Simon Wasiela
email: swasiela@laas.fr

Marco Cognetti
email: mcognetti@laas.fr

Paolo Robuffo Giordano

Juan Cortés
email: jcortes@laas.fr

Thierry Siméon
email: simeon@laas.fr

Learned Sensitivity Metrics for Robust and Accurate Motion Planning

 to produce robust global plans, emphasizing the generation of low sensitivity trajectories. However, a bottleneck of this method remains the very high computational cost of the uncertainty tubes. In this paper, we mitigate this problem by proposing a novel framework that first incorporates a Long Short-Term Memory [5] (LSTM) neural network (NN) to provide fast and accurate uncertainty tubes estimation, and then reduces tracking errors at given points on the trajectory. We validate our framework on a full 3D-quadrotor UAV model performing a 'ring-recovering' task requiring high accuracy. Our results show the computational gain of the LSTM-based robust planning and that the subsequent optimization stage significantly improves the accuracy of the trajectory execution.

I. INTRODUCTION

Nowadays, motion planners can generate feasible and globally-optimal paths for high-dimensional systems and complex constraints/environments (e.g. see the recent survey [START_REF] Gammel | A survey of asymptotically optimal sampling-based motion planning methods[END_REF]). However, most planners do not consider the unavoidable presence of uncertainties in the robot/environment model, and of a feedback action that will track the planned trajectories in presence of these uncertainties. This can often lead to a poor robustness and potential loss of optimality at runtime.

Efforts have been made to merge control and planning together. For example, the well known Model Predictive Control (MPC) technique [START_REF] Houska | Robust optimization for mpc[END_REF] provides a "less local" control strategy. This technique consists in re-planning a local optimal trajectory taking into account a state feedback and a prediction of the evolution of the system state over a finite horizon. Nevertheless, MPC remains local in the vicinity of the reference trajectory. On the other hand, the global control-aware motion planner proposed in [START_REF] Tognon | Control-aware motion planning for task-constrained aerial manipulation[END_REF] relies on some coupling between planning and control, but uncertainties are not explicitly considered.

Other approaches based on contraction theory [START_REF] Manchester | Robust direct trajectory optimization using approximate invariant funnels[END_REF]- [START_REF] Singh | Safe motion planning with tubes and contraction metrics[END_REF] or the so-called 'feedback motion planning' [START_REF] Tedrake | Lqrtrees: Feedback motion planning via sums-of-squares verification[END_REF], [START_REF] Majumdar | Funnel libraries for real-time robust feedback motion planning[END_REF] synthesize or rely on a specific robust controller that ensures that the trajectory remains within some uncertainty tubes, which can then be used in global planners as RRT [START_REF] Lavalle | Rapidly-exploring random trees: A new tool for path planning[END_REF]. These methods, Fig. 1: Scenario with a drone that has to grasp a ring. (a) the uncertainty associated with its end-effector position is too large and the execution fails. (b) with a lower uncertainty the robot is able to successfully accomplish the task. however, remain limited to a specific form of control strategy and are often applicable only to specific class of systems for which the controller derivation is feasible in practice.

To overcome some of these problems, the sensitivityaware motion planner (SAMP) [START_REF] Wasiela | A sensitivity-aware motion planner (samp) to generate intrinsicallyrobust trajectories[END_REF] exploits the derivation of the uncertainty tubes in [START_REF] Brault | Tube-based trajectory optimization for robots with parametric uncertainty[END_REF] (based on the so-called closed-loop sensitivity matrix [START_REF] Giordano | Trajectory generation for minimum closed-loop state sensitivity[END_REF], [START_REF] Brault | Robust trajectory planning with parametric uncertainties[END_REF]) to generate globally robust trajectories for any controller and any robot dynamics. However, this planner suffers from the high computational cost of calculating the uncertainty tubes.

The contribution presented in this paper is twofold. We first propose a more efficient sampling-based motion planner (SBMP) relying on a Long Short-Term Memory (LSTM) [START_REF] Hochreiter | Long short-term memory[END_REF] network that quickly and accurately estimates the uncertainty tubes and control input profiles along trajectories. In addition, the proposed framework locally optimizes the planned trajectory together with the controller gains in order to maximize the accuracy at a set of waypoints. Simulation results show the higher computational efficiency of the planning framework. Also, we tested our approach for the scenario shown in Fig. 1 where a 3D-quadrotor with uncertain parameters has to perform an in-flight ring recovery task. The results confirm a better accuracy and robustness of the plan.

The paper is organized as follows. Sect. II first provides a reminder of the closed-loop sensitivity notions, and then describes our machine learning approach. Sect. III presents a framework to generate robust and accurate trajectories, and explains the incorporation of the LSTM-based neural network into a global planner. The dynamics of a 3D quadrotor, the application of the learning method to the latter, and the planning scenario are described in Sect. IV. Simulations results are provided in Sect. V. Finally we draw some conclusions and future directions in Sect. VI.

II. LEARNING SENSITIVITY METRICS

A. Closed-loop sensitivity : Reminder

The notion of closed-loop state sensitivity [START_REF] Giordano | Trajectory generation for minimum closed-loop state sensitivity[END_REF], [START_REF] Brault | Robust trajectory planning with parametric uncertainties[END_REF] quantifies deviations of the closed-loop trajectory of any robot/controller pair against variations of uncertain parameters in the robot model. Consider a generic robot dynamics q = f (q, u, p), q(t 0 ) = q 0 , (

where q ∈ R nq is the state vector, u ∈ R nu the input vector, and p ∈ R np the vector containing (possibly uncertain) model parameters. Also assume presence of a tracking controller of any form to track a reference trajectory r d (a, t) parameterized by vector a s.t.,

ξ = g(ξ, q, a, p c , k c , t), ξ(t 0 ) = ξ 0 u = h(ξ, q, a, p c , k c , t), (2)
where ξ ∈ R n ξ are the internal states of the controller (e.g., an integral action), k c ∈ R n k the controller gains and p c ∈ R np the vector of nominal robot parameters used in the control loop.

In order to quantify how sensible the system is w.r.t. parameter variations, let the state sensitivity matrix Π be defined as (see [START_REF] Giordano | Trajectory generation for minimum closed-loop state sensitivity[END_REF])

Π(t) = ∂q(t) ∂p p=p c ∈ R nq×np , (3)
and the input sensitivity matrix as (see [START_REF] Brault | Robust trajectory planning with parametric uncertainties[END_REF])

Θ(t) = ∂u(t) ∂p p=p c ∈ R nu×np . (4)
These two matrices quantify, respectively, how sensible the states q(t) and the inputs u(t) are w.r.t. variations of p (w.r.t. the 'nominal' p c ) for the closed-loop system (1-2). They do not have in general a closed-form expression, but it is possible to obtain a closed-expression for their dynamics. Therefore, the behavior of Π(t) and Θ(t) is obtained in practice by numerical integration of a first-order differential equation along a planned trajectory.

The sensitivity framework has been extended in [START_REF] Brault | Tube-based trajectory optimization for robots with parametric uncertainty[END_REF] in the case where each parameter p i is assumed to vary within a range δp i centered on the parameter nominal value p ci s.t. p i ∈ [p ci -δp i , p ci + δp i ]. In these conditions, the socalled uncertainty tubes can be computed as the envelope of the perturbed state/input trajectories obtained when the parameters vary in the given range. In order to compute these tubes, let W = diag(δp 2 i ) be a weighting matrix and

∆p T W -1 ∆p = 1, (5)
be an ellipsoid in parameter space centered at p c and semiaxis δp i , with ∆p = pp c . Assuming small variations of the parameters, one has ∆q ≈ Π(t)∆p, and it is possible to Fig. 2: A simplified architecture of the proposed LSTM NN. Blue blocks correspond to the inputs of the NN that are composed of a sequence of states q k and an initial tuple (h 0 , c 0 ). Green blocks refer to the outputs of the NN which are a sequence of radii and actuator's inputs (R q k , R u k , U k ), and the final tuple (h end , c end ).

obtain -see [START_REF] Brault | Tube-based trajectory optimization for robots with parametric uncertainty[END_REF] for details -the corresponding ellipsoids in the state and the control spaces as

∆q T (ΠW Π T ) -1 ∆q = 1, (6)
∆u T (ΘW Θ T ) -1 ∆u = 1, (7)
where ∆q = qq nom , ∆u = uu nom , while q nom (resp. u nom ) is the state (resp. input) evolution of the closed-loop system in eqs. (1-2) in the nominal case (p = p c ). These ellipsoids represent the sets where the states and the inputs can vary in case the parameters vary in the specified ranges. Following the procedure given in [START_REF] Brault | Tube-based trajectory optimization for robots with parametric uncertainty[END_REF], it is further possible to compute the radius r i (t) along the i-th component of the state that bounds its evolution over time. In order words,

q i,nom (t) -r i (t) ≤ q i (t) ≤ q i,nom (t) + r i (t). (8)
A similar derivation can also be done for the input ellipsoid. Such radii were used in [START_REF] Wasiela | A sensitivity-aware motion planner (samp) to generate intrinsicallyrobust trajectories[END_REF] to perform robust collision checking within a motion planning framework. However, their computations rely on the knowledge of Π(t) and Θ(t) that have been shown to be computationally expensive in the context of sampling-based motion planning, resulting in high planning times even for simple problems.

B. LSTM-based learning method

To leverage this computational issue, we propose a learning-based method to quickly and accurately estimate the tube radii in eq. ( 8) and the input profiles in eq. ( 2).

LSTM [START_REF] Hochreiter | Long short-term memory[END_REF] is a recurrent neural network (NN) that has feedback connections encoding past events thanks to the socalled hidden and cell states. LSTM NN has already been used in recent years for motion planning applications, e.g., to quickly predict the surrounding state of the robot [START_REF] Jeong | Surround vehicle motion prediction using lstm-rnn for motion planning of autonomous vehicles at multi-lane turn intersections[END_REF], [START_REF] Everett | Motion planning among dynamic, decision-making agents with deep reinforcement learning[END_REF], or to predict trajectories in sampling based algorithms [START_REF] Nair | Robotic path planning using recurrent neural networks[END_REF]. Since LSTM NNs work very well in processing sequences of data -in particular time series -they perfectly fit with our framework, since the robot trajectory can be discretized in some points (hereafter referred to as state) associated with some time instants, that will be treated as input sequences by the LSTM NN.

