Vincent Drevelle
email: vincent.drevelle@ensta-bretagne.fr

Luc Jaulin
email: luc.jaulin@ensta-bretagne.fr

Benoit Zerr
email: benoit.zerr@ensta-bretagne.fr

Guaranteed Characterization of the Explored Space of a Mobile Robot by using Subpavings

Keywords: interval analysis, mobile robots, exploration, sets, mapping, uncertainty

This paper proposes a method to characterize the space explored by a mobile robot during a mission. Because of localization uncertainty, the area osculated by a sensor at a given time is uncertain too. The problem is modeled by using intervals to represent trajectory uncertainties and a "visibility function" to describe the area in view at a given time. A setinversion method is then applied to compute a "guaranteed visible area" and a "possible visible area" with respect to positioning uncertainty. A bracketing of the actual explored area between a "guaranteed explored area" and a "possible explored area" for the whole mission is finally obtained by respectively taking the union of the guaranteed and possible areas. Results from a simulated underwater exploration mission are presented.

INTRODUCTION

Mobile robots are often the only safe way to perform measurements and observations in dangerous, hard to reach or extreme environments, like underwater or radioactive areas. The development of autonomous robots has also led to new applications in domestic environments. Some missions require a robot to fully cover a defined area with its embedded sensors or actuators. This is the case for mapping, search and recovery of lost items, but also lawnmowing and vacuum-cleaning.

Estimation of the area that has been sensed (or touched by the robot's tool) enables to assess the completion of an area-covering mission. Since tools and sensors are attached to the body-frame of the robot, the area that has been covered during the mission is linked to the robot's trajectory. Estimation of the robot's explored area thus depends on trajectory accuracy. The uncertainty of position estimates needs to be taken into account when trying to characterize the explored area.

Set-membership methods have successfully been used to reliably deal with uncertainty, especially in non-linear problems. They have been employed for localization of robots (see, e.g, [START_REF] Meizel | Initial localization by set inversion[END_REF] for an initial localization problem with string non-linearities, [START_REF] Caiti | Setmembership acoustic tracking of autonomous underwater vehicles[END_REF] for an underwater positioning system, and [START_REF] Drevelle | Interval-based fault detection and identification applied to global positioning[END_REF] for fault detection and identification applied to GPS), but also simultaneous localization and mapping [START_REF] Jaulin | Range-only slam with occupancy maps: A setmembership approach[END_REF]). Problems such as state estimation of non-linear systems have successfully been addressed [START_REF] Raıssi | Set membership state and parameter estimation for systems described by nonlinear differential equations[END_REF]) even in the presence of fleeting data (Le [START_REF] Bars | Setmembership state estimation with fleeting data[END_REF]), and interval based methods have been applied in control of uncertain dynamical systems [START_REF] Rauh | Robust and optimal control of uncertain dynamical systems with state-dependent switchings using interval arithmetic[END_REF]).

In this paper, an interval-based set-membership method is proposed to compute the area explored by a mobile robot and characterize its uncertainty. The explored area problem is introduced in Section 2. In Section 3, intervals and associated tools for solving set-inversion problems are presented. The explored area characterization with uncertain localization is then detailed and solved by using interval methods in Section 4. Finally, in Section 5, the method is applied to two simulated test cases of representative underwater exploration missions, and experimental results are reported.

PROBLEM STATEMENT

Let us consider a mobile robot equipped with actuators and sensors. The robot is classically represented by the following state equations

ẋ(t) = f (x(t), u(t)) y(t) = g (x(t)) , (1)
where x denotes the robot's state vector (e.g. position, velocity...), u is the input vector and y is the observation vector. The robot's evolution is modeled by the function f and g is the observation function.

The robot uses a sensor for searching or mapping, that can cover a given area. The area auscultated by the robot's sensor depends on its technology, geometry and physics, but also on the robot's state (position, velocity...). Let V be the set-valued function that returns the area which is in the robot's field of view at each time. V is defined as

V (t) = z ∈ R 2 : v (z, x(t)) ≤ 0 .
(2) The set V (t) is called the visible area at time t, i.e. the points of the sensed space that are in the range of the robot's sensor (Fig. 1). The visible area is defined by the visibility function v, such that v (z, x(t)) is negative if and only if the point z of the sensed space is in the range of the sensor for the given the robot state x(t).

Fig. 1. Visible areas at times t and t k , and current explored area M(t).

As the robot moves, its visible area changes accordingly, which enables to explore space. Let M(t) be the map of the current explored area at time t, i.e the set of all points in the sensed space that have been in the range of the robot's sensor at least once until time t. It is shown in red in Figure 1. M(t) is the union of all the visible areas over the whole trajectory, from the mission start t 0 to current time t:

M(t) = τ ∈[t0,t] V(τ ). (3)
The mission's explored area M is the area that has been covered by the robot's sensor at the end of the exploration mission. With t f denoting the time at the end of mission, the mission's explored area is defined such as M = M(t f ).

In this paper, the terms explored area refer to the mission's explored area.

In practice, due to measurement noise and model inaccuracies, the robot trajectory is uncertain. This uncertainty can be represented by covariance in Bayesian filtering methods, or by a set of possible values. In this paper, we use intervals to model uncertainty. Next section presents intervals and some basic tools to manipulate them.

INTERVAL ANALYSIS AND SET-INVERSION

Interval analysis

Interval analysis [START_REF] Moore | Interval analysis[END_REF], see [START_REF] Jaulin | Applied Interval Analysis[END_REF] for algorithms and applications) is based upon computations with intervals and their multidimensional extension, interval vectors (or boxes). The width of an interval is defined as width

([x]) = x -x.
The width of a box is the width of its longest interval component:

width([x]) = max i width([x i ]).
Interval arithmetic allows performing computations on intervals and boxes thanks to the interval extension of classical real arithmetic operators +, -, × and ÷.

[x] + [y] = [x + y, x + y], [x] -[y] = [x -y, x -y] In the same way, elementary functions such as tan, sin and exp can be extended to intervals. This is done by returning the smallest interval covering the range of the input through the function.

The image of a box by a function f : R n → R m is generally not itself a box, but an arbitrary set. This problem is solved using the so-called inclusion functions: The interval function

[f ] from IR n to IR m is an inclusion function for f if the image of [x] by f is included in the image of [x] by [f ], i.e. ∀[x] ∈ IR n , f ([x]) ⊂ [f ]([x]
). The natural inclusion function obtained by replacing each operator in the expression of the function by its interval counterpart.

Extensions of intervals

In addition to real intervals and boxes, closed intervals can be defined for different sets of mathematical objects, providing they form a complete lattice.

Tubes

The set F = {f : R → Rn } of all functions from R to Rn is a complete lattice with the partial order

f ≤ g ⇔ ∀t ∈ R, f (t) ≤ g(t). An interval of F is an interval of functions, called a tube.

Set intervals Since the set 2

Rn of all subsets of Rn is a complete lattice with the partial order ⊂, set intervals can also be defined. A set interval contains all sets that are subsets of its upper-bound and supersets of its lowerbound.

Set inversion and subpavings

The set inversion problem consists in determining the set

X = f -1 ([y]) such as X = {x | f (x) ∈ [y])},
where [y] is a known interval vector. To approximate compact sets in a guaranteed way, subpavings can be used. A subpaving of R n is the union of non-empty and non-overlapping boxes of R n . X X X Fig. 2. Approximation of a set X between an inner subpaving X and an outer subpaving X

The solution X = f -1 ([y]) can be approximated in a guaranteed way by using interval analysis. The Set Inversion Via Interval Analysi s algorithm (SIVIA) [START_REF] Jaulin | Applied Interval Analysis[END_REF]) computes two subpavings X and X such that X ⊆ X ⊆ X, i.e a set interval [X, X] that contains the solution (Fig. 2). The algorithm starts from an arbitrarily big initial box, and consists in recursively testing the inclusion of a box in the solution set. If the box cannot be proven to be inside or outside the solution set, then it is bisected into two boxes. SIVIA is described in Algorithm 1. It uses a list of boxes L that is generally implemented as a stack, so that the algorithm employs a depth-first strategy. The parameter controls the sharpness of the approximation between the two subpavings X and X. The algorithm stops when the width of boxes falls below .

Algorithm 1 SIVIA(in:

[x 0 ], [f ], [y], , out: X, X) X ← ∅; X ← ∅ // inner and outer subpavings push([x 0 ], L) while L is not empty [x] ←grab the first box of L if [f ]([x]) ∩ [y] = ∅ then continue else if [f ]([x]) ⊂ [y] then X ← X ∪ [x] else if width([x]) < then X ← X ∪ [x] else ([x 1 ], [x 2 ]) ← bisect([x]) push [x 1 ] into L; push [x 2 ] into L endif end return [X, X]

EXPLORED AREA CHARACTERIZATION

Explored area with an uncertain trajectory

As previously stated, we aim to characterize the explored area, given an uncertain robot trajectory. Let us introduce the robot trajectory tube [x](t) which encloses the robot trajectory, i.e ∀t ∈ [t], x(t) ∈ [x](t). This tube is a bounded estimate of the robot state at each time. The uncertain explored area mapping problem is now defined as follows:

       x(t) ∈ [x](t) V (t) = z ∈ R 2 : v (z, x(t)) ≤ 0 M (t) = τ ∈[t0,t] V(τ ). (4)
Uncertainty about the robot state leads to uncertainty about its visible area. We thus define the guaranteed visible area V ∀ as the set of points that have necessarily been observed, regardless of the robot's state uncertainty:

V ∀ (t) = z ∈ R 2 : ∀x ∈ [x](t), v (z, x) ≤ 0 (5)
The guaranteed visible area is the set of points in the sensed space for which the visibility function is negative for all states in the state uncertainty domain. Similarly, the possible visible area V ∃ is the set of all the points that may have been in the robot's field of view:

V ∃ (t) = z ∈ R 2 : ∃x ∈ [x](t), v (z, x) ≤ 0 (6)
A point of the sensed space belongs to the possible visible area if it exists a state in the state uncertainty domain for which the visibility function of this point is negative.

