Raphael Chekroun

Thomas Gilles

Marin Toromanoff

Sascha Hornauer

Fabien Moutarde

MBAPPE: MCTS-Built-Around Prediction for Planning Explicitly

We present MBAPPE, a novel approach to motion planning for autonomous driving combining tree search with a partially-learned model of the environment. Leveraging the inherent explainable exploration and optimization capabilities of the Monte-Carlo Search Tree (MCTS), our method addresses complex decision-making in a dynamic environment. We propose a framework that combines MCTS with supervised learning, enabling the autonomous vehicle to effectively navigate through diverse scenarios. Experimental results demonstrate the effectiveness and adaptability of our approach, showcasing improved real-time decision-making and collision avoidance. This paper contributes to the field by providing a robust solution for motion planning in autonomous driving systems, enhancing their explainability and reliability.

I. INTRODUCTION

Innovations in machine learning techniques have led to significant advancements in self-driving technology. Particularly, the use of deep learning has greatly improved the perception stage of autonomous driving. These developments have been complemented by progress in sensor technology and mapping methods. As a result, the focus is now shifting to the next challenges of autonomous driving, and motion planning emerges as a pivotal component. After identifying roads and monitoring nearby vehicles and object entities, the autonomous driving system must now decide its future path and plan its trajectory accordingly to ensure a collision-free route while respecting traffic rules.

Therefore, this study centers on the mid-to-end stage of autonomous driving, presuming that perception tasks have already been accomplished and working toward an efficient and explainable motion planning. In this realm, recent research mostly focus on Imitation Learning (IL) [START_REF] Gilles | Gohome: Graph-oriented heatmap output for future motion estimation[END_REF]- [START_REF] Renz | Plant: Explainable planning transformers via object-level representations[END_REF] or hybrid IL and rule-based methods [START_REF] Dauner | Parting with misconceptions about learningbased vehicle motion planning[END_REF], [START_REF] Hallgarten | From prediction to planning with goal conditioned lane graph traversals[END_REF].

However, rule-based methods for autonomous driving are limited by their lack of scalability, adaptability, robustness in complex and ambiguous situations, and their inability to handle unconventional scenarios. This contrasts with machinelearning based approaches that address these limitations through data-driven learning and adaptability.

Nonetheless, while Neural Networks (NN) provide a powerful and flexible tool for learning to drive using supervised labels with IL methods [START_REF] Gilles | Gohome: Graph-oriented heatmap output for future motion estimation[END_REF], [START_REF] Bojarski | End to end learning for self-driving cars[END_REF], [START_REF] Chitta | Transfuser: Imitation with transformerbased sensor fusion for autonomous driving[END_REF], they remain limited in the long-term understanding of the consequences of their Fig. 1. Visualization of the exploration done by MBAPPE in one planning step. We display the bird-eye-view trajectory pieces in xy coordinates. As the road is turning right, the MCTS explores multiple steering angle and acceleration configurations to correctly take the turn. MBAPPE finally selects the path which maximizes the Q-value (in green).

actions. Therefore, they may not comprehend the full scope of interactions with the map and other agents. Deep Reinforcement Learning (Deep RL) based methods [START_REF] Kendall | Learning to drive in a day[END_REF]- [START_REF] Chekroun | Gri: General reinforced imitation and its application to vision-based autonomous driving[END_REF] aim to incorporate long-term returns of such consequences in the training of these networks. However, this causal understanding remains implicit and not guaranteed, and Deep RL training is most often sample inefficient.

Our approach aims to get the best of both worlds by using an IL prior to guide a MCTS [START_REF] Coulom | Efficient selectivity and backup operators in monte-carlo tree search[END_REF], [START_REF] Kocsis | Bandit based montecarlo planning[END_REF] into explicitly exploring the consequences of actions, validating the NN trajectory if it respects driving constraints, or exploring new actions if required, see Figure 1. The main challenge in running a MCTS is that it assumes environment transitions to be deterministic and perfectly known. While this is true for the displacement of the ego vehicle given its actions, and for the update of the map that remains the same, other agents will also move on their own accord. In order to have a realistic world model, we developed an IL model to predict all the other agents future trajectories. This way we get an approximate of the future transitions that enables us to roll out the consequences of our chosen actions on multiple timesteps.

