Legislation concerning pollutant emissions of diesel passenger cars is becoming increasingly restrictive, especially for nitrogen oxide (NOx) and particulate matter (PM). This article proposes to apply a CRONE control design methodology on a diesel engine in order to adapt the air-path and fuel-path of the engine and minimize NOx emissions. As the multivariable CRONE control strategies need a nominal transfer function (G 0 (s)) and some frequency response of the system (G(s)), several test-bench experiments and a linear identification of the system were performed. The aim of this approach was to find a decoupling and stabilizing controller for the combustion engine that minimized NOx emissions at each operating point considered and during transient of torque/engine speed. The system is a square multivariable system with three inputs: Exhaust gas recirculation valve (EGR), variable geometry turbine (VGT), and start of injection (SOI); and three outputs: mass air flow (MAF), boost pressure (Pboost) and NOx level (NOx). The CRONE control approach developed for multivariable square plants is based on the third generation scalar CRONE methodology. Fractional order transfer functions were used to define all the components of the diagonal open-loop transfer matrix, β 0 . Optimisation gave the best fractional open-loop transfer matrix and finally, frequency domain system identification was used to find a robust controller 𝑲(𝒔) = 𝑮 𝟎 -𝟏 (𝒔)𝛃 𝟎 (𝐬). Performances of the proposed control structure were tested and validated with a number of experiments on a high dynamic test bed (NEDC driving cycle).

I. INTRODUCTION

Current interest in halting global warming has put pressure on the automobile industry to produce vehicles/engines that are more environmentally friendly. This has led to the development of increasingly complex engine feedback control systems. Nowadays, these control systems are mainly based on experimental data. For every type of engine, measurements concerning fuel economy and pollutant emissions must be made. These measurements include successive changes to the many parameters involved in order to cover all the operating conditions of the engine. This is very expensive and time consuming. Moreover, variations in engine-out emissions due to ageing, component drift or production tolerances pose a serious problem. One way to tackle this problem is to add control strategies on pollutant emission. This is an emerging topic driven by the development of cheap sensors that can easily measure pollutant production. [START_REF] Bessai | Emissions reduction potential of closed-loop intake oxygen control[END_REF] demonstrated the advantages of precisely controlling the quantities of O 2 entering the D. Nelson-Gruel is with the University of Orleans, Laboratoire PRISME, 8 rue Léonard de Vinci, 45000 Orleans, FRANCE (phone: +332 38 49 46 21; e-mail: dominique-gruel-nelson@univ-orleans.fr).

G. Colin, Y. Chamaillard and A. Charlet are with the University of Orleans.

cylinder to solve the pollutant emissions problem. In [START_REF] Zentner | Model-based injection and EGR adaptation and its impact on transient emissions and drivability of a diesel engine[END_REF], the impact of adapting the time response between fuel-path and air-path to lower PM emissions was studied. In [START_REF] Tschanz | Control of diesel engines using NOx emission feedback[END_REF][START_REF] Tschanz | Feedback control of particulate matter and nitrogen oxide emissions in diesel engines[END_REF] the authors combined air-path variables (boost pressure and exhaust gas recirculation rate, swirl valve) and a fuel-path variable (start of injection) in order to control NOx and PM emissions. A model-based observer for the engine-out emissions was used to cope with sensor lag and delay.

To solve the pollutant emissions minimisation problem using feedback, a fast and accurate sensor or a virtual sensor must be used [START_REF] Tschanz | Feedback control of particulate matter and nitrogen oxide emissions in diesel engines[END_REF][START_REF] Kato | Performance of thick film NOx sensor on diesel and gasoline engines[END_REF]. A model based on in-cylinder measurements that use the advantages of an empirical and phenomenological model was developed in [START_REF] Kato | Performance of thick film NOx sensor on diesel and gasoline engines[END_REF]. This model extracts the most relevant physical phenomena and extends them by physically motivated empirical elements. The resulting model is a real-time model that shows good performances. While the topic is intensively researched, the majority of this work is based on the well-known extended Zeldovich mechanism which gives a relation to calculate the rate of NO formation using the concentration of the different gas species involved in the process. This mechanism gives good results (Fig. 1) but cannot be run in real time unless rather sweeping assumptions are made. Fig. 1 shows some results using this mechanism. The time taken to find each NOx emission level estimated value was around 10 seconds. One way to counteract the problem of designing a pollutant observer or estimator is to use a cheap pollutant emissions sensor. This study was primarily conducted to demonstrate the feasibility of a robust control during torque transient. Be able to control this variable in a robust way offers one hand the possibility of playing trajectories of NOx emissions and secondly to win some precious ppm of NOx emissions during transient of torque/engine speed. This article proposes a NOx emissions robust control strategy that uses a sensor from Siemens VD, a trademark of the Continental Corporation,

Robust control applied to minimize NOx emissions

Nelson-Gruel D., Chamaillard Y., Charlet A., Colin G. that measures NOx levels with a fast response time (around 0.6sec) but variable time-delay due to gas transportation. After section 2 in which the system identification process is presented, section 3 focuses on the robust control system design. Finally section 4 presents the performances of the proposed control structure, that were validated using test-bed experiments.

II. SYSTEM IDENTIFICATION

All the experiments conducted in this work were carried out on a high dynamic Engine-Dynamometer test-bed that consists of a dynamical mechanical load provided by an asynchronous machine and a Peugeot S.A. DV6, a 1.6 liter diesel engine with 4 cylinders, common-rail injection system, cooled EGR, and VGT turbocharger. The test-bed engine is equipped with a fast prototyping system based on xPCTarget from Matlab. With this module and adequate software it is possible to read the actual values of every variable calculated and measured by the ECU (Bosch, EDC 17) and modify every map and parameter contained in the ECU code. It is also possible to deploy new real-time control structures and to bypass some variables calculated or measured by the ECU.

A. System description and problem formulation

The system is a 1560 cm3 diesel engine with 4 cylinders and 68kW at 3750rpm. The air-path of the system is equipped with two actuators: a variable geometry turbine (VGT) and an exhaust gas recirculation valve (EGR). The fresh air coming from the atmosphere (Mass air flow: MAF) is compressed and warmed up by the compressor. The exchanger cools it down which increases the density of flow and decreases the boost pressure (pboost). The Exhaust Gas Recirculation system dilutes the fresh air entering the cylinder. The mixture of intake flow and exhaust flow decreases the mean combustion temperature, thus producing the pollutant emissions trade-off. Lower PM emissions need high temperature and oxygen in the combustion chamber where these same parameters increase the level of NOx pollutants (Fig 2 ). Finally, the exhaust flow that cannot go to the intake manifold by the EGR valve flows through the turbine, and speeds it up. This energy is transmitted by a shaft to the compressor which adjusts the boost pressure .The turbine speed can be tuned by adjusting the turbine (VGT) position. The exhaust gas returns to the atmosphere and just before the NOx and PM sensors are placed. The NOx sensor used for the on-board measurement of the NOx concentration (Siemens-VDO, measuring range between 0 and 1500 ppm) is a smaller and cheaper device whose working principle is briefly explained in [START_REF] Kato | Performance of thick film NOx sensor on diesel and gasoline engines[END_REF][START_REF] Kato | Thick film Zr02 NOx sensor for the measurement of low NOx concentration[END_REF][START_REF] Kato | Thick film ZrO2 NOx sensor[END_REF][START_REF] Alfieri | Emission-controlled diesel engines[END_REF].

