T Sim

Dacre-Wright

A Practical Motion Planner for All-terrain Mobile Robots

This paper addresses the motion planning problem for wheeled vehicules moving on rough terrains 1 . First, we formalize the placement problem for the case of a rather complex locomotion system consisting of n wheels attached to the robot body by passive suspensions. We next analyze the geometric and kinematic constraints acting on the placements of the robot. Finally, we present a planning method that computes a safe and feasible path between two given placements of the robot. The approach basically consists in searching a path into a graph built incrementally during the exploration of a discrete 3D con guration space. The algorithms have been implemented and simulation results are reported at the end of the paper.

Introduction

There is an increasing interest in developping mobile robots for applications requiring autonomous navigation on natural terrains (planetary exploration 4] 5], public safety robotics and other hazardous missions 8] 9]). This paper addresses the path planning problem for such all-terrain mobile robots.

Research in motion planing has been very active over the past decade. Most of the work has addressed the problem of nding a collision-free path for manipulators or for mobile robots moving in planar environments (see 6] for a detailed survey).

However, motion planning is almost inexistent in the litterature for mobile robots moving on non-planar terrains. There already exists all-terrain mobile robots which use simple path generation techniques for their autonomous navigation. These approches use the terrain model to characterize the traversability of small terrain patches (roughness of the patch, preferred crossing direction,. .. ). In 4] 10], paths are computed from this characterization by gradient propaga-tion techniques. The AMR robot 8] uses a 2D pathplanner similar to the one presented in 2] to plan a path that avoids the patches classi ed as obstacle.

These simple techniques are certainly su cient for the case of benign terrains. However, they will fail to nd a safe path for a robot moving on a rough terrain: in this case, the binary notion of obstacles and non obstacles regions does not hold anymore; the obstacles depend on the ability of the robot to cross over the irregularities of the terrain and their characterization requires to better formalize the constraints acting on the placement of the robot on the terrain.

We are aware of a very few contributions that consider this new path planning problem. A geometric 3D planner is described in 12] for the very simple case of a 3-wheels robot moving on a polygonal terrain. Related work is reported in 9] for the Intelligent Locomotion of a four tiltable track robot. We recently proposed 3] a free-space structuring algorithm based on the characterization of con guration space regions for which the locomotion architecture guarantees terrain irregularities absorption and stability of the vehicle. Finally, Shiller addressed in 11] the problem of nding a time optimal trajectory for a point robot moving on a terrain. The dynamics of the vehicle is used to take into account tip-over constraints.

In this paper, we present an extension of the planning approach proposed in 12]. This extension allows the planner to deal with more complex (and realistic) locomotion structures. We also describe several algorithms which signi cantly improve the e ciency of the planner.

2 General statements

Overview of the Approach

We consider an articulated robot moving on a terrain. The robot consists of a body and n wheels attached to it by passive suspensions. These suspensions allow the wheels to remain in contact with the terrain. However, they also complicate the placement of the robot which results from the interaction between the wheels and the terrain, and from the balance of the suspensions. We consider that a safe trajectory needs to satisfy the following constraints, called placement constraints:

(C1) the wheels remain in contact with the ground. (C2) the suspensions cannot be stretched beyond some limit length. (C3) the robot does not tip-over, which requires that the projection of its gravity center remains inside the convex hull of the projections of all the contact points (called the support polygon). (C4) the robot does not collide with the terrain. Given an initial and a goal placement of the robot, our purpose is to plan a feasible trajectory (with respect to the non-holonomic constraint of the robot) that satis es these placement constraints. The remaining of this section describes the models used to represent the vehicle and the terrain. In section 3, we give a formal statement of the problem and we de ne the three dimensional con guration space CS which will be used to search for a solution. Section 4 details several algorihms that are used by the path-planner presented in the last section.

The Vehicle Model

The body of the robot is modeled by a polyhedron R. We de ne a local frame R rob = (G; u; v; w), where G is the gravity center of the robot, and (u; v; w) are respectively its longitudinal, lateral and vertical axis (see Fig. 1). The n wheels are attached to R by passive suspensions which are modeled by springs. We assume that, when all the springs are in their steady state, the wheels belong to the same plane P S perpendicular to w axis, at height w 0 in the local frame. Then, the coordinates of wheel i are (u i ; v i ; w 0 +l i ) where u i and v i are some xed values related to the geometry of the robot, and l i is the algebraic extension of the spring (l i = 0 being its natural length). That means that the springs always keep a vertical orientation in the robot's frame. Fig. 1 shows an example of a 6-wheels robot, with the parameters detailed above.

Moreover we consider that two control parameters allow to drive and to steer the vehicle: the linear velocity v lin (mesured along u) and the angular velocity v rot (mesured around w).

The Terrain Model

The terrain is known through a discrete elevation map, that is the elevation values z on a discrete regular grid in (x; y). For each patch de ned by this grid, the terrain is modeled by the non planar face z = a:x + b:y + c:x:y + d which interpolates the four corresponding 3D points of the elevation map. The coe cients (a,b,c,d) associated to the patch (i; j) are directly obtained from the elevations z i;j ,z i+1;j ,z i+1;j+1 ,z i;j+1 and from the size ter of the patch. Fig. 2 shows an example of a rough terrain.

M(p) = T (x; y; z)R(w; )R(v; )R(u; ):
Therefore, a complete placement of the robot is given by (6 + n) independant parameters : the 6-dimensional vector p = (x; y; z; ; ; ) for the position of the robot's body the n spring extensions l i , for the wheel positions.

The Con guration Space

Nevertheless, the interactions with the terrain constrain these parameters and therefore reduce the dimension of the robot's con guration space. We consider the three dimensional Con guration Space CS = R 2 S 1 induced by the parameters x; y and of vector p. To any con guration q = (x; y; ) corresponds a complete placement of the robot. Section 3.3 explains how its n + 3 remaining parameters z(q), (q), (q) and the l i (q) can be obtained.

We de ne the admissible con guration space CS free CS as the set of all con gurations q 2 CS for which the associated placement satis es the placement contraints. The planning problem can be therefore formulated as the problem of computing a path connecting two given con gurations and lying in CS free .

The Placement Problem

The placement of the robot results from its weight and the reaction of the ground exerted through the springs. The static equilibrium state is reached when the total energy of the robot is minimized. In the following, we consider a simple energy function, including only the compression energy of the springs:

E = P n i=1 kl i 2
where k is the sti ness coe cient of the springs.

Moreover, we only need to consider the placements which keep all the wheels in contact with the terrain (C1). Let us denote by L i (p) the function which associates to a given value of the vector p, the value of the spring extension l i such that the wheel i is in contact (without intersecting) with the terrain (see Fig. 3).

Therefore, the energy can be expressed as a function of the placement E(p) = P n i=1 kL 2 i (p) and for a given q, the remaining parameters of vector p result from the minimization of this function. Vector (z(q); (q); (q)) is the solution of: The spring extensions l i (q) are obtained from the evaluation of the functions L i (p) for the computed placement. Section 4.1 details more precisely the algorithms which have been implemented to solve this problem.

min z; ; n X i=1 L 2 i (p) (1)

The Nonholonomic Constraint

In order to establish the nonholonomic constraint applying to the motions of the vehicle, let us consider the velocity vector v G of the origin G of R rob . Since the axis of the wheels always remain colinear to the lateral axis v of R rob , the velocity vector v G is perpendicular to v: v G = v lin :( u + w)

This expression is similar to the classical nonholonomic contraint _ y = _ xtan established for the case of a mobile robot moving in a two dimensional workspace (see for example 7] 1]). We recall that such a constraint restricts the set of achievable velocities at any con guration to a two dimensional subspace of the tangent space ( _ x; _ y; _ ). However the system remains fully controllable, that is: any two con gurations lying in the same connected component of CS free can be connected by a path respecting the kinematic constraint (3).

In our case, the equations of the feasible motions are nevertheless more involved than the one obtained for the planar case. We describe in section 4.3 a simple method to produce paths which satisfy approximatively this constraint.

We describe now the algorithms which have been developped to solve some of the problems mentionned above. These algorithms are used by the path-planner presented in Section 5.

Placement Computation

Two algorithms have been implemented to obtain a solution to the placement problem. The rst one, denoted PLACE(q), is based on standard minimization techniques which compute the minimum of a multivariable function (Eq. 1). This method simply requires to evaluate the functions L i (p). This evaluation is described in section 4.1.1. The second algorithm, denoted PLACE APP (p) allows to compute much more e ciently an approximate placement. Section 4.1.2 describes this algorithm and discusses the reliability of the solution.

Computing the L i (p)

For a given value of p, the n functions L i (p) are computed as follow: Let us rst consider the case of a ponctual wheel (identi ed to its center). Its position is determined in R rob by the vector (u i ; v i ; w 0 + l i ).

Thus, the parameter l i allows to move this point along the w axis of R rob . This motion corresponds to a line parametrized in the reference frame by the point (x i ; y i ; z i ; 1) t = M(p)(u i ; v i ; w 0 ; 1) t and the direction n = M(p)(0; 0; 1; 0) t . Let z = f(x; y) denote the analytic expression of the terrain surface. A positive (resp. negative) value of z i f(x i ; y i ) means that for a null value of l i , the wheel lies over (resp. under) the terrain. Therefore the value of L i (p) can be simply determined from the computation of the rst intersection point between the terrain model and the half-line issued from this point (x i ; y i ; z i ) t in direction n (resp. in direction n). The same algorithm can be extented to account for the shape of the wheels by considering a discrete number of \control points" placed on its surface. In this case, L i (p) corresponds to the minimum of the values obtained for each of the control points.