A simplified architecture of our NN is presented in Fig. 2, where the tuple (h 0 , c 0 ) represents the initial hidden and cell states, respectively. The input sequence consists of a series of states, denoted with q k , evaluated along a trajectory at a given time step. The output is a sequence consisting of the inputs values U k and of R q k and R u k , that represent the radii of the uncertainty tubes, estimated at the k-th state of the trajectory, along the desired direction of the state and of the input spaces respectively. Finally, the tuple (h end , c end ) corresponds to the hidden and the cell states at the last point of our sequence (i.e., the last state of our trajectory). The importance of such initial and final tuples is discussed in Sect. III-B. Training and prediction results are presented in Sect. V, as well as a discussion on the limitations.

III. ROBUST AND ACCURATE MOTION PLANNING VIA LEARNED SENSITIVITY

METRICS We first present the overall planning framework proposed to generate both robust and accurate trajectories in Sect. III-A. The two components of this framework described next: Sect. III-B shows how to integrate the sensitivity learning method within a sampling-based motion planner, Sect. III-C then explains the accuracy optimization stage.

A. Robust and accurate planning framework (RA-SAMP)

In this section, we present RA-SAMP, a planning framework that generates robust and accurate trajectories. It works in two stages: (i) first, it generates a robust trajectory based on a Robust Sensitivity-Aware Motion Planner (R-SAMP) integrating the LSTM-based computation of the uncertainty tubes ; (ii) second, it optimizes the accuracy at some given points of this trajectory by minimizing the size of the uncertainty tubes at these locations. The motivation behind the second stage is to improve the accuracy of the planned robust trajectory for tasks -e.g., pick-and-place or insertion tasks -where the precision is important only at specific designed locations, as for picking the ring in Fig. 1.

We present RA-SAMP in its most general form in Alg.1. It takes as inputs the list of waypoints list wpt = (w 0 , . . . , w n ) for which the accuracy should be optimized, and the values of the nominal controller gains.

Algorithm 1 RA-SAMP [list wpt , gains init ] 1: {π tot , gains best } ← {∅, gains init } ; 2: for (i = 1; i < len(list wpt ); i = i + 1) do 3:

π i ← R SAM P (list wpt (i -1), list wpt (i)); 4:
π tot ← π tot + π i ; 5: end for 6: {π tot , gains best } ← A Optim(π tot , gains best ); 7: return {π tot , gains best };

The first step of the algorithm consists in generating robust trajectories between successive waypoints in the list (line 3 of Alg. 1) by means of a SBMP framework called R-SAMP that utilizes our learning approach. These trajectories are concatenated into a global one, interconnecting all the waypoints (lines 2-5 in Alg. 1).

Then, the trajectory from R-SAMP is locally modified by A-Optim (line 6 in Alg. 1), an algorithm whose aim is to optimize the accuracy at given waypoints along the input trajectory. In particular, this algorithm samples, at each iteration, both the trajectory from R-SAMP and the controller's gains, modifying the former in order to minimize the uncertainty at the waypoints. The outputs of the algorithm are then: (i) a robust trajectory where the accuracy is maximized at the desired waypoints; (ii) the optimal controller gains.

Note that, even if R-SAMP benefits from the neural network, A-Optim cannot employ it because the controller gains are different from those used for training the network.

B. Robust sensitivity-aware motion planning (R-SAMP)

In this section, we describe how the learned uncertainty tubes can be incorporated in any tree-based SBMP in order to generate a robust sensitivity-aware motion planner (R-SAMP). As discussed before, one issue for computing the sensitivity metrics along a given trajectory comes from the possibly high computational time of the numerical integration of the dynamics for obtaining Π(t) and Θ(t). This time might span from tens of milliseconds to several seconds -depending on the trajectory duration -and it sensibly increases the planning time for a SBMP. Moreover, an additional problem -that is specific when integrating the sensitivity machinery within a SBMP -comes from the fact that, for computing the sensitivity for a given node of a SBMP, the overall path for arriving at that node is needed.

However, this is not a problem for our framework thanks to the LSTM network, that naturally encodes this information within the hidden and the cell states. To this aim, these states are saved for each node of the tree built by the SBMP. Then, when expanding a node, the starting hidden and cell states (as for the tuple (h 0 , c 0 ) of Fig. 2) are already available from previous iterations, and the final ones (h end , c end ) are embedded within the node generated by the expansion. This last tuple can then be reused in future extensions as the initial condition tuple (h 0 , c 0 ). Note that such mechanism of using the tuples (h, c) limits its validity to tree-based planners (e.g., [START_REF] Karaman | Sampling-based algorithms for optimal motion planning[END_REF]- [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF]), where each node has a single parent. Therefore, planners whose nodes may have multiple parents (e.g., PRM [START_REF] Kavraki | Probabilistic roadmaps for path planning in high-dimensional configuration spaces[END_REF]) cannot employ such mechanism.

The LSTM network is used by the tree-based planner inside the function RobustCC N N whose pseudocode is reported in Alg.2. Its role is to validate the trajectory provided as input, together with the tuple (h 0 , c 0 ) of the first trajectory state. The outputs of this function are a boolean value (validity) that specifies if the trajectory is valid or not, and the tuple (h end , c end ), computed for the final state of the validated trajectory. The trajectory to be checked (π) is first discretized (π d ) using a time step ∆T (line 2). Then, all the radii and the inputs profiles (R q , R u , U ) on this trajectory are predicted by the LSTM network by means of the SensiNN function (line 3 in Alg. 2). This function takes into account the initial trajectory conditions encoded in the tuple (h 0 , c 0 ), and it returns the above-mentioned radii and inputs, together with the pair (h end , c end ) by using the LSTM network.

For each state q k of the discretized trajectory, the function IsValid (line 5 in Alg. 2) performs a robust collision checking, testing if there are no collisions despite the state uncertainty, and if the inputs are within some bounds that the system can exert. Since the first operation is known to be computationally expensive, the input bounds are tested first and, in case they are respected, the collisions are checked between the robot and the environment.

Algorithm 2 RobustCC N N [π, (h 0 , c 0 )] 1: validity ← true; 2: π d ← DiscretizedT raj(π, ∆T ); 3: {R q , R u , U, (h end , c end )} ← SensiN N (π d , (h 0 , c 0 )); 4: for each q k in π d do 5: if not IsV alid(R k u , U k , R k q , q k ) then 6:
validity ← f alse;

7:

break;

8:

end if 9: end for 10: return {validity, (h end , c end )};

Note that this robust collision checker can be employed within any tree-based planner. An example on how to include RobustCC N N for the case of a standard RRT planner is given in Alg. 3 with the pseudocode of the R-SARRT function, as a particular instance of R-SAMP planner. The same notation is used in Sect. V. As shown in lines 7-12 of Alg. 3, a valid output from RobustCC N N simply corresponds to a successful extension from a node, and the final state of the trajectory is inserted in the tree as a new node, storing in it also (h end , c end ).

Algorithm 3 R-SARRT [q init , q goal ] 1: T ← {q init , q goal } ; 2: for k = 0 to K do 3:

q rand ← Sample(); 4:
q near ← N earest(T, q rand );

5:

π ← Steer(q near , q rand );

6:

(h 0 , c 0 ) ← q near .getHidden();

7: {valid, (h end , c end )} ← RobustCC N N (π, (h 0 , c 0 )) 8:
if valid then 9: q rand .setHidden(h end , c end ); T.addV ertex(q rand ); 11:

T.addEdge(q near , q rand ); end if 13: end for 14: return T ;

C. Accuracy optimization (A-Optim)

The choice to use a local optimization is justified by the cost function considered in order to optimize the accuracy at desired waypoints. Indeed, the latter is defined as:

c = E[R q ] + V[R q ] (9)
which aims at minimizing the average size of the radii and their variance at each desired waypoints. The variance is considered in this cost function so that the minimization of a radius at a given point does not lead to a growth of another radius at another waypoint. This function is then neither additive (i.e considering two trajectories (π 1 , π 2 ), the cost of their concatenation c(π 1 |π 2 ) ̸ = c(π 1 ) + c(π 2 )), nor monotonic, which makes it impossible to optimize in most global planners. This cost function is then optimized within the A-Optim method while other cost function can be optimized in the R-SAMP (e.g. path length). Given that we do not have the analytic form of the cost function derivatives and that estimating them would be expensive, the accuracy optimization has to be performed by a derivative-free (or black-box) method, e.g., the random shortcut algorithm [START_REF] Geraerts | Creating high-quality paths for motion planning[END_REF].

IV. APPLICATION TO A 3D-QUADROTOR

In Sect.IV-A, we introduce the scenario on which we tested our framework, using a quadrotor as robotic platform. Then, in Sect. IV-B, we explain how we learned the uncertainty tubes for the quadrotor case.

A. 3D-quadrotor application and planning scenario

The dynamic model of the robot is the same full 3D quadrotor model as described in [START_REF] Brault | Tube-based trajectory optimization for robots with parametric uncertainty[END_REF]. The tracking controller considered in this work is the so-called Lee (or geometric) controller [START_REF] Lee | Geometric tracking control of a quadrotor uav on se(3)[END_REF] where the control inputs are the squared rotor speeds u = [ω 2 1 ω 2 2 ω 2 3 ω 2 4 ] T . An in-flight ring recovery task is considered for testing our accurate optimization framework. In particular, the quadrotor is tasked to recover some rings by means of a perch mounted along its x-axis, as depicted in Fig. 1. The task is performed in the environment shown in Fig. 3, in which the robot must first recover 3 rings in the departure room (red rectangle in the figure), then it must pass through a window of dimension 1.5m × 1m (blue rectangle) for reaching the second room (green rectangle) and collecting other 4 rings. Finally, it has to return to the departure room, passing again through the small window. In Fig. 3, each ring is represented by a black dot, it has an inner radius of 0.06m and a mass of 50g.

For this scenario we consider the uncertain parameters p = [m g x I x I y I z ] T where m denotes the mass of the system, g x the position of its center of mass along the xaxis of the body frame, and I x , I y , I z , are the principal moments of inertia in the body frame. Recovered rings will remain attached to the perch, modifying the mass of the quadrotor along its x-axis. This justifies why we considered as uncertain g x only and not g y , due to the fact that the mass and its distribution becomes mostly uncertain along the x-axis of the UAV. We chose our nominal parameters as p c = [1.5, 0.0, 0.01, 0.01, 0.02] T and their associated uncertainty range δp = [10%, 5cm, 5%, 5%, 5%] T which represents the percentage variation of the parameters w.r.t. their associated nominal values except for g x whose nominal Fig. 3: Environment of the 'ring recovery task' scenario. The position of the 7 rings is represented by a black dot. The departure room of the drone (red rectangle) contains 3 rings and is connected by a small window (blue rectangle) to a second room room with 4 rings. value is null. The quadrotor trajectories are planned using the Kinosplines steering method of [START_REF] Boeuf | Motion planning[END_REF], and a RRT * algorithm [START_REF] Karaman | Sampling-based algorithms for optimal motion planning[END_REF] minimizing the time-length. Robust collision checking is performed by simply considering a bounding sphere of the UAV increased by the predicted state uncertainty radii R q .