As described above, NOx emissions are essentially defined by the local temperature trajectory and by the availability of oxygen in the cylinder, which are influenced by the intake conditions, the burn gas rate (air-path variables) and the SOI (fuel-path variable). It was shown in [START_REF] Helmantel | Visualization of the effects of post injection and swirl on the combustion process of a passenger car common rail DI diesel engine[END_REF][START_REF] Tschanz | Feedback control of particulate matter and nitrogen oxide emissions in diesel engines[END_REF] that NOx control is clearly a multivariable control problem with a high coupling phenomenon that is provided by coupling between the air and fuel-path variables used to control this output.

B. System identification

The frequency-domain control-system-design (CSD) approach used in this work requires high fidelity linear dynamic models that approximate the underlying dynamics of the engine. Thus, a frequency domain system identification methodology was used to obtain a linear timeinvariant model that approximates the dynamics of the diesel engine. The studied system is a MIMO system with three inputs and three outputs (3x3).

( ) ( ) ∑ + = = N k k k k t f A t u 1 2 cos ϕ π , (1)
where:

-N: number of harmonics, -f k : harmonic frequency, φk : initial phase of ea ch harmonic, -Ak : harmonic amplitude.

Step signals are first used to define the bandwidth where the outputs can be excited (range of f k ) and the acceptable amplitude A k is chosen in such a way that the system gives a linear response. The multisine excitation signal is chosen with a sampling time of 200Hz and a frequency range from 0.1 Hz to 20 Hz. After that, using the superposition theorem, the multisine signal is applied on the system to find the frequency response of each input-output transfer function of the system. This process is repeated for fourteen operating points on the overall range of operating points (Fig. 4). Fig. 5 shows the results obtained with this identification method applied on fourteen operating points. The frequency domain identification provides a nonparametric model (Fig. 5). The phase deviation and gain variation observed demonstrate that our system is a nonlinear one that can be approximated at each operating point by a matrix of linear time-delay transfer function. A parametric identification of one of the fourteen operating points gives the following matrix:

𝐺 0 (𝑠) = � 𝑔 11 (𝑠) ⋯ 𝑔 13 (𝑠) ⋮ ⋱ ⋮ 𝑔 31 (𝑠) ⋯ 𝑔 33 (𝑠) �, (2)
with 𝑔 𝑖𝑗 (𝑠) = ℎ 𝑖𝑗 (𝑠)𝑒 -𝐿 𝑖𝑗 𝑠 , ℎ 𝑖𝑗 (𝑠) a strictly proper timedelay free transfer function and 𝐿 𝑖𝑗 ∈ ℝ * + . The bode diagram of this matrix transfer function called the nominal plant is also presented on Fig. 5 in red.

III. ROBUST CONTROL IN DIESEL ENGINES

The robust control strategies proposed in this section used the CRONE control methodology [START_REF] Oustaloup | La commande CRONE, 2nd edition[END_REF] and more precisely its development on a time-delay multivariable system [START_REF] Nelson-Gruel | Extension de la commande CRONE multivariable aux systèmes non carrés : application à un système d'air de moteurs essence et diesel[END_REF][START_REF] Gruel | Robust control design for multivariable plants with time-delays[END_REF]. The aim of the multivariable (MIMO) CRONE control approach is to robustify closed-loop dynamic performance through robustness of the damping factor or the resonant control peaks, when plant parameters vary. Contrary to some methods, CRONE control and design does not deal with robustness of the closed loop bandwidth and thus limits the control effort. The CRONE CSD is based on the common unity-feedback configuration, Fig. 6. The CRONE methodology used consists in finding the nominal diagonal and optimal open-loop transfer matrix with 3 fractional order transfer elements [START_REF] Oustaloup | La commande CRONE, 2nd edition[END_REF][START_REF] Oustaloup | Robust control of LTI square MIMO plants using two CRONE control design approaches[END_REF]:

𝛽 0 (𝑠) = 𝐺 0 (𝑠)𝐾(𝑠) = � 𝛽 0 11 (𝑠) ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ 𝛽 0 33 (𝑠) �. ( 3
)
Each element, 𝛽 0𝑖𝑖 (𝑠), of the diagonal open-loop matrix 𝛽 0 (𝑠) is based on the third generation CRONE single-input single-output methodology [START_REF] Oustaloup | La commande CRONE, 2nd edition[END_REF]. The principle of this methodology is to optimize the parameters of the nominal open-loop transfer function 𝛽 0 (𝑠) that includes band-limited complex fractional order integration over a frequency range[𝜔 𝑙 , 𝜔 ℎ ]. The complex fractional order, n = a+ib, enables a straight line of any direction to be created in the Nichols chart which is called the generalized template (Fig. 7). The open-loop transfer functions 𝛽 0𝑖𝑖 (𝑠) around the resonant frequency, ω r is defined by:

𝛽 0𝑖𝑖 = 𝛽 li (𝑠)𝛽 mi (𝑠)𝛽 hi (𝑠), (4) where:
( )

( ) ( ) b - b a b mi s s C e s s C s sign i l h g /i l h sign 1 1 1 1                             + + ℜ ×         + + = ω ω ω ω β , (5)
( ) ( ) [ ] 3 1 0 1 0 0 )) ( β 1 ( 1 β S ≤ ≤ -       + = + = i ii s diag s I s , (6) ( ) ( ) [ ] ( ) 3 1 0 0 0 1 0 0 )) ( β 1 ( ) ( β β β T ≤ ≤ -       + = + = i ii ii s s diag s s I s ,(7) ( ) ( ) [ ] ) ( S ) ( β ) ( S 0 1 0 U0 s s K s I s K s = + = - , (8)
( ) ( ) [ ] ) ( ) ( T ) ( β S 1 0 1 0 i0 s K s s G s I s - - = + = . ( 9
) ( ) ( 1 ) ( 1 ) ( ) ( β s S s S s T s T s ii ii ii ii ii - = - = . ( 10
) Figure 7 shows that the resonant peak 𝑀 𝑟 variation of the complementary sensitivity function is reduced by optimizing the position of the generalized template in the Nichols chart (Fig. 7b and7c). The robustness cost function is given by

𝐽 = (𝑠𝑢𝑝|𝑀 r | -inf|𝑀 r |) 2 , (11)
whith:

-𝑠𝑢𝑝|𝑀 r | = max 𝐺 sup 𝜔 �𝑇 𝑖𝑖 (𝑗𝜔)�, -𝑖𝑛𝑓|𝑀 r | = min 𝐺 sup 𝜔 �𝑇 𝑖𝑖 (𝑗𝜔)�, where G is the set of all the operating points of the diesel engine, and while respecting the frequency-domain inequalities below for 𝜔 ∈ ℝ + and 𝑖, 𝑗 ∈ 𝑁:

sup 𝐺 �𝑇 𝑖𝑗 (j𝜔)� ≤ 𝑇 𝑖𝑗 up (𝜔), ( 12
) inf 𝐺 |𝑇 𝑖𝑗 (j𝜔) ≥ 𝑇 𝑖𝑗 low (𝜔), ( 13
) sup 𝐺 �𝑆 𝑖𝑗 (j𝜔)� ≤ 𝑆 𝑖𝑗 up (𝜔), ( 14
) sup 𝐺 |𝐾𝑆 𝑖𝑗 (j𝜔) ≤ 𝐾𝑆 𝑖𝑗 up (𝜔), ( 15
) sup 𝐺 |𝑆𝐺 𝑖𝑗 (j𝜔) ≤ 𝑆𝐺 𝑖𝑗 up (𝜔).
(16) As the uncertainties are taken into account by the least conservative method, a non-linear optimization method must be used to find the optimal values of the independent parameters of the fractional open-loop, and consequently to find an optimal placement of the equivalent open-loop frequency response.