Approximate Placement

The method consists in applying iteratively a least square algorithm to improve an initial estimation [START_REF] Barraquand | Robot Motion Planning: A distributed Representation Approach[END_REF] of the parameters z, and . Each iteration is aimed to decrease the value of E(p). Let z k , k and k denote the value of the placement parameters at the beginning of iteration k. For the corresponding placement denoted p k , the algorithm L i (q) described in the previous section allows to compute the value E k = E(p k ) [START_REF] Barraquand | Robot Motion Planning: A distributed Representation Approach[END_REF] the initial values are 0 = 0 = 0 and z 0 = f (x G ; y G ) and the n contact points P i between the wheels and the terrain. The least square method is then used to obtain the equation of the plane which minimizes the quadratic mean of the distances to the points P i . The new values of the placement parameters are deduced from this plane: k+1 and k+1 are computed such that the vertical axis w of R rob coincides with the plane normal. z k+1 is computed such that all the wheels contact this plane for a null deformation of the springs (see Fig. 4).

The procedure is iterated while E k < E k 1 . When the algorithm stops at iteration k, it simply returns the vector p k 1 and the spring elongations L i (p k 1 ).

Obviously, this iterative method is not garanteed to exactly converge to the solution of equation 1. However, the following remarks justify its interest: First, it is much more e cient than the algorithm PLACE(q). Second, experimental tests performed with several terrain models, show that this simple method returns a placement very close to the one computed with PLACE(q) when the portion of the terrain lying under the robot is relatively smooth. For the case of large terrain irregularities, PLACE APP (q) does not always succeed in decreasing E to its minimal value and therefore a larger error is possibly introduced by the algorithm. However, when this case occurs, some of the computed values l i (q) are generally too large to satisfy condition (C2) and consequently, the placement will not be considered as valid.

Validity of a Con guration

We consider now the problem of checking wether a given con guration q belongs to CS free or not.

Deformation of the Suspensions

Let L max be the maximal deformation allowed for the springs. A con guration q veri es (C2) i : 8i 2 1; n]; jl i (q)j < L max (4)

Stability of the Placement

According to constraint (C3), the vertical projection of G has to belong to the support polygon. The shape of this polygon is clearly a function of , and of the lengths (l i ) i=1:::n . However, we assume that the less stable position is obtained when all the springs are the longest. The stability thus only depends on and , and the subset S ] 2 ; 2 2 verifying this condition can be easily determined [START_REF] Dacre-Wright | Free Space Representation for a Mobile Robot moving on a Rough Terrain[END_REF] . Thus, constraint C2 is veri ed for a given q i : ( (q); (q)) 2 S

(5)

Collision-free Placement

Figure 5: The hierarchical model (levels 5,6,7,8) for the terrain shown in Figure 2 Basically, the collision checker consists in verifying that the polygonal faces5 of the polyhedron R(q) do not intersect any of the underlying surface patches of the terrain model.

In order to improve the e ciency of the algorithm, we construct a hierarchical model (a quadtree) from the surfacic model of the terrain. The root of the quadtree (ie. the rectangloid cell corresponding to the de nition domain of the terrain) is recursively subdivided into smaller cells. To each of these cells, we associate the extremal elevations z min and z max of the corresponding portion of the terrain. Thus, each level of the quadtree determines a set of cuboids that approximate the terrain geometry. The maximal level is obtained when the size of the cells is equal to the resolution ter of the elevation map. Figure 5 shows the higher levels of the quadtree decomposition for the terrain model shown in Figure 2. The following procedure is recursively applied, starting from the root of the quadtree, to e ciently check the non collision between a polygonal face P of the polyhedron R(q) and the terrain. If the upper and lower horizontal faces of the cuboid associated to a given node do not intersect P (see Fig 6-a), then we are certain that P does not collide with the terrain. Similarly, when both faces intersect P (see Fig 6-b) we can directly conclude the existence of a collision. Otherwise, we need to consider a ner approximation of the terrain by analyzing the four descendant of this node. When a leaf of the quadtree is reached and does not allow to conclude [START_REF] Giralt | The French Planetary Rover VAP: Concept and Current Developments[END_REF] , a more expensive test with the corresponding patch surface can be applied.

Computing Feasible Trajectories

Given a constant control (v lin ; v rot ) applied when the vehicle is at con guration q 0 = (x 0 ; y 0 ; 0 ), we want to compute the con guration q 1 = (x 1 ; y 1 ; 1 ) reached after the application of the control during a short time interval dt.

Let R 0 = (G 0 ; u 0 ; v 0 ; w 0 ) be the frame which coincides with R rob when the robot is at q 0 . We simplify the problem by assuming that, during the motion from q 0 to q 1 , G remains in the plane de ned by (G 0 ; u 0 ; v 0 ) (see Fig 7).

Under this assumption, and for xed values of (v lin ; v rot ), the trajectory of G relatively to R 0 corresponds to a circular arc [START_REF] Latombe | Robot Motion Planning[END_REF] in the plane (G 0 ; u 0 ; v 0 ). This circular arc is centered at (0; ; 0) and its radius is given by = v lin =v rot . Therefore, after the time interval dt, the origne G of R rob arrives at position 6 this case rarely occurs [START_REF] Latombe | Robot Motion Planning[END_REF] or a straight line segment when vrot = 0 5 The Path Planner

Principle

Given two con gurations q i and q g , we want to compute a feasible path connecting q i to q g and lying in CS free .

The planner is based on a slighly modi ed version of the planning approach proposed in 1] for the optimal maneuvering of non-holonomic mobile robots moving in a two dimensional workspace. We recall that this approach basically consists in generating a graph G of discrete con gurations that can be reached from q i by applying sequences of xed controls during a short time interval. The xed controls generally correspond to drive forward or backward with a null or a maximal angular velocity which steers the vehicle toward the left or the right: (v lin ; v rot ) 2 f V lin ; V lin g f V rot ; 0; V rot g (6) In order to limit the size of the graph, the con guration space is initially decomposed into an array of m small cuboid cells. This array is used during the search to keep track of small CS-regions (the cuboids) which have already been crossed by some trajectory. The successors generated into a marked cell are discarded and therefore, one node is at most generated in each cell.

We use a classical A algorithm to search the graph G. Starting with q i as current node, this node is expanded ie. its successors are computed and are stored into a list. The next iteration selects the best element of the list, which becomes in turn the current node to be expanded. The procedure is repeated until the goal is reached. six controls de ned in (6), the algorithm tries to compute a neighbor q next as follows: For a given control (v lin ; v rot ) a successor q 0 of q cur is rst computed as indicated in section 4.3. The algorithms described in section 4.1 and 4.2 allow to obtain the corresponding placement and to check the validity of q 0 . If q 0 does not satisfy the placement constraints, the current control does not allow any node creation and the next control is considered. Otherwise, the same process is repeated from q 0 until a cell C next adjacent to C cur is reached. A graph node is associated to the reached con guration q next only if the cell C next has not been yet visited. The corresponding control and its duration are stored into the arc linking q cur to q next .

Neighbors of the Current Node

Cost of the Arcs

The cost assigned to the arc connecting two adjacent nodes is computed from the distance between the two con gurations associated to these nodes. This distance is ponderated in order to penalize the changes of control and the trajectories for which the angles (q), (q) or some of the lengths l i (q) are close to the limits imposed by the placement constraints (C2) and (C3). Therefore, the minimum-cost trajectory returned by the planner realizes a compromise between the distance crossed by the vehicle, the security along the path and a small number of maneuvers.

Choice of the Parameters and Complexity Issues

Note that during the node expansion, the placement constraints are checked in a discrete way after each incremental motion (v lin :dt; v rot :dt). In order to be garanteed that the placement constraints remain satis ed during the incremental motions, the choice of these parameters needs to be related to the resolution ter of the elevation map. They are chosen in such a way that the horizontal motion of any point of the robot is less than ter. An upper-bound dep max of this displacement can be estimated as follows: Let D max be the maximal distance from the origin G of R rob to any point of the robot and let us consider that a linear velocity v lin is applied during the time interval dt with a xed radius of curvature = v lin =v rot . The horizontal motion of any point of the robot can be upper-bounded by dep max = v lin :dt + v rot :D max . Therefore dl = v lin :dt is chosen such that: dl + D max : ter

The richness of the search space (ie. the size of graph G) is directly related to the cell decomposition of CS. Note that several incremental motions are generally needed to compute, for a given control, the neighbor of the current con guration (ie. to move from C cur to C next ). A decomposition into large cells allows the planner to search e ciently for a solution into a reduced search space. For the case of constrained environments, requiring important maneuvering capacities of the vehicle, this reduced search space is unlikely to contain a solution, and the planner needs therefore to be called with a ner decomposition.

Let O(n cs ) be the number of discretization points along each coordinate axis of CS and let O(n 2 ter ) be the number of patches describing the terrain model. The graph G contains in the worst case O(n 3 cs ) nodes (and arcs). Each node expansion requires 8 O(n ter =n cs ) calls to the algorithms described in section 4. Therefore these algorithms are called at most O(n ter :n 2 cs ) times during the search. n ter is given by the precision of the terrain model. n cs can be seen as a \tuning" parameter which allows to realize a compromize between the completeness of the planner and its e ciency.