V ∀ (t) and V ∃ (t) form a bracketing of the actual visible area V (t). They can be seen as the lower and upper bounds of a set interval that contains the visible area:

∀t ∈ [t], V ∀ (t) ⊂ V (t) ⊂ V ∃ (t) (7)
Proof. Let us first prove that V ∀ (t) ⊂ V (t):

p ∈ V ∀ (t) (5) ⇔ ∀x ∈ [x](t), v (p, x) ≤ 0 x(t)∈[x](t) ⇒ v (p, x(t)) ≤ 0 ⇒ p ∈ V(t)
Now let us prove that V (t) ⊂ V ∃ (t): Figure 3 shows the guaranteed and possible visible area of an omnidirectional sensor with v (z, x) = zx 2 -r 2 , where r is the maximum range of the sensor. V ∀ and V ∃ are plotted for state-uncertainty boxes of increasing width. It illustrates the erosion of the guaranteed visible area as state uncertainty increases, and simultaneously the expansion of the possible visible area with growing uncertainty. With large state uncertainty, the guaranteed visible area becomes empty (see lower-right of Fig. 3).

p ∈ V(t) ⇔ v (p, x(t)) ≤ 0 x(t)∈[x](t) ⇒ ∃x = x(t) ∈ [x](t), v (p, x) ≤ 0 (6) ⇒ p ∈ V ∃ (t) V ∀ V ∃ [x]
The notion of guaranteed and possible areas extends to the explored areas, by taking the union over time. The guaranteed explored area M ∀ is defined as the union of all the guaranteed visible areas

M ∀ = t∈[t0,t f ] V ∀ (t), (8)
and the possible explored area M ∃ is defined as the union of all the possible visible areas over time

M ∃ = t∈[t0,t f ] V ∃ (t). (9)
Thus, a bracketing of the actual explored area M is given by

M ∀ ⊂ M ⊂ M ∃ . ( 10
)

Quantifier elimination

The ∀ and ∃ quantifiers appear in the expressions of the guaranteed and possible visible areas V ∀ (t) and V ∃ (t)

given by equations ( 5) and ( 6). Solving set-inversion problems that involve quantifiers can be quite inefficient. To simplify the visible areas computations, quantifier-free expressions of V ∀ (t) and V ∃ (t) are derived in this sub-section.

We consider a sensor that sees inside a robot-centered disk of radius r. It can be described by the following visibility function:

v (z, x) = (z 1 -x 1 ) 2 + (z 2 -x 2 ) 2 -r 2 . (11) Let us denote by [v] (z, [x]
) the natural inclusion function for v with respect to x.

[v] (z, [x]) = (z 1 -[x 1 ]) 2 + (z 2 -[x 2 ]) 2 -r 2 .
(12) Since v is continuous and the x i 's occur only once in the expression of v, we have [START_REF] Moore | Interval analysis[END_REF]) 14) is thus true when the upper bound v of [v] (z, [x]) is negative:

[v] (z, [x]) = {v (z, x) , x ∈ [x]} , ( 13
) The guaranteed visible area condition ∀x ∈ [x], v (z, x) ≤ 0 from formula (5) is equivalent to [v] (z, [x]) ⊂ [-∞, 0]. (14) Inclusion (
z ∈ V ∀ (t) ⇔ v (z, [x]) ≤ 0. ( 15
)
Similarly, by using the natural inclusion function [v], the possible visible area formula (6), ∃x ∈

[x], v (z, x) ≤ 0 can be rewritten [v] (z, [x]) ∩ [-∞, 0] = ∅.
(16) which can be also expressed as a negativity condition on the lower bound v of [v]:

z ∈ V ∃ (t) ⇔ v (z, [x]) ≤ 0. ( 17
)
This way, quantifiers have been eliminated from the expressions V ∀ (t) and V ∃ (t). The visible areas are now defined by inequalities involving the bounds of [v] (z, [x]).

Expressions of the upper bound v and and of the lower bound v and can be derived by using symbolic interval arithmetic [START_REF] Jaulin | Resolution of nonlinear interval problems using symbolic interval arithmetic[END_REF]). The lower bound is given by

v (z, [x]) = H((z1-x1)(z1-x1)) min (z1-x1) 2 ,(z1-x1) 2 +H((z2-x2)(z2-x2)) min (z2-x2) 2 ,(z2-x2) 2 -r 2 (18)
where H denotes the Heaviside step function. The expression obtained for the lower bound is

v (z, [x]) = max (z 1 -x 1 ) 2 , z 1 -x 1 2 + max (z 2 -x 2 ) 2 , z 2 -x 2 2 -r 2 (19)

Explored area mapping

It has been shown in Section 4.1 that the explored area M is bracketed between the guaranteed explored area M ∀ and the possible explored area

M ∃ such that M ∀ ⊂ M ⊂ M ∃ .
Similarly, the visible area V(t) is bracketed between the guaranteed visible area V ∀ (t) and the possible visible area

V ∃ (t) such that V ∀ (t) ⊂ V(t) ⊂ V ∃ (t).
Visible area Visible areas are arbitrary sets whose shape depends on sensor aperture, environment and robot state. Such arbitrary sets cannot be precisely described by a single box, but they can be approximated to any desired precision by subpavings.

At each time t, the SIVIA algorithm can be used to compute a bracketing of the guaranteed visible area between an inner subpaving V ∀ (t) and an outer subpaving V ∀ (t).

Similarly, a guaranteed approximation of the possible visible area between the two subpavings V ∃ (t) and V ∃ (t) can be computed. We thus have

V ∀ (t) ⊂ V ∀ (t) ⊂ V ∀ (t) (20) V ∃ (t) ⊂ V ∃ (t) ⊂ V ∃ (t) (21)
From ( 20) and ( 21), we obtain a bracketing of V(t) between the two subpavings V ∀ (t) and V ∃ (t) such that

V ∀ (t) ⊂ V(t) ⊂ V ∃ (t). ( 22
)
The visible area V(t) is thus known to be inside the set-interval [V(t)] made of a lower-bound V ∀ (t) of the guaranteed visible area and an upper-bound V ∃ (t) of the possible visible area. Figure ( 4) shows the fusion of the SIVIA computed set-intervals for V ∀ (t) and V ∃ (t) to obtain a bracketing of V(t). Explored area As previously described in ( 8), the guaranteed explored area is the union of all guaranteed visible areas over the duration of the mission:

[V ∀ (t)] [V(t)] [V ∃ (t)]
M ∀ = t∈[t] V ∀ (t).
Let us define M ∀ = t∈[t] V ∀ (t), the union of all the computed inner subpavings of V ∀ . From the inclusion relation 20), by applying the union operation, we obtain M ∀ ⊂ M ∀ . Similarly, let M ∃ = t∈[t] V ∃ (t) be the union of the computed outer subpavings of the possible visible areas. Equations ( 9) and ( 21) lead to M ∃ ⊂ M ∃ . Hence we have the inclusion relation

V ∀ (t) ⊂ V ∀ (t) of (
M ∀ ⊂ M ∀ ⊂ M ⊂ M ∃ ⊂ M ∃ . ( 23
)
The computed solution [M ∀ , M ∃ ] thus form a set interval that contains the actual explored area M.

EXPERIMENTAL VALIDATION

Underwater exploration simulation

To validate experimentally the proposed method, let us characterize the exploration of an area by an autonomous underwater vehicle (AUV). The mission of the AUV is to explore and fully cover a 500 m × 300 m rectangular target area. Exploration is done with a sensor whose range is a 40-meter radius disk.

An AUV simulator has been developed in C++ with Qt and OpenGL (Fig 5). The simulated AUV is equipped with a GPS receiver, an Inertial Measurement Unit (IMU) and a Doppler Velocity Log (DVL). The DVL provides the robot with speed measurements, either relative to water or to the seafloor. A set-membership estimator-predictor provides real-time onboard positioning. This system computes a box in which the submarine is located. The center of the box is used as a point position estimate, and fed to the control system. The AUV is programmed to follow a "lawnmower pattern" that covers the target area. The spacing between the lanes in the reference trajectory is lower than the maximum spacing allowed by the sensor theoretical maximum range, in order to have some exploration overlap between successive lanes. This enables to cope with small navigation errors and also with environment effects on sensor performances.

All navigation data is saved and retrieved at the end of the mission for post-processing. Moreover, the true explored area is also computed by the simulator, which enables comparison with the computed solution sets.

Two test-cases have been simulated, both corresponding to a 30-minute mission:

• In the first test-case, the AUV starts from surface, where GPS is available, then dives to perform its exploration mission, and finally returns to surface when the mission is finished. Since GPS is not available underwater, there are only two position fixes: at the beginning and the end of the mission. When the AUV is underwater, positioning is only done by deadreckoning. • The second test-case is similar to the first, but an acoustic ranging system made of two GPS buoys has been deployed. Now, position fixes are also available underwater, which enables higher accuracy in positioning.

Figure 6 shows the trajectories actually followed by the AUV in the two test-cases, along with the reference "lawnmower pattern" trajectory. The actual explored area M is shown in green. Since the AUV is controlled from the center of its estimated position box, positioning errors induce errors in the followed trajectory. Without acoustic positioning during the mission, the AUV clearly drifts from the reference trajectory, which leads to uncovered zones in the bottom-left of the target area (Fig. 6a). In the second test-case, with acoustic positioning, the reference trajectory is more closely followed by the AUV, which provides a near perfect coverage of the target area (Fig. 6b).

Results

Figure 7 shows in light blue the real-time estimated position boxes of the AUV in the two test cases. The boxes are consistent with the actual robot position during the whole mission. In the first test case, position boxes width increases with time since the robot only relies on deadreckoning for localization (Fig. 7a). Contrarily, positioning uncertainty is prevented from growing in test case 2 thanks to the use of an acoustic localization system (Fig. 7b).

Before applying the explored area characterization algorithm, the AUV trajectory is post-processed with constraint propagation [START_REF] Benhamou | Revising hull and box consistency[END_REF]). The AUV motion model is applied to contract the position uncertainty boxes in backward order, from the end of the mission to the start. This enables to retro-propagate the final GPS position fix to the whole trajectory. Moreover, in the second test-case, acoustic positioning corrections are also propagated back in time. The trajectory tubes obtained after post-processing are shown in dark blue in Figure 7.

The second half of the first test case is greatly improved (Fig. 7a), the second test case is less improved since realtime positioning was already rather precise (Fig. 7b). Comparison of Fig. 8a with Fig. 8b clearly shows the influence of positioning uncertainty (i.e. the width of the trajectory tube) on the possible and guaranteed explored areas. Areas of the computed guaranteed and possible explored areas in both test cases are reported in Table 1.