A. Decoupling and optimized controller

Let G 0 be the nominal plant transfer matrix and considering (3), the aim of the CRONE control approach for MIMO plants is to parameterize 𝛽 0 (𝑠) to satisfy the following four objectives:

-perfect decoupling for the nominal plant, -accuracy specifications at low frequencies, -required nominal stability margins of the closed loops (behaviours around the required cut-off frequencies), -specifications on the n control efforts at high frequencies. As G 0 is not diagonal, the problem is to find a decoupling and stabilizing controller K(s). This controller exists if and only if the following hypotheses are verified:

𝐻 1 : [𝐺 0 (𝑠)] -1 exists, ( 17
) 𝐻 2 : 𝑍 + [𝐺 0 (𝑠)] ∩ 𝑃 + [𝐺 0 (𝑠)] = 0, (18)
where 𝑍 + [𝐺 0 (𝑠)] and 𝑃 + [𝐺 0 (𝑠)] indicate the positive real part zero and pole sets. Once β 0 (𝑠) has been optimized, the controller is given by:

𝑲(𝑠) = 𝐆 0 -1 (𝑠)𝛃 0 (𝑠), (19)
where 𝐆 0 -1 (s) is the inverse of the nominal plant G 0 (s). In [START_REF] Gruel | Robust control design for multivariable plants with time-delays[END_REF], the author demonstrates that when 𝐺 0 (𝑠) is defined by (2) P(s) can be written:

𝐆 0 -1 (𝑠) = 𝐏(𝑠) = � 𝑃 11 (𝑠)𝑒 𝛾 11 𝑠 ⋯ 𝑃 1𝑛 (𝑠)𝑒 𝛾 13 𝑠 ⋮ ⋱ ⋮ 𝑃 31 (𝑠)𝑒 𝛾 31 𝑠 ⋯ 𝑃 𝑛𝑛 (𝑠)𝑒 𝛾 33 𝑠 �, (20)
where 𝑃 𝑖𝑗 (𝑠) is the non-zero transfer function and 𝛾 𝑖𝑗 ∈ ℝ * + . Each element of the controller is obtained from relations ( 19) and ( 20): 𝐾 𝑖𝑗 (j𝜔) = 𝑃 𝑖𝑗 (j𝜔)𝑒 𝛾 𝑖𝑗 j𝜔 𝛽 0 𝑗𝑗 (j𝜔).

(21) To make the controller achievable and the closed loop fully stable for unstable and under-damped systems with nonminimum phase (RHP zeros or time-delays), the open-loop transfer function must include a calculated nominal timedelay, under-damped modes and right half plane zeros and poles of 𝐺 0 (𝑠) and 𝐺 0 -1 (𝑠) [START_REF] Nelson-Gruel | Extension de la commande CRONE multivariable aux systèmes non carrés : application à un système d'air de moteurs essence et diesel[END_REF][START_REF] Gruel | Robust control design for multivariable plants with time-delays[END_REF].

IV. APPLICATION : EXPERIMENTAL RESULTS

The issue of minimizing NOx emissions can be relaxed if a NOx sensor is integrated into a feedback loop. In [START_REF] Tschanz | Feedback control of particulate matter and nitrogen oxide emissions in diesel engines[END_REF] a model-based observer and classical proportional and integral controller are used for feedback NOx emissions. In [START_REF] Alfieri | Emission-controlled diesel engines[END_REF] a multivariable feedback controller of NOx emissions and air/fuel ratio (PM indicator) was designed. The controlled inputs used were EGR valve and injection timing. In [START_REF] Stefanopoulou | Control of variable geometry turbocharged diesel engines for reduced emissions[END_REF] the control design objective was to coordinate EGR and VGT actuators to fully use their effect on engine emission performance. Air/fuel ratio and burned gas fraction in the intake manifold were regulated to meet a new optimum equilibrium. In this section, the robust multivariable controller for NOx emissions is presented. The performance of the proposed control structure has been tested and validated with a number of load-step experiments and with the NEDC driving cycle. The studied diesel engine is a MIMO time-delay system with three inputs and three outputs (3x3

G i1 : from EGR input (%) to respectively MAF (kg/h) for i=1, Pboost (mbar) for i=2 and NOx level for i=3, G i2 : from VGT input (%) to respectively MAF (kg/h) for i=1, Pboost (mbar) for i=2 and NOx level for i=3, G i3 : from SOI input (°CA) to respectively MAF (kg/h) for i=1, Pboost (mbar) for i=2 and NOx level for i=3.

The determinant of G 0 (s) has a right half plane pole (+15.597) that thus needs to be included (as zeros) in β 011 (s), β 022 (s) and β 033 (s) for the stabilization of the CS(s) transfer function matrix. Low frequency accuracy specifications are ensured by n l = 1 for β 011 (s), n l = 1 for β 022 (s) and n l = 1 for β 033 (s). The high-frequency control efforts are limited with n h = 4 for β 011 (s), n h = 3 for β 022 (s) and by n h = 4 for β 033 (s). The nominal resonant peak for β 011 (s) is 0, M r022 = 0 for β 022 (s) and M r033 = 0.5 for β 033 (s).

The highest value of the resonant peak of each |T ii (jω)| (related to the overshoot specification) must not exceed 3dB. Using cost function [START_REF] Nelson-Gruel | Extension de la commande CRONE multivariable aux systèmes non carrés : application à un système d'air de moteurs essence et diesel[END_REF] to solve this control problem, some frequency-domain constraints of ( 12) to ( 16) are very simply defined:

-T iiu (ω) = +3dB, -S iiu (ω) = +6dB (for a 0.5 modulus margin).