Simulation results

The algorithms presented above have been implemented in C and the planner runs on a Silicon Graphics Indigo Workstation. We experimented the planner with several simulated robot (with up to 8 wheels) and di erent terrain models. The size of the terrains was approximatively ten times superior to the size of the vehicle. For a discretization of CS into 64 3 cells 9 the computation times ranged from a 10 seconds up to a few minutes to nd a solution (or to report failure). Figures 9 and10 show two examples of trajectories computed by the planner for a six-wheels robot. [START_REF] Laumond | Feasible Trajectories for Mobile Robots with Kinematic and Environment Constraints[END_REF] the number of incremental motions linearly depends on the ratio between size of the CS cells and the length dl which is proportional to the size ter of the terrain patches. [START_REF] Laurette | Supervision and Control of the AMR intervention robot[END_REF] for a unit size vehicle, this correponds to cells whose size is 1/6 along the x and y axis and 5 degrees along the axis 6 Conclusion In this paper, we have addressed the path planning problem for the case of a mobile robot moving on rough terrains. From a formalization of the placement problem and of the constraints acting on the robot placements, we have proposed a discrete con guration space approach to solve the problem. We have described e cient algorithms which have been implemented in a path planner. The experiments show the ability of the planner to solve problems of practical interest in a reasonable amount of time.

Figure 1 :

 1 Figure 1: Model of the vehicle

Figure 2 :

 2 Figure 2: An example of terrain

Figure 3 :

 3 Figure 3: De nition of L i (p)

  v G in the reference frame yields the following constraint: _ xsin _ ycos = :sin

Figure 4 :

 4 Figure 4: Iterative computation of the approximate placement

Figure 6 :

 6 Figure 6: Polygon/quadtree collision checking

Figure 7 :

 7 Figure 7: The kinematic constraint ( :sin ; :(1 cos ); 0) where = v rot :dt corresponds to the angle between u 0 and u.The coordinates of the con guration q 1 are obtained by expressing these values into the reference frame (O; x; y; z) from the matrix M(p 0 ).

Figure 8 Figure 8 :

 88 Figure 8 details how the current node q cur (belonging to the cell C cur ) is expanded. For each of the

This work has been done in the framework of the Automatic Planetary Rover project conducted by the French Spatial Agency. It was partially supported by C.N.E.S. and by the ECC Esprit 3 Program within Project 6546 PROMotion.

j j < 2 ; j j < 2 .

In the current implementation S is simply approximated by an enclosed rectangular domain max; max] max; max]

In fact only the ones whose outer normal points toward z


Alain Hait

Thierry Sim

Motion planning on rough terrain for an articulated vehicle in presence of uncertainties

This paper addresses motion planning for a mobile robot moving on a rough terrain. We proposed in 14] a geometrical planner for a particular architecture of robot. The approach was based on a discrete search technique operating in the (x; y; ) con guration space of the robot, and on the evaluation of elementary feasible paths between two con gurations. The overall e ciency of the approach was made possible by the use of fast algorithms for solving the placement problem and checking the validity of such placements. The contribution of this paper is twofold. First, we study the extension of this approach to an articulated vehicle composed of three axles connected to the chassis by joints allowing the roll and pitch movements. We also propose new algorithms to improve the robustness of the planner by considering additionnal constraints: uncertainties in the terrain model and existence of a free channel around the computed trajectory. Some simulation results presented at the end of the paper show the e ectiveness of the planner which turns out to be both fast and capable of solving di cult problems.

Introduction

Autonomous navigation on natural terrains is a complex and challenging problem with potential applications ranging from intervention robots in hazardous environments to planetary exploration.

Several systems for outdoor navigation have already been developped and demonstrated for speci c tasks, e.g., road following 15], or motion in rather limited environment conditions [START_REF] Thorpe | Toward autonomous driving : the cmu navlab. part i : Perception[END_REF][START_REF] Weisbin | Evolving directions in nasa's planetary rover requirements end technology[END_REF]. The UGV 7], as well as Ratler 8] achieve autonomous runs avoiding obstacles, but not coping to our knowledge with irregular terrain. The adaptive navigation approach currently developped at LAAS within the framework of the EDEN experiment 4] demonstrates fully autonomous navigation in a natural environment, gradually discovered by the robot. The approach combines various navigation modes in order to adapt the robot behaviour to the complexity of the environment.

In this paper, we concentrate on the motion planning algorithms required for the 3D navigation mode This work has been done in the framework of the Automatic Planetary Rover project conducted by the French Spatial Agency. It was partially supported by C.N.E.S. 12] which is applied when the terrain to be crossed is uneven. On such terrain, irregularities are important enough and a binary partition into crossable/forbidden regions is not anymore su cient: the notion of obstacle clearly depends on the capacity of the locomotion system to overcome terrain irregularities and also on speci c constraints acting on the placement of the robot over the terrain. The trajectory planner therefore requires a 3D description of the terrain, based on the elevation map, and a precise model of the robot geometry in order to produce collision-free trajectories that also guarantee vehicle stability and take into account its kinematic constraints.

Although a large amount of work has been devoted to motion planning 10], only a few contributions have been recently reported for the case of a vehicle moving on a terrain. First works 13] 11] addressed the problem of computing time optimal trajectories for a point robot subject to simple dynamic constraints. The planners proposed in 14] 6] 9] consider a geometric model of the robot by using discrete search techniques operating in the con guration space. Other interesting contributions studied the problem of simulating the motions of the vehicle along a precomputed path. The kinematic simulator described in 3] turns the problem into a minimization under constraints. The dynamic behavior of the robot can also be predicted by modeling the physics of the interactions between the wheels and the ground 2] 5]. As proposed in 5], both geometric and physical models could be combined during the planning phase. However, because of the high computational cost, it is generally preferable to favour a two phases approach which simulates the behaviour of the vehicle along a path precomputed by a geometric planner.

The paper is structured as follows: after a brief overview in section 2 of the planning approach of 14], the contributions of the paper, ie. the extension to an articulated vehicle and the integration of uncertainty constraints, are respectively detailed in sections 3 and 4. Finally, some experimental results are presented in the last section.

Given the models of the terrain surface and of the vehicle geometry, the problem is to nd a feasible motion between two con gurations, while respecting a set of geometric constraints related to the safeness of the motion. Typical validity constraints are: stability of the vehicle. collision avoidance of terrain irregularities. mechanical constraints expressing that the contact between the wheels and the terrain can be maintained without exceeding the limits of the articulations. The terrain is described by ruled surface patches dened from an elevation map in z associated with a regular grid in (x; y). The robot has an articulated chassis with passive joints allowing to adapt its shape to the terrain irregularities. Its placement p = (q; r(q)) is de ned by a con guration vector q = (x; y; ) specifying the horizontal position/heading, and by a vector r(q) of the n parameters associated to the values of the joints. The dependancies between the parameters of r and the con guration q come from the contact relations between the wheels and the terrain. The search space is thus reduced to the con guration space CS = (x; y; ) and we denote by C free the subset of CS where the validity constraints are veri ed. The motion planning problem can be classicaly formulated as the problem of nding a path connecting two given con gurations and lying in C free . Determining the validity of a con guration q however requires to compute its associated placement (q; r(q)). The next section details an e cient algorithm for solving this problem for a robot composed of several articulated axles.

The planning approach used in 14] builds incrementally a graph of discrete con gurations that can be reached from the initial position by applying sequences of discrete controls during a short time interval. Typical controls consist in driving forward or backwards with a null or a maximal angular velocity. Each arc of the graph corresponds to a trajectory portion computed for a given control. Only the arcs verifying the placement constraints mentionned above are considered during the search. In order to limit the size of the graph, the con guration space is initially decomposed into an array of small cuboid cells. This array is used during the search to keep track of small CS-regions which have already been crossed by some trajectory. The con gurations generated into a visited cell are discarded and therefore, one node is at most generated in each cell.

The A algorithm used to explore the graph returns a minimum cost trajectory which realizes a compromise between the distance crossed by the vehicle, the terrain di culty along the path and a small number of maneuvers. The heuristic function used to e ciently guide the search requires a preprocessing step: a cost bitmap is rst computed by evaluating for each patch of the terrain model, the slope and the roughness of a circular domain centered at this position, with a radius related to the size of the robot. A potential bitmap is then computed by using classical wave propagation techniques which integrate the cost across the bitmap, starting with a null potential at the goal position of the robot and propagating in priority the lowest cost pixels. During the planning step, the heuristic H(q) is computed, as in 1], by a linear combination of the potential evaluated at two control points of the robot.

3 Application to an Articulated Robot

Model of the robot

Let us consider a three-axle articulated robot (Fig. 1). We de ne a local frame R robot (M;x; ỹ;z) where M is the center of the middle axle, x is the longitudinal axis of the robot and z the vertical axis. Each axle is articulated around the x-axis; ' <axle> is the roll angle of an axle, measured with respect to the horizontal ỹ-axis. The axles are linked by two rigid bodies articulated around the ỹ-axis; F and R are the pitch angles of the front and the rear body, measured with respect to the horizontal x-axis. For this locomotion system, q = (x M ; y M ; ) and the other placement parameters of r are the roll angles ' F ; ' M ; ' R of the axles, the pitch angles F ; R of the bodies and the elevation z M of the middle axle.

The Placement Algorithm

As mentionned earlier, the role of this algorithm is to compute the vector r(q) associated with a given con guration q. After considering the case of a single axle, we show how this basic algorithm can be used for the placement of the chassis. Finally, the last subsection describes a preprocessing step which allows to signi cantly improve the e ciency of the algorithm when used by the planner.