B. Learning uncertainty tubes for the 3D-quadrotor

As mentioned in Sect. II-B, our LSTM-based network predicts the uncertainty tubes' radii and the inputs of the system. In the quadrotor case, the control inputs to be predicted are U = [U 1 , U 2 , U 3 , U 4 ] T , with U i = ω 2 i . Regarding the uncertainty tubes, the LSTM-based network predicts R q =[R x , R y , R z ] T (with R k , k ∈ {x, y, z} the radius of the state uncertainty tube along the {x, y, z}-axis) and R u = [R u1 , R u2 , R u3 , R u4 ] T (with R ui the radius of the input uncertainty tube associated with the i-th control input of the system).

Then, as shown in eq.( 6), the computation of these radii is strongly related to the one of the state/input sensitivity matrices [START_REF] Brault | Tube-based trajectory optimization for robots with parametric uncertainty[END_REF][START_REF] Wasiela | A sensitivity-aware motion planner (samp) to generate intrinsicallyrobust trajectories[END_REF]. Such matrices can be computed numerically by forward integration and thus strongly rely on the Jacobian of the system dynamics. This justifies our choice of using the global velocities and accelerations as well as the yaw angle (Ψ) along the trajectory to be the components of q i =[cos(Ψ) sin(Ψ) qd qd ] T evaluated at time i∆T , where q d =[x y z Ψ] T and ∆T is the same time step that will be used for the collision checking by the planner.

Finally, the LSTM-based network is trained using the MSE criterion on 10.000 randomly generated trajectories with an execution time of 15s. In order to evaluate the accuracy of the network, we generated an evaluation set composed of 1.000 trajectories whose duration is slightly longer (17s) w.r.t. the ones used in the training set. The performance of the learning is illustrated in Table I that reports the accuracy for each radius according to the L1 error norm.

V. SIMULATION RESULTS

This section first presents results showing the quality of the learning-based computation uncertainty tubes and its high efficiency when used for robust motion planning. Then, we illustrate the ability of the proposed RA-SAMP planning approach to generate high accuracy trajectories for the scenario illustrated by Figure 3. or the Π dynamics integration (red), as done in [START_REF] Wasiela | A sensitivity-aware motion planner (samp) to generate intrinsicallyrobust trajectories[END_REF].

A. Performance of the learning-based tube computation

inputs U as well as on the radii R u1 , R u3 , R x , R y while a lower accuracy is observed on R u2 , R u4 , R z . However, note that the absolute values of these radii are much smaller compared to the others. In other words, the relative accuracy (or, equivalently, the relative error, normalized by the reference value) is comparable and similar in all the radii, confirming the validity of the prediction of the LSTM-based network. Moreover, in order to guarantee the prediction robustness, we add for each component of the predicted vector the quartile of its relative error observed on the evaluation set.

Fig. 5 shows the significant performance improvement of using this learning-based prediction within a SBMP for checking the robustness of the local tree expansions using the RobustCC N N function (see Alg. 3), against the previous version [4] integrating the Π dynamics. Results provided for RRT and RRT * compare the number of iterations of the main loop of the algorithm a function of computing time, showing for both cases a significant gain thanks to the proposed learning method. Note that in the RRT case this time gain is constant (45 times faster) because the expansion benefits from the neural network only once per iteration. In the RRT * case, the denser the tree, the more robust collision tests are required for the rewiring connection phase. Therefore, more time is saved by using the learning method. In particular, the gain on the planning time can reach more than two-orders of magnitudes for problems requiring a significant amount of iterations.

Note that the application of the learning method is limited to trajectories having a shorter execution time than those used for training, which constraints the time-length of the local paths used by the planner for the tree expansions. Also, the predictions are only valid for the variation of the parameters δp chosen during the generation of the training set, and the model is trained for given values of the controller gains.

B. Accuracy optimization evaluation

Finally, we demonstrate the efficiency of our accuracy optimization framework on the in-flight ring recovery task scenario by planning trajectories that minimize the uncertainties for the end effector position of the perch at the location of the rings. The rings that are collected by the robot's perch modify the quadrotor mass at run time. The planned trajectories are executed in the Gazebo simulator.

For this experiment, twenty trajectories are planned, using the classic RRT * , a robust version of the latter (R SARRT * ), and a robust version also optimizing the accuracy (RA SARRT * ), where the A-Optim function is a simple robust variant of the shortcut algorithm [START_REF] Geraerts | Creating high-quality paths for motion planning[END_REF] in which the controller gains are also sampled between 50% and 150% of their nominal values. Table II shows the average execution failure1 percentage for each type of trajectory, as well as the average number of rings recovered. We can see that LSTM-based tubes prediction allows to generate more robust trajectories than the standard RRT * , and that the accuracy optimization allows to recover even more rings. Finally, Fig. 6 shows an example of uncertainty ellipsoids before and after the accuracy optimization (i.e., R SARRT * vs. RA SARRT * ) at one ring location. In particular, the uncertainty, that was larger than the radius of the ring, is reduced and becomes smaller after optimization.

VI. CONCLUSION In this paper, we propose a motion planner able to generate trajectories that are intrinsically robust against parametric uncertainties for any robot/controller pair. It is hinged on a LSTM-based learning approach that quickly and accurately estimates the control inputs and the uncertainty tubes of the state and of the inputs. The results confirm the efficiency of the proposed learning method and highlight the impact of integrating it within a motion planner, resulting in a significant reduction of the planning times. Moreover, we showed that our framework is able to locally optimize the planned trajectory in order to minimize the size of the uncertainty tubes of the state at some desired locations, allowing the system to accurately perform a precision task. Future works will focus on considering uncertainties not only at the parametric level, by extending the computation of the tubes for external disturbances. Finally, we aim to experimentally validate the proposed framework on a real robotic platform.

Fig. 4 :

 4 Fig. 4: Example of network predictions along a trajectory (orange) against true values (blue). R x,y,z are expressed in m, and input associated values (R ui , U i ) i=1,4 in rpm.

Figure 4

 4 Figure 4 compares the learning-based prediction of the tubes radii and inputs wrt. their real values. The curves illustrate the excellent accuracy on the predictions of the

Fig. 5 :

 5 Fig.5: Number of (a) RRT / (b) RRT * iterations as a function of planning time using the learning method (green) or the Π dynamics integration (red), as done in[START_REF] Wasiela | A sensitivity-aware motion planner (samp) to generate intrinsicallyrobust trajectories[END_REF].

Fig. 6 :

 6 Fig. 6: Example of uncertainty ellipsoid at the first ring location, before (pink) and after (purple) accuracy optimization, displayed along the XY plane (left) and XZ plane (right). The ring shape is displayed as a black rectangle. Similar results are observed for the other rings.

TABLE

TABLE II :

 II Average number of failures, together with the average number of rings picked over 20 simulations.

An execution failure is characterized by zero ring recovered.

* This work was supported by the project ANR-20-CE33-0003 "CAMP"


F Ossant
email: ossant@med.univ-tours.fr

R Libgot

P Coupé

P Lermusiaux

F Patat

High frequency ultrasound characterization of the coagulation process of whole blood

Keywords: high frequency ultrasound, blood clotting, red blood cell aggregation

This study was designed to characterize the blood clotting process in vitro by following changes in its acoustic properties. High frequency (from 20 to 45 MHz) ultrasound parameters were measured both in double transmission (sound velocity) and backscattering (backscatter coefficient, integrated backscatter coefficient and effective scatterer size) mode. Whole blood samples were collected from healthy volunteers. The protocol to initiate the coagulation process is describe. During the blood clotting process (two hours' observation), acoustic parameters were measured with 15 seconds time resolution for the transmission parameters and 1 minute for the backscattering parameters. The results clearly showed that changes in several acoustic parameters are able to identify several stages in the in vitro blood clotting process, in particular, red blood cell aggregation and blood solidification.

INTRODUCTION

The clinical interest in studying the blood clotting process is very old and wide : clotting deficiency linked to diseases, hematological or physiological parameters governing thrombus formation, thrombogenicity of material used for implants, etc. Ultrasound techniques have the major advantage of using of non-invasive method to describe the blood clotting process through non-transparent tissue or media. Several studies performed in-vitro or in-vivo have shown quantitatively the potentials of several ultrasound parameters such as velocity, attenuation coefficient, and backscatter coefficient [START_REF] Shung | Ultrasonic characterization of blood during coagulation[END_REF]. Nevertheless, these studies were limited by the ultrasound frequency used (<10 MHz) or the small number of acoustic parameters measured.

Our contribution is to propose in-vitro analysis of the interaction of high frequency ultrasound ( from 20 to 40 MHz) with whole blood during the clotting process. This analysis was based on the simultaneous measurement of both transmission and backscatter parameters. These measurements were performed with static blood, with reference to previous studies, notably their of Fatkin et al. [START_REF] Fatkin | Inhibition of red cell aggregation prevents spontaneous echocardiographic contrast formation in human blood[END_REF], which confirmed that low or zero flow maximizes formation of red blood cell (RBC) aggregates. Therefore we studied both whole blood coagulation and sedimentation phenomena with several clotting and anti-clotting products.

II. MATERIALS AND METHODS

A. Transducer characteristics

For backscattering measurement, we used a high frequency echographic device named Dermcup2020 [START_REF] Berson | High-resolution realtime ultrasonic scanner[END_REF]. The probe has a single element focused transducer with linear mechanical scanning and provides a real-time image of 5mmx6mm. The transducer has a 20 MHz central frequency with a 55% bandwidth (Fig. 1). For transmission measurement, we used a 45 MHz focused transducer with a broadband (200 MHz) pulser/receiver (both designed by Panametrics). The characteristics, i.e. impulse response and power spectrum, are shown in Fig. 2. These characteristics were measured in double transmission and after crossing a division (0.5 mm) dividing blood and water chambers in the measurement cell (see part II.B. Measurement cell).

B. Measurement cell

The measurement cell (Fig. 3) was made in PMMA (Plexiglas) material. It comprised a 3 ml blood chamber with a propagation path of 5 mm and with water chambers allowing acoustic coupling of the two transducers. The focal depth of the single transducer was located in the middle of the propagation path. Blood and water chambers were divided by a thin layer of plastic (15µm) in the case of backscattering measurement and a layer of 0.5 mm (PMMA material) in the case of double transmission measurement. Measurements in both transmission and backscattering were performed at the mid height of the blood compartment. To avoid liquid evaporation and to maintain a constant temperature in the measurement cell, a lid of molded silicon was placed in the cell during measurement.