The nominal plant and the whole set of the measured frequency-responses are used to optimize at the same time the parameters of β 011 (s), β 022 (s) and β 033 (s). the optimal parameters are: Y r = 8dB, ω r = 0.05rad/s, ω l = 0.01rad/s, ω h = 100rad/s. Thus a 0 = 1.22, b 0 = -0.08 and K 3 =1.41. Figure 8 shows the optimized open-loop frequency response and Fig. 9 shows the nominal and reparametered magnitude of the complementary sensitivity matrix transfer function. The final values of the cost function are respectively 1.3 dB, 0.6 dB, 1dB and all sensitivity constraints are met The designed controller was assessed with some time domain tests on the test-bed. The proposed controller is compared to the results obtained with a conventional diesel engine control (standard ECU control). The standard ECU control consists of two single input single output controllers. The first one control MAF with EGR valve and the second one control Pboost with VGT. The two loops of the standard ECU controller have the same bandwidth of the first two loops of the robust controller designed. Figure 11 and12 show some load-steps that validated the robust behavior of the control structure. Figure 13 focuses on the validation of NOx control during a driving cycle. The NOx setpoint trajectory was fixed at 5% lower than the NOx level obtained with a conventional diesel engine controller. Results obtained during an NEDC driving cycle proved the feasibility of the proposed robust controller.

V. CONCLUSION

The CRONE methodology has been applied to feedback NOx emissions. To treat this kind of plant, a square 3x3 time-delay multivariable system, some time-delay and right half plane poles of G 0 or its inverse must be introduced in each open-loop. A PSA DV6 diesel engine was used to improve the proposed approach. The time domain data show that the CRONE control approach successfully states the robust stability of the closed-loops, the robust decoupling and actually minimizes the amount of NOx produced. As mentioned in section 2, reduce the amount of NOx produced leads irrevocably to increase the amount of PM produced. The next step of this work would be to design a control law that would take into account these two variables at the same time.

Figure 1

 1 Figure 1 NOx estimated value compared to NOx measurements for different couples of EGR and VGT positions on a Diesel engine (1800rpm and 54N.m) using the extended Zeldovich Mechanism.

Figure 2

 2 Figure 2 PM and NOx trade-off

Figure 3

 3 Figure 3 System representation To identify the system described Fig. 3, some step and multisine signals are used. A multisine is a combination of sinusoids with various frequencies. The equation of this signal is written:

Figure 4 Figure 5

 45 Figure 4 Speed-Torque map of the diesel engine (blue stars) and fourteen operating points used to identify the system (red circle)

Figure 6

 6 Figure 6 Common CRONE control-system diagram

Figure 7 (

 7 Figure 7 (a) template with real fractional order, (b) template with complex fractional order, (c) optimal template

With-,+ 1 ),-

 1 𝛽 l𝑖 (𝑠) = 𝐶 li � order n li fixes the accuracy of each closed-loop, -𝛽 h𝑖 (𝑠) = 𝐶 h𝑖 ( 𝑛 h𝑖 , order n hi permits the elements of the controller to be proper, -𝐶 𝑔 = � The gains 𝐶, 𝐶 l𝑖 and 𝐶 h𝑖 are such that 𝜔 r is the closed-loop resonant frequency (K i = 𝐶. 𝐶 l𝑖 . 𝐶 h𝑖 ).

  nominal sensitivity, complementary sensitivity, input sensitivity and input-disturbance sensitivity function transfer matrices are:

  ) For plants other than the nominal, the closed-loop transfer matrices T(s) and S(s) are no longer diagonal. Each diagonal element ( ) can be interpreted as a closed-loop transfer function resulting from a scalar open-loop transfer function ) ( β s ii called equivalent open-loop transfer function:

  For the MAF open-loop β 011 (s), the optimal parameters are: Y r = 5dB, ω r = 0.1rad/s, ω l = 0.01rad/s, ω 1 = 10rad/s, ω h = 100rad/s, a +1 = -1, and b +1 = 0. Parameters a 0 = 1.10, b 0 = -0.51 and K 1 =10.05 are computed from these optimized values. For the Pboost open-loop β 022 (s), the optimal parameters are: Y r = 3dB, ω r = 0.01rad/s, ω l = 0.005rad/s, ω h = 5rad/s. Thus a 0 = 1.32, b 0 = -0.60 and K 2 =10. For the NOx open-loop β 033 (s),

Figure 8 Figure 9 Figure 10

 8910 Figure 8 Optimized nominal (red dash-dot line) and equivalent open-loop frequency responses (grey solid line)

Figure 10 MIMO

 10 Figure 10 MIMO controller frequency response

Figure 11 Figure 12 Figure 13

 111213 Figure 11 For a variation of torque: MAF, pboost and NOx emissions are measured (green measures, blue setpoints)

  ).

	𝑌 1	𝐺 11 𝐺 12 𝐺 13	𝑈 1
	� 𝑌 2	� = � 𝐺 21 𝐺 22 𝐺 23	� � 𝑈 2	� ,
	𝑌 3	𝐺 31 𝐺 32 𝐺 33	𝑈 3


Olivier Le Meur

Zhi Liu

Keywords:

published or not. The documents may come

Saliency aggregation: Does unity make strength?

O. Le Meur (olemeur@irisa.fr) & Z. Liu Motivation: we investigate whether we could improve on the saliency quality by aggregating a set of predicted saliency maps. Does the linear combination improve the prediction?

• Uniform: weights w are uniform and spatially invariant, The robustness of the prediction can be enhanced by:  averaging the saliency maps of the top 2 models;  considering a dedicated training dataset.

𝑤 𝑘 = 1
Unsupervised methods to compute the weights The supervised method might improve the quality of saliency map, provided that we succeed in finding an image similar to the input one.

•

  𝑘 is the probability of an image pixel x from the saliency map 𝑀 𝑘 to be salient, The classical least-squares method (LS) • LS with the sum-to-one constraint of the weights (LLE) • LS with positive weights (NMF) • Robust least-squares (LSR) the learned weights of the most similar image Conclusion The WMSI method gets the lowest performance WMSI = Weights of the Most similar Image ACCV 2014


Annie Luciani
email: annie.luciani@imag.fr

Being There & Being With: The Philosophical and Cognitive Notions of Presence and Embodiment in Virtual Instruments

In this paper, we will discuss two main concepts, associated with the development of Virtual Worlds, which are "Presence" and "Embodiment". Presence is stamped as the sense of "Being there", that has to be reconstructed in Local world to render Distant Worlds accessible by networked or mediated communications. "Embodiment" could be the property of a Virtual entity to be incorporated by human as a second nature. We will show then, how (1) the first situation can be seen as a definition of "immateriality" and its correlative concept of infinity, (2) the second situation can be seen as a definition of "tangibility" with its correlative concept of instrumental embodiment. After exploring the complementary properties of these situations in detail, we will focus on the second one, identified as "the instrumental situation". We will propose some of its relevant properties, those that are able to trigger the sense of embodiment, as the main property supported in the real physical world by the feature of "tangibility". Consequently, we estimate that "embodiment" is more important than the tangibility in itself and we examine some criteria able to help us to recreate them in digital representations.

HUMAN-WORLD FUNCTIONNAL RE-LATIONSHIPS

Let start with a rough look at the diversity of the tasks humans can perform when they interact sensorially, cognitively and physically with the real world. We may observe that they could be represented along an axis putting the emphasis on two complementary situations (Figure 1): -The immersive situation, in which humans are at the center of a surrounding world, such as when we are exploring large landscapes, mainly through exteroceptive sensory channels such as vision and audition, (Figure 1 on the left of the horizontal axis) -The vis-à-vis situation in which humans are interacting with a vis-à-vis objects, in hand, supported by physical contacts and interactions through the propriotactilo-kinesthetic sensory-motor modality, such as haptic, tactile and gestural interactions (Figure 1 on the right of the horizontal axis).