Case of a single axle

Given the (x; y) position of the axle center and its orientation , the placement basically consists in nding the ' angle for which the right and left wheels, W r and W l have the same vertical distance to the terrain 1 . Let dist = F(') be the distance from W l to the terrain when W r is put in contact. Then we have: F(') = 2l sin ' (z l (') z r ('))

(1) where z l ('); z r (')) are the elevations of the wheels contacting the terrain for the xy-positions of their center associated with the angle ' (see Fig. 2). The placement is obtained for the solution ' sol of the equation F(') = 0. This equation cannot be solved analyt- The algorithm Place axle(x; y; ) presented below uses this remark to iteratively re ne an approximation of ' sol . At step i, evaluating z l (') z r (') for a value ' i and applying Eq. 2, allows to get the slope which would be the solution for a planar approximation of the terrain. The next value ' i+1 is computed from ' i and . begin i = 0; ' 0 = 0 dist 0 = F(' 0 ) while dist i > 1. estimate of ' i+1 as if the terrain was at: determination of (cf g.2) and dist = F( ) 2. computation of ' i+1 : the line passing through ( ; F( )) and (' i ; F(' i )) cuts the horizontal axis (F(') = 0) at ' i+1 . dist i+1 = F(' i+1 ) 3. i = i + 1 ' sol = ' i end Tests performed on highly irregular terrains show that function F(') varies very smoothly and that the risk of local minima is very limited between ' = 0 and the solution ' sol . In many cases, the solution is obtained after one iteration.

Placement of the chassis

The placement consists of three steps: the middle axle is rst placed by using the algorithm presented above. The parameters of the front and rear axles are then determined by another algorithm based on the same principle, but adapted in order to introduce the link with the middle axle as an additionnal constraint. Consider the case of the front axle 2 . Knowing the elevation z M of the middle axle, we can compute for a given value of parameter F , the coordinates (x F ; y F ; z F ) of the front axle's center F. Applying Place axle(x F ; y F ; ) determines ' F and the elevation z of F when the front axle is placed on the terrain, regardless of the link with the middle axle. Let G( F ) = z F z denote the di erence between both elevations. The constraint imposed by the link is veri ed for the solution of G( F ) = 0. The values of the parameters F and ' F are computed successively by an iterative algorithm Place other axle similar to the previous one. Each iteration rst evaluates i+1 regardless of the link with the middle axle: is determined from z, z M and the distance between both axles. Then we compute i+1 such that the line passing through ( ; G( )) and ( i ; G( i )) cuts the horizontal axis (G( ) = 0) at i+1 . Note that in this case, the evaluation of G( F ) requires a call to the function Place axle which is then used once for the initialisation and twice for each step of the algorithm. Again the solution is generally found in only one iteration. Figure 3 shows an example of placement computed by the algorithm.

Placement precomputation

The motion planner extensively uses the placement algorithms when evaluating the validity of the elementary motions generated during the search. Moreover the placement of the chassis requires itself several calls to the function Place axle. The aim of this preprocessing step is to signi cantly reduce the computationnal cost of the placement algorithm when used by the planner. It consists in slicing the orientation parameter, and in computing two surfaces denoted S ' (x; y) and S z (x; y) for each slice i . These surfaces respectively correspond to the roll angle and the elevation of the axle when it is placed at position (x; y), with an orientation i . Like the terrain, both surfaces are represented by ruled surfaces patches de ned from a elevation map in ' (or z axle ) associated with a regular grid in (x; y). They are computed by applying the function Place axle at every point of the grid 3 .

The online placement of the chassis simply computes the ' (or z) parameter for a position (x; y; ) of the axle, as follows:

for lying between i and i+1 = i + of the slicing, let S i ' and S i+1

' denote the associated 'surfaces. ' i = S i ' (x; y) and ' i+1 = S i+1 ' (x; y). the roll angle ' is obtained by a linear interpolation: ' = (' i+1 ' i ) i i+1 i + ' i

Validity constraints

These constraints are checked all along the elementary motions generated during the search for limiting the exploration to the C free regions.

Stability

The constraint used to check that some static stability conditions (eg. no tip-over and absence of sliding) are satis ed simply consists in verifying that the global roll and pitch angles of the robot do not exceed some prede ned stability limits. The global roll angle of the robot is de ned by the average of the three roll angles of the axles.

' F + ' M + ' R 3 < ' StabMax
The global pitch angle is de ned by the angle between the horizontal plane, and the line going through the centers of the front/rear axles. The pitch stability constraint is:

StabMin < R F 2 < StabMax

Mechanical constraints

These constraints correspond to angular limits for the relative angle between two successive axles j' M ' R j < ' max and j' M ' F j < ' max and for the angle made by the two bodies (concave or convex con guration of the robot) Min < F + R + < Max 3 to minimize the number of steps, the angle ' is initialized with the value computed for the previous point of the grid.

Collision

The last validity constraint considered in the current implementation guarantees that, except the wheels, the other parts of the locomotion system do not collide with the terrain irregularities. The algorithm described in 14] allows to e ciently check the collision between polygonal faces and the terrain surface. Applying this algorithm to eight rectangular faces is su cient to detect the collisions of the robot's axles/bodies. Each axle is represented by two faces, each being placed under the semi-axle and tangent to it (see Fig. 4). Only the lower faces of the two bodies are considered by the collision checker. Dealing with uncertainties constitutes an important issue of motion planning 4 since robots operating in real world setting are faced to several sources of uncertainties arising from inaccurate models of the environment, control errors and limited sensing accuracy. Consequently, the use of planners which do not explicitly consider uncertainties is limited to some simple situations where the errors remain small with respect to the task tolerances. This is generally not the case in the context of outdoor navigation. First, the terrain model is incrementally built from sensors data and the errors in some areas can be rather important. The complex physical interactions between the wheels and the terrain also result into possibly large control errors, and the robot does not precisely execute the planned motions. This section shows how to improve the robustness of the planner by the introduction of uncertainty constraints in the algorithms described above.

Uncertainties of the Terrain Model

The uncertainties can be propagated through the di erent steps of the terrain modelling in order to produce an elevation map with an error interval associated with each elevation of the grid points. The terrain is therefore represented by two surfaces (T min ; T max ) corresponding to the enveloppes obtained from the minimal/maximal elevations. The problem is to guarantee that the validity constraints imposed to the computed for the maximal R regions of the wheels tested between the lower faces of these volumes and the terrain surface (or with the upper envelope T max if the model uncertainties are also considered).

Experimental results

The algorithms have been implemented in C on a Silicon graphics indigo workstation with an R4000 processor, and the planner has been tested onto a number of di erent terrains. We describe below some of the experimental results obtained during these tests.

The terrain of the rst example is represented by a 100 75 elevation map. For this example, Figure 8 illustrates some intermediate data computed during the preprocessing step: the cost and potential used to guide the search (cf. Fig. 8-b) and surfaces S ' computed for -slices of 0 and 90 degrees (cf. Fig. 8c). Finally, the trajectory computed by the planner is shown in Fig. 8-d. For this example, we also give some indications concerning the performances of the algorithms described in the paper.

Preprocessing step: The CPU times and memory requirements of this step are reported in the following Table . The left/right columns respectively correspond to the case without/with model/control uncertainties. The rst line corresponds to the computation the parameters surfaces for ten -slices covering the interval 0; . The second line includes the cost/potential computation, and also the hierarchical terrain model used by the collision checker. After a preprocessing step of 8 sec., the trajectory of the rst example (Fig. 8-d) was found by the planner after less than one second. In this paper, we considered the di cult problem of planning safe motions for an articulated vehicle moving on rough terrains. The overall approach essentially consists in using discrete search techniques operating in the con guration space of the robot, and in evaluating the validity of elementary motions. This approach is made possible by the use of e cient algorithms to compute the robot's placements and to check their validity. We also proposed techniques which improve the robustness of the solution in presence of model and control errors. Experiments conducted with this planner on various terrains have demonstrated its capacity to solve rather di cult problems in a very reasonable amount of time.

Current work concerns the introduction into the planner of constraints related to the visibility and to the selection of landmarks which could be tracked at execution in order to decrease errors in localization. We also plan to integrate this planner into the outdoor navigation approach 4] currently developped at LAAS within the framework of the \EDEN" experiment, and to validate its e cacy in real world settings.

Figure 1 :

 1 Figure 1: Model of the robot

Figure 2 :

 2 Figure 2: Placement of an axleically since z l ('); z r (') closely depend on the terrain geometry. However one can remark that for the case of a at terrain having a slope , we would have: z l (') z r (') = cos ' tan (2) and that the solution ' sol would equal the slope .

Figure 3 :

 3 Figure 3: Example of placement

Figure 4 :

 4 Figure 4: Collision of an axle with the terrain

Figure 8 :

 8 Figure 8: a/ the terrain model and the initial/ nal congurations. b/ the associated cost and potential functions. c/ the S' surfaces for = 0 and 90deg:. d/ the trajectory found by the plannerUncertainties:The second example illustrates the in uence of the uncertainties on the solutions produced by the planner. A rst trajectory (Fig.9-b) was generated in 2:5sec: without considering the uncertainties. Then we introduced the errors shown by Figure9.c in the terrain model of Figure9.a, and we imposed a 30cm width for the safety channel around the trajectory. The rst trajectory traversing the canyon is not anymore safe, and the solution found by the planner in 14:5sec: is shown in the last Figure.

Figure 9 :

 9 Figure 9: a/ the terrain model and the initial/ nal con gurations. b/ a rst trajectory computed without considering uncertainties. c/ the uncertainties of the terrain model. d/ the trajectory computed in presence of model/position uncertainties

afterwards, the elevation of its center is easily deduced

Only two surfaces are used for all the wheels. They are

planner are satis ed for whatever terrain lying between both enveloppes.

Robot placement

The placement of the robot is now de ned by a vector (q; r(q)) where r represents, at con guration q, the possible intervals for the joints values. These intervals are computed by applying the algorithms described in x3.2 for the wheels placed either on the lower or upper enveloppes:

The minimal (resp. maximal) elevation of an axle is obtained when both wheels are placed on T min (resp. T max ).

The minimal (resp. maximal) value of ' <axle> is obtained when the left wheel is placed on T min and the right one on T max .

