simulink R .

Regarding the scenario tested, a real experiment in a french road has been conducted by the Group Renault to test only vehicle dynamics. We use the steering wheel angle, the acceleration pedal, and the brake pedal inputs registered to generate longitudinal speed and yaw rate targets and then evaluate the influence that would have the proposed control logic on the vehicle motion. Driving modes are changed manually in Simulink R by means of a rotary switch.

Fig. 1 and2 show the variation of the longitudinal acceleration and the lateral one respectively when changing the driving modes. We can see that the control allocation algorithm allows different behaviors, and therefore different motion feelings using the same inputs. This comes without significance variation of the yaw rate to stay in the stability envelope as Fig. 3 shows. This is mainly due to the prioritization of the yaw rate control with respect to the longitudinal speed control.

This influence how chassis systems are solicited. Fig. 4 shows the braking torque variation of the front-left tire for example from a driving mode to another. As expected, to give a more comfortable feeling, the use of brakes is minimized, while it is maximized in a more sportive behavior. The same remark holds for the rear steering angle as Fig. 5 illustrates. In a sportive behavior, the rear axle is more agile, while it is slowed to give a more comfortable feeling. It should be noted also that this vari-Figure 4: Front-left tire braking torque depending on driving behavior.

ation respects the physical behavior of tires. Thanks to the linear tire model integrated with varying parameters, variation of the rear lateral tire stiffness variation due to brake activation has been estimated to adapt generation of the rear angle to the real potential of the tire (see Fig. 6).

The rear steering angle sign could be even changed to steer in the same direction than the front angle, which would give a sort of a lateral transitional motion of the car as experienced drivers do when drifting. Weights of each objective could also be variable depending on the driving mode (including autonomous or not). This is not shown here to keep the idea simple. A further investigation could be needed in the future.

OPEN CHALLENGES FOR FUTURE CARS

Autonomous vehicles seems to be the next big revolution in automotive industries. All car manufacturers are concentrating their efforts to their development. Several challenges still need to be overcome.

Industrial Constraints

One of the challenges is the fact that different stakeholders are concerned. These actors should have a common framework in which each one can operate at ease. However, the know-how of several stakeholders manifests in their control algorithms. The overall control architecture should be elaborated in such a way to allow a plug-and-play way of operating where each actor can protect its intellectual properties. For this reason, in [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF], several characteristics that the overall control architecture should respect have been determined:

• Adaptability to face environment changes and drivers behaviors [START_REF] Coelingh | Openinterface definitions for automotive systems -Application to a Brake by Wire System[END_REF]. A high-level control based on gain scheduled H ∞ controller satisfies an adaptive and robust control.

• Fault-tolerance to propose some degraded modes and keep ensuring safety even if a chassis system break down. In the control allocation framework, this is easily taken into account by adding in the matrix effectiveness the different systems' flags to update this matrix when a failure is detected. This has been tested by simulation and will be published in a future work.

• Dynamic reconfiguration to ensure soft switching and prevent loss of stability [START_REF] Wills | An open platform for reconfigurable control[END_REF]. A way to add this feature is to tune the weighting functions used in control allocation [START_REF] Tor | Control allocation -A survey[END_REF].

• Extensibility to rapidly insert additional technologies without redesigning the whole architecture [START_REF] Coelingh | Openinterface definitions for automotive systems -Application to a Brake by Wire System[END_REF]. This is one of the major industrial concerns as autonomous vehicles needs are not frozen yet. Control allocation methods are designed to handle over-actuated systems with a dimension of R m×n . The same algorithm presented in this paper could be applied to a bigger set, which makes it extensible.

• Modularity to ensure flexibility, which is already the case in most of vehicle dynamics control architectures.

• Openness to support various systems from different sources without jeopardizing the intellectual property rights of the different stakeholders [START_REF] Coelingh | Openinterface definitions for automotive systems -Application to a Brake by Wire System[END_REF]. This supposes interfacing modification, which needs a tight collaboration between car manufacturers and equipment suppliers.

It seems clear then that the different stakeholders should start thinking about joining forces to implement this control allocation layer for future cars by enabling a certain degree of openness of their algorithms.

Human Acceptance

Another autonomous vehicles challenge is their acceptance by humans. Here, the feeling that generates the vehicle behavior plays a major role. Not only the trajectory tracking is important but also how this trajectory is followed. The motion of the car should be done in a way to make drivers trust their vehicle. A discussion about human trust and autonomous systems is provided in [START_REF] Stormont | Analyzing Human Trust of Autonomous Systems in Hazardous Environments[END_REF]. The difficulty is the fact that the definition of comfort or excitement differs from a driver to another due to inter-individual variability. Current commercial vehicles enable you choose manually the driving mode. We could expect that future vehicles would learn and remember your preferences. However, the most suitable behavior may differ from the three main drive modes. A continuous space defining car behavior tuning would be preferred to make driving experience more personalized. This is one of the main innovations of the Group Renault 4 . This tuning is done at the reference calculation level. Again, the vehicle should be able to respond correctly and generate the expected feeling. A smart coordination between chassis systems should be ensured. This could be done by formalizing a multiobjective problem. As it is depicted in Section 3, formalizing an objective related to the vehicle's acceleration allows allocating the commands differently to increase or reduce the acceleration with respect to a neutral behavior. This comes without jeopardizing the vehicle's stability by means of higher weight for the stability objective. The additional acceleration term vary with the driving mode. As a consequence, commands fed to different subsystems vary from a behavior to another. This can be generalized to a bigger set of subsystems. To do so, the effectiveness matrices should be simply updated. However, precautions should be taken. The more complex the problem gets, the more time and calculation effort the solver require. Depending on the financial decisions the car manufacturer would take regarding its calculators, the set of subsystems to integrate with a feasible real-time coordination will be limited.