The path from the first to the second (and vice-versa), that is a usual daily experience, is not so trivial to analyze and implies deep transformations in the cognitive humanworld relationship. We propose first an exercise that consists in a course along this path from the left side to the right side in order to bring out some relevant features of the complexity of the cognitive processes going from the sense of "being there" to the sense of "being with", and vice-versa.

Being there ?

On the left part of the scale axis, the concept of immersive environments (Figure 2), is placed, based on large spatial spaces in which spatial properties are essential: sizes, scales, large free body motion, etc. leading to body oriented VR platforms. The main task characterizing such situations are environment exploration, including localization, navigation, path finding. The aim is to be able to perform the task of exploration of a "landscape" as well as possible, as immersed within them (landscape, cities, houses, other bodies). The basic principles are: free motion as much as possible (position changing) in a 3D space, no occlusion for these free motion and the perceived results, free focus of observation (scale changing), knowing where we are (self localization). The concerned perceptual channels are visual and/or acoustical via 3D sounds. On the extreme right of the scale (Figure 3), the vis-à-vis object is now close in hand or "present-to-hand" and its exploration allows to extract other features such as rigidity, fluentness, weight, which are more physical than geometrical properties. Objet recognition and identification of physical features is performed by means of physical manipulation, such as squeezing, stretching, hitting, etc. and proprioceptive and kinesthesic sensory modalities. We reach the concept of intimate instrumentality. Here, the focus is put on the physical manipulation of objects. Physical means that what it is expected is based on the physical behaviors of objects; vibrations, deformations, sticking, fractures, resistance to the displacements, dynamics of collisions and of hitting, cohesions, ways of deformations (elastic, plastic, etc.). This type of task corresponds to "ergotic 1 tasks" in Cadoz's typology [START_REF] Cadoz | Le geste, canal de communication homme/machine. La communication instrumentale[END_REF], in which there is an energetic exchange between the humans who act on an object (directly or via an intermediate physical organ), which is significant as well as for the performance task than for its results.

The fuzzy figure of the notion of "object"

This imaginary course along a scale axis allows to identify two sides separated by a cognitive frontier. Onto this frontier (Figure 4), the fuzzy notion of "vis-à-vis object" is being cognitively negotiated, as it is, like the Janus, either looking on the left, toward "immersion" and "surrounding environment", or on the right, toward "instrumental situation". We identify this frontier really as a cognitive gap. 1 Do not confuse "ergotic" and "ergodic". "Ergotic" is a term coined by C. Cadoz to name a type of interaction functionality on which physical energy ("erg" is an unity of energy). In gestural interaction between a human and an object, this function integrates the haptic (or gestural) perception and the physical (or gestural) action. The fuzzy state of vis-à-vis object: the transition from "near-in-hand" to "present-in-hand" via "ready-to-hand"

On the left of this frontier, the notion of "object" starts to be cognitively constructed, not as a part of the environment but as it is considered near the body, "ready-tohand". The size of the possibly manipulated thing is smaller than the environment, near to the size of the hand or a part of the body. Relatively to the human body, it plays the role of a "vis-à-vis". In that situation, the relevant main task is to recognize or identify the spatial and topological features. Such exploration is performed through spatial actions (positioning) and exteroceptive sensory channels (vision). On the right of the frontier, once the position of vis-à-vis established, the object exploration and recognition of the surface state (rugosity, micro shapes, sharp edges, etc.) is taking over from "in hand situation" by manipulation such as palpating, brushing, skimming, etc., and by tactile sensory channels During a brief instant, "object" could be either a part of the surrounding environment just be near the hand (or near the body) -said "ready to hand" -or "an object in hand", prelude of an instrumental situation.

The transition between the both sides of the frontier is the location of a task discontinuity that is the selection task (Figure 5). The transformations consists in -at least -for the human, to become an instrumentalist when object in hand, and symmetrically, for the object, to become an instrument. We see that both transformations -of the human and of the object -are correlated, simultaneous and non separable. The human remains instrumentalist as long as the object remains an instrument and vice-versa. The reverse transformation occurs when the object being unhanded comes back to a part of the environment and the instrumentalist comes back to a human performing other tasks.

Three criteria for featuring the "immersive/Vis-àvis" transformation

The reversible transformation that occurs when crossing the "immersive / vis-à-vis" frontier, separate spaces of very different nature. Here are three criteria that allow to distinguish between these both sides: 1. In the immersive space -the human-centered philosophy -the human-world relationship is an overview rela-tionship, insisting on the extensiveness -we can say the infinity -of the space. Spatial properties are essential: sizes, scales, large body motion, etc. 2. In the instrumental space, the human-objet relationship is centered, neither on the human nor in the object but more at the place (the frontier) of their physical coupling, insisting more on the "intensiveness" of the energetic coupling Temporal properties are essential: frequencies bandwidth, reaction delay, etc. 3. The duality of both situations is also traced by another duality, we called "the concave/convex transformation". It consists in the fact that: (1) in immersive one, the environment surrounding humans and that containing things appears as concave to the human; (2) conversely, when things become as a vis-à-vis and ready-to-hand, they appear as convex. And then, we want to use hands to explore the non seen parts, either by tactile or by rotating the object which is in front of us.

We will show then, how (1) the first situation can be seen as a definition of "immateriality" and its correlative concept of infinity, (2) the second situation can be seen as a definition of "tangibility" with its correlative concept of instrumental embodiment.

THE COMPLEXITY OF THE TRANS-FORMATION FROM AN OBJECT TO AN INSTRUMENT

We will now discuss the main characteristics of both situations, focusing more on the instrumental situation, with the aim of being able to reconstruct it within the field of computerized tools.

The intimate relation between human and object during the performance of an instrumental task (i.e. a task performed by means of an instrumental human-world relationship as defined before) leads to the emergence of cognitive features such as those of the embodiment process or of considering the instrument as a second nature [START_REF] Stewart | Transparency_1[END_REF]. Indeed, the process articulates the following stages:

(1) seeing or hearing an object, distant in space and thus constituting a part of the environment, (2) choosing it, (3) touching it and grasping it, (4) manipulating it and ( 5) using and playing it in the performance of the task, and this process is everything but trivial. In that process, the object is progressively transformed in an instrument, so being a part of the human body ("his second nature") and the human is progressively transformed in an instrumentalist, so being a part of the instrument ("its human nature"). All along the playing of the instrument by his instrumentalist, the instrument became his own. Because the instrument is intrinsically a physical external object, the human being has always and at each time the capability to leave instantaneously the instrumental state and to render the instrument to its status of a trivial physical object of the environment. Alternately, the instrument plays as a temporary extension of the human organology and as a part of the external environment. Thus, it is a locus on which some complex cognitive processes can take place. The symmetric process, strictly correlative to the embodiment process here, and permitted by principle by the status of external object, is the disembodiment process.