The minimal values of F and R are computed for the middle axle (both wheels) placed on T min and the other axle on T max (conversely for the maximal value). For each slice , the preprocessing step is applied four times to produce the surfaces S zmin ,S zmax and S 'min ,S 'max which represent the bounds on the axle parameters as functions of the (x; y) position. During the online placement of the chassis, the middle axle parameters z M and ' M are directly obtained from the precomputed surfaces. The function Place other axle is then applied to these surfaces to compute the parameter intervals ' F ; F and ' R ; R for the front and rear axles.

Validity constraints

The constraints are checked in the worst case situation obtained from the bounds of the placement intervals.

Stability:

The global roll angle is checked for the extreme values of ' <axle> :

The minimal pitch angle is obtained when the rear axle is placed on T max and the front one on T min (and conversely for the maximal value). This value may also vary as a function of the middle axle placement. However, we assume that this variation is small and the middle axle is placed on T min . Let Rtermin (resp.

Ftermin ) denote the pitch angle computed for the middle and rear (resp. front) axles placed on T min (cf.

Fig. 5). Then we have:

Mechanical constraints: The angular limit between two successive axles is checked when the roll angle of one is maximum and the other minimum:

MAX(j' Mmin ' Rmax j; j' Mmax ' Rmin j) < ' max MAX(j' Mmin ' Fmax j; j' Mmax ' Fmin j) < ' max and the minimal angle formed by the bodies is attained for the minimum value of both pitch angles (conversely for the maximum):

Collision Concerning the collision checker, the worst case corresponds to a placement of the robot on T min and a test of intersection with T max .

Uncertainty on the Robot Position

The robustness to the control errors is achieved by imposing the validity of a con guration domain around the planned trajectory. To guarantee the validity of the domain, we introduce the notion of neighbourhood N(q) induced by two parameters ( l; ): at any q, the robot may be translated by l along the segment normal to the trajectory, with an orientation (see Fig. 6). The free con guration space is now de ned as CS 0 free = fq 2 CS = N(q) CS free g. A con guration q is declared valid, only if all the congurations of its neighbourhood satisfy the validity constraints.

Robot placement

For the placement, we have to compute the vector interval r(q) giving the limits of the parameter values for any con guration of N(q). The method proposed to solve this problem consists in transforming the position uncertainty into uncertainties on the elevations of the terrain model.

For a given neighbourhood N(q), the wheel elevations belong to an interval de ned by the extreme elevations, for any horizontal position of the wheel induced by N(q). As illustrated by Figure 7, this position domain can be approximated by a rectangular region R. Its size depends on ( l; ) and on the distance from the wheel center to the origin M of the robot's frame. Although it may overconstraint the problem when the terrain slope is important, ie. the produced placement intervals are larger than the expected ones, the advantage of this method is to handle position uncertainty with a low additionnal cost. Also, it allows to fuse both types of model/position errors in a very simple way, ie. by the union of the elevation intervals resulting from each source of uncertainty. The surfaces T 0 min are computed from the lower terrain enveloppe T min and conversely for maximal case.

Validity constraints

The stability and mechanical constraints are checked as for the case of the model uncertainty. The only adaptation concerns the faces considered by the collision checker. We rst compute the volume swept by the lower faces for the placement domain r computed at con guration q. The collisions are then


Laurent Libessart

Rebiha Anceur

Chafika Djelal

Abdulhadi Aljawish

Michel Millares

Synthesis and characterization of release agent from used cooking oil at the concrete/formwork interface

Keywords: aesthetic aspect, formulation, friction, lubrification, surface tension, used cooking oil

For this preliminary study, the lubricating properties of six formulations containing used cooking oils were tested. The physicochemical properties involved were determined by measuring viscosities at temperatures between 0° and 40°C as well as by calculating adhesion energies. The formwork/concrete interface was then studied on the steel surface by means of both tribological measurements and analysis of facing quality at 1 day and 7 days after stripping. The results obtained were compared with a marketed vegetable-based oil. The physicochemical results revealed attractive parameters despite a viscosity that remained high. The liquid/vapor surface tensions and wettabilities measured satisfied the recommendations, i.e. greater than 30 mN/m and less than 30°. The selected formulation offered the best compromise between composition and the physicochemical recommendations. At the formwork/concrete interface and for a scraped application, satisfactory criteria were derived, with a 35% reduction in friction and an acceptable facing quality for this initial study.

Introduction

Used cooking oils (UCO) are edible oils of either vegetable origin, such as sunflower, rapeseed, and palm, or animal origin. They are used to cook food, with a change in both properties and use [START_REF] Loizides | Circular Bioeconomy in Action: Collection and Recycling of Domestic Used Cooking Oil through a Social, Reverse Logistics System[END_REF]. UCOs mainly stem from the agri-food industry, households, and the hotel, catering, and collective catering sectors [START_REF] Orjuela | Green chemicals from used cooking oils: Trends, challenges, and opportunities[END_REF]. It has been estimated that at least 16.54 million tons (Mt) of UCO are produced annually among the largest producing countries, namely China, Malaysia, the United States, European nations, Taiwan, Canada and Japan [START_REF] Loizides | Circular Bioeconomy in Action: Collection and Recycling of Domestic Used Cooking Oil through a Social, Reverse Logistics System[END_REF][START_REF] Gui | Feasibility of edible oil vs. non-edible oil vs. waste edible oil as biodiesel feedstock[END_REF]. The current world production is actually estimated to lie between 20% and 32% of total vegetable oil consumption Mt/year) [START_REF] Ribau | Quantitative assessment of the valorization of used cooking oils in 23 countries[END_REF]. In Europe, recent estimates suggest that 1.66 Mt of UCO are available, with 0.854 Mt generated from the household sector and 0.806 Mt from the commercial sector [START_REF] Loizides | Circular Bioeconomy in Action: Collection and Recycling of Domestic Used Cooking Oil through a Social, Reverse Logistics System[END_REF][START_REF] Ribau | Quantitative assessment of the valorization of used cooking oils in 23 countries[END_REF][START_REF] Greenea | Analysis of the current development of household UCO collection systems in the EU[END_REF].

Most vegetable oils contain very high concentrations of both monounsaturated and polyunsaturated fatty acids and moreover are usually liquid at room temperature [START_REF] Loizides | Circular Bioeconomy in Action: Collection and Recycling of Domestic Used Cooking Oil through a Social, Reverse Logistics System[END_REF][START_REF] Gui | Feasibility of edible oil vs. non-edible oil vs. waste edible oil as biodiesel feedstock[END_REF]. When these oils are heated in the presence of oxygen or of water, they undergo quite significant degradation. Oils with a high level of monounsaturated fatty acids, such as olive oil and peanut oil, are more stable and can be reused many times after heating, unlike oils with a high level of polyunsaturated fatty acids, e.g. corn oil and soybean oil [START_REF] Ammar | Stability and Change in Fatty Acids Composition of Soybean, Corn, and Sunflower Oils during the Heating Process[END_REF].

In France, the collection of UCOs has become a legal obligation. As of January 1, 2012, "any person who produces or holds large quantities of waste composed mainly of biowaste, is required to set up sorting at the source and biological recovery or, when it is not carried out by a third party, a selective collection of this waste to allow for the recovery of the material in order to limit greenhouse gas emissions and encourage a return to the ground [START_REF] Walker | Chapter 16 -Surface Water Pollution[END_REF]. Indeed, this waste is considered non-hazardous but still cannot be mixed with household waste. In addition, used cooking oils pollute water and groundwater, clog wastewater pipes and disrupt the operation of treatment plant operations. It is estimated that a single liter of oil can contaminate one million liters of water, thus rendering the water unfit for human and animal consumption [8].

For UCOs, restaurateurs, food industry companies, recycling centers and local authorities have since 2016 been required to submit their used cooking oil and waste to a recycling specialist once the oil volume reaches 60 liters per year. The recycling of UCO highlights a company's social and environmental responsibility while reducing both hydrocarbon consumption and greenhouse gas emissions. The combined effects of greater corporate responsibility and the legal obligation to recycle UCO now result in the vast majority of the 100,000 to 150,000 liters of used oil produced each year to be collected and recycled [START_REF] Choe | Chemistry of deep-fat frying oils[END_REF]. These oils are mainly transformed into biofuels [START_REF] Fonseca | Biodiesel from waste frying oils: Methods of production and purification[END_REF][START_REF] Kumar | Use of Waste Frying Oil as C.I. Engine Fuel-A Review[END_REF], in particular biodiesel. It should be noted that since 2001, used oils can no longer be transformed into products intended for human or animal consumption [START_REF] Gui | Feasibility of edible oil vs. non-edible oil vs. waste edible oil as biodiesel feedstock[END_REF]. On the other hand, cosmetics industry uses, in the form of soaps or detergents following biochemical operations [START_REF] Sajid | Biosurfactants: Potential applications as immuno-modulator drugs[END_REF], constitute a significant outlet for oil recovery [START_REF] De | Environmental assessment of four waste cooking oil valorization pathways[END_REF][START_REF] Kim | Valorization of waste-cooking oil into sophorolipids and application of their methyl hydroxyl branched fatty acid derivatives to produce engineering bioplastics[END_REF]. In addition, a proportion of these oils is employed in producing green electricity, via adapted power plants, or else in implementing asphalt [START_REF] Dokandari | Topal A Implementing waste oils with reclaimed asphalt pavement[END_REF].

Another promising avenue for recovery would be as a release agent in the construction industry [START_REF] De Brito | Evaluation of the technical performance of concrete vegetable oil-based release agents[END_REF].