In the second test case, thanks to the improved positioning accuracy, the guaranteed explored area M ∀ is more than three time larger than in the first test case. Moreover, the possible explored area is also tightened in the second test case. Indeed, while only 24.4% of the possible explored area has been guaranteed in the first test case, 88.9% of the computed M ∃ belongs to the guaranteed explored area in the second test case. Reduction of positioning uncertainty has thus a great impact on explored area uncertainty.

Two other interesting figures for mission assessment are presented in Table 1: the parts of the target area that have been possibly and guaranteedly explored. In both test cases, the whole target area belongs to the possible explored area. This means that, with the given positioning uncertainty, it is not possible to prove that a portion of the target area has not been covered. In the first test case, only 32% of the target area has been proven to have been explored. But in the second test case, 99.7% of the target is proven to have been explored. Moreover, contrarily to the first test case where the non-guaranteed explorer area is mostly located in the center of the mission zone, in the second test case, the 0.3% of the target area that have not been guaranteedly explored are located on the edge of the target rectangle.

With a sensor that provides images or than can detect landmarks, the remaining possible but not guaranteed explored area can be assessed by searching in the gathered data for overlap between two successive passes of the robot near the same area. Without analysis of the gathered data, the computed exploration map can also be used to plan a second mission to fill uncovered areas.

CONCLUSION

An interval based method has been presented to characterize the area explored by a robot. Due to localization uncertainty, the method computes a set interval that brackets the actual explored area between a guaranteed explored area and a possible explored area. As positioning uncertainty increases, the guaranteed explored area gets smaller and the possible explored area grows. Inversely, the computed explored area interval tightens as positioning uncertainty decreases.

Experimental results on a simulated 30-minute underwater exploration mission shows the feasibility of the approach, yielding results in less than a minute. The computed setinterval of the explored area can be used after a search mission to ensure that space has been fully covered, to manually check possible but non-guaranteed explored areas, and to plan a complementary mission if necessary.

Another use is for system design and mission planning, to ensure that positioning system accuracy and programmed navigation trajectory enable full exploration of a target area.

Future work will be focused on application to cooperative exploration with multiple robots and on improvement of the guaranteed explored area by the use of additional constraints.

Fig. 3 .

 3 Fig. 3. V ∀ (in red) and V ∃ (union of yellow and red) for increasing position uncertainty (black squares).

Fig. 4 .

 4 Fig. 4. The guaranteed visible area set-interval [V ∀ (t)] and the possible visible area set-interval [V ∀ (t)] are combined to obtain a bracketing of V(t).

Fig. 5 .

 5 Fig. 5. 3D display of the AUV simulator. The green box is the position uncertainty domain of the AUV positioning algorithm.

  Fig. 6. Actual trajectory of the AUV (thick blue line), reference trajectory (dashed line) and actual explored area (light green area). The rectangle represents the target area.

  Fig. 7. Real-time estimated position tubes (painted in light blue), post-processed position tubes (dark blue) and true trajectory (black line). The rectangle represents the target area. The guaranteed explored area M ∀ and the possible explored area M ∃ are computed from the post-processed trajectories of both test cases. Computation of the explored area for the 30-minute long simulated mission takes less than a minute on a standard computer. Since M ∀ ⊂ M ∃ , they can both be represented on the same figure.Figure 8 shows the guaranteed explored area in red; the possible explored area corresponds to the union of red and yellow. The outline of the actual explored area M is drawn in black. It can be seen of the figure that the computed M ∀ and M ∃ form a bracketing of M, such that M ∀ ⊂ M ⊂ M ∃ .

  Figure 8 shows the guaranteed explored area in red; the possible explored area corresponds to the union of red and yellow. The outline of the actual explored area M is drawn in black. It can be seen of the figure that the computed M ∀ and M ∃ form a bracketing of M, such that M ∀ ⊂ M ⊂ M ∃ .

  Fig. 8. Guaranteed explored area (red), Possible explored area (union of yellow and red) and actual explored area border (black).

Table 1 .

 1

		Test case 1	Test case 2
	Area of M ∀	51,865 m 2	157,578 m 2
	Area of M ∃	212,827 m 2	177,220 m 2
	Part of M ∃ covered by M ∀	24.4%	88.9%
	Part of target covered by M ∃	100%	100%
	Part of target covered by M ∀	32.0%	99.7%


Fabrice Le Bars
email: fabrice.le_bars@ensta-bretagne.fr

Luc Jaulin
email: luc.jaulin@ensta-bretagne.fr

Olivier Ménage
email: olivier.menage@ifremer.fr

Suivi de ligne pour un voilier : application au robot voilier autonome VAIMOS pour l'océanographie

Bien que les humains utilisent des voiliers depuis des siècles, peu de robots voiliers autonomes existent à ce jour. L'une des principales difficultés pour un robot voilier par rapport à un robot bateau à moteur est de suivre précisément une trajectoire voulue malgré les manoeuvres inhérentes au fonctionnement d'un voilier (lorsque la trajectoire désirée est face au vent par exemple). Dans cet article, nous allons décrire le fonctionnement, le processus de validation et les performances d'un algorithme de contrôle simple permettant à un robot voilier de suivre précisément une trajectoire de manière totalement autonome, à travers des tests effectués avec le robot voilier VAIMOS (Voilier Autonome Instrumenté pour Mesures Océanographiques de Surface) de l'Ifremer, construit pour effectuer des mesures océanographiques. Mots clésrobotique, voilier autonome, suivi de ligne, océanographie.

 Une sonde et des pompes permettant de mesurer divers paramètres à la surface de l'eau et à un mètre de profondeur (température, salinité, oxygène, chlorophylle, turbidité…).

 Un ordinateur embarqué sous Linux.  Une station météo qui donne la direction et la force du vent ainsi que la position GPS.  Une AHRS (Attitude and Heading Reference System) donnant les angles, vitesses de rotation et accélérations du robot.  Un système de communication Wifi et Iridium.  Les actionneurs nécessaires au contrôle de sa voile et du gouvernail : moteur pas-à-pas qui contrôle l'angle maximal d'ouverture de la voile et servomoteur qui contrôle l'angle du gouvernail. De plus, une balise SPOT, un déflecteur radar, une lumière clignotante et un émetteur VHF sont parfois installés pour minimiser les risques de perdre le robot.

Introduction

Pour pouvoir effectuer des mesures océanographiques, l'Ifremer a réalisé un robot voilier (voir par exemple [1] [START_REF] Brière | The First Microtransat challenge[END_REF] [3] [4] [START_REF] Erckens | Navigation Strategy and Trajectory Following Controller for an Autonomous Sailing Vessel[END_REF] [6] [START_REF] Bruder | Model Sailboats as a Testbed for Artificial Intelligence Methods[END_REF] [8] [START_REF] Stelzer | Autonomous sailboat navigation for short course racing[END_REF] pour plus d'informations sur les robots voiliers autonomes) de 3.65 m basé sur une coque de Mini-J et un gréement de type balestron : VAIMOS (Voilier Autonome Instrumenté pour Mesures Océanographiques de Surface, voir [START_REF] Gorgues | An innovative approach of the surface layer sampling[END_REF] [START_REF] Jaulin | Suivi de route pour un robot voilier[END_REF] [12] [START_REF] Bars | An experimental validation of a robust controller with the VAIMOS autonomous sailboat[END_REF]). Ce robot a : capteur qui émet si on souhaite rester furtif). L'ajout de voiliers autonomes de surface à ces meutes pourrait résoudre certains problèmes : transport sur de longues distances, récupération d'énergie, communications avec la base et les bateaux environnants, localisation grâce au GPS… VAIMOS a été automatisé pour qu'il soit capable de réaliser de manière autonome un quadrillage de zone aussi précis que possible, tout en consommant le moins d'énergie possible. Pour cela, un algorithme de suivi de ligne [START_REF] Jaulin | Suivi de route pour un robot voilier[END_REF] [17] a été mis au point. L'objectif est de garantir que le robot reste toujours dans un couloir prédéterminé d'une largeur de 25 m par exemple, malgré les manoeuvres liées aux changements de cap, remontée au vent… inhérentes au fonctionnement d'un voilier. Le voilier devient alors aussi précis qu'un bateau à moteur. L'idée de cet article est de montrer que pour obtenir un robot autonome fiable, une validation théorique de ses algorithmes en utilisant le calcul par intervalles (voir [START_REF] Jaulin | Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics[END_REF] par exemple pour plus d'informations sur le calcul par intervalles) par exemple peut être faite, mais il faut ensuite valider les hypothèses faites (équations d'état, bornes sur les erreurs, coefficients,…) à l'aide d'autres méthodes. Ainsi une validation théorique du régulateur a d'abord été faite en utilisant le calcul par intervalles et les méthodes de Lyapunov [START_REF] Jaulin | An interval approach for stability analysis; Application to sailboat robotics[END_REF]. Ensuite, un simulateur HIL (Hardware In the Loop) de VAIMOS a été mis au point. Enfin, des expériences en conditions réelles avec le vrai robot dans la rade de Brest et vers Douarnenez (Bretagne, France) ont été faites, avant une utilisation lors d'une campagne de mesures océanographiques au milieu de l'Atlantique. Le régulateur de robot voilier développé sera expliqué dans la section 2. La section 3 abordera la validation théorique de ce régulateur. Le simulateur HIL utilisé comme méthode validation supplémentaire et outil pour planifier les expériences réelles sera décrit dans la section 4. Enfin, la section 5 montrera les résultats des tests réels avec VAIMOS.

Régulateur

Du fait du fonctionnement d'un voilier, certains caps sont difficiles à suivre selon l'orientation du vent. Ainsi, la plupart des régulateurs ont 2 modes différents : nominal, lorsque le cap à suivre est tenable, ou remontée au vent i.e. oscillations autour de la direction du vent + ou -45° (angle de près) lorsque le cap à suivre n'est pas directement tenable. La plupart des régulateurs existants ne font qu'un suivi de waypoints de base au lieu d'un suivi de ligne pour les caps tenables [START_REF] Sliwka | Autonomous robotic boat of ENSIETA[END_REF] :

 Le robot suit un cap en direction de son waypoint.