So, the mutation process of an object into instrument (and of the human into an instrumentalist) is the supportas well as the material representation -of the dual cognitive processes of embodiment and disembodiment, the first one stressing his integration within the world and the second one, maintaining his individuality. The precise point and instant during which the object becomes in physical contact with the human body is then of an existentialistic critical point. First, it is no less than the point in which the human cognitively creates the notion of the sense of matter. That consists not only in the notion of the object in the sense of non simultaneous space occupation, such one being also supported by visual or tactile experiences. It also consists in the experience of something that is, at the first, resistant [START_REF] Gapenne | Resistance as constraint and auxiliary for proximal and distant interaction[END_REF] and more, of something that opposes and proposes complex behaviors to human sensory-motor acts: from elasticity and viscosity to dry friction and other more complex ones. Such behaviors are precisely learned and intimately used by humans during the instrumental playing: playing musical instruments, molding a soft paste, manual drawing, etc (Figure 6).

PROPERTIES OF INSTRUMENALL HUMAN-WORLD RELATIONSHIP

Since primary experiences such as those in which a human hits a tree with another piece of wood to alert his congeners by means of specific sounds and rhythms, the fundamentals of the instrumental paradigm were launched. In this paragraph, we enounce, in three points, the main properties of what is for us « an instrument », in order to examine further what is the epistemological break introduced by the information technologies and how it can be crossed over.

The instrument as a physical object

In the instrumental relationship between humans and the world, an instrument is, at first, a part of the physical word, i.e. a physical object, chosen by humans and modeled or not by them. Moreover, it is used to perform a task that humans cannot perform without it. In this respect, it provides morphological, physical and functional adaptations of the human morphology to the physical world. As an example of morphological adaptation, a screwdriver allows to perform continuous rotation that is impossible to perform only by hand and fingers. As example of physical adaptation, the wax spread under skis optimizes the dynamic adherence in order to move faster.

As an example of functional adaptation, a musical in-strument is a physical object that transforms gestures into sounds, in order to enlarge the capabilities of the human beings to produce sounds, because, except with his vocal cords, the human is a very poor acoustic vibrating structure. Thus, as the Janus figure, an instrument has two faces, and one can say, strictly speaking, that it is an interface.

Alternately, it can be considered as a part of the physical environment, seen or heard by humans, or an extension of human body when near the body and taken in hand. As when an object is not in hands, its appraisal by human can be perceptual or formal. But when in hand and during the performance of the task, it is felt, and consequently known, through the human sensory-motor capabilities so that one cannot say who manipulates which and vice-versa (of the human and of the object). Human and object constitute a single system, we can say a single instrumental system, mediating a human intention (implicit or explicit) to others humans through the performed task. Consequently, we cannot speak of instrument or instrumentalist, separately, but only of the instrumental relationship between them, during which they constitute a single instrumental system.

The instrumental system as a dynamic system

Such an instrumental system exhibits specific and rich properties. The relation between the human and the physical object is more than a sensory-motor relation like hand-vision sensory-motor relationship when showing an object by pointing it with the finger. When in hand, human body and the physical object are not only like two things in contact. They constitute an inseparable closed loop dynamic system (Figure 7), really a single object. This single object is a complex dynamic system composed of an active part and of passive part as shown in the Figure 8. We use the term "active", not in the sense that humans are subjects able to have intentions, but in the sense that a system embeds an internal source of energy able to internally modify its internal states. Indeed, the human bodies have the capability to modify the tonicity of their muscles during a jump. It is not necessary that the instrument is also active to dispose of the minimal functionalities able to characterize the instrumental system as a dynamic system. Figure 8. The basic instrumental system as a dynamic closed-loop system Considering the instrumental system as a dynamic complex system allows to better understand why it is able to exhibit features that cannot be found in other types of human-world relationships, for example in the handvision relationship. Indeed, the instrumental system composed of the closed-loop coupling between a human and a physical object exhibits dynamic properties such as energetic exchanges consistency, reactivity or dynamic adaptation. Such properties are not necessary to perform types of tasks such as those that can be performed through formal communication by signs and languages or by openloop command systems. But they are necessary to perform tasks that, either by principle or until new technologies prove otherwise, cannot be performed by the first types of tools. The distinction between both is well represented by the concept of ergotic and non-ergotic tasks proposed by C. Cadoz [START_REF] Cadoz | Le geste, canal de communication homme/machine. La communication instrumentale[END_REF]. Let us illustrate that with emblematic cases as those shown in Figure 6: playing a cello, rubbing a surface and sculpting with clay. During such instrumental performances, the physical body of the instrumentalist and the instrument are closely dynamically coupled, being then able to produce non-predictable emergent effects: timbre changing, sticking, cracking, breaking, transients, bifurcations, stability regions, etc. In the finger-glass system, the sound can appear or not; timbre can change or not. And all of these effects cannot relate simply to only parameters control processes: the intensity of the sound is not directly correlated only to the pressure force or to the finger velocity. When the sound is started, the pressure and the velocity can be relaxed to maintain it. It is the same in the bowed string playing during which human gestures are able to manage very complex dynamic patterns: relaxing the pressure, increasing or decreasing the velocity of the bow, at the right state of this complex dynamic system, etc. When succeeding in such tasks, the expression used is: "He/she is one with his/her instrument".

CONDITION FOR EMBODIMENT IN DIGITAL INSTRUMENTAL RELA-TIONSHIP

Digital instrumental relationship as a representation

In the previous paragraph, we detailed basic functional, technical and cognitive properties of the instrumental relationship. We do not pretend to have exhausted all the questions around it. But, we hope, at first, that the reader is now convinced of the necessity of such relationship. Nevertheless, all the topics discussed above are necessary for examining why and how the instrumental relationship can be implemented in information technologies. One can consider that mechanical instruments perfectly serve all the instrumental tasks and that electrical, and/or computer technologies, have been designed to develop other types of tools for other types of tasks. Let us notice that the constraints imposed by mechanics in the optimal design of such instruments is a critical limitation for the three types of adaptivity we spoke above: morphological, physical and functional. No doubt that electromechanical teleoperated master-slave systems designed to extend the space, to improve the accuracy of the manipulation, or to secure humans who are manipulating, were necessary. No doubt neither that synthesis processes enlarge considerably the variety of sounds and images that humans are able to produce. But what is the main and fundamental difference between a pure mechanical instrument, such as a violin or a puppet, and electrical or information-based ones? A first and obvious answer is: In such implementation of the relationship between the human and the system which performs the task, the coupling, as described before, as well as the sensations of the matter which naturally exist in mechanical interaction, are lost. They are not naturally supported by electrical technologies, and thus, if necessary, we have to (re) construct them.

Such a very simple observation first leads to one remark, and secondly to one new concept. First, the mediated relation between humans and the physical world by means of electrical and computer technologies cannot be an instrumental relationship. And second the electricalbased instrumental relationship that could exhibit the main properties of the mechanical one, cannot be anything else than a representation of the instrumental situation, as introduced by C. Cadoz [START_REF] Cadoz | Informatique et Outil de Création Musicale[END_REF] and developed in [START_REF] Cadoz | Simuler pour connaître, Connaître pour simuler[END_REF] [START_REF] Luciani | Towards a complete representation by Means of Computer[END_REF]. Such representation has not to be understood as a representation of specific instrumental cases, such as playing violin or piano, but the representation of the principles of the instrumental situation. Consequently, we ask, and try to answer, on what are the main technological and conceptual bottlenecks for the implementation of a representation of the instrumental relationship within electrical and computer technologies.