Despite recent studies [START_REF] Spitz | On functional signatures of bare and coated formwork skin surfaces[END_REF][START_REF] Chadfeau | Characterization of the surface of formworks -Influence of the surface energy and surface texture parameters on the demolding forces[END_REF] conducted on formwork surfaces without the application of formwork products, oil-based formulations are still quite widespread in both the building and prefabrication sectors. They facilitate the release of concrete, in yielding good facing quality without leaving any defects on the walls and protecting the formwork surfaces against corrosion to prolong their life. Several families of release agents can be distinguished: mineral-based, vegetable-based, and synthetic-based [START_REF] De Caro | Influence of the nature of demoulding agent on the properties of the formwork/concrete interface[END_REF][START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF].

Oils derived from petrochemicals are remain the most widely used on construction sites and in prefabrication, given their technical efficiency as well as the ease of control over their formulation. However, these oils contain aromatic chemical compounds, which cause of many occupational diseases and contribute to global warming through greenhouse gas emissions. To combat these phenomena, alternatives must be sought that are both more ecological and respectful of sustainable development principles. In this aim, many applications have turned to the use of vegetable oils [START_REF] Uppar | A critical review on vegetable oil-based bio-lubricants: preparation, characterization, and challenges[END_REF], emulsions or recycled vegetable oils. To develop these new products, it is necessary to know the physicochemical mechanisms taking place at the formwork/concrete interface. In addition to recovering UCOs via biodiesel [START_REF] Fonseca | Biodiesel from waste frying oils: Methods of production and purification[END_REF][START_REF] Kumar | Use of Waste Frying Oil as C.I. Engine Fuel-A Review[END_REF] or industrial lubrication (in machine tools) [START_REF] Mannu | Available Technologies and Materials for Waste Cooking Oil Recycling[END_REF], the purpose of this study is to demonstrate their potential use as a release agent. To accomplish this, it is important to analyze the physicochemical stability of UCO (viscosity, wetting, adhesion properties) and verify their ability to reduce friction in the concrete and yield high-quality facings. For this preliminary study, mixtures with additives and a solvent have been produced from UCO in the catering industry. A physicochemical study has been carried out to identify an optimal mixture. In considering the knowledge acquired by our previous research on release agents [START_REF] Libessart | Correlation between adhesion energy of release agents on the formwork and demoulding performances[END_REF][START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF], it was advisable to introduce a streamlined application and a homogeneous film thickness to yield a dynamic viscosity below 30mPa.s, a liquid-vapor (L/V) surface tension above 30 mN/m and a drop (wetting) angle less than 30°. This research proposes an experimental approach based on our previous works [START_REF] De Caro | Influence of the nature of demoulding agent on the properties of the formwork/concrete interface[END_REF][START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF] Libessart | Correlation between adhesion energy of release agents on the formwork and demoulding performances[END_REF][START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF][START_REF] Libessart | Influence of the emulsions to the interface formwork/concrete[END_REF][START_REF] Libessart | Comparative study of the tribological behaviour of emulsions and demoulding oils at the concrete/formwork interface[END_REF].

Friction tests have been conducted to clarify the effectiveness of formulations derived from UCO on the concrete/oil/formwork interface. These tests make use of a plane/plane tribometer designed to study the friction of complex media. A comparison of the tribological behavior of mixtures based on both UCO and a commercial oil has also been performed.

Facing aesthetics are indeed a concern within the construction industry given that concrete walls need to reflect the quality of the completed work; these walls must not contain zero defects, such as color variation or bubbling. Facings are increasingly being left in their raw state, as the absence of finishing saves time and money. One of the parameters influencing facing quality is the release agent and especially its application. The last part of this paper will be devoted to facing quality.

To better utilize the results obtained, these preliminary tests have been carried out on the steel surface. This research was conducted at the Civil Engineering Institute of Bethune (France) within the Civil Engineering and geo-Environment Laboratory (LGCgE) as part of a Master's degree internship held between February and September 2021.

Materials and Method

Formulations based on used cooking oil

A release agent is a mixture of various components, including the base oil, solvent, and additives (anti-corrosion, flow point depressor), aimed at achieving a high-performance formulation to ease concrete stripping without encountering any defects. For purposes of this study, the used cooking oils (UCOs) are generally composed of a mixture of edible oils, based mainly on rapeseed and sunflower. The UCO composition for this study is given in Table 1. to rely on plant esters as the solvent.

To complete these mixtures, various additives are needed in order to obtain a finished product with the desired use properties, which may be corrosion protection, viscosity correction and antifoaming power. On the other hand, these additives can also modify the surface tension characteristics and improve surface wetting properties. During the formulation step, such additives can constitute up to 30% of the total mixture [START_REF]Lubricant Additives -A Practical Guide[END_REF].

The main additives are listed below [START_REF] Mechanic | A Practical Guide To Understanding Engine Oil Additives[END_REF]:

-Anti-corrosion (Ac)
An anti-corrosion additive offers release agents the power to protect surfaces against corrosion by forming a passivated layer; this layer is typically an oxide playing the role of a protective surface film.

-Pour-point depressants (PPD)

Oils are known for their high sensitivity to temperature changes; as a matter of fact, at low temperature they tend to gel and thicken.

PPD ensures that the oil remains more fluid at very low temperatures; these additives are generally polymers or copolymers, such as:

-Copolymer olefins;

-Polymethacrylate polymers;

-Styrene-butadienes.

-Thickener (T)

Thickeners are commonly used to provide adhesion to a fluid lubricant. These additives are generally very high molecular weight polymers. The quantity to be introduced must facilitate the search for a compromise between adhesion and viscosity.

To achieve an optimal formulation that complies with the physicochemical specifications, six mixtures were prepared using used cooking oil mixed with Fatty Acid Ethyl Ester (FAEE) as the solvent and the three additives described above. Given that the proportions to be introduced were unknown for this study, it was decided to adopt average rates of anti-corrosion (Ac) and pourpoint depressant (PPD), set respectively for all the mixtures at 0.1% and 0.5%. The influence of thickness is observed on the formulations Ha-1, Ha-2 and Ha-3. By taking an average value of thickener at 9%, the Hc-1, Hc-2 and Hc-3 formulations vary the solvent while trying to maintain roughly 30% additives. Table 2 details the various mixture compositions. The mixtures were homogenized, and Figure 1 shows the finished products. The color remains homogeneous after thermal solubilization.

To study the effect of the chemical composition of mixtures with or without a solvent, in addition to defining the role of additives and fully understanding their influence on the properties and characteristics of the ultimate mixtures, it was necessary to know their physicochemical properties, such as viscosity, wettability and liquid/vapor (L/V) surface tension. These blends were then compared to a marketed vegetable-based formulation (VO), which was pure vegetable liquid in nature, yellow to light brown in color and with a density of about 0.90.

Formulation of conventional concrete

A CEMI 52.5 CP2 type of Portland cement was used for this investigation, while the concrete employed was of a conventional variety containing 28% cement paste [START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF] with a mass density of 2,388 kg/m 3 . Workability, as measured by the Abrams cone test, is lies between 12 and 14 cm. [START_REF] Libessart | Influence of the emulsions to the interface formwork/concrete[END_REF][START_REF] Libessart | Comparative study of the tribological behaviour of emulsions and demoulding oils at the concrete/formwork interface[END_REF].

This new studied formwork surface was homogeneous and devoid of any defects or particularities as regards its lamination. Its roughness was measured at 1.07 μm.

Mixing was carried out in accordance with Standard NF P 18-404, entitled "Concretes: Mix design, suitability and inspection tests -Casting and storage of test specimens", which specifies the following operating procedure:

Tests were conducted in the laboratory at room temperature (around 20°C).

At construction project sites, the release agent is most often sprayed onto the formwork or spread after spraying with a rubber scraper to remove excess product specific to each individual layer.

For this experimental campaign, only the application followed by scraping was studied in order to control the thickness of the film being applied.

To determine the oil film thickness before testing, pellets cut directly from a formwork were employed (Fig. 2). Spraying was performed with an Ecospray device [START_REF] Mannu | Available Technologies and Materials for Waste Cooking Oil Recycling[END_REF] and then scraped (Fig. 2). with S (m 2 ), ρ (kg/m 3 ), m (kg) and the thickness e (m).

Previous works have shown that values obtained by the weighing method were very close to measurements carried out by PIXE [START_REF] Djelal | Influence of the thickness of demoulding oils on the aesthetic quality of facings[END_REF].

Physicochemical characterization 2.3.1. Rheological properties

The rheological properties of release agents exert a powerful influence on the behavior of the concrete/oil/formwork interface. This influence is directly felt on: wettability, friction stresses at the concrete/formwork interface, and ultimate cladding quality [START_REF] Libessart | Correlation between adhesion energy of release agents on the formwork and demoulding performances[END_REF][START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF]. The viscosity of oils is determined using a HAAKE VT550 single-speed viscometer, fitted with a 1° (PK5) cone. A constant volume of oil (v = 0.6 cm 3 ) is deposited on the plate with a pipette; the cone is then lowered toward the plate. To obtain an accurate measurement, a 5-to 10-min wait time (depending on measurement temperature and after depositing the oil on the plate) is required for the oil to reach the desired temperature. During the testing phase, the temperature must be held constant so as not to bias the reading. For this study, viscosity measurements were conducted at five constant temperatures (0°C, 10°C, 20°C, 30°C and 40°C).

Surface tension

The L/V surface tension of a liquid is correlated with the value of the contact angle formed by a drop on a support [START_REF] Chappuis | Contribution to Study of Wetting -Analysis of a Measuring Method[END_REF]. Contact angles are a readily observable physical manifestation of the more fundamental concepts of energy and surface tension. This insight serves to determine the properties of wettability and adhesion of a film, which in turn makes it possible to predict the properties of a lining or detect the traces of surface pollutants. As part of a theoretical approach, adhesion energy values are calculated based on contact angle data.