C. Ultrasound transmission parameters

For double transmission measurement, acoustic signals were digitized at 500 Mhz with 8-bit resolution (LC534A, Lecroy). The transmission parameters were measured with 15 seconds time resolution. In order to reduce noise of signals and thus increase measurement precision, acoustic signals were time averaged (averaging was performed with 16 signals).

• Acoustic Velocity

The technique used to measure acoustic velocity (m/s) was a classical differential pulse echo method. The ultrasound pulse was transmitted into the blood sample through the water/blood division and reflected by the bottom of the blood chamber. We then measured the time interval between ultrasound pulses reflected from the sides of the water/blood division in contact with blood (t 1 ) and the bottom of the blood chamber (t 2 ). As the time interval from the water/blood division was constant (for a constant temperature), variations in the differences in the two time intervals was due to changes in velocity in the blood sample along the propagation path (L B ). The blood velocity, V b, can thus be estimate by the equation [START_REF] Shung | Ultrasonic characterization of blood during coagulation[END_REF].

V b =2L B /(t 2 -t 1 ) (1)
We used a cross-correlation method to estimate variations in time interval t 2 . Cross-correlation points were interpolated to increase resolution. Precision in velocity measurement was estimated better than 1 cm/s.

D. Ultrasound Backscattering parameters

For backscattering measurement, RF signals were digitized at 100 MHz with 8-bit resolution. Parameters were estimated in a region of interest (ROI) positioned 100 µm below the 15 µm layer with 224 x 252 pixels (i.e. 8.6 mm 2 ). The focal depth of the probe was positioned in the middle of the ROI. The backscatter parameters were measured with 1 minute time resolution

• Backscatter coefficient

The backscatter coefficient, σ b, represents the quantity of acoustic energy backscattered by a volume of tissue. σ b was calculated following the expression established by Insana et al. [START_REF] Insana | Describing smallscale structure in random media using pulse-echo ultrasound[END_REF]. The ROI was subdivided into 13 windows, each window representing 32x252 pixels in which the signal was thought to be stationary, the windows overlapping by 50 %. In part III Results, we will present σ b value averaged on the 13 values estimated in the 13 windows. This parameter was attenuation and diffraction-corrected. The two parameters below were assessed from the backscatter coefficient.

• Integrated backscatter coefficient (IBC)

The integrated backscatter coefficient, IBC(sr -1 .cm -1 ), was calculated according to equation ( 2

• Effective scatterer size (ESS) Effective scatterer size (µm) was determined from the frequency dependence of the backscatter coefficient following the method described by Insana [START_REF] Fatkin | Inhibition of red cell aggregation prevents spontaneous echocardiographic contrast formation in human blood[END_REF]. As for σ b, 13 ESS values were calculated for each ROI and averaged values are presented in part III.

Note that attenuation coefficient, IBC and EES were estimated in the 10-30 MHz frequency range.

E. Sampling of whole blood and preparation protocol

• Coagulation protocol of the whole blood: Whole blood samples were collected from healthy volunteers into 3.5 ml vacuum sodium citrate tubes (3.2 %). Each tube was initially heated at 37 ± 0.1°C in an incubator and replaced in the incubator with the blood sample for 30 min. After this time, the coagulation process was initiated by adding calcium chloride (100 µl at 0.5M concentration), the prepared blood sample was then transferred to the blood chamber of the cell measurement and acoustic measurement began immediately. All measurements were performed in the incubator at 37 ±0.1°C. Hematocrit and fibrin concentration were determined for each blood sample.

• Sedimentation protocol for whole blood: Whole blood samples were collected from healthy volunteers into 3.5 ml citrated and 6 ml heparin tubes under the same temperature conditions as above. Blood samples were then transferred from heparinized or citrated tubes to the measurement chamber and acoustic measurement began immediately.

III.

RESULTS

The curves shown below are typical of 20 experiments for coagulation and 10 experiments for sedimentation of whole blood.

A. Coagulation of whole blood • Ultrasound transmission parameters

Temporal variations in the acoustic velocity parameters during the coagulation process are shown in Fig. 5 for two volunteers. Several characteristics differentiate of these two coagulation dynamics : the time from which the velocity increased strongly (about 40 and 20 min for volunteers 1 and 2, respectively) and the final velocity value reached at 120 min (1625 and 1610 m/s, respectively).

B. Sedimentation of whole blood

In order to validate and understand variations in the parameter values of the clotting process better, we also measure acoustic parameters during the sedimentation of the whole blood (see II.E). Acoustic velocities as a function of time are shown in Fig. 7, for one volunteer. We first observed that the amplitude of the variations with sedimentation were very low (a few m/s in 140 min). The kinetics of these curves were different, with a quasi linear variation for citrated blood (dashed line) in contrast to heparinized blood (continuous line). IBC as a function of time is shown during blood sedimentation for two volunteers in Fig. 8. Variations in values measured in citrated blood (broken line) were noised and decreased slowly. Values measured in heparinized blood (continuous line) were noised only during the first 40 minutes and then the curve was smooth with a slow decrease.

Finally, we compared ESS values as a function of time for citrated blood (broken line) and heparinized blood (continuous line) for one volunteer (Fig. 9). For citrated blood, ESS values remained at zero (corresponding to Rayleigh scattering) for ten to twenty minutes and then increased to values between 10 and 15 µm with a noised curve. For heparinized blood, values rapidly increased from zero to about 25-30 and then slowly decreased to 20 µm with a smooth curve.

----Citrated blood Heparinized blood

C. Discussion

The findings linked to whole blood sedimentation (Fig. 7,8 & 9) confirmed several phenomena :

• ESS values for heparinized blood immediately increased to reach about 30 µm. This was due to RBC aggregate formation (rouleaux) in heparinized blood, an established hematological phenomenon. The slow decrease in ESS values from about 40 min might be linked to the sedimentation of these RBC aggregates; • As a result of the lack of RBC aggregates with citrated blood (established phenomenon), ESS values increased only after 25 minutes with small size (about 12 µm) and might only have been the effect of sedimentation. • Time velocity variations were low compared to those of the blood clotting process (Fig. 5), because no major mechanical property of blood is affected during sedimentation. Note also that the difference between the kinetics of the two curves in Fig. 7, mentioned above and underlying more rapid sedimentation of heparinized blood, was probably due to the presence of RBC aggregates in this blood sample. The findings linked to whole blood clotting emphasized specific phenomena (Fig. 5,6 & 10):

• Increase in ESS values starting after a few minutes reflected RBC aggregates with an effective size 10 times larger than a RBC; • Sudden increase in velocity specifically emphasized the blood clotting process (blood solidification). The fact that this clotting did not affect ESS is an important result and probably means that clot structures are governed by RBC aggregates preceding clot formation. • Increase in IBC values during the first minutes could be linked to the formation of small RBC aggregates (not measurable at 20 MHz).

IV. CONCLUSION

Measurement of transmission and backscattering parameters allowed us to describe the blood clotting process both in terms of mechanical properties (blood solidification) and spatial distribution of structures (RBC aggregates). Future investigations with standardized blood samples will provide better understanding of stages in the overall blood clotting process.

ACKNOWLEDGMENT

Figure 1 :

 1 Figure 1: Impulse response (left) and associated power spectrum (right) of transducer used for backscattering measurement.

Figure 2 :

 2 Figure 2: Impulse response (left) and associated power spectrum (right) of transducer used for double transmission measurement (Panametrics)

Figure 3 :

 3 Figure 3: Photograph of the measurement cell, the 45 MHz transducer and the 20 MHz probe.

Figure 5 :

 5 Figure 5 : Acoustic velocity as a function of time measured for volunteers 1 (Ht=40,8%) and 2 (Ht=36%) during the coagulation process. • Ultrasound backscatter parameters : Integrated backscatter coefficient (broken line) and effective scatterer size (continuous line) as a function of time during the coagulation process are shown in Fig. 6. Typically, IBC values increased rapidly over the first minutes and then decreased. Initial ESS values were zero (corresponding to Rayleigh scattering) for a few minutes and then increased strongly during the next few minutes to reach a plateau with values typically in the order of 35 µm.

Figure 6 :

 6 Figure 6 : Integrated backscatter coefficient (broken line) and effective scatterer size (continuous line) as a function of time for one volunteer during the whole blood clotting process.

Figure 7 :

 7 Figure 7 : Acoustic velocity as a function of time measured for one volunteer during sedimentation of two blood samples : citrated blood ( dashed line) and heparinized blood (continuous line).

Figure 8 :

 8 Figure 8 : IBC as a function of time measured for two volunteers during sedimentation : citrated blood (Ht=40.6%, broken line) and heparinized blood (Ht=44.3%, continuous line).

Figure 9 :

 9 Figure 9 : ESS as a function of time measured for two volunteers during sedimentation : citrated blood (Ht=40.6%, broken line) and heparinized blood (Ht=44.3%, continuous line).

Figure 10 :

 10 Figure 10 : Velocity, IBC and ESS parameters (normalized linear scale) as a function of time measured for one volunteer (same as in figure 6) during blood clotting process.

ml blood chamber

We thank Professor Y. Gruel (Hematology Dept., Univ. Hospital, Tours) for his help in the implementation of the whole blood clotting protocol.


Denise Dalbosco
email: denise.ddd3@gmail.com

Dell ' Aglio

Tayeh Nadim

INRAE Agroécologie

Responsiveness of the broad bean weevil, Bruchus rufimanus, to Vicia faba genotypes

Keywords: bruchid beetle, faba bean, seed quality, resistance, oviposition, preference, Coleoptera, Chrysomelidae, Fabaceae, agricultural pest, cultivars, breeding

The broad bean weevil, Bruchus rufimanus Boh. (Coleoptera: Chrysomelidae), also called bruchid beetle, is a major pest of Vicia faba L. (Fabaceae) given that larvae develop inside the seeds causing direct quality losses in agricultural products. Recurrent chemical applications are inappropriate because they represent a serious threat to pollinators in general. In addition, biological control approaches that have been attempted so far showed limited effectiveness, which makes studies of methods to control bruchid populations extremely important.

Breeding resistant cultivars is the most adequate approach to achieve efficient levels of pest resistance and promote sustainable agriculture. To explore the mechanisms underlying bruchid resistance, we explored B. rufimanus behavior at different life stages and preference in plant feeding, oviposition, and larval survival into adulthood on a range of susceptible and resistant broad bean cultivars (genotypes), both in greenhouse experiments and in the field.