The information technologies started from the notions of electrical transducers and signals. Indeed, electrical transducers and signals, and thus, all the electrical sciences including computer sciences, operate the fundamental historical shift from mechanically coupled systems to input-output systems [START_REF] Fontana | Afferent -Efferent Channel[END_REF], breaking the mechanical-based closed loop and thus having to represent it as well in the formal representations as in the electrical and information systems. The input-output representation formalism introduces a causality, that does not exist in the mechanical systems, between what is the input and what is the output. Consequently, in the representation of coupled systems, it obliges to separate the two intimately stuck parts, for example the cellist and the cello, each of them being then represented by an input-output block as shown in the Figure 9. It obliges then to represent their coupling by connecting the output of the one onto the input of the other. So the representation of the instrumental system introduces a cascade of two causal relations: the cellist is considered as an input of the cello and the cello as an input of the cellist. The input-output representations ground the sensorsactuators (more generally transducers) and signals technologies and information systems, and vice-versa. The outputs of a system are then sensors that acquire its behaviors and transform them into signals and the inputs are actuators that receive these signals. We do not discuss about the reduction due to the fact that the sensors, the actuators and the signals so produced represent only some parts of the physical behaviors 3 . But, we will focus on the fact that the coupling is not totally representable in electrical and in computers systems. Then, the questions are: Is it possible to restore the sensation of physical matter? How can we implement the input-output correlations to preserve the representation of the coupling? In the following, we propose two aspects, one conceptual, two technological, which can help us to answers such questions.

"Transparency of the system or new representation of the instrumental universe"

The approach we present here differs conceptually and pragmatically from that which is usual in teleoperation in the field of robotics. A common engineering goal in Robotics and teleoperation is to replicate at the best a real situation. The concept is that of "transparency" of the new electromechanical system, i.e. how can we render the behaviors introduced by the new electromechanical system as transparently as possible? This concept derivates from the electrical teleoperation in which one tried to render the new components added to the mechanical teleoperation as functionally "transparent". Although the answer is that it is not absolutely possible [START_REF] Fontana | Transparency_3[END_REF][9], the main stream in teleoperation worked to solve this question of transparency.

Our approach is near from a more anthropological point of view. It does not consist in reproducing existing instrumental situations by rendering the specificities brought by novel technologies as non-existent as possible, but in developing new instruments under specific conditions and assumptions. These conditions are to take care of the fundamentals of human-world couplings, in order to develop not only new systems, but those that will be able to preserve the fundamentals expressed above and to experiment their role in human cognition as well in the performance of the tasks. Our approach is then taskindependent, and can be expressed as: how do we specify the scheme represented on the right of the Figure 9 and implement it in information technologies to obtain, at the best for the human, the instrumental situation represented on the left of the same Figure 9? A temptation could be to consider that the answer could be only on the human side and that the question can be solved by human-based design of robotic systems after having performed psychophysical and cognitive preliminary experiments. We outline here that it will be not sufficient: first because the instrumental problem is not the same as risen by transparency in the teleoperation chain [START_REF] Luciani | Transparency_2[END_REF]; secondly, because for centuries the instrumental paradigm has not consisted in copying previous instruments and previous situations, but in creating new instruments for new tasks for new instrumentalists, and thirdly, because the humanmechanical object system is not observable and needs new experimental workbenches to be better known. The basic technical schema that represents the instrumental situation within the domain of information technology is given in Figure 10.

Figure 10. The representation if instrumental situation in the framework of Information Technology

Notice that in the part of the instrument: (1) sensors and actuators are electromechanical devices that have to be designed to preserve the properties of the instrumental coupling as sketched before; and (2) the real time computer algorithms have to maintain the consistency of the instrumental coupling between the inputs and the outputs of the interaction devices.

Notice that, if we called Z1 the impedance on frontier (1) of the right part of the whole system seen by the left part of the human and Z2 the impedance on frontier (2), the transparency assumption leads to have Z1=Z2, that corresponds to a deny of the intermediate instrumental part. Conversely, the instrumental concept allows that Z1≠Z2. This means that the design the new "instrument" allows to render it to support at the best the "embodiment" and the "second nature" processes.

Thus, the question becomes: what are the necessary and minimal conditions we must preserve to benefit from instrumental properties from the human side when shifting the technologies. We can say, what could be the "task-independent axioms" of the instrumental situation. We now sketch two minimal elements of these basic properties, and their correlated technological needs.

A first minimal dynamic property: perceiving the resistance of the matter

First of all, when used in computer technologies, i.e. when the system that receives the inputs from sensors and produces the outputs to actuators, is based on or includes computers, the causality introduced between inputs and outputs is transformed in a temporal causality. Indeed, a non instantaneous computation process is inserted between the inputs and the outputs. In the electromechanical coupling between humans and such systems by force feedback transducers, this question is related to that of the bandwidth of the system device / computer algorithms. This bandwidth obviously depends on the dynamical properties of the device itself but also on the computer algorithms and the communications systems between both. These two last can be expressed by the temporal latency between the outputs of the device (resp. inputs of the computer) and its inputs (resp. outputs of the computer). The higher this bandwidth is, and lower the latency is, the better the restitution of coupling between rigid systems will be. That is a critical point in force feedback transducers design, known under the terms "Stability" or "Bandwidth problem" [START_REF] Gil | Stability[END_REF].

Having in mind the previous discussions [START_REF] Gapenne | Resistance as constraint and auxiliary for proximal and distant interaction[END_REF] about the fact that the contact situation conveys the sense of resistance of the external matter and further of the matter itself, the rendering of contacts is also a critical point for a perceptual, cognitive, and further existentialistic point of view on the side of the human being. Consequently, all the technical components (force feedback transducers including sensors, actuators, mechanical embedding of them and electronic regulation processes) must be used coherently and consistently to render, at the best -the interaction during collisions and contacts between a human and a simulated resistant matter in the computer. It will be in the same time a workbench in order to experiment [START_REF] Cadoz | Le geste, canal de communication homme/machine. La communication instrumentale[END_REF] what is the cognitive role of the contact situation in the trade-off from "environment" to "instrument" via the intermediate stages of "object -near the hand" and the "object -in -hand"; and (2) how it could be a necessary component for considering the instrument as a "second nature" of the instrumentalist. Couroussé and colleagues, in [START_REF] Couroussé | Effects of stiffness on tapping performance[END_REF] tacked these questions in a specific research on haptic-audio tapping. Using the high quality TELLURIS platform, in which all the systems and processes run at 44 kHz, they show that, when hitting an acoustical surface, the properties of the matter (its non-linear elasticity and viscosity), are influencing the maximum of the frequency of the hits. To sum up, according to the critical role played by the existence of the matter, revealed during the contact and collision situation, in the instrumental situation, the rigidity during contact is the first axiom of the instrumental relationship to be rendered at the best in the framework on information technologies.