In this paper, we extend the MCTS paradigm to partiallylearned environment and apply it to autonomous driving. Next, we validate our performance on nuPlan [START_REF] Caesar | Nuplan: A closedloop ml-based planning benchmark for autonomous vehicles[END_REF] simulation environment and compare to other existing baselines. Lastly, we highlight the explainability of our approach which allows easy observation and analysis of the steps leading to any given decision via its decision tree.

II. RELATED WORK

MBAPPE seeks to leverage imitation learning (IL) to guide a MCTS model in exploring the outcomes of its actions. As such, this section is dedicated to examining rulebased and learning-based motion planning techniques, and strategies integrating MCTS with deep learning. a) Rule-based methods: Rule-based methods employ explicit rules to dictate the behavior of autonomous vehicle, making them interpretable by nature [START_REF] Thrun | Stanley: The robot that won the darpa grand challenge[END_REF]- [START_REF] Bacha | Odin: Team victortango's entry in the darpa urban challenge[END_REF]. A notable instance is the Intelligent Driver Model (IDM) [START_REF] Treiber | Congested traffic states in empirical observations and microscopic simulations[END_REF], designed to track leading vehicles while maintaining safe distances through computation of optimal acceleration based on the leading vehicle's speed. Rule-based methods were extended in predictive rule-based approaches which anticipate future environmental states to improve collision avoidance [START_REF] Karkus | Diffstack: A differentiable and modular control stack for autonomous vehicles[END_REF]- [START_REF] Zeng | End-to-end interpretable neural motion planner[END_REF]. However, rule-based methods are inflexible and rely on perfect and consistent representation of the environment. This characteristic make them struggle with generalization to novel scenarios or with the inherent variability of real-world conditions.

b) Imitation learning methods: Imitation learning methods allow to learn how to drive from supervised data, leading to more generalizability than rule-based methods. Some of these methods directly create driving plans or commands [START_REF] Chitta | Transfuser: Imitation with transformerbased sensor fusion for autonomous driving[END_REF], [START_REF] Scheel | Urban driver: Learning to drive from real-world demonstrations using policy gradients[END_REF], but they suffer from a lack of interpretability and general robustness. To address these issues, some other approaches focus on making the planning decisions more interpretable. For instance, Dauner et al. developed Predictive Driver Model (PDM) [START_REF] Dauner | Parting with misconceptions about learningbased vehicle motion planning[END_REF] to combine an interpretable IDM with a simple neural network. Some methods deal with the robustness problem by generating multiple planning options with deep learning and then choosing the best one with the lowest cost [START_REF] Cui | Lookout: Diverse multi-future prediction and planning for self-driving[END_REF]- [START_REF] Zeng | Dsdnet: Deep structured self-driving network[END_REF] or by refining deep-based predictions [START_REF] Huang | Gameformer: Gametheoretic modeling and learning of transformer-based interactive prediction and planning for autonomous driving[END_REF], [START_REF] Aydemir | Adapt: Efficient multi-agent trajectory prediction with adaptation[END_REF]. However, IL methods still suffers from distribution mismatch where agent fails to recover from accumulation error thus leading to increasingly out of expert distribution states, and lacks of long-time reasoning. c) Reinforcement learning methods: Instead of copying human behavior like IL, RL models use a reward system to judge how good a strategy is. This can lead to improved decision-making, sometimes even outperforming humans [START_REF] Silver | Mastering the game of go with deep neural networks and tree search[END_REF]. Model-free reinforcement learning focuses on learning optimal actions directly from observed states and rewards without creating an explicit model of the driving environment. Even though RL is successful for simple autonomous driving tasks [START_REF] Kendall | Learning to drive in a day[END_REF], up to now, no published work has reported sucess of exclusively RL-based method in autonomous driving for complex urban environments [START_REF] Chen | End-to-end autonomous driving: Challenges and frontiers[END_REF]. Furthermore, RL suffers from sample inefficiency and lack of convergence guarantees and interpretability. Recent works leveraged supervised learning in RL pipelines to overcome these limitations [START_REF] Chekroun | Gri: General reinforced imitation and its application to vision-based autonomous driving[END_REF], [START_REF] Toromanoff | Endto-end model-free reinforcement learning for urban driving using implicit affordances[END_REF], thus compensating the weakness of the RL gradient during training.