Our greenhouse results showed that females, compared to males, prefer flowers from some genotypes over others, although the choices made did not correspond with egg-laying preference. Egg-laying preference was also affected by cultivars. This attraction for egglaying was associated with the number of seeds per pod produced by the genotypes. In the field flowering date influenced bruchid infestation. Also the survival of larvae into adulthood was greater in certain genotypes over others. The results of our study lay the groundwork for further analyses to finely dissect V. faba resistance towards bruchids and pave the way for the development of methods to predict potential resistant genotypes in research and breeding programs.

Introduction

Vicia faba L. (Fabaceae), commonly referred to as broad bean or faba bean, is a grain legume crop which provides seeds with high content of proteins, starch, and micronutrients that are widely used as food resource for humans and feed for livestock [START_REF] Crépon | Nutritional value of faba bean (Vicia faba L.) seeds for feed and food[END_REF]. Faba bean also brings environmental and agricultural benefits due to its ability to improve soil fertility by fixing nitrogen and increasing crop yields when used in crop rotations with cereals [START_REF] Köpke | Ecological services of faba bean[END_REF]. Nevertheless, it is sensitive to various abiotic and biotic stresses such as frost, drought, fungal diseases, and insect pests, which reduce crop productivity [START_REF] Torres | Faba bean breeding for resistance against biotic stresses: towards application of marker technology[END_REF]. A common pest worldwide is the broad bean weevil, Bruchus rufimanus Boheman (Coleoptera: Chrysomelidae, Bruchinae), also called bruchid beetle, which infests seeds of leguminous plants. The larvae of bruchids develop in forming seeds of faba bean, causing direct quality losses to the seed industry. Therefore, the study of methods to control bruchid populations is of great economic importance [START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF].

The B. rufimanus life cycle strongly depends on host plant phenology. Adults hibernate during winter, hiding under the bark of trees or leaf litter before coming out to feed on flowering bean crops [START_REF] Dupont | Contribution à l'étude des Populations de la Bruche de la Fève Bruchus rufimanus (Boh). Analyse des Relations Spatio-Temporelles entre la Bruche et sa Plante Hôte[END_REF][START_REF] Tran | Changes in responsiveness to factors inducing diapause termination in Bruchus rufimanus (Boh.) (Coleoptera: Bruchidae)[END_REF]. During spring under natural conditions, the signal to terminate diapause is when the photoperiod reaches 16 h per day and the diurnal temperature reaches on average 16 °C [START_REF] Tran | Interactions between photoperiod and food affect the termination of reproductive diapause in Bruchus rufimanus[END_REF]Roubinet, 2016;[START_REF] Segers | Varietal and environmental effects on the production of faba bean (Vicia faba L.) seeds for the food industry by confrontation of agricultural and nutritional traits with resistance against Bruchus spp. (Coleoptera: Chrysomelidae, Bruchinae)[END_REF]. Males and females colonize faba bean crops and consume their pollen, essential for females to acquire sexual maturation [START_REF] Tran | Changes in responsiveness to factors inducing diapause termination in Bruchus rufimanus (Boh.) (Coleoptera: Bruchidae)[END_REF]. After mating, females lay eggs on the surface of developing pods during the flowering period, and are able to deposit up to 100 eggs while they are sexually active. The emerging larvae burrow into the underlying seeds, devouring the seed endosperm. After pupation in the seeds, the young adult beetles emerge through a hole that they make in the seed before or after harvest, thereby completing the life cycle [START_REF] Hamani | Biological cycle and populations dynamics of bean weevil Bruchus rufimanus (Coleoptera: Bruchinae) on two parcels: Vicia faba major (Seville) and Vicia faba minor (Field bean) in the region of Haizer (Bouira, Algeria)[END_REF]Roubinet, 2016;[START_REF] Hamidi | Physiological synchrony of the broad bean weevil, Bruchus rufimanus Boh., to the host plant phenology, Vicia faba[END_REF][START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF]. These holes are the main damage to the crop, as they affect the dry seed weight and germination rate [START_REF] Titouhi | Status of coleopteran insects infesting faba bean in Tunisia with emphasis on population dynamics and damage of Bruchus rufimanus (Chrysomylidae)[END_REF][START_REF] Ward | The Biology and Ecology of Bruchus rufimanus (Bean Seed Beetle)[END_REF]. Export quality standards are strict; seed lots with >3% and >10% infested seeds are not acceptable for human consumption and for animal feed, respectively (Institut du Végétal Arvalis, 2014).

Previous efforts on the management of broad bean weevils depended on the use of chemical insecticides. However, many of these have been banned, as they have a negative impact on the environment and pollinators. Biological control methods have been attempted but their application is still limited [START_REF] Sabbour | Efficiency of some bioinsecticides against broad bean beetle, Bruchus rufimanus (Coleoptera: Bruchidae)[END_REF][START_REF] Titouhi | Protective effects of three Artemisia essential oils against Callosobruchus maculatus and Bruchus rufimanus (Coleoptera: Chrysomelidae) and the extended side-effects on their natural enemies[END_REF].

Kairomones transmitted from faba bean plants and pheromones from broad bean weevil males have also been studied [START_REF] Bruce | Development of semiochemical attractants for monitoring bean seed beetle, Bruchus rufimanus[END_REF][START_REF] Johansson | Scent Traps and Trap Crops for Broad Bean Weevil (Bruchus rufimanus) Control[END_REF] but totally efficient semiochemical traps have not been reported to date. In this context, breeding resistant cultivars is the most appropriate approach to achieve effective levels of resistance and promote sustainable agriculture.

In faba bean, mechanisms of bruchid resistance have not yet been identified. Although bruchids are known to be attracted by flower chemicals [START_REF] Bruce | Development of semiochemical attractants for monitoring bean seed beetle, Bruchus rufimanus[END_REF], their preferences and the general behavior in response to various plant attractants are poorly understood. From previous studies, some accessions showed more resistance to bruchids than others but the reason for that remains unknown [START_REF] Carrillo-Perdomo | Identification of novel sources of resistance to seed weevils (Bruchus spp.) in a faba bean germplasm collection[END_REF][START_REF] Segers | Varietal and environmental effects on the production of faba bean (Vicia faba L.) seeds for the food industry by confrontation of agricultural and nutritional traits with resistance against Bruchus spp. (Coleoptera: Chrysomelidae, Bruchinae)[END_REF]. A biparental population of V. faba resulting from a cross between a partially resistant genotype (Nova Gradiska) and a susceptible winter variety (Hiverna) was developed and contrasted recombinant inbred lines for their resistance or susceptibility to bruchids in the field could be identified [START_REF] Carrillo-Perdomo | Development of new genetic resources for faba bean (Vicia faba L.) breeding through the discovery of gene-based SNP markers and the construction of a high-density consensus map[END_REF].

As a starting point to explore the mechanisms behind the plant resistance against bruchids and to address key gaps in the current knowledge of this study system, we observed B. rufimanus behavior at different life stages to identify plant preference in (1) feeding, (2) oviposition, and (3) larval survival into adulthood. In the feeding experiment, the role of volatile stimuli from faba bean flowers in the mechanism of plant choice by B. rufimanus was explored in both males and females in a Y-tube apparatus. A multiple-choice oviposition experiment was performed, under glasshouse conditions, to identify plant preference by egglaying females in order to understand the high infestation observed in the seeds of some genotypes in past research, and consequently egg-to-adult survival was also considered. In parallel, we also performed a field experiment using multiple genotypes to access different phenotypic traits impacting bruchid infestation. Our aim was to understand the mechanisms of resistance and susceptibility in faba bean that would help the future management of bruchids.

Material and methods

Insect culture and experimental plants

Bruchus rufimanus adults were collected from infested seeds harvested during the 2020 season in Escacena del Campo, Spain (37°27'17"N, 6°21'46"W). Males and females were stored at 4 °C to keep them in cold diapause for 8 months until the experiment. In order to break the overwinter diapause, insects were left at room temperature for 1-2 h until they were actively moving and looking for food. Sex determination was based on the presence of a small spine on the tibia of the middle leg in male individuals (Yus- Ramos et al., 2014). Males and females were kept separately in a climate chamber (20 °C, 60% r.h., and L16:D8). Fresh faba bean flowers and water were provided 3× a week for 15 days to allow males and females to sexually mature, as the end of reproductive diapause results from the interaction between a 16-h photoperiod and the ingestion of pollen from the host [START_REF] Tran | Interactions between photoperiod and food affect the termination of reproductive diapause in Bruchus rufimanus[END_REF]. To avoid feeding bias, bruchids were fed with pollen of all genotypes at the same time.

Five faba bean accessions showing different levels of B. rufimanus infestation in previous years were selected. The accession 'Nova Gradiska', hereafter referred to as '159B', is a landrace originating from Croatia and presenting partial resistance to the attack of bruchids [START_REF] Carrillo-Perdomo | Identification of novel sources of resistance to seed weevils (Bruchus spp.) in a faba bean germplasm collection[END_REF]. 'Hiverna' is a winter German cultivar susceptible to bruchids. The two recombinant inbred lines, POP1-R1 and POP1-S1, are from the population POP1 derived from the cross between 159B and Hiverna [START_REF] Carrillo-Perdomo | Development of new genetic resources for faba bean (Vicia faba L.) breeding through the discovery of gene-based SNP markers and the construction of a high-density consensus map[END_REF].

Those two lines previously showed a contrasted response to bruchid infestation in field conditions: POP1.R1 (resistant) was one of the less attacked, in contrast to POP1.S1 (susceptible) (E Carrillo-Perdomo, unpubl.) The cultivar 'Acequia', producing large seeds and demonstrated to have a high infestation rate, was selected as a susceptible accession.

Infestation results for 159B, Hiverna, and Acequia were confirmed through a field study conducted in seven localities across Europe by the ERA-NET SusCrop project PROFABA in 2020 (E Carrillo-Perdomo, unpubl.). Plants were grown in the greenhouse under controlled conditions in two separate experiments. The first group of plants was used as pollen supply for adult insects and provided flowers for the flower attractiveness behavioral experiment.

The second batch of plants was grown inside a cage (see below). To ensure a sufficient supply of fresh flowers and pods at a required stage, accessions were sown at various dates. Plants were drip irrigated with a nutrient solution (Liquoplant FD34; Plantin, Courthézon, France) until full saturation, and no pesticides were applied.