We saw that our approach is different for conceptual reasons of that of teleoperation, based on the transparency concept. It is also technically different than the main stream of researches in Virtual Realities. In Virtual environments and virtual reality systems, most of the work is dedicated to the immersion of humans within virtual environments. This immersion is simultaneously physical by means of systems such as Caves in which 3D images and sounds are surrounding the human beings, and virtual by means of avatars of the human beings representing them in the virtual environment. The core problem here is the wideness of the represented spatial environments and systems that put the emphasis on the navigation and the exploration of large spatial and geometrical 3D scenes. The collisions problem is processed from a geometrically-based point of view, the critical problem being that of the geometrical computation of the intersection between two complex geometrical shapes to prevent interpenetration. There are many works developed in computer graphics and applied in teleoperation when complex manufactured objects are colliding. The related scientific questions are summarized in [START_REF] Boulic | Collision Detection Algorithm[END_REF]. In such applications, the dynamic of the contact remains a secondary problem, while it is one of the first generic properties that systems have to render in the instrumental paradigm, as it works in the musical creation.

A second minimal dynamic property : perceiving the dynamic texture of the matter

Having created the minimal conditions to restore the sense of the matter through its physical resistance within information-based technological systems, and reminding, as explained above, that humans use the other properties of the matter (other than and in addition with its resistance) in the instrumental tasks, a second stage consists in restoring such behaviors as well as possible. Some other behaviors of the matter such as all the viscoelastic effects able to render all types of deformability are easily derived from the rigidity effects discussed above. The second critical dynamic feature for most of complex instrumental tasks is then the friction effect. Different from the collision processing that led to much work in virtual reality, there are very few works that tackle the friction effect. Florens and coworkers [START_REF] Florens | Real time Bowed String Synthesis with Force Feedback Gesture[END_REF] [START_REF] Luciani | Ergotic sounds: A New Way to Improve the Playability, Believability and Presence of Virtual Musical Instruments[END_REF] demonstrate that when the friction between a bow and a string is simulated by the computer and returned to the force feedback transducer manipulated by the instrumentalist at a high frequency, typically 1500 Hz in [START_REF] Florens | Real time Bowed String Synthesis with Force Feedback Gesture[END_REF] and 44 kHz in [START_REF] Luciani | Ergotic sounds: A New Way to Improve the Playability, Believability and Presence of Virtual Musical Instruments[END_REF], the sensation of the presence of the vibrating bowed string increased significantly. The instrument became more and more playable and new gestures and exploratory manipulations happened due to the fact of wide possibilities of dynamic gestural adaptations and learning, by allowing the instrumentalist to play with non predictable effects as those occurring in the bow-string interaction. Hereto, the rendering, at the best, of the usual properties of the matter when instrument are in hand, such as friction, will allow to better know what is its role in the cognitive appraisal of the instrumental situation and in different criteria characterizing the performed task: efficiency, playability, handleability, creativity.

CONCLUSION AND FURTHER QUES-TIONS

We compared two complementary human-word relationships.

In a first situation, in which we are immersed in a landscape, humans develop the sense of "being there", looking far away from his (her) place towards large scales by means of exteroceptive sensory modalities such as vision and audition. Such a situation, drastically extended by networked and distant exploration, can be seen as a definition of "immateriality" and its correlative concept of infinity.

In a second situation, in which humans are confronted face-to-face to a thing, placed in vis-à-vis, extracted from a surrounding environment to acquire the state of an "object" able to be handled, humans develop the sense of "being with". Progressively, objects are transformed into instruments and humans into instrumentalists. Such a situation leads to the embodiment of the object as a "second nature " or as a part of the human body or as an extension of the human organology. It can then be seen as a definition of "tangibility" with its correlative concept of instrumental embodiment.

We developed here the idea that to implement such an instrumental situation in a computer context, not in the aim to mimic our relation with the mechanical world or to mimic the notion of tangibility in the real mechanical universe, but rather, in order to have at our disposal within the new contemporary digital creative context, the minimal properties necessary to ground the embodiment process, some properties of the instrumental relation ship have to be reached.

We have not examined here questions such as the morphological ones (number of sensors and actuators and morphological arrangements). They undoubtedly play an important role in human manipulation of physical objects. Indeed, some drastic limitations of the existing force feedback devices are related to the fact that they allow only punctual contacts. However, we demonstrated that dynamic properties of the close-loop coupling between human and a physical object, are a necessary condition, (even if it is not a sufficient one), to have access to behaviors that are the specificities of the instrumental system and that cannot emerge otherwise. Based on primary functions of the instrumental paradigm, we showed how the central concept of teleoperation, i.e. the transparency of the electrical and information parts of the system, despite the huge development of interactive teleoperators including haptics, does not match with the instrumental paradigm. We showed also that Virtual Reality, despite the wide uses of haptic devices, does not fit either within such an instrumental paradigm. So, the field of instrumental situations in computerized environments remains to be developed and is still a subject for the future. We have to know more, to build more, to experiment more around the non trivial concept of instrument and instrumental relationship, from an anthropological point of view, within the scope of information technologies.

Several other fundamental issues remain pending. Taking the examples of Arts, such as Musical Arts, Visual Dynamic Arts, Choreographic Arts, no doubt that the instrumental relation, in the meanings developed in this paper, is fundamental to produce subtle sensory effects. But further, if we include the very long process to design an instrument, process in which the physical matter is also pointed out, we could see that the instrument is not only a way to adapt the human and the world to perform tasks that humans cannot do, but more a way to organize and structure, in the same movement, the physical world and the human gestures.

Figure 1 .

 1 Figure 1. From Immersive to the embodied instrument: a bilateral complex cognitive process.

Figure 2 . 1 . 2

 212 Figure 2. Immersive situation: environment as surrounding humans and exteroceptive exploration tasks

Figure 3 .

 3 Figure 3. Physically-oriented manipulation task

Figure 4 .

 4 Figure 4. The fuzzy state of vis-à-vis object: the transition from "near-in-hand" to "present-in-hand" via "ready-to-hand"

Figure 5 .

 5 Figure 5. The selection task

Figure 6 .

 6 Figure 6. Three emblematic cases of the instrumental situation

Figure 7 .

 7 Figure 7. The intimate instrumental relationship 2

Figure 9 .

 9 Figure 9. The two shifts in the representation of the instrumental system. Left: the instrumental system; Middle: its splitting in two input -output systems; Right: the input-output representation of their coupling

Proceedings ICMC|SMC|201414-20 September 2014, Athens, Greece

Thanks to Jean-Loup Florens for his particularly expressive representation of the coupling human -physical object.

That is of course a true critical question, widely examined in electrical engineering and transducers theories and systems.

ACKNOWLEDGEMENTS

The work presented here has been supported by the French Ministry of Culture and by Grenoble Institute of Technology. Thanks to Claude Cadoz and Jean-Loup Florens, who enlightened my thoughts and my feelings around the notions discussed in this paper, all along inestimable hours of discussions.