 Le waypoint est atteint quand on s'en approche dans un rayon prédéfini.  Malheureusement, rien ne l'empêche de dériver entre les waypoints (à cause du courant, du vent,...). Certains utilisent aussi des champs de potentiels pour définir des zones interdites pour le voilier [START_REF] Romero-Ramirez | Contribution à la commande de voiliers robotisés[END_REF], des fonctions de coût, de la logique floue et la polaire des vitesses du voilier (voir VMG : Velocity Made Good) [START_REF] Stelzer | Autonomous sailboat navigation for short course racing[END_REF]. L'un des premiers robots voiliers utilisant une stratégie de suivi de ligne était Atlantis (et HWT X-1, son successeur) [1] [START_REF] Elkaim | An Energy Scavenging Autonomous Surface Vehicle for Littoral Surveillance[END_REF]. Les entrées d'un voilier tel que VAIMOS sont l'angle du gouvernail et l'angle maximum d'ouverture de voile ( l'angle de la voile dépend de ce dernier et de l'orientation du vent par rapport à l'orientation du voilier). Les sorties sont la position du voilier obtenue grâce au GPS, la vitesse et l'orientation du vent retournés par la station météo (on utilise le vent vrai calculé par la station) et l'orientation du voilier avec l'AHRS, utilisée comme boussole. On peut noter qu'il serait possible de se passer de la station météo et de garder l'angle maximal d'ouverture de la voile constant en utilisant les méthodes décrites dans [START_REF] Sliwka | A wind-independent control strategy for autonomous sailboats based on voronoi diagram[END_REF]. Le régulateur par suivi de ligne de VAIMOS (décrit en détails dans [START_REF] Jaulin | A simple controller for line following of sailboats[END_REF], [START_REF] Jaulin | Suivi de route pour un robot voilier[END_REF] et [START_REF] Jaulin | An interval approach for stability analysis; Application to sailboat robotics[END_REF]) est composé de plusieurs parties :

 Un premier étage de régulation en cap. L'angle du gouvernail est réglé proportionnellement à la différence entre le cap voulu et le cap actuel si le robot est proche du cap voulu, ou avec une régulation de type bang-bang autrement :  Expériences réelles dans la rade de Brest et entre Brest et Douarnenez. Une nouvelle méthode par intervalles pour l'analyse de stabilité de systèmes linéaires a été mise au point (ceci est décrit en détail dans [START_REF] Jaulin | An interval approach for stability analysis; Application to sailboat robotics[END_REF]). Le principe de cette approche est de représenter les systèmes incertains par des inclusions différentielles et d'appliquer ensuite des méthodes d'analyse de Lyapunov pour transformer le problème de stabilité en un problème d'inversion ensembliste (voir [START_REF] Jaulin | Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics[END_REF] et [START_REF] Jaulin | Set inversion via interval analysis for nonlinear bounded-error estimation[END_REF] pour plus d'informations sur le calcul par intervalles et l'inversion ensembliste). De cette manière, il est possible de démontrer que pour toutes les perturbations possibles :

{ ( ) ( ) ( (
 Il y a un sous-ensemble de l'espace d'état d'où le système ne peut s'échapper dès qu'il y entre.  Si le système est en-dehors de ce sous-ensemble, il ne va pas rester en-dehors pour toujours. Cependant, même si ces méthodes permettent de valider théoriquement la robustesse du régulateur (i.e. le fait que le robot va bien suivre sa ligne et rester dans son couloir), des méthodes supplémentaires doivent être utilisées pour ajuster les hypothèses faites (équations d'état, bornes sur les erreurs de mesures des capteurs,…). Un simulateur (inspiré par [START_REF] Jaulin | Modélisation et commande d'un bateau à voile[END_REF]) Hardware In the Loop permettant de simuler la trajectoire du robot sur ordinateur selon le trajet demandé et les conditions de vent et de mer prévues tout en faisant bouger les actionneurs du robot comme s'il se croyait en mer pour étudier leur fatigue a donc été développé et utilisé pour préparer au mieux les expériences de validation réelles.

Simulateur HIL

La plupart des simulateurs existants utilisent la polaire des vitesses du voilier ou de nombreux scénarios prédéfinis pour déterminer son mouvement. De ce fait, ils évitent certaines situations singulières qu'il faudrait détecter et vérifier pour valider totalement le régulateur. Des équations d'état inspirées de [START_REF] Jaulin | Modélisation et commande d'un bateau à voile[END_REF] ont été utilisées pour tenter de valider notre régulateur :

Expériences avec un robot réel

Des expériences réelles avec des motifs de trajectoire particuliers ont été faites en rade Brest pour tester VAIMOS dans un maximum de conditions de vent différentes tout en faisant des mesures océanographiques pour l'Ifremer. Ces tests réels courts ont été importants pour détecter certains problèmes, telles que des perturbations magnétiques sur l'AHRS à cause de certaines parties du voilier, nécessitant de la séparer du reste de l'électronique embarquée, problèmes qui ne pouvaient a priori pas être détectés simplement avec les méthodes de validation décrites précédemment.

Figure 1 :

 1 Figure 1 : VAIMOS en mer

Figure 2 :

 2 Figure 2 : Notations: et sont l'orientation et la vitesse du vent, est la force du vent sur la voile et l'angle de la voile, est la force de l'eau sur le gouvernail et l'angle du gouvernail, et sont la position et l'orientation du voilier

Figure 3 :

 3 Figure 3 : Principe du régulateur par suivi de ligne de VAIMOS

  du voilier, sa vitesse de rotation, son roulis supposé pendulaire, avec les coefficients (frottement fluide), (hauteur du point d'application de la force sur la voile), (masse du pendule équivalent), (longueur du pendule équivalent), (moment d'inertie), et la vitesse du courant marin et son orientation, la hauteur des vagues, le coefficient de la dérive due au vent, , , , , divers coefficients de frottement fluide et , les distances du centre de masse au gouvernail et au mat respectivement. Ensuite, le comportement de ces équations a été testé sur un simulateur en 3D. A la suite de ces résultats, un simulateur HIL (Hardware In the Loop) a été finalement développé pour générer la trajectoire du robot et les données de ses capteurs en fonction des lignes à suivre, des conditions de vent et de mer attendues et d'une position initiale données en entrée, tout en utilisant le régulateur développé sur l'ordinateur embarqué du voilier pour contrôler les actionneurs du robot comme si le voilier était à l'eau, et ainsi étudier la fatigue mécanique de certaines pièces ainsi que la robustesse de l'électronique embarquée. Une simulation HIL signifie que des parties du robot réel (ici l'ordinateur embraqué et les actionneurs) sont utilisées dans la simulation :  D'abord, le simulateur utilisant les équations définies précédemment est démarré sur un ordinateur normal avec un état initial prédéfini. Il génère des données capteurs simulées ( , , ) à partir des commandes du gouvernail ( ) et de la voile ( ) en entrées déterminées par le régulateur et des conditions de mer ( , , ) et de vent ( , ) prédéfinies.  Ensuite, le régulateur est démarré sur l'ordinateur embarqué du voilier. Il prend en entrée une liste de lignes à suivre (formée par des waypoints , ) de la même façon que lors d'une expérience réelle et contrôle les actionneurs tout en envoyant une copie de ses sorties actionneurs ( et ) au simulateur, et en utilisant les données capteurs ( , , ) simulées au lieu des données des vrais capteurs.  Enfin, les fichiers logs générés par le régulateur sont récupérés et affichés en temps réel dans Google Earth et un tableau de bord spécifique. Les communications sont rendues possibles par le fait que tous les éléments embarqués (capteurs, actionneurs et ordinateur) sont accessibles via Wifi.

Figure 4 :

 4 Figure 4 : Principe du simulateur HIL de VAIMOS

Figure 5 :

 5 Figure 5 : Simulation de VAIMOS allant de Brest à Douarnenez. La trajectoire désirée (ligne rouges formées par les waypoints jaunes) et la trajectoire (simulée) effective (en vert) semblent superposées.Cependant, en zoomant, on s'aperçoit qu'il y a bien des phases de remontée au vent avec changements de bords. On peut aussi distinguer les étapes de recalibration du moteur de voile (toutes les 2 h), où le voilier dérive pendant une minute

Figure 6 :

 6 Figure 6 : Tests en rade de Brest. Le vent était de Sud-Ouest dans les 2 cas

Figure 7 :

 7 Figure 7 : Brest-Douarnenez. Le robot a dû être dévié 2 fois pour éviter un sous-marin et un bateau sur sa trajectoire. Pendant ces perturbations, le robot a été dévié manuellement par notre bateau suiveur et son programme autonome n'a pas été stoppé. Ainsi, ses déviations illustrent aussi la robustesse du régulateur, qui a été capable de continuer la mission comme s'il n'y avait rien eu

Figure 8 :

 8 Figure 8 : Campagne STRASSE sur le navire océanographique Thalassa

  Remerciements: Le robot VAIMOS a été construit dans le cadre d'une collaboration entre le LPO (Laboratoire de Physique des Océans), le RDT (Recherches et Développements Technologiques) d'Ifremer (Institut Français de Recherche pour l'Exploitation de la Mer) et l'ENSTA Bretagne (Ecole Nationale Supérieure de Techniques Avancées Bretagne). Les auteurs souhaitent remercier le LPO et RDT pour avoir mis à disposition VAIMOS en tant que vecteur pour tester des algorithmes de l'ENSTA Bretagne. Ils remercient aussi toutes les personnes ayant participé au projet VAIMOS: Yves Auffret, Patrick Rousseaux, Sébastien Prigent, Loïc Dussud, Stéphane Barbot, Loïc Quemeneur, Bertrand Forest (RDT, Ifremer) et Fabienne Gaillard, Thomas Gorgues, Thierry Terre (LPO, Ifremer). Elkaim G.H., Kelbley R. (2006), Station Keeping and Segmented Trajectory Control of a Wind-Propelled Autonomous Catamaran, In Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, USA.

	7. Bibliographie
	[1]


S Mezghani
email: sabeur.mezghani@ensam.eu

I Demirci

M El Mansori

M Yousfi

Mutual influence of crosshatch angle and superficial roughness of honed surfaces on friction in ring-pack tribo-system

Keywords: Honing, Plateau roughness, Friction, Cylinder engine. 0 Ambient temperature and pressure density, kg.m -3 Equivalent shear stress, Pa Characteristic

The cylinder bore surface texture widely produced by honing technique, is an essential factor for a good engine performance (friction, oil consumption, running-in, wear…). This explains the improvement and development of various new honing techniques. These different honing processes generate surfaces with various texture features characteristics (roughness, valleys depth, crosshatch angle…).