Experiments under controlled conditions

Flower attractiveness assay

The attractiveness of the faba bean flowers was tested using a Y-tube glass olfactometer (Figure S1A). This apparatus was inspired by previous studies on preference of beetles to odor sources in dual-choice tests [START_REF] Bartlet | The responses of the cabbage seed weevil (Ceutorhynchus assimilis) to the odour of oilseed rape (Brassica napus) and to some volatile isothiocyanates[END_REF][START_REF] Salisbury | Odour-mediated orientation behaviour of the lily beetle Lilioceris lilii[END_REF]. The experiments were divided in one-flower and two-flower choices. In a one-flower choice assay, faba bean flowers were tested vs. clean air. Naïve adults were tested in order to explore whether insects were willing to move towards the plant and/or had a plant preference before being sexually matured. In a two-flowers choice assay, four faba bean genotypes had their flowers tested against each other (159B, Hiverna, POP1.S1, and POP1.R1) and, because of short flower availability, Acequia was tested only against 159B (see Table S1 for details). Both reproductive states were tested, naïve and mature adults. Naïve adults were tested as soon as they were removed from the cold condition and therefore were still not fed with pollen.

Individuals were tested once as naïve and once as mature in random comparisons, resulting in two releases for each comparison (see Table S1 for details).

Three fresh flowers of each faba bean genotype were cut and placed inside the container at the end of each side of the olfactometer (Figure S1). These containers were open at both sides and the openings were protected by a white mesh, preventing bruchids to reach the flowers and ensuring the air flow. The position of all apparatus and genotypes were switched every test to avoid biases due the positional effects. Also, the apparatus was cleaned and rinsed with distilled water and 70% ethanol to avoid chemical trails. For each experiment, two olfactometers were used at the same time, one with males and the other with females. The experiment was performed at room temperature (20-24 °C) and the apparatus was covered with a green mesh to exclude visual stimuli and to avoid potential influence of light. Ten individuals were inserted at the base of the apparatus and left for 1 h to choose one arm of the tube. At the end of the arm, there was a funnel which let the individuals go in, but prevented them from going back (Figure S1B). At the end, we registered the total number of individuals at each arm of the tube (Table S1).

Flower attractiveness was analyzed using Pearson's χ 2 test by comparing the observed frequencies against 0.5 (expected frequency of random choice, no preference). A generalized linear mixed-effects model (glmer), package lme4 [START_REF] Bates | Fitting linear mixed-effects models Using lme4[END_REF], was used to analyze the influence of sex (female/male) and status (naïve/matured) in the choices taken (observed frequencies, binomial test) using 'compared genotype pair' as random factor and adding w (weights), followed by ANOVA Type II χ 2 test.

Oviposition preference and larval success into adulthood assay

The plants were grown inside one cage (6 × 4 × 2 m) covered with an insect-proof white mesh. In the same cage, there were three replicates for the five genotypes, each consisting of one 4-l pot with three plants of the same genotype, totaling 15 pots inside the cage. The cage was under optimal conditions for bruchids (24 °C day, 18 °C night, 60-70% r.h., and L16:D8 photoperiod). Inside the cage, flowers were manually fertilized and labelled at the moment of fertilization to have the age of pods in days. At the start of the experiment, all five genotypes had flowers and pods at early seed filling stage (ca. 10 days since hand pollination). Sexually matured adult bruchids (30 females and 15 males) were released inside the cage to feed, mate, and oviposit freely. Adults were released in three batches of 10 females and five males every week to maintain the population size and to control for mortality. The cage was monitored daily to assess the number of new eggs laid (per pod, per genotype, and per replicate). New eggs are bright yellow when recently laid, whereas older eggs are opaque white. After larvae penetrate inside the pod, empty transparent shells are left together with dark holes [START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF].

At the end of the experiment (after 25 days), no more active bruchids were found in the cage. Labelled pods were manually harvested when they reached maturity (dry pods).

Pods were stored at room conditions (25 °C, 60-70% r.h., and natural light cycle) for approximately 3 months to favor a homogeneous development of the larval stage into pupae and adults. Thereafter, pods were carefully opened and healthy and damaged seeds were quantified and weighed. A seed was considered damaged if it showed one or more circular emergence holes caused by an adult bruchid [START_REF] Carrillo-Perdomo | Identification of novel sources of resistance to seed weevils (Bruchus spp.) in a faba bean germplasm collection[END_REF][START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF], otherwise the seed was considered healthy.

Whether pod age (days since hand pollination) influenced the laying of new eggs, a glmer model (package lme4) was used with a binary category (pods with or without new eggs) as response factor, pod age as predictor factor, and genotype and replicate as random factors (family binomial). To analyze the difference in eggs laid between genotypes, a linear mixedeffects model (lmer, package lme4) was performed for each week of the experiment using number of eggs as response factor, genotype as predictor factor, and replicate as random factor, followed by post-hoc Tukey tests.

To check the influence of seeds on egg laying and adult survival, we used lmer models (package lme4) using replicate as random factor followed by an ANOVA to analyze whether single application of an insecticide (Karate K, active substances: pyrimicarb (100 g l -1 ) and lambda-cyhalothrin (5 g l -1 ), at 1 ml l -1 ; Syngenta Agro, Basel, Switzerland) was performed on 12 May 2021 to manage an infestation of pea aphid, Acyrthosiphon pisum Harris. In the field, plants were monitored daily for presence of bruchids and phenology traits such as flowering time (days since sowing), flowering duration, and pod setting period. At maturity, plant height was measured and pods were manually harvested (20 July 2021-2 August 2021). Harvested pods were kept at room temperature (25 °C) to favor a homogeneous development of the weevils. One-hundred seeds of each genotype and replicate were randomly selected and weighed for the quantification of healthy seeds, following the same methodology described previously. A seed was considered infested if it showed a circular emergence hole caused by an adult bruchid and/or a hole caused by adults of parasitoid wasps (Braconidae) that develop within the larvae of the seed weevil [START_REF] Carrillo-Perdomo | Identification of novel sources of resistance to seed weevils (Bruchus spp.) in a faba bean germplasm collection[END_REF][START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF].

Finlay-Wilkinson mixed model analysis with the package statgenGxE (van Rossum, 2021) was used to calculate the effects of environment (two sowing dates) and genotypes on the percentage of healthy seeds. A general linear model (GLM) followed by an ANOVA was performed to analyze the influence of phenological traits, such as flowering time, plant height, and 100-seed weight, on bruchid infestation levels. All statistical analyses were done using R (R Core Team, 2021) and graphs were made using the package ggplot2 (Wickham, 2016).

Results

Flower attractiveness

Naïve and sexually mature bruchids were evaluated for their preference of faba bean flowers using Y-tube olfactometers in two sets of experiments. First, we tested the attractiveness of faba bean flowers vs. clean air using only unfed naïve adults. Flowers from five genotypes were considered, separately. Only flowers from one genotype (POP1.R1) significantly attracted females (χ 2 = 7.36, d.f. = 1, P = 0.006; Figure 1A). No particular preference was seen in male bruchids when the flowers were presented (Figure 1B). On the other hand, we found that flowers from Hiverna conferred aversion to naïve adult females (χ 2 = 6.25, P = 0.012; Figure 1A) and Acequia to naïve adult males (χ 2 = 5.4, P = 0.02, both d.f. = 1; Figure 1B).

Interestingly, some bruchids did not choose any arm of the Y-tube (159B: 45%, Hiverna: 20%, POP1.R1: 47%, and Acequia: 17%; Table S1), apart from POP1.S1 in which all individuals made a choice.

In the two-flowers choice experiment, naïve and sexually mature individuals were tested. All flowers were attractive to some degree, as most of the individuals ended up in one arm of the Y-tube in all trials (Table S1, Figure 1C,D). Acequia was preferred over 159B by insects of both sexes (χ 2 = 4.5, d.f. = 1, P = 0.034). For females, 159B was preferred over Hiverna (χ 2 = 10.8, P = 0.001) and POP1.R1 (χ 2 = 6.2, P = 0.013, both d.f. = 1). Also, females preferred POP1.R1 over POP1.S1 (χ 2 = 8.0, d.f. = 1, P = 0.005). The choices differed between sexes but not between statuses (sex: χ 2 = 12.4, P = 0.0004; status: χ 2 = 0.62, P = 0.62; sex*status: χ 2 = 2.8, P = 0.09, all d.f. = 1), with the females being choosier than the males.

Oviposition preference

In a monitored bruchid infestation inside the cage, female adults freely laid eggs in the five selected genotypes, to estimate oviposition preference. After 25 days, 250 pods and 1276 eggs were observed. On average, 42.5 eggs were laid per female, assuming all were actively fertile.

In this multiple-choice test, bruchids had pods from all genotypes at seed filling stages available to oviposit. The pod stage (days since pollination) had influence on the laying of new eggs (z = -7.86, P<0.001), although it varied depending on the genotype (Figure 2A).

In the 1st week of releasing bruchids, females laid more eggs on pods from Acequia (week 1: χ 2 = 22.75, d.f. = 4, P<0.001; Figure 2B). At the end of the experiment, POP1.S1 elicited significantly more B. rufinamus females to lay eggs than any other genotype inside the greenhouse cage (week 4: χ 2 = 42.93, d.f. = 4, P<0.001; Figure 2B). The number of eggs on 159B and Acequia was not different from the number on the other genotypes and the fewest eggs were laid on Hiverna and POP1.R1 (Figure 2B, Table 1).

Egg-to-adult survival

At maturity, and following the monitored bruchid infestation inside a cage in the greenhouse, pods were harvested to assess larval survival rate difference between faba bean genotypes. Some pods collected did not produce seeds, therefore we analyzed 225 pods. A total of 313 larvae successfully finished their development into adults inside the seeds, representing an egg-to-adult survival rate of 25% (Table 1). The genotype with the highest percentage of healthy seeds (98%), and thus exhibiting the lowest egg-to-adult survival rate, was 159B.

Acequia was the most damaged with only 16% healthy seeds having also the highest number of emergence holes (Table 1).

We observed more eggs laid on POP1.S1 pods than on any other genotype. The number of laid eggs is likely influenced by the number of seeds inside each pod, and not by the genotype (seeds: χ 2 = 21.8, d.f. = 1, P<0.001; genotype: χ 2 = 1.1, d.f. = 4, P = 0.88). POP1.S1 is the genotype which produced the highest number of seeds and pods in our experiment (Table 1). The number of damaged seeds was influenced by both the number of eggs on the pod and the genotype (eggs: χ 2 = 13.3, d.f. = 1; genotype: χ 2 = 99.3, d.f. = 4, both P<0.001). The number of eggs had a positive influence on the seed infestation rate in genotypes Acequia, Hiverna, and POP1.S1, but did not influence POP1.R1 and 159B (Figure 3A). The number of emergence holes per seed was higher in Acequia (Table 1). The number of emergence holes could be predicted by the weight of the seed, but not by genotype (weight: χ 2 = 8.7, d.f. = 1, P = 0.003; genotype: χ 2 = 8.9, d.f. = 4, P = 0.063; Figure 3B).