It may be considered that the liquid/solid adhesion energy value is representative of the adhesive strength between the liquid and the support.

Young [START_REF] Zisman | Relation of the Equilibrium Contact angle to Liquid and Solid Constitution[END_REF] was the first researcher to derive an equation for the equilibrium of a drop of liquid placed on a given solid. This resulting equation is expressed in the following form:

LV  cos() = SV -LS → LS = SV -LV  cos() ( 2
)
where θ is the contact angle formed by the surface and the plane tangent to the meniscus, SV the solid surface energy, LV the liquid/vapor surface tension et LS the liquid/solid interfacial tension.

The liquid/solid adhesion energy (LS) value is also representative of the adhesive force between a liquid and its support. It is calculated according to Zisman's Equation [START_REF] Mechanic | A Practical Guide To Understanding Engine Oil Additives[END_REF]:

LS = LV  (1+cos()) (3)
To determine the solid/liquid adhesion energy, it is necessary to measure both the contact angle of the oil and the liquid/vapor surface tension.

The liquid/vapor surface tension was measured using Wilhelmy's plate method at 20°C. The device employed is a tensiometer manufactured by the CAD firm fitted with a platinum blade.

According to this method, a thin platinum plate is hooked up to a Kahn scale and then immersed into a liquid contained in a tank. The surface tension is indicated by the meniscus formed along the plate boundary. The measurement accuracy is ± 0.3 mN/m.

The material contact angle was determined using a PGX type of mobile goniometer. This device measures the contact angle at the interface between a liquid drop and the substrate surface where it had been deposited. The studied surface is directly obtained in a new steel formwork. The measurement accuracy is ± 0.3°.

Tribological study

The principle behind this type of measurement device is as follows (see Fig. 3): an interchangeable plate slides between two concrete samples, with plate movement taking place by means of a motor coupled to an auger [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF] Djelal | Analysis of friction and lubrication conditions of concrete/formwork interfaces[END_REF]. The plate speed is controlled by an automaton.

The samples are pressurized by activating jacks, to a pressure of between 50 and 1,000 kPa. The sample holders are cylinders fitted with a hatch for introducing the concrete. A tension sensor hooked up to the plate serves to measure the tangential friction stresses. Fig. 3. Plane/Plane tribometer principle [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF].

The selected parameters retained are those used in our previous studies [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF] Libessart | Comparative study of the tribological behaviour of emulsions and demoulding oils at the concrete/formwork interface[END_REF][START_REF] Spitz | Characterizing tribological behavior of fresh concrete against formwork surfaces[END_REF] and completely mastered on the device. For our experimental campaign, these test parameters replicated jobsite conditions in order to approximate the stresses being exerted on the oil film by the concrete. The casting speed and pressures at the formwork base constitute this study's key parameters. Tests were conducted on a plate cut out from a formwork wall with roughness values of Ra = 1.07 μm.

A speed of 3 m/h (0.84 mm/s) was used for our testing campaign, which corresponds to the speed commonly practiced on worksites.

Formwork heights ranging from 3 to 4.5 m have been evaluated; they correspond to pressures in the range of 75 to 115 kPa.

Aesthetic study

The cladding analysis relies on molds measuring 30*30*30 cm 3 [START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF]. The concrete is cast in three layers and then vibrated at 5 points for 10 seconds per layer using a 40-mm diameter vibrating needle. This vibration step is carried out in five 10-second sequences per layer with the 40-mm needle.

The most significant cladding defect is a color variation, which produces a visual differentiation between large adjacent surface zones [START_REF]Bétons et ouvrages d'art -La maîtrise esthétique des parements en béton[END_REF][START_REF] Lemaire | Evaluating concrete surfaces using an image analysis process[END_REF]. This kind of alteration typically affects concrete over several millimeters of thickness. Two types of color variation exist, namely those between different concrete mixes on a single cladding, and those on the same mix. A rating scale with 7

shades of gray has been developed by CIB [START_REF] Cib | Tolérances sur les défauts d'aspect du béton[END_REF]. French Standard P18-503 also offers a guideline for evaluating the surface appearance of concrete cladding [START_REF] St P | Concrete surfaces and facing. Identification elements[END_REF]. This standard is based on three characterization criteria: flatness, texture (bubbling), and hue. To analyze the cladding and formwork surfaces, the rating criteria selected were those adopted by our team when testing for the influence of mix designs on cladding quality. For this cladding, the rating was determined 24

hours after formwork removal.

The facing aspect (FA), micro-bubbling (MB), dusting (DU), dirtying (DI) and attachment points (AP) are all parameters capable of characterizing formwork removal quality [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF]. Table 4 lists the rating criteria used. The cladding obtained was photographed on Days 1 and 7 following formwork removal. The concrete blocks were released 12 hours after casting and then stored indoors at a temperature of 20°C +/-2°C and constant humidity of 60% +/-5%. The first measurement stage consisted of a general assessment of the surface, complete with snapshots of its overall appearance.

Results and discussion

Viscosity analysis

Measurements were recorded as an average of three readings. The addition of the thickener led to an increase in the dynamic viscosity of the mixtures at low temperature (Fig. 4). This variation is due to the nature of vegetable oils, which are rich in vegetable esters [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF]. These molecules can interact with each other, hence their sensitivity to temperature changes, and such differences may be restrictive when seeking to obtain a homogeneous film since the application by spraying will not be completely controlled, thus making it necessary to scrape the film.

The presence of solvent (Fig. 5) improved the viscosity at low temperature, yielding more stable values closer to those of the commercial formulation. This presence will engender a contribution beneficial to the application. The viscosity value remains high compared to the recommendation of 30 mPa.s at 20°C [START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF]. The viscosity values found in the literature lie between 0.02 Pa.s and 0.05 Pa.s [START_REF] Libessart | Influence of the type of release oil on steel formwork corrosion and facing aesthetics[END_REF][START_REF] Bouharoun | Effect of a superplasticizer on the properties of the concrete/oil/formwork interface[END_REF][START_REF] León-Martínez | Laboratory and field performance of biodegradable release agents for hydraulic concrete[END_REF][START_REF] Barnat-Hunek | Influence of biodegradable release oils on the physical and mechanical properties of ligt-colored architectural concrete[END_REF]. However, Hashin Mohseni's [START_REF] Mohseni | Effect of formwork surface texture features on surface morphology, roughness parameters, and the demolding force of cementitious materials[END_REF] and Loh's [START_REF] Loh | Palm olein lubricates and removes freshly baked concrete from its formwork[END_REF] research on vegetable oils (palm) demonstrated an improved mold release functionality due to its higher viscosity qualities.

This analysis is encouraging for the pursuit of this study.

Continuing the analysis makes it possible to derive the interfacial parameters necessary for an improved adhesion of the oil on the formwork surface.

Surface tension analysis

The corresponding values are given in Table 4. The liquid/vapor surface tensions lie between 34 and 37 mN/m, which correspond to the recommendations promulgated for other release agents [START_REF] Uppar | A critical review on vegetable oil-based bio-lubricants: preparation, characterization, and challenges[END_REF]. It had previously been shown that a minimum value of 30 mN/m made it possible to obtain effective adhesion energy.

Courard et al. [START_REF] Courard | Influence of the reuse of OSB and marine plywood formworks on concrete surface aesthetics[END_REF] reached the same conclusions regarding interfacial properties, i. that adding the thickener is favorable to the L/V surface tension yet degrades wettability. The presence of solvent acts upon the wettability of mixtures, making it possible to retain a good amount of adhesion energy. The mixtures obtained display a higher adhesion energy value than that of the commercial vegetable formulation. In a previous study [START_REF] Woma | Vegetable Oil Based Lubricants: Challenges and Prospects[END_REF] on recycled vegetablebased oils, the presence of solvent had influenced the viscosity in yielding values close to those of a commercial formulation while maintaining stable surface tension properties. The solvent did not improve facing quality.

In considering physicochemical results, the study continues with the Hc-2 formulation, which allows for a compromise between a large quantity of base cooking oil used and the solvent, thereby both stabilizing viscosity and reducing wettability. The weighing measurements provided the oil film thickness values, which lie between 5 and 7 µm for the Hc-2 formulation and between 3 and 5 µm for the vegetable oil (VO).

Friction analysis

To reproduce the implementation of the concrete in the formwork, tests were carried out with a plane/plane tribometer [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF]Lubricant Additives -A Practical Guide[END_REF][START_REF] Zisman | Relation of the Equilibrium Contact angle to Liquid and Solid Constitution[END_REF]. Such tests served to validate the mechanisms at the formwork/concrete interface due to the presence of a physical effect or a chemical effect [START_REF] De Brito | Evaluation of the technical performance of concrete vegetable oil-based release agents[END_REF].

The Hc-2 formulation was to be compared with the marketed vegetable-based formulation (VO).

The evolution in the friction constraints of the concrete and the demolding oil films is displayed in Figure 6.

Fig. 6. Friction stresses as a function of contact pressure For this measurement range, the concrete is submitted to the following Coulomb Law:

f =   P (4)
with f the tangential stress (Pa) and P the contact pressure (Pa).

The results in Figure 6 show great efficiency of the Hc-2 mixture in reducing concrete friction:

the Hc-2 mixture reduces concrete friction by an average of 35% vs. roughly 45% for the vegetable formulation (VO). These results are similar to those reported in previous studies [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF]Lubricant Additives -A Practical Guide[END_REF][START_REF] Zisman | Relation of the Equilibrium Contact angle to Liquid and Solid Constitution[END_REF]. Leon-Martinez et al. [START_REF] León-Martínez | Laboratory and field performance of biodegradable release agents for hydraulic concrete[END_REF] showed similar results on refined oils. Their measurements revealed a reduction in tangential adhesion of 64% compared to a surface free of a release agent.