This paper addresses a comparison of ring-pack friction for cylinder surfaces produced respectively by plateau honing and helical slide honing. It takes in consideration the mutual effect of superficial plateau roughness amplitude and honing angle. A numerical model is developed to predict friction within the cylinder ring-pack system in mixed lubrication regime. The results show the effectiveness of helical slide honed surface texture in comparison to plateau honed bore surfaces.

Introduction

With a stringent legislation for the limitation of harmful polluting emissions, the improvement of environment efficiency of vehicle engine is became a fundamental objective [START_REF] Sabeur | Energy efficiency optimization of engine by frictional reduction of functional surfaces of cylinder ring-pack system[END_REF]. It is evident actually, based on several experimental and numerical studies, that cylinder engine surface texture considerably influences functional performances (running-in, friction, oil consumption, wear…) of the ring-pack tribo-system [START_REF] Pawlus | Effects of honed cylinder surface topography on the wear of piston-piston ringcylinder assemblies under artificially increased dustiness conditions[END_REF][START_REF] Shinkarenko | The effect of surface texturing in soft elastohydrodynamic lubrication[END_REF][START_REF] Jocsak | The Effects of Surface Finish on Piston Ring-pack friction[END_REF].

Honing is a widely used finishing process for cylinder surfaces after drilling or turning operation to guarantee reproducibility with efficient productivity in mass production of cylinder liners [START_REF] Sabri | Multiscale study of finish-honing process in mass production of cylinder liner[END_REF]. In honing, abrasive stones are loaded against the bore and simultaneously rotated and oscillated. The industrial honing involves graduated stages of abrasive finishing processes, using at first a coarse abrasive stones, and then progressively finer grades, so that a very structured surface of liner is produced. Characteristically, the resulting structured surface consists of low rough plateau textures separated by two or more bands of parallel deep valleys with stochastic angular position [START_REF] Sabri | Functional optimisation of production by honing engine cylinder liner[END_REF].

Hence, effort has been made in last decade for the improvement of honing process for cylinder liners finishing. Moreover, various new surface textures was proposed by the development of innovate honing techniques (slide honing, glide honing, brush honing…) [START_REF] Johansson | New cylinder surfaces for low oil consumption[END_REF][START_REF] Haasis | New honing technique reduces oil consumption[END_REF][START_REF] Dimkovski | Optimization of cylinder liner surface finish by slide honing Manufacture[END_REF][START_REF] Hoen | Less Wear and Oil Consumption trough Helical Slide Honing of Engines by Deutz[END_REF][START_REF] Tomanik | Friction and wear bench tests of different engine liner surface finishes[END_REF] and surface texturing methods to meet both actual and future functional requirements [START_REF] Ma | An optimum design model for textured surface with elliptical-shape dimples under hydrodynamic lubrication[END_REF][START_REF] Kovalchenko | The effect of laser surface texturing on transitions in lubrication regimes during unidirectional sliding contact[END_REF].

Unfortunately, the whole effect of different cylinder liner finishes on ring-pack performance is not well understood [START_REF] Tomanik | Friction and wear bench tests of different engine liner surface finishes[END_REF]. Furthermore, the engineered optimized functional surface is still not well defined. Then, it is important to define the optimum texture characteristics to obtain the best functional properties.

Some topographical and lateral geometric properties of the cylinder bores affect considerably the functional performances of the ring-pack contact, particularly, the crosshatch angle [START_REF] Mezghani | The effect of groove texture patterns on piston-ring pack friction[END_REF][START_REF] Jocsak | Analyzing the effect of three dimensional cylinder liner surface texture on ring-pack performance with a focus on honing groove cross-hatch angle[END_REF][START_REF] Shi | Effects of groove textures on fully lubricated sliding with cavitation[END_REF][START_REF] Yuan | Orientation effects of micro-grooves on sliding surfaces[END_REF][START_REF] Křupka | Effect of real longitudinal surface roughness on lubrication film formation within line elastohydrodynamic contact[END_REF], superficial plateau roughness [START_REF] Larsson | Modelling the effect of surface roughness on lubrication in all regimes[END_REF][START_REF] Demirci | The scale effect of roughness on hydrodynamic contact friction[END_REF] and the valley and surface patterns depth [START_REF] Mezghani | The effect of groove texture patterns on piston-ring pack friction[END_REF] and density [START_REF] Mezghani | The effect of groove texture patterns on piston-ring pack friction[END_REF]. It believed that liner surfaces that have smaller valleys and smoother plateaus would reduce friction and oil consumption [START_REF] Dimkovski | Optimization of cylinder liner surface finish by slide honing Manufacture[END_REF]. Moreover, the orientation of micro-grooves has a strong effect on the friction performance of sliding surfaces and optimal orientation is closely dependent on the contact conditions [START_REF] Yuan | Orientation effects of micro-grooves on sliding surfaces[END_REF]. In hydrodynamic lubrication condition, two optimal range of crosshatch angle was determined [40°-60°] and [120°-140°] [START_REF] Mezghani | The effect of groove texture patterns on piston-ring pack friction[END_REF]. However, [START_REF] Johansson | New cylinder surfaces for low oil consumption[END_REF] shows that the steep honing angle did not present any improvement in ring-pack friction and wear at the top dead center of the cylinder but it yields to less oil consumption over the entire engine course in comparison to 40° honing angle [START_REF] Haasis | New honing technique reduces oil consumption[END_REF][START_REF] Hoen | Less Wear and Oil Consumption trough Helical Slide Honing of Engines by Deutz[END_REF].

In this paper, the mutual influence of honing angle and superficial plateau roughness was investigated based on comparison of surface textures generated by two kind of honing processes: the widely used Plateau honing with honing angle in the range of 40°-60° and helical slide honing with grooves arranged in the direction of the piston in an elongated spiral (120-140° honing angle). Thus, to predict friction of the produced textures in ring-pack tribosystem, simulation model in mixed lubrication regime was developed. Then, an algorithm involving the generation of 3D surface topographies with controlled superficial plateau roughness and total surface height is established. Finally, a comparison between these two processes and possible friction reduction strategy in ring-pack system is analysed and discussed.

Numerical model for hydrodynamic friction simulation in piston ringpack system

A numerical model was developed to estimate the friction generated between rough surfaces.

The model considered the real topography of the cylinder bore surfaces. The objective of this model is to compare the predicted friction coefficient between two kinds of cylinder bore textures in accordance with their superficial plateau roughness amplitude.

Elastohydrodynamic equations

The generalized Reynolds' equation introduced by Najji [START_REF] Najji | New Formulation for Lubrication with Non-Newtonian Fluids[END_REF] has been used to estimate the pressure distribution, film thickness, and the friction coefficient. This equation has the advantage of not being restricted to a particular non-Newtonian law. The steady state equation in the dimensionless form is given by: 33 22 The effective viscosities could be calculated as considering the shear-thinning effect (Eyring fluid):

1 1 1 sinh m m (2) with 0 me
, where, τ 0 is a reference shear stress and Higginson formula [START_REF] Dowson | Elastohydrodynamic Lubrication; The Fundamentals of Roller and Gear Lubrication[END_REF] (Eq. 3) and Roelands law [START_REF] Roelands | Correlational aspects of the viscosity-temperature-pressure relationships of lubricant oil[END_REF] (Eq. 4) were used: where, µ 0 is the viscosity at ambient pressure, p r is a constant equal to 1.96 x 10 8

, and z r is the pressure viscosity index.

Finally, the boundary condition P = 0 and the cavitation P(X,Y) ≥ 0 , XYmust be satisfied during the simulation.

The film thickness equation is given in dimensionless form by the following equation:

22 0 , , , , , , 22 h XY H X Y T H T X Y T Z X Y T (5)
Where, Z h is the height surface topography at each position , XY and ,, X Y T is the dimensionless surface deformation calculated by 2 22 ,, 2 ,,

P X Y T dX dY X Y T X X Y Y (6)
The global force balance condition is given by: 2 ,,

3 c P X Y T dXdY T (7)

Numerical procedure

The Reynolds equation was solved by the finite difference method in order to obtain the film pressure distribution. A second order accuracy with respect to both space and time [START_REF] Venner | Amplitude reduction of small-amplitude waviness in transient elastohydrodynamically lubricated line contacts[END_REF], was used. The discredited equation was solved by the Jacobi line relaxation [START_REF] Venner | Multilevel methods in lubrication[END_REF]. The full-scale mixed EHL approach developed by Hu and Zhu [START_REF] Hu | A full numerical solution to the mixed lubrication in point contacts[END_REF] was used in the present study. The multi-grid method [START_REF] Venner | Multilevel methods in lubrication[END_REF] was applied in order to accelerate the solution convergence. The elastic deformation calculation was conducted by using the discrete convolution and fast integration [START_REF] Venner | Multilevel methods in lubrication[END_REF]. The integral terms in the generalized Reynolds' equation were calculated at each step using the solution obtained at the previous stage. A classical Newton-Raphson procedure was used to determine the shear stress and the effective viscosities. The solution domain was determined as 2.5 1.5 X and 2.0 2.0 Y . The computational grid covering the domain consisted of equally spaced 512x512 or 1024x1024 nodes. Using rough surfaces in EHL simulation could yield localized asperity contact pressure peaks usually higher than the average EHL pressure resulting in high subsurface stress that exceeds the material yielding limit [START_REF] Ren | Plasto-elastohydrodynamic lubrication (PEHL) in point contacts[END_REF]. To limit the contact pressure, the elastic-perfectly plastic behavior of a material was approximately simulated by using a cut-off value, i.e. the hardness of the material. The normal load F N and contact speed u m are respectively equal to 50 N and 300 rpm [START_REF] Bolander | Lubrication regime transitions at the piston ring-cylinder liner interface[END_REF]. It simulate the piston ring-cylinder bore contact in mixed regime that occur near the Top Dead Center (TDC) and Bottom Dead Center (BDC) [START_REF] Bolander | Lubrication regime transitions at the piston ring-cylinder liner interface[END_REF].