Phenological factors influencing seed weevil infestation in the field

Thirty-two faba bean accessions were evaluated for bruchid resistance in the field in Bretenière, France, in the spring of 2021, including the five genotypes studied in the greenhouse experiments. Two sowing dates were considered. Bruchids were observed on the flowers and pods during a period of 23 days (3 June 2021-25 June 2021). We observed strong associations between phenological traits and bruchid infestation: early flowering and short accessions with large seeds exhibited the highest bruchid infestation rates (Table 2). The influence of flowering time is more pronounced when each sowing is considered. As the second sowing had its flowering time later in the year -start of flowering time on 10 May 2021 (sowing 1) and on 24 May 2021 (sowing 2) -seeds harvested from the second sowing date had a lower infestation rate than seeds from the first sowing (68.3% healthy seeds from sowing 1, 82.4% from sowing 2; ANOVA: F1,63 = 5.14, P = 0.027), confirming again that flowering time and bruchid infestation are strongly positively correlated (Figure 4). The accessions varied in their response to bruchid infestation (Table S3). The results showed a significant genotypic main effect on seed infestation in this field experiment (Table 3).

Genotype explained 58.1% of the variance observed and the heritability estimate was high (0.83).

Discussion

The objective of this study was to answer three main questions: (1) do bruchids have preference for flowers from particular faba bean genotypes? (2) Do female bruchids have preference for laying eggs on pods of particular genotypes? And (3) does egg-to-adult survival rate in B. rufimanus differ between faba bean genotypes? A group of five faba bean genotypes, known from previous field experiments to vary in the percentage of seed infestation by bruchids, was considered. These genotypes were phenotypically evaluated both in the field and under greenhouse conditions. The list of genotypes was extended for the field trial. Results clearly showed that females, compared to males, have preferences for some flowers over others although the choices made did not correspond with the laying preference.

Females also laid more eggs in some genotypes compared to others. This attraction matched the number of seeds produced by the genotypes. Finally, the survival of larvae into adults was higher in certain genotypes over others. Whereas the same strategies identified under greenhouse conditions might apply in the field and contribute to lower infestation rates in some genotypes, flowering time had an important impact on bruchid infestation rate in the field.

Do bruchids have preferences for flowers from specific faba bean genotypes?

The reproduction of B. rufimanus is synchronized with the flowering and fructification cycles in faba bean [START_REF] Medjdoub-Bensaad | Bioecology of broad bean bruchid Bruchus rufimanus Boh. (Coleoptera: Bruchidae) in a region of Kabylia in Algeria[END_REF][START_REF] Hamidi | Physiological synchrony of the broad bean weevil, Bruchus rufimanus Boh., to the host plant phenology, Vicia faba[END_REF]. Therefore, the colonization of faba bean cultures strongly depends on plant flower availability, as pollen consumption provides the insect with nutrition and induces females into reproduction [START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF]. However, we found inconclusive results testing flower attraction. In fact, we could not observe a strong flower preference for a particular genotype by the males, and the female choice results did not correspond with the oviposition preference. In our experiment, floral odor differences might not have been strong enough or the methodology used was not adequate for individuals to have a clear attraction.

Previous experiments in semiochemical attractants with B. rufimanus showed that host-plant floral odors were attractive to both sexes [START_REF] Bruce | Development of semiochemical attractants for monitoring bean seed beetle, Bruchus rufimanus[END_REF][START_REF] Johansson | Scent Traps and Trap Crops for Broad Bean Weevil (Bruchus rufimanus) Control[END_REF].

Here, naïve and mature females were choosier than males, suggesting that they might have a higher sensibility when searching for plants. Moreover, the reproductive state of the adult bruchid was not a significant factor influencing the choice of the flowers, whereas in an experiment with lily beetles, the beetle state (in diapause vs. pre-diapause) was important in moving towards the host plant [START_REF] Salisbury | Odour-mediated orientation behaviour of the lily beetle Lilioceris lilii[END_REF]. It is also unknown whether hostspecific oviposition is driven by larval dietary or female feeding preference [START_REF] Thompson | Evolutionary ecology of the relationship between oviposition preference and performance of offspring in phytophagous insects[END_REF] and bruchids are known to use a diversity of pollen in their diet [START_REF] Hamidi | Physiological synchrony of the broad bean weevil, Bruchus rufimanus Boh., to the host plant phenology, Vicia faba[END_REF].

From our results, flower attractants do not seem to be an important cue for ovipositing females and thus might not explain the difference in bruchid infestation rate between genotypes.

Do female bruchids have preference for laying eggs on pods from particular faba bean genotypes?

Our results showed that some genotypes were significantly more attractive to egg-laying B. rufimanus females than others. Pods from all genotypes and at all development stages were available for adults during oviposition in our experimental design but females laid more eggs on POP1.S1 and fewer on Hiverna and POP1.R1. This partly matched the number of seeds per pod but the genotype POP1.S1 produced also more pods per plant in comparison to other genotypes. This indicates that females might be attracted by some chemical cues elicited by seeds or pods on the plant, strongly signaling that the plant is suitable for egg-laying -the number of seeds or pods on the plant could then influence the strength of the signal.

Bruchid oviposition repellence or attraction to pods might be due to mechanical or chemical defense mechanisms. Secondary metabolites such as volatiles or plant defense responses to insect presence could interfere in oviposition. A study demonstrated that volatiles released by Pisum sativum L. at different phenological stages elicited behavioral responses from both males and females of the pea weevil, Bruchus pisorum (L.), although females could better discriminate volatiles from pods than males [START_REF] Ceballos | Electrophysiological and behavioral responses of pea weevil Bruchus pisorum L. (Coleoptera: Bruchidae) to volatiles collected from its host Pisum sativum L[END_REF]. Pod morphological traits such as surface wax, trichomes, and the toughness of the plant tissues may also play a role in the egg-laying female decision. These traits were not explored here; however, weevil resistance mechanisms and oviposition preference related to wax layers and pod thickness have been documented for B. pisorum (White & Eigenbrode, 2000;[START_REF] Mendesil | Oviposition preference of pea weevil, Bruchus pisorum L. Among host and non-host plants and its implication for pest management[END_REF], and for the pod borer of Vigna unguiculata (L.) Walp [START_REF] Oghiakhe | Pod wall toughness has no effect on cowpea resistance to the legume pod borer Maruca testulalis Geyer (Lepidoptera: Pyralidae)[END_REF] although no clear relationships were found between pod structural traits and pest infestation.

Does egg-to-adult survival rate in Bruchus rufimanus differ between faba bean genotypes?

We observed that Acequia was the genotype in which the survival of bruchids was the highest, resulting in the lowest percentage of healthy seeds, with only 16%. In contrast, 159B was the most resistant genotype with 98% healthy seeds, and although its pods received a fair amount of eggs, the larvae did not penetrate the pod and/or could not penetrate and/or survive in the seed. Genotype 159B is a consistently resistant accession, as it was also ranked as resistant to bruchid infestation in previous work on bruchid infestation in the field [START_REF] Carrillo-Perdomo | Identification of novel sources of resistance to seed weevils (Bruchus spp.) in a faba bean germplasm collection[END_REF]. The genotypes selected for our greenhouse experiments presented similar results in the field (Table S2). The pressure of bruchid infestation was clearly higher in the cage, especially due to optimal growth conditions and the constant release of bruchids, which resulted in high adult survival and high female oviposition.

In our greenhouse experiment, larval survival into adulthood ranged from 1 to 54%, which is not uncommon and matches field results [START_REF] Seidenglanz | Effects of faba bean (Vicia faba) varieties on the development of Bruchus rufimanus[END_REF][START_REF] Pölitz | Studies on biology and infestation dynamics of the bean seed beetle (Coleoptera, Bruchidae: Bruchus rufimanus) in Saxon[END_REF]. A previous field study has shown that larval mortality in the seeds ranged from 64 to 99% and it was the most important factor in reducing bruchid populations, showing that larval development differed greatly between faba bean varieties [START_REF] Seidenglanz | Effects of faba bean (Vicia faba) varieties on the development of Bruchus rufimanus[END_REF]. Several components of seed quality may facilitate or inhibit larval performance. Seed hardness and chemistry -such as toxins, plant defense proteins, feeding deterrents, and low nutrient content -can be effective barriers to the entry and survival of bruchid larvae [START_REF] Janzen | How southern cowpea weevil larvae (Bruchidae: Callosobruchus maculatus) die on nonhost seeds[END_REF][START_REF] Tsialtas | Exit of seed weevil and its parasitoid changed testa color but not phenolic and tannin contents in faba beans[END_REF]Zhang et al., 2021). We did not test longevity of adults, but it could also be affected by chemical barriers. Further experiments testing larval development on a wider range of seeds are necessary to investigate larval and adult mortality and efficient control strategies.

Factors impacting bruchid infestation in the field

The resistance of genotypes to B. rufimanus was evaluated in a field experiment under natural conditions. Despite the particular climatic conditions represented by unusual rain episodes and low temperatures (Figure S2), we found that phenotypic traits significantly affected bruchid infestation. Early flowering accessions provided pods first, and for that reason, the oviposition started earlier and lasted longer on the pods of these genotypes, resulting in a higher rate of bruchid infestation. This outcome has been documented in previous studies in which several faba bean varieties are grown together in the field [START_REF] Seidenglanz | Effects of faba bean (Vicia faba) varieties on the development of Bruchus rufimanus[END_REF][START_REF] Carrillo-Perdomo | Identification of novel sources of resistance to seed weevils (Bruchus spp.) in a faba bean germplasm collection[END_REF][START_REF] Hamidi | Physiological synchrony of the broad bean weevil, Bruchus rufimanus Boh., to the host plant phenology, Vicia faba[END_REF]. Our results also showed that shorter plants were more attacked by bruchids, and this could be simply explained by the fact that spring-type accessions flower earlier than winter-type, being shorter.

Our field result showing that seed size (i.e., 100-seed weight) influences bruchid infestation might be discussed in light of our greenhouse results. Acequia, which also produces large seeds, was the most affected genotype and also had more holes per seed, showing that bigger seeds are an advantage for bruchids, offering more food resource for larvae and tolerating more larvae inside the seed than other genotypes.