Bouharoun et al. [START_REF] Bouharoun | Effect of a superplasticizer on the properties of the concrete/oil/formwork interface[END_REF] also exposed the effectiveness of vegetable oils in reducing the friction of self-compacting concrete. For comparison in the field of industrial lubrification [START_REF] Bahari | Friction and wear response of vegetable oils and their blends with mineral engine oil in a reciprocating sliding contact at severe contact conditions[END_REF][START_REF] Pawar | Recent advancements in synthesis, rheological characterization, and tribological performance of vegetable oil-based lubricants enhanced with nanoparticles for sustainable lubrication[END_REF][START_REF] Reeves | The influence of fatty acids on tribological and thermal properties of natural oils as sustainable biolubricants[END_REF],

formulations based on vegetable oil are often studied and exhibit good lubrication performance.

All these studies were carried out on unprocessed products, hence the great interest in pursuing effective with a lower applied thickness. However, the Hc-2 formulation has a thicker film and appears to be more cohesive on the surface. Its high adhesion energy can also pose a constraint on the lubricating effect of the film and therefore limit its effectiveness on friction. These analyses have allowed us to add a criterion to our specifications, namely an adhesion energy of less than 65 mN/m, along with an L/V surface tension above 30 mN/m and a drop angle smaller than 30°.

To complete the action process at the formwork/concrete interface, the slopes of the two straight lines seem to be similar and not parallel to the concrete, which would indicate that UCOs form a double layer (esters and soap), as is typical of vegetable-based formulations. The physical and chemical effects are therefore combined (Fig. 7), as has been demonstrated in previous studies [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF] and confirmed by the research of both Leon-Martinez et al. [START_REF] León-Martínez | Laboratory and field performance of biodegradable release agents for hydraulic concrete[END_REF] and Loh et al. [START_REF] Loh | Palm olein lubricates and removes freshly baked concrete from its formwork[END_REF]. The film is thus more resistant and effective during the passage of concrete. Fig. 7. Organization of the concrete/formwork interface in the presence of vegetable oil [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF] To finalize this initial approach, the facing aesthetics will now be analyzed.

Concrete (hyrophilic environment)

Vegetable oil film

Calcium oleate

Ester molecule Formwork Soap film Aggregate

Analysis of surfaces of molds and concrete facings

Figure 8 shows the surface condition of the mold after stripping. The surface of the formwork with Hc-2 contains more dirt and sticking points; it remains "fatty" and is difficult to clean compared to the commercial formulation (VO). [START_REF] Djelal | Comprehension of demoulding mechanics at the formwork/oil/concrete interface[END_REF][START_REF] Cib | Tolérances sur les défauts d'aspect du béton[END_REF]. Similar and interesting results were obtained from feasibility studies to develop palm olein-based lubricants with a tackifier [START_REF] Loh | Palm olein lubricates and removes freshly baked concrete from its formwork[END_REF] or edible oil-based release oils [START_REF] Barnat-Hunek | Influence of biodegradable release oils on the physical and mechanical properties of ligt-colored architectural concrete[END_REF] with respect to both dismantling and the performance on finished concrete blocks. These outcomes were of higher quality than the facings obtained during a previous study on recycled vegetable industrial oils [START_REF] Woma | Vegetable Oil Based Lubricants: Challenges and Prospects[END_REF]. 5 summarizes results according to the observed criteria. The notation used is the average of 4 surfaces, as derived by two observers. The concrete surfaces reveal little micro-bubbling and dusting. Micro-bubbling was determined by means of image analysis [START_REF] Woma | Vegetable Oil Based Lubricants: Challenges and Prospects[END_REF]. Facing quality improved at 7 days. The phenomenon of concrete maturity [START_REF] Lukpanov | Performance of maturity method for estimation of concrete strength based on cubic specimens[END_REF] leads to an evolution in its color; in fact, the concrete tends to lighten over time. The Hc-2 mixture mainly loses points on formwork surface quality due to a greater presence of fouling.

Conclusion

This initial study of mixtures based on used cooking oil (UCO) as a mold release agent has yielded noteworthy conclusions as well as prospects for further research. First, the physicochemical characterizations showed that the formulated products can behave similarly to commercial formulations. However, the products still need to be optimized in order to improve viscosity and facilitate application. The addition of a thickener is not currently recommended for UCOs.

Indeed, application by spraying alone has not yet been mastered at this stage of the study. The interfacial parameters potentially stand out, given that the tribometer measurements indicate a higher frictional resistance for the Hc-2 oil film (6 μm thick). Film thickness therefore is not the main parameter associated with this study, and moreover it is recommended to limit the adhesion energy to a maximum of 65 mN/m. In addition, vegetable-based formulations involve more of a chemical process by creating a saponification film at the interface. Consequently, it is critical to control the quantity deposited in order to avoid excessive dusting or dirtying.

An analysis in the presence of concrete has offered positive conclusions regarding the friction reduction of the selected Hc-2 product for a scraped application after spraying. The chemical effect is predominant and allowed for effective lubrication. The concrete facings obtained were of good quality at 7 days; however, as mentioned above, the mold surface remained heavily clogged and difficult to clean.

Following this study, it will be necessary to refine the Hc-2 mixture from a physicochemical standpoint to both improve its application (through spraying alone) and verify its stability over time. It would also be worthwhile to quantify the performance of the product relative to steel formwork corrosion by means of electrochemical impedance spectroscopy measurements. It would indeed be interesting to compare the results by measurements on wooden surfaces. Lastly, tests on building sites would need to be carried out to validate its marketing feasibility.

Table 2 . 3 OilFig. 1 .

 231 Fig. 1. Photographs of the various mixtures

Fig 2 .

 2 Fig 2. Sprayed Hc-2 film (a), rubber scraper (b), Scraped Hc-2 film (c),

Fig. 4 .Fig. 5 .

 45 Fig. 4. Dynamic viscosities of mixtures without solvent as a function of temperature

  e. low wettability and high surface tension on steel and plywood formwork surfaces. Results indicate 0

  UCOs. In addition,Reeves et al. [49] demonstrated that lubrication performance is correlated with viscosity and depends on the nature of the oils. Commercial oil remains more

Fig. 8 .

 8 Fig. 8. Surface condition of the molds after stripping: VO on the left, Hc-2 on the right

Fig. 9 .

 9 Fig. 9. Concrete facing obtained after 1 day: VO on the left, Hc-2 on the right

Table 1 . Physicochemical characteristics of the used cooking oil

 1 The goal of this work is to derive a finished product as ecological as possible and the most environmentally friendly over the entire molecular scale. It is therefore preferable

	Parameters	Values
	Acidity index (mg KOH/g)	< 1
	Dynamic viscosity (Pa.s) at 20°C	0.11  0.05
	Average Molar Mass Triglycerides (g/mol)	> 800
	Average Molar Mass Fatty Acid (g/mol)	> 200
	Average length of the carbon chain C

Table 3 .

 3 Concrete mix design

	Concrete	C28
	Paste volume (%)	28
	Cement CEMI 52,5 CP2 (kg/m 3 )	232
	Limestone (kg/m 3 )	77
	Sand 0/4 (kg/m 3 )	838
	Gravel 4/8 (kg/m 3 )	287
	Gravel 6/20 (kg/m 3 )	778
	Water (l)	176
	W/B	0.57
	2.2.1. Implementation protocol

Metal formwork has been adopted for this study, given its extensive use within the building trades; it serves to streamline concrete setting and enhances worksite productivity. Formwork reuse possibilities are substantial for structural elements being repeated throughout a project, e.g. vertical shear walls, floors, columns. The introduction of stiffeners enables extending elements over larger surface areas

Table 4 .

 4 Grading criteria

	Facing Aspect Degree of	Micro-bubbling	Dusting, Dirtying,	Degree of
		importance		Attachment points	importance
	Perfect	9	0/0.2%	None	3
	Excellent	8 / 6	0.4%	Slight	2
	Good	5 / 3	0.6%	A little	1
	Average	2 / 0	0.8%	Normal	0
	Fair	-1 / -3	1%	Many	-1
	Poor	-4 / -6	1.2%	Important	-2
	Very poor	-7 / -9	> 1.2%	Very important	-3

Table 4 .

 4 Interface parameter values

		L/V (mN/m)	 (°)	L/S (mN/m)
	H0	34.5	18.8	67.2
	Ha-1	34.9	23.1	67.0
	Ha-2	35.7	24.9	68.1
	Ha-3	36.9	25.6	70.2
	Hc-1	35.5	18.3	69.2
	Hc-2	35.1	18.1	68.5
	Hc-3	34.6	17.4	67.6
	VO	33.5	15.2	65.8
	3.3. Influence of UCOs at the formwork/concrete interface

Table 5 .

 5 Notation of formwork surfaces and concrete facings

				Concrete facing				Mold surfaces		Total	Total
		FA	FA	MB DU Total /15	Total /15	DI	DU	AP	Total	/24	/24
		(1day)	(7days)		(1day)	(7days)				/9	(1day)	(7days)
					Steel surface (spray application + scraping)
	VO	6	8	2	2	10	12	2	2	1	5	15	17
	Hc-2	4	7	2	1	7	10	1	1	1	3	10	13

Acknowledgment

The authors acknowledge GECCO company for the donation of materials used for experiments.

Conflict of interest

The authors declare that they have no conflict of interest. Partial financial support was received from GECCO company for the Rebiha Anceur's Master's internship.