Mastered honed surface topographies generation

The honed surface texture of cylinder liners is composed of 3D superficial rough surface separated by deep valleys with defined crosshatch angle. These two elements play different roles in the cylinder-ring contact [START_REF] Decencière | Morphological decomposition of the surface topography of an internal combustion engine cylinder to characterize wear[END_REF]. The superficial plateau morphology replaces partially initial run-in and related to friction and wear. The valleys component is related to lubricant circulation and retention.

The morphological filtering approach described in [START_REF] Decencière | Morphological decomposition of the surface topography of an internal combustion engine cylinder to characterize wear[END_REF], provides a powerful tool capable of separating these two principal components of the honed surface topography data. This approach, use an alternate sequential filter with a disc structuring element, as non-linear image processing operator. The surface topography is filtered recursively with increasing the filter size after each filtering operation until reach the smallest form elements. Figure 1 To investigate the mutual effect of crosshatch angle and the plateau surface roughness on frictional losses at the interface between a piston ring and cylinder liner, an approach for generating controlled surface topography based on real surface measurement data was developed. The algorithm of the method used for surface topographies generation is described in Figure 2. It is applied for creation of surface topographies with different specified amplitude ratio plateau/valleys and having the same total surface height Sz (ISO 25178-2 standard) from two original honed surfaces plateau honed (PH) and helical slide honed (HSH) surfaces taken from mass production of cylinder liners (Figure 3).

Plateau honing very widely used process is a succession of three honing stages [START_REF] Sabri | Multiscale study of finish-honing process in mass production of cylinder liner[END_REF][START_REF] Sabri | Functional optimisation of production by honing engine cylinder liner[END_REF]. The first stage often categorized as rough honing establishes the form of the bore. The so called ″finish honing″ which creates the basic surface texture of the hole is the second operation.

This enables the third honing operationplateau stageto serve for removing the surface peaks, increasing plateau surface area and then reducing the plateau valleys amplitude ratio.

HSH is achieved with the same stages succession but generate surface with steep honing crosshatch angle by reducing the rotational speed of the honing tool and increasing the stroke rate to limit the reduction in the stroke removal rate. The principal difference between the real PH and HSH surface textures is the honing angle between the two groove orientations, the maximum height of the surface and the plateau valleys amplitude ratio. For considered surfaces (Figure 3), the honing angle is about 50° for PH surface and is beyond 130° for HSH surface, the ratio S parameter plateau honed surface and 0.54 for the original helical slide honed surface. These two surface textures have almost the same texture aspect parameters that affect friction such as grooves density (≈600 grooves/mm 2 ) and grooves balance (≈0.5). The method of quantification of these lateral texture characteristics and theirs influence on friction are detailed in [START_REF] Sabri | Functional optimisation of production by honing engine cylinder liner[END_REF][START_REF] Mezghani | The effect of groove texture patterns on piston-ring pack friction[END_REF]. Using this methodology, the comparison between surface textures generated by plateau honing and helical slide honing is performed with the same total surface height (Sz).

Moreover, all surface feature characteristics (groove density, groove width,…) are realistic and remains unchanged. Three total surface height (Sz=2.5µm, Sz=5µm and Sz=10µm) and six plateau/valleys amplitude ratio between 0.1 and 0.8 were considered. A ratio equal to 0 corresponds to an ''ideal'' smooth plateaued surface. A ratio equal to 1 represents a nonplateaued surface finish.

Results and discussion

The numerical model presented in Section 2 was used to predict friction in the ring-linerpiston contact and to analyze the mutual effect of crosshatch angle and superficial plateau roughness on friction. Moreover, as shown in Figure 5 which shows the evolution of metal to metal contact and the average film thickness between the friction pairs function of the plateau/valleys amplitude ratio, steep honing angle (130° crosshatch angle) reduce the oil film thickness average and leads to lower dry contact area and tightens therefore to a hydrodynamic lubrication regime.

The frictional performance of helical slide honed cylinder is three times less sensitive to superficial plateau roughness (Figure 4). Table 1 In contrary, Surface textures with 140° cross-hatch angles are very less sensitive to superficial surface peaks in particular with 5 Sz µm (Table 1). Therefore, this third honing operation can be canceled in production process of HSH surface textures. So, with only two-stage honing operations, more efficient production of cylinder liners at industrial level is guaranteed.

Finally, optimal surface texture is characteristically defined by steep honed angle with

Conclusion

The mutual effect of crosshatch angle and superficial plateau roughness of honed surface textures of cylinder liners in mixed lubrication contact regime was investigated. Then, two real honed surface textures produced respectively by plateau honing (50° honing angle) and helical slide honing (130° honing angle) were considered. An algorithm for generation of surface topographies with mastered plateau/valleys amplitude ratio and specified total surface height from real three-dimensional surface data was developed. Then, the friction performance of a cylinder ring-pack system in mixed lubrication regime was predicted.

Finally, results of numerical simulations show that:

1. For 50° honing angle and surface total height greater than 10 µm, the reduction of the superficial plateau roughness decreases considerably the friction in mixed lubrication contact regime;

2. The 130°-honed liner (helical slide honing) leads to an improvement in friction, film thickness and reduce the dislocation of the boundary layer in comparison to 50° crosshatch angle (plateau honing);

3. With helical slide honed liners, friction is much less sensitive to superficial plateau roughness than with plateau honed liners. Then, the industrial helical slide honing process can be set up in only two process stage instead of the three stage required for plateau honing in mass production of cylinder engines.

  y Radius of curvature in x and y direction respectively, m R Equivalent radius of curvature, m Srr Slide to roll ratio : Srr = 2(u1-u2)/(u1+u 2 viscosity index (Roelands), z r = p r /(ln(η 0 )+9.67) Pressure-viscosity coefficient Pa -1 Dimensionless elastic deflection of the contacting bodies Effective viscosities

y

  is the equivalent shear stress inside the lubricant film. The lubricant's viscosity and density are assumed to depend on pressure. The Dowson and

Figure 1

 1 Figure 1 Example of decomposition of a cylinder liner surface topography using alternate sequential filtering; (a) tri-dimensional topography of plateau honed surface, (b) superficial plateau (in red) and valleys components (in blue).

Figure 2

 2 Figure 2 Algorithm of reconstruction of honed surfaces with mastered plateau/valleys amplitude ratio and total surface height (Sz) from a original honed surface texture.

Figure 3

 3 Figure 3 Three-dimensional topographies of typical (a) plateau-honed surfaces and (b) helical slide honing surface showing a different cross-hatch angle respectively 50° and 130°.

Figure 4 and

 4 Figure 4 and Figure 5 resume the obtained simulation results performed in this study.

Figure 4

 4 Figure 4 depicts the influence of superficial plateau roughness on friction coefficient of PH (50° honing angle) and HSH (130° honing angle) cylinder liner surfaces for three level of liner surface roughness Sz. One can see that, in mixed lubrication conditions, friction coefficient (COF) increases with increasing liner surface roughness for both PH and HSH

Figure 4 Friction

 4 Figure 4 Friction Coefficients of PH and HSH cylinder liner surfaces function of the ratio Spq/Svq and for three different total surface height (a) Sz=2.5µm, (b) Sz=5µm and (c) Sz=10µm.

4 )

 4 resumes the rate of friction variation function of plateau-valleys ratio for PH and HSH surfaces. Plateau honed surfaces are very sensitive to superficial plateau roughness particularly when . Therefore, the third honing stage in plateau honing process has a decisive influence since it allows to reduce considerably friction by reducing plateau roughness amplitude. Furthermore, a b c this reduction of superficial plateau peaks yields to diminish the metal to metal contact area and thereby to less lubricant film dislocation.

Figure 5

 5 Figure 5 Contact area ratio (a) and film thickness average (b) of PH and HSH cylinder liner surfaces function of the ratio Spq/Svq and for three different total surface height (1) Sz=2.5µm, (2) Sz=5µm and (3) Sz=10µm.

  to the lower friction and oil film thickness average and with dry contact area less than 2%.

Table 1 .

 1 Rate of friction variation function of plateau-valleys ratio changes

	Surface total height	PH		HSH
	Sz = 2.5 µm	7.13%	2.44%
		S	S	S	S
		pq	pq	pq	pq
		0.3	0.3	0.3	0.3
		S	S	S	S
		vq	vq	vq	vq
	Sz = 5 µm	20.28%	7.78%	7.8%	4.3%
	Sz = 10 µm	45.3%	1.6%	13.8%	0.3%


Ioana Bilegan

Carlos Alberto Nunes Cosenza

Sergio Gonzalez-Rojo

A maximum entropy approach to update airlines demand distributions

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


The Alsatian Altenberg : a seven centuries laboratory for silver metallurgy

Introduction

First lode silver mining district for the present French territory regarding its accumulated production, the Sainte-Marie-aux-Mines vein structure develops itself in the central area of Vosges mountains (almost a replica, on the western side of the Rhine Graben, of the Schwarzwald)(fig. 1) 1 . In detail, mineral parageneses are complex there. One can although define three different mining sectors, based on mineralogical, geological, geographical and historic criteria (fig. 2).

The area located on the left side of the Lièpvrette river is called "Lorraine side", it was property of the Duke of Lorraine until the French Revolution. Ore lodes are oriented NW-SE and characterized by antimoniferous tetrahedrites containing high amount of silver. Some were exploited during the Middle Ages, but the most important mining activities took place during the 16 th c.

On the right side, in the South of a village called Echery, the Neuenberg area is composed of seven main veins oriented E-W or NW-SE. It presents very various mineralization, and particularly arsenic-tetrahedrites containing fluctuating amounts of silver (up to 1%). Besides, some veins of native arsenic were also noticed there, as lead and cobalt ores. Its name is due to the relatively late discovering of its metal resources, in the middle of the 16 th century.

In both of these sectors, some lodes have offered high-amount silver ores and even native silver.

The third area, called Altenberg, is located in the North-East of the Neuenberg, still on the right side of the Lièpvrette. This side was owned by the alsatian Lord of Ribeaupierre. Its vein structure is oriented NNE-SSW. Tetrahedrites can accessorily be noticed but the almost only silver-containing mineralization there is galena (silver amount lower than 0,1%), contained in a gangue of siderite and compact quartz. As its name seems to indicate, mining was initiated earlier in this area. Historians meet enormous difficulties in defining activities during the medieval period, due to a serious lack of reliable sources. The Richer de Senones' Chronicle (around 1265) set the beginning of silver exploitation, by a monk called Blidulphe, around 938. We don't know anything about those mining activities sustainability, if not their total abandonment at beginning of the 14 th c. An agreement between Guillaume de Ribeaupierreaffrighted by the Duke of Lorraineand Sigismond of Austria, signed in 1486, allowed the resumption of the mining industry, effective in 1502.