There was a significant genotypic main effect on seed infestation in the field experiment. This could be partly explained by the influence of flowering time on bruchid damage to seeds, as this phenological trait is under genetic control (Weller & Ortega, 2015).

In the faba bean plants selected for this study, there was a mix of spring and winter-type accessions, which are known to have different flowering times [START_REF] Flores | Faba bean adaptation to autumn sowing under European climates[END_REF].

The influence of sowing date acted together with flowering time in affecting bruchid infestation in this study. Previous studies already pointed out the importance of timing in controlling bruchids, highlighting that delayed flowering and delayed pod-forming plants induced lower oviposition and, as a consequence, less seed damage [START_REF] Szafirowska | The role of cultivars and sowing date in control of broad bean weevil (Bruchus rufimanus Boh.) in organic cultivation[END_REF][START_REF] Bachmann | Control of bean seed beetle reproduction through cultivar selection and harvesting time[END_REF][START_REF] Hamidi | Physiological synchrony of the broad bean weevil, Bruchus rufimanus Boh., to the host plant phenology, Vicia faba[END_REF]. Strategies to manage bruchid infestation should take into consideration both sowing date and flowering time. Screening new lines and varieties for bruchid resistance in the field should also consider the impact of these parameters and consider dissociating the genetic component of resistance from the escape strategy.

Conclusions

Numerous studies with bruchid species and legume crops explored key elements about insect pest resistance, such as in Vigna sp. [START_REF] Mishra | Bruchid pest management in pulses: past practices, present status and use of modern breeding tools for development of resistant varieties: bruchid pest management in pulses[END_REF], in chickpea, Cicer arietinum L. [START_REF] Shaheen | Resistance of chickpea (Cicer arietinum L.) cultivars against pulse beetle[END_REF], and in pea, P. sativum [START_REF] Morton | Bean alfa-mylase inhibitor 1 in transgenic peas (Pisum sativum) provides complete protection from pea weevil (Bruchus pisorum) under field conditions[END_REF][START_REF] Clement | Variation among accessions of Pisum fulvum for resistance to pea weevil[END_REF].

However, there is still much information missing for faba bean and the biology of B. rufimanus, and specific studies are rare [START_REF] Hamidi | Physiological synchrony of the broad bean weevil, Bruchus rufimanus Boh., to the host plant phenology, Vicia faba[END_REF][START_REF] Segers | Overview of Bruchus rufimanus Boheman 1833 (Coleoptera: Chrysomelidae): biology, chemical ecology and semiochemical opportunities in integrated pest management programs[END_REF] rufimanus differed substantially between the genotypes, and studies could advance into investigating physical and chemical barriers to larval penetration and survival in the seed, especially focusing on the resistant accession 159B. Future studies could focus on exploring specific characteristics that may be selected genetically. Our methodology and results could be used to predict potential resistant genotypes, boost breeding efforts towards developing resistant varieties, and transfer knowledge to species closely-related to faba bean including pea and lentil (Lens culinaris Medik.), which are also highly susceptible to bruchids.

  (1) the number of laid eggs was influenced by the genotype or by the number of seeds inside the pod, (2) the number of damaged seeds was influenced by the number of eggs on the pod or by the genotype, and (3) the number of emergence holes depended on the weight (g) of the seed or on the genotype.Field experimentFaba bean genotypes showing different levels of bruchid infestation in previous years (Camillo-Perdomo et al., 2019) were selected essentially from the collection available at the National Research Institute for Agriculture, Food and Environment (INRAE) at Dijon, France, and from the material composing the diversity panel of the PROFABA project. Fifteen susceptible genotypes and 15 genotypes less damaged by bruchids were selected, including the genotypes evaluated previously in the greenhouse: 159B, Hiverna, and Acequia. We also added the two recombinant inbred lines from the POP1 population, POP1.S1 and POP1.R1. The experiment was conducted at the INRAE experimental farm of Epoisses in Bretenière, France (47°24′10′′N, 5°11′40′′E). Seeds were sown in two replicates, at 1 month apart (sowing 1: 24 February 2021, sowing 2: 23 March 2021). The field plan was carried out with a randomized design. For each accession, 20 seeds were sown in two consecutives rows, with intra-and inter-row distances of 40 cm and 1 m, respectively. As the experimental farm has a known history of seed weevil infestation, we relied on natural infestation. No fungicides were sprayed on the experimental plot or surrounding fields during the experiments and a

  Our study brings new key elements of the behavior of B. rufimanus and adds more questions to the field. Moreover, we showed the advantages of characterizing the mechanisms underlying bruchid resistance in faba bean under greenhouse conditions. Experiments in the field are largely influenced by weather conditions and by flowering time for some genotypes, which can both be controlled indoors. Considering our present results, the successful development of B.

Table 3

 3 ANOVA table for the fitted model. Effects of the environment (sowing) and genotypes on the healthy seeds' percentage in the field trials

		d.f.	SS	MS	% variance	F	P
					explained
	Sowing	1	2999.1	2999.05	13.94	15.8	0.0004
	Genotype	31	28698.2	925.75	58.16	4.9	<0.001
	Residuals	27	5095.7	188.73	27.90
	Total	59

Acknowledgments

We thank INRAE technical staff for efficient management of the trials, in the field at U2E Époisses (Bretenière, France) and in the greenhouse at INRAE (Dijon, France). We particularly thank Valérie Dufayet, Franck Zenk, and Damien Gironde for their assistance.

The authors are also grateful to Jean-Bernard Magnin-Robert, Hervé Houtin, Pascale Ducloux, Elodie Vouaux, and Sabrina Pedreira for their help in preparing, sowing, harvesting, and phenotyping the seeds. We thank Gregoire Aubert for helpful insights on the manuscript. This project was financially supported by ERA-NET Cofund SusCrop project ProFaba.

Supporting Information

Additional Supporting Information may be found in the online version of this article.

Table S1 Number of females and males of Bruchus rufimanus used in each olfactometer test, states tested and total number of individuals evaluated at the end of the experiments.

Table S2

Mean percentage of healthy seeds on the selected Vicia faba accessions under field conditions in previous studies (PROFABA, not published) and in the present study.

Table S3 Field data for the two replicates: flowering time (days since sowing), plant height at maturity (cm), 100-seed weight (g), and healthy seeds (%).


is a remarkable year for Green Chemistry and Green Materials

Sylvain CAILLOL ICGM, Univ Montpellier, CNRS, ENSCM, Montpellier, France I take advantage of this editorial at the beginning of the year to wish a very happy New Year 2023 to our readers and to our journal Green Materials. We hope that this New Year will be marked by the development of technological responses adapted to environmental and societal challenges on a global scale. Our modern societies indeed base many hopes on the technological answers to these essential questions. Chemistry is a science that feeds an industry upstream of all the others, and therefore very much in demand in all technological developments. Green Chemistry can provide much-awaited answers to these sustainability issues.

Moreover, this year 2023 is particularly remarkable because we are celebrating several anniversaries around Green Chemistry. In particular, we celebrate the 25 th anniversary of the 12 principles of Green Chemistry described in the groundbreaking book "Green Chemistry: Theory and Practice" coauthored by Paul Anastas and John C. Warner and published in 1998. However, the phrase "Green Chemistry" was officially coined in 1991 by EPA Office of Pollution and Toxins Prevention staff that sowed the seeds for productive collaboration between government, industry, and academia. Indeed, the Pollution Prevention Act of 1990 marked a regulatory policy shift from pollution control to pollution prevention as the most effective strategy for these environmental problems. Hence, in the early 1990s, the Chemistry Council of the European Community published articles on the subject, including the influential book "Chemistry for a Clean World". Moreover, 2023 is also remarkable since it is the 10 th anniversary of Green Materials journal. The first issue was released in March 2013, with an editorial by Michael Shaver who served as the first editorin-chief.

With these aspects in mind, this issue of Green Materials follows the principles of Green Chemistry, particularly with the use of renewable resources, the substitution of harmful chemicals, and an environmentally driven approach.

The underlying idea of the study reported in first paper 1 was conceived after numerous reports of marine oil spill occurrences and the often-inefficient mitigation efforts. Physical and chemical efforts are commonly made but prove to be unsustainable in the long run. Bioremediation efforts are more environmentally friendly; however, the efficiency needs to be tweaked. Hence, maintaining a high biomass of oil-degrading bacteria has proved challenging. Here, a carrier that enables simultaneous bacterial immobilization and oil absorption is proposed as a solution. Porous cellulose triacetate beads (PCTBs) derived from cellulose triacetate powder were obtained through the acetylation of kapok fibres. This study revealed, that PCTBs with oil-degrading bacteria are potentially able to absorb and degrade oil simultaneously, thus highlighting the novelty of a working alternative for sustainable oil spill mitigation.

The second paper 2 studied the replacement of petroleum-based polymers by biobased polymers in air cushions in transport packaging brings in order to reduce environmental damage due to discarded packaging. Hence, the authors proposed to combine fatty-based dimer acid polyamide films with montmorillonite (MMT). The layer structure of MMT and the heterogeneous nucleation effect augment the crystal content of the g-crystal phase. The oxygen permeability and thermal stability of the film improve as the MMT content is increased. Hence, the results showed that dimer acid polyamide/MMT film can fully meet the requirements of air cushions for short-term transportation.

The purpose of the work reported in the third paper 3 was to obtain the thermal conductivity of a biomaterial based on cornstalk, as well as the hygroscopic properties that demonstrate the possibility of its use in different applications as insulating material. The thermal conductivity obtained at 30°C for the insulating material show that the hydrothermal properties of this material make it suitable as a thermal insulator, having a thermal conductivity value of 0.043 W/(m K) and absorbing less than 9% humidity in environments of up to 85% relative humidity.

In the fourth paper 4 , the authors proposed to use simultaneously eggshells (ES), waste grinding sludge (GS) and chromium (Cr) as reinforcement content in the fabrication of aluminum/magnesium alloy based composites. Thus, ES and GS were used as primary and secondary reinforcement contents. Chromium was further used to prevent the grain growth of the composite material during the solidification process. These hard phases were accountable for improving the mechanical properties of the fabricated composite.

Taken together, the articles in this issue reveal not only the growing attention paid to the use of renewable resources and the substitution of harmful substances, following the trends in society, but also all the interest and promises of this chemistry for the improvement of current materials and the design of new green materials.

1

  DOI : 10.1680/jgrma.21.00064 2 DOI : 10.1680/jgrma.22.00027 3 DOI : 10.1680/jgrma.21.00046 4 DOI : 10.1680/jgrma.21.00035