Motion Feelings Formalization

Knowing that the vehicle behavior influence the passengers feelings, these motion feelings should be formalized in a way to make an autonomous vehicle behavior predictable and reliable. Research on motion sickness related discomfort to high acceleration values. ISO 2631-1 defines standards of the r.m.s. (road motion sickness) overall acceleration related to passengers comfort (Table 1) [START_REF] Raimondi | Fuzzy motion control strategy for cooperation of multiple automated vehicles with passengers comfort[END_REF]: However, these researches concerned ground Very uncomfortable a rms >2. [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF] Extremely uncomfortable vehicles in general, without differentiating cars from buses for example. In a bus, passengers could be standing. One cannot generalize the comfort notion to any type of ground vehicles without taking into account the passengers' postures.

Other researches have related ride quality to jerk, which is the time derivative of acceleration [START_REF] Kawabe | Speed Control Method of Electric Vehicle for Improving Passenger Ride Quality[END_REF]. Unfortunately, it is hard to obtain good results by deriving the acceleration signal in real time, as this latter is already noisy and corrupted by the gravitational acceleration.

However, in hazardous situations, high acceleration values are often required to stabilize the vehicle. This does not go into contradiction with ISO 2631-1, as this latter concerns only the r.m.s. of the overall acceleration. In other words, high accelerations must not be maintained for a long period of time. Nevertheless, high values of acceleration or jerk can cause discomfort even during a short period of time [START_REF] Svensson | Tuning for Ride Quality in Autonomous Vehicle : Application to Linear Quadratic Path Planning Algorithm[END_REF]. Maximum allowable values of acceleration should be identified separately. According to [START_REF] Kilinc | Determination of minimum horizontal curve radius used in the design of transportation structures, depending on the limit value of comfort criterion lateral jerk[END_REF], discomfort threshold lies around 1m/s 2 to 1.47m/s 2 . These values were set for different means of transport including buses and trains. Again, this has generalized the problem to both seated and standing passengers. Since we are interested in cars where passengers are always seated, it might be reasonable to set the maximum acceleration values up to 2m/s 2 [START_REF] Svensson | Tuning for Ride Quality in Autonomous Vehicle : Application to Linear Quadratic Path Planning Algorithm[END_REF]. This shows the gap in the literature regarding motion feelings formalization. This field still should be investigated to facilitate autonomous vehicles introduction to the society.

The major problem is the fact that motion feelings are perceived differently from a driver to another due to the interindividual variability. In this work, we supposed that the driver itself can select the behavior desired as in driving modes proposed by recent cars. These modes should be extended to personalized behaviors. Experimental studies are needed to associate a certain vehicle behavior to motion feelings and drivers' profiles. The reverse could be then imagined then when the driver profile can be estimated, control allocation weights would be automatically updated in order to generate the expected motion feeling in an autonomous mode.

CONCLUSIONS

In this paper, a new problematic regarding motion feelings and vehicle dynamics control has been introduced. A solution using multi-objectives control allocation algorithm has been proposed in order to tune vehicle's motion. This method is based on amplifying or reducing the acceleration generated by tire forces to generate different feelings. A co-simulation between Matlab/Simulink R and AMESim R has been realized in order to validate complex algorithms in high-fidelity models. Results showed different use of subsystem when it comes to motion feelings. This comes without jeopardizing the vehicle's stability ensured by the high-level control layer.

This demonstrates the need of implementing such algorithms in future cars, especially for autonomous cars so their behavior stays predictable and fit best drivers' preferences.

The goal of this paper is to sensitize and start a debate about the objectives that future cars should satisfy. The authors recognize that more evidence should be provided by means of real experiments before proposing any standards. A closer collaboration with car manufacturers is expected for this reason.

Finally, the control allocation framework offers richer possibilities as fault-tolerance. Conflicted chassis systems can be used to complete each other maneuvers. In this way, if a system fails, the other one will easily take over. This will be detailed in a future work to prove that with this approach, both safety and comfort can be ensured.

Figure 1 :

 1 Figure 1: Longitudinal acceleration depending on driving behavior.

Figure 2 :

 2 Figure 2: Lateral acceleration depending on driving behavior.

Figure 3 :

 3 Figure 3: Vehicle's yaw rate depending on driving behavior.

Figure 5 :

 5 Figure 5: Rear steering angle depending on driving behavior.

Figure 6 :

 6 Figure 6: Rear lateral tire stiffness depending on driving behavior.

Table 1 :

 1

	ISO 2631-1 standard
	r.m.s. overall acceleration m/s 2	Passenger comfort level
	a rms < 0.315	Not uncomfortable
	0.315< a rms <0.63	A little uncomfortable
	0.5< a rms <1	Fairly uncomfortable
	0.8< a rms <1.6	Uncomfortable
	1.25< a rms <2.5

Basically the mass and moment of inertia.

Due to the negligence of vertical motions.

The Multi-Sense project.