Initiated in 1981, archaeological excavations on the Altenberg were led by different teams, nearly without interruption until 1996, focused on the underground mining works but also on some surface sites. We can approximate that 70 percent of investigations concerned the Renaissance period 2 . Some characteristics, as the mining works' shape, the exploitation of lodes crests by pits (Pingen), the slag mineralogy, testified an important medieval industry. Nevertheless, datings were scarce (only three sites dated for this six centuries period). This disparity of information between Renaissance and Middle Age period led to elaborate a new research program focused on three questionings: which remarkably fits with the Renaissance context, due to an exponential production of archive documents, isn't at all adapted to medieval times. Moreover, the unearthed archaeological material linked to this period has been very scarce for this sector. So another methodology had to be defined: it is mainly based on multiplying archaeological surveys and excavations that could supply absolute dating supports.

A new research program was so initiated in 2006, consisting first on several geophysical and archaeological surveys, that led to a Collective Research Program from 2008 to 20114 . Furthermore, a new program is currently being elaborated, for the 2012-2014 period, concerning a larger region of study, i.e. the Oberrhein.

Context of study

A first chronological synthesis of the mining activities in Sainte-Marie-aux-Mines can be drawn, based on the results of this six-year work : twenty archaeological surveys, two archaeological, nine geophysical and one geochemical prospections, four excavations, seven underground investigations, an airborne laser-scanning survey, one experimental archaeology program, and three historical researches investigating "new" archives collections (fig. 3). Only 5 to 10 percents of the Altenberg's estimated archaeological potential have so far been investigated. Some great evolutions in mining and metallurgic techniques can be drawn. At first, the major conclusion is that we are forced to reconsider totally what was thought till now about mining activities chronology in this region. Between the settlement of the first Echery monks in about 938 and the ending of the Thirty Years War in 1637, no major interruption of mining and metallurgic activities appears to have occurred. Fig. 4 shows the synthetic chronological diagram for mining-and metallurgy sites on the Altenberg. Most of these data has been obtained by radiocarbon dating5 , less frequently by thermoluminescence or dendrochronological dating. Some groups can be distinguished on it, on the base of chronological and geographical criteria. However, these groups can also be influenced by the choice of sites to be investigated. These groups are defined as follows (n.b. most of the locations don't carry their original names!):

-A first "Haut-Altenberg" group (located most nearly from the top of the Altenberg, height 850 m), dated from the 10 th and maybe 11 th c.

-A "Saint-Philippe" group (so-called Pfaffenloch, Patris, Charlotte sites), from the first half of the 11 th c.

-A "Fertrupt" group (sector of the forthcoming Rumpapump mine), in the 12 th c. and around 1200.

-The Echery foundry site, which occupation began in the late 13 th c.; its activity restarted in the 14 th c. after having been interrupted

-A late "Haut-Altenbergand Pfaffenloch-group", from 1350 until the end of the 15 th c.

-Several sites in the Saint-Philippe small valley (Charlotte, Bergarmuth, Sapin Vert), which occupation took place in the late 15 th c.

This chronological division will be respected through the following development, trying to highlight, for each period, major technical and social features.

A new defined Altenberg chronological pattern

1-The Pingen period

From the time monk Blidulphe had presumably settled on the Altenberg, in 938, several hundred pits6 were dug on the crests of Altenberg vein structure (fig. 5); their density made possible to restitute its absolute extension. Only the ones located on Haut Altenberg sector were dated (the dating matched the textual sources about Blidulphe !), but it can be assumed that most of these structures were dug during a relatively short period. Indeed, once the first outcrops located, it was much easier for surveyors to determine the veins' azimuths and extensions, and to excavate it step by step. Archaeological surveys accomplished on those structures have shown that first medieval prospectors took a particular care in removing surrounding altered rock before digging the pits. Archaeologists faced a huge problem while performing excavations on such structures, due to the poor stability of highly faulted gneissic substratum as a wall rock. Nevertheless, some underground investigations, centred in the remote parts of the Porte de Fer mine, permitted to access pits bases and to observe the underground parts of the Pingen exploitation system. Lodes were there intensively excavated on a height range of about a hundred meters. The best-matching comparison in archival sources could certainly be the picture of Kutna Hora's gradual (from Mathis, in 1490), describing mine shafts which morphology seem to be closely adapted to the vein's, resulting in very deformed shapes. Though adits showed a cramped and egg-shaped profile, the use of fire was rarely observed.

2-First adits

At the turn of the millennium, the exploitation tends to take the form of galleries dug lower on the mountain slopes, in order to cross the lodes previously exploited from their crests. The technique of such crosscut tunnels became the norm in this sector. A good example of those first adits is part of the Patris mine, dated from the early 11 th c. (few years after 1014 by dendrochronology7 ). 1,2 m high and less than one meter wide, it was dug using fire and maybe Fimmeln (sort of ancient handleless iron tool, cf Agricola), because no continuity in tool traces can be noticed. Some similar galleries have been studied in the Cep de Vigne and Hans Franz mines; the latter, dated from about 1200, intended to exploit lower parts of lodes already worked by Pingen. Surface facilities, located a hundred meters from it, were surveyed. They consist on a wooden building of late 11 th or 12 th c., destroyed by fire. Ceramic, which remains are scarce, is rather characteristic of the 12 th -13 th transition. The corresponding gallery was studied in 1996. It was reshaped in the 1520's, and renamed Rumpapump, according to textual sources.

3-First smelting places

Foundries where built within the surface facilities located near those adits, and on other places. Meticulous archaeological prospecting has allowed to identify ten smelting sites for the strict Saint-Philippe small valley, a number which certainly may seriously underestimate the reality, due to the generally important thickness of colluviums in this sector. These smelting places can be attested by the presence of fayalitic slags concentrations (fig. 6 and7).

In some cases, geophysical surveys have led to spot the most important concentration areas within the slag spreadings, which allows focusing further surveys.

Archaeological excavations were performed on three smelting sites: the so-called Pfaffenloch, Patris and Charlotte. All of them presented strata dated from the 11 th c., but these sites present one or more other periodsgenerally more recentof metallurgy-linked activities. None of them revealed conserved furnaces, although furnace fragments were observed. At the most some rubefacted areas were excavated, which purpose was certainly ore-roasting, maybe smelting (their soils may contain some significant lead amounts). Nevertheless, no conserved structure has been discovered, due to the relatively bad taphonomic conditions generally encountered on Altenberg sites.

4-Later foundries

A fayalitic slag spreading has been spotted at the foot of the Altenberg, in the Echery village surroundings. A geophysical survey has allowed locating the most important slag concentration, which was investigated through two successive years of archaeological surveying (2006-2007) and an excavation campaign (2008). The site revealed itself complex and multiphased. Archaeological material and absolute dating have permitted to distinguish three periods of occupation. The first goes back to the second half of 13 th c. (y. 1261-1284). It shows an important innovation : it is, for the Altenberg, the oldest example of the smelters' will to settle farther from the veins (distant of approximately two kilometers), and in a stream's proximity. This happened right during the gothic's advent in the Rhine regions. The facilities scale and situation may suggest that it could have been supplied by different Altenberg mines. Moreover, the end of this period seems to coincide with some historians' assumptions that exploitation would have ceased in 1280 : could these information be put in relation?

This site knew a second period of activity during the 14 th century, which is attested by a strong masonry, as by large quantities of material such as stove tiles, cooking pottery and furnace tuyères, and also by abundant industrial wastes (charcoal, fayalitic slags,…).

Another slag concentration site has been spotted on the foot of the Altenberg, at the bottom of Saint-Philippe small valley. Its location could have been motivated by a stream's proximity, but with no certainty. Its dating (2 sigma 1039-1212) ought to be confirmed.

5-The hydraulic energy innovation and the first ore-washing facilities

In the middle of 14 th century took place what we call the late Middle Ages technical breakthrough. Its oldest clue is the surface facilities 8 that were renamed, 170 years later, Vieux-Saint-Guillaume. This upheaval is first characterized by the establishment of an altitude small canal of about 1,5 km length in order to operate a large pumping machinery in a big shaft. The canal structure itself hasn't been unearthed (maybe it was a wooden structure), but some remains were found by surveying several trenches, consisting on alternated sand and silt deposits.

Downstream of the structure we could call Vieux-Saint-Guillaume shaft, this canal could have been used for ore-washing operations, which remains consist on important sandy sediments and schlamms buildups up to several meters thick. Further down, about 300 meters from it, the older site Pfaffenloch knew a new period of activity. In the middle of the 14 th c. 9 , the slag heap in this place is interspersed with tailing waste materials and ore-washing wastessandy and silt sedimentslayers. This could corroborate the first "hand-made" stamp milling operations.

This site also provides us with clues of new metallurgical practices that one can qualify as a "technical revolution" in this context. Till then, siderite as gangue rock was introduced in furnace with the lead ore. This process explains the concomitant presence of slag and tailing wastes within the slag heaps, the latter stemming from a crude sorting. This mixture produces, as activity wastes, slags presenting an iron silicate framework, fayalite (fig. 7). The evoked 8 Dated by thermoluminescence on a cooking pottery fragment.

innovation consists on sorting extracted material by water, after "hand-made" milling. Thus galena is sorted from its gangue by gravity in facilities we qualified as "proto-laveries", which remains are those layers of sand and schlamms in stratigraphy. Through the smelting process, the ore produces an iron-depleted slag, presenting a more vitreous structure, which was found in the most recent layers of the Pfaffenloch slag heap (fig. 8). An astonishing fact is the resilience, for even one and a half century, of the ancient process in some places of the Altenberg. For example, the metallurgy site called Charlotte has known its last activity period in the second half of the 15 th century, after a gap of about 400 years. Metallurgical wastes there still present a fayalitic facies. Moreover, two hearths were unearthed in this sequence; one of them offers some similarity with a structure which was found in the Westphalian Altenberg10 . Thus, during a 250-years time laps, the Altenberg constituted an original place to observe the strong promiscuity of innovations and old-fashioned processes' resilience.

Other sites, investigated during the research program, furnished information about this 15 th century, for which we suffered a lack of knowledge11 . The medium part of the Altenberg is centered on a cluster of mines, which at beginning of the 16 th c. were named Berg Armo; in their vicinity, several surveying trenches were performed in 2011 (a site called "Bergarmuth"). They revealed an unconformity between tailing wastes layers dated from the middle of 15 th c., interspersed by gangue rocks stemming from "hand-milling"12 (fig. 9), and layers of sediment in a double ore-washing basin dated from the turn of the 16 th c..

6-Late Middle Ages galleries… and the textual sources explosion

Most of medieval galleries opened and explored in the 1970's and 1980's are today condemned. Elaborating a typology is still possible, since meticulous measurements, topographic surveys and photographs were performed there, as for the Weinstock mine.

Unfortunately, no dating support could have been found there. Nevertheless, some mines furnished such elements, as the Vieux-Rimpy mine, on the top part of Altenberg. There, the 16 th -century exploitation partly redrafted the former structures, which remain unchanged in some other parts of the mine. The galleries then appear wider than Renaissance's, and tool marks (Agricola's Fimmeln ?) show themselves more disorganized. A crosscut tunnel was dug using fire, and has been dated from the first half of the 15 th c., thanks to the soot adhering on the gallery's wall.

The number of dated mines which original name is known from us also allowed attempting an onomastic approach. Assuming that no considerable interruption had struck mining activities in Altenberg, why would have the Renaissance people absolutely renamed the former mine porches? Names that aren't linked to a religious lexical field, such as Einhorren, Weinstock, Grüntann, der Stein, der Greiff, Backofen… might constitute toponymical remnants. A study led on written sources is currently led following this hypothesis.

7-At the turn of the 16 th century

The last noticeable technical change, at the turn of 16 th c., is the adoption of a water-powered stamp milling, concomitantly with a new generation of foundries. These reflect technical systems that Biringuccio, and then Agricola, have described. In the lower part of the Fertrupt village, the most northern part of Altenberg, remains of a foundry, coupled to an habitat, were investigated in the vicinity of a mine called Fundgrube, where exploitation was initiated in 1502 (or 1506) by Lord Brunon of Ribeaupierre. It revealed an hypothetic furnace base crudely elaborated, but also numerous vitreous slags including massive lead quantities, as if the new metallurgical processes applied to well-prepared ore wasn't mastered then.

The most well-achieved facility among smelting works of the very flourishing period (1520-1530) is the Echery foundry. It was edified by the Austrian archduke and the Lord of Ribeaupierre on the ruins of the precedent buildings (see § 4). Archaeological excavations have revealed a part of it; but it's especially well illustrated by exceptional archive documents filled with a number of technical details.

Conclusion

Datings obtained in 2008 and 2009 have totally infirmed the paradigm, elaborated following historical information, of a total lack of activity in this sector during the end of the Middle Ages.

Way is now open to consider an uninterrupted (or nearly-uninterrupted) mining and metallurgical activity in a 700-year period. From now, the research issues precise themselves : to link the different successive phases of this mining industry with major events that have struck the local history (as the transition from a monastic to a seigniorial economy, the advent of Echery nobles, the edification of their castle,…) and the regional one (increasing importance of minting,…) throughout the medieval period. The major mining districts' organization at the scale of the Oberrhein also has to be considered. Thus, for the 2012-2014 period, we envisage to extend this Collective Research Program to consider those questionings. For example, it is planned to perform isotopic analyses on lead found in different mining or smelting sitesas the Altenbergand to confront it to architectural lead from monuments in the Rhine region. It appears as an essential step evaluating the metal's spreading. Moreover, two PhD works were initiated in 2010 and 2011, to a further development of historical and archaeological approaches.

Figures1245

  Figures

  Les résultats de ces investigations bouleversent ce qu'on croyait savoir : entre l'instant des premiers moines d'Echery, vers 937, et les derniers soubresauts de la Guerre de trente ans, en 1637, aucune interruption durable n'affecta l'activité extractive. Tout au plus peut-on, dans cette longue durée, détecter quelques « pics » de plus grande prospérité, autant de jalons de l'histoire : l'ère des puits alignés par centaines sur les crêtes des filons au X e s., le boom de l'an Mil avec l'éclosion des fonderies et la généralisation des travers-bancs, le XIII  première fonderie hydraulique vers 1250, qui fait le choix de s'éloigner des filons pour se fixer sur le voisinage des cours d'eau  révolution technique du Bas-Moyen-Age, initiée vers 1350 par le tracé d'un canal d'altitude pour un dispositif d'exhaure  abandon progressif de la métallurgie traditionnelle, qui consistait à verser dans les fours la galène et sa gangue de sidérite simplement fragmentées, et qui génère des scories fayalitiques … pour une métallurgie appuyée sur le minerai bocardé manuellement et donc trié par l'eau, un process qui génère des scories vitreuses. Les premières « protolaveries » apparaissent ainsi dès la seconde moitié du XIV e s. et se multiplient au courant du XV e s., au côté de fonderies résiduelles jouant la carte de l'inertie vis-à-vis de l'innovation  à la charnière des XV e et XVI e siècles, le bocardage hydraulique induit un changement d'échelle dans le domaine des laveries et des fonderies. Le projet pour 2012-2014 prévoit d'étendre la « méthode Altenberg » à divers sites médiévaux d'extraction et de métallurgie de non-ferreux d'Alsace, afin de tendre vers une géographie économique des différentes époques de l'histoire, qui pourra être mise en perspective avec les découpages territoriaux, les événements politiques et économiques et le développement des sociétés dans l'ensemble de l'Oberrhein.

	e , le XIV e , le XV e s. … Mais cette histoire est
	jalonnée d'initiatives innovantes :
	doctorants, IRAMAT, CRESAT
	Une renaissance de l'archéologie des mines et des métaux à Sainte-Marie-aux-Mines (Alsace,
	France) s'est esquissée en 2006, qui aboutit à la structuration d'un projet collectif de recherches
	pluriannuel (2008-2011) « Mines et métallurgie de l'argent à l'Altenberg, X	e -XVII	e siècles ».
	Pionnière en Europe à une telle échelle, l'archéologie minière fortement impulsée dans les années
	1980 avait abouti à l'affirmation d'une « école sainte-marienne », caractérisée par un va et vient
	permanent entre l'archive et le terrain, appliquée au domaine des sites miniers de la Renaissance. Le
	nouveau programme 2006-2011 s'adresse à des problématiques qui embrassent les techniques, les
	économies et les sociétés pour la très longue période qui précède. Mais le Moyen-Age n'a pas livré de
	textes, et le mobilier datant se révèle rare dans les fouilles : la méthode était donc totalement à revoir.

A l'Altenberg, berceau de l'extraction minière et de la métallurgie à Sainte-Marie-aux-Mines, l'enquête s'appuie sur la multiplication des sites sondés ou fouillés, assortis de datations absolues.

NOTE IMPORTANTE : depuis la présentation de ces résultats le 1.07.2011 à l'occasion de la Troisième

Conférence Internationale « Archéométallurgie en Europe », des datations nouvelles ont permis d'étendre l'activité minière et métallurgique à l'Altenberg à l'époque carolingienne.

FLUCK P., Sainte-Marie-aux-Mines, les mines du rêve, Editions du Patrimoine Minier, Soultz,

2000, 205 p.

-Chronology. When did really the medieval mining activities begin ? Is it possible to distinguish several activity sequences, separated by episodes of interruption ? And when did it end ?

-Extracting, ore-washing and metallurgical techniques. Assuming that the Pingen technique seems to characterize the beginning of the activities, is it possible to establish a chronologic typology of underground mining works? Why are the fayalitic slags found on the former metallurgy sites so different from those, which offer a glassy texture, characterizing the Renaissance sites? How was a medieval silver-production unit organized? Did it really work without any hydraulic energy, since smelting places set in altitude, near or not far from the mines ?

-At another scale, how did the mining activities impact on the local economic geography? Although extracting structures are compelled by the ore locations, where were the ore treatment and metallurgical structures set? What was the pressure of these activities on the lumber resources? And finally, where and how did metalworkers and miners live ?Between 1981 and 1996, mining archaeology in Sainte-Marie-aux-Mines had been strongly characterized by a very close relation between archives and fieldwork. Indeed, it particularly allowed an improved interpretation of underground mining networks, benefitting from some rare topographic surveys that have been done during the 16 th c. exploitation 3 . This method, 2 For the best synthesis, see FLUCK P., Mines et fonderies de l'Altenberg. Les leçons des fouilles 1982-1996. Société d'Histoire du Val de Lièpvre, 28 e cahier, 2006, pp. 26-60 3 FLUCK P., Saint-Louis-Eisenthür (Sainte-Marie-aux-Mines, France de l'Est) : sans doute la plus belle mine d'argent de la Renaissance. Bientôt vingt ans d'ouverture au public, 13 e Congrès International TICCIH, Italie (2006) [on line site hal-archives ouvertes]

These operations were managed by P. Fluck, co-director of the CRESAT (Centre de Recherche sur les Economies, les Sociétés, les Arts et les Techniques) of the Upper-Alsace University. Among the main partners, we notice the University of Technology of Belfort-Montbéliard, the geophysical laboratories of the Universities of Strasbourg (Pr. M. Munschy) and Paris VI (Pr. N. Florsch), the CEA -Saclay center, the National Institute for Preventive Archaeological Research (INRAP) and the Pôle Archéologique Interdépartemental Rhénan. From a practical point of view, operations were performed during "Young Volunteers Operations" led by the ASEPAM (Speleological Association for Study and Protection of Ancient Mines) and Mining Heritage Federation.

Most of them in the Archeolabs laboratory, Saint-Bonnet-de-Chavagne (Isère).

The map indexing them indicates 191 pits. A part of them can be seen on fig.5.

Performed on a sawn plank unearthed in the gallery by P. Clerc (INRAP).

DAHM C., LOBBEDEY U., WEISGERBER G., Der Altenberg : Bergwerk und Siedlung aus dem 13. Jahrhundert imSiegerland, Bonn, R. Habelt, 1998, 2 vol.

Dating of basins in the lower part of the Vieux-Saint-Guillaume (first and second half of 15 th c.) area, and the later Pfaffenloch foundry (middle of 15 th c.).

A "Scheidstein" (mortar for ore crushing) was discovered in the same layers.