d) Methods integrating MCTS with deep learning: Integrating MCTS with deep learning techniques has emerged as a compelling approach to enhance decision-making processes in various domains. Silver et al. [START_REF] Silver | Mastering the game of go with deep neural networks and tree search[END_REF] pioneered this fusion by combining MCTS with deep supervised learning to achieve groundbreaking results in the game of Go with AlphaGo. This paradigm was extended with AlphaZero [START_REF] Silver | Mastering chess and shogi by self-play with a general reinforcement learning algorithm[END_REF] by relying solely on self-play and RL. MuZero [START_REF] Schrittwieser | Mastering atari, go, chess and shogi by planning with a learned model[END_REF] finally embraced implicitness and extended the generality of these approaches by employing learned models to simulate outcomes and inform strategic decision-making.

In the realm of autonomous driving, Chen et al.

[32] integrated MCTS with deep learning but relied on implicitness for the tree transitions and prior computation, possibly leading to inexplicable behaviors which are not desirable for this domain of application. Other published methods lack generalizability and constraint their applicative fields to simplified custom environments such as highway driving without possibility for public benchmarks comparison [START_REF] Shu | Autonomous driving at intersections: A critical-turning-point approach for left turns[END_REF], [START_REF] Ha | Vehicle control with prediction model based monte-carlo tree search[END_REF], or high level tactical decisions [START_REF] Hoel | Combining planning and deep reinforcement learning in tactical decision making for autonomous driving[END_REF].

III. METHOD

In this section, we introduce MBAPPE and its components. In particular, we present the known and learned features of the world model, and technical details of our MCTS design and exploration steps.

Q Q Q Q Q+u(P)
Q+u(P) Q+u(P) Q+u(P) Fig. 3. MCTS steps a) Each simulation pass in the tree follows a trade-off between exploitation of the best Q value of an action, and the exploration term u(P ) that encourages to explore nodes with less visits N along the prior P . b) The leaf node is possibly expanded following some probabilities depending on the prior P and the continuity constraints. c) After the simulation, the leaf node is evaluated by explicitly computing the reward r described in Section III-C. d) Q-values are updated so means of the rewards r in the sub-tree below each actions are tracked.

A. MBAPPE framework

At each time-step, a neural network (based on an openloop version of Urban Driver [START_REF] Scheel | Urban driver: Learning to drive from real-world demonstrations using policy gradients[END_REF]) predicts an estimation of the ego trajectory and of the future trajectories of every other agents around the ego. This information is fed to the MCTS, which will deploy an internal lightweight simulation where the ego trajectory is used as a prior to guide the first steps of exploration, and other agents trajectories are leveraged to build the world model. At each simulation-step, which follow a planning time axis inside the tree, the MCTS explores the possible actions and internally simulates the evolution of the environment to check how those explored actions will impact its driving performances (driving out of area, check for collisions with static objects, check collisions with other agents thanks to their estimated trajectory, etc).

The global pipeline is represented in Figure 2.

B. World Model

The Monte-Carlo tree search leverages an internal simplified representation of the world where it can quickly iterate to explore possible sequences of actions and their consequences. This environment is made of two categories of features:

• Known features:

-The map information, including traffic light, -Static objects such as traffic cones and barriers -Dynamic objects such as neighboring vehicles, traffic cones or pedestrians, which we will consider as other agents evolving in the simulated environment

• Learned features:

-Estimated future trajectories of other agents given by the NN prediction.

C. MCTS design and tree steps

Our MCTS is based on a kinematic bicycle model of the vehicle. Actions are defined as a tuple (a, δ), where a is the acceleration and δ the steering angle. Accelerations and steering are discretized in 13 values each, in the respective range of [-3, 3] m.s -2 and [-π/4, π/4] rad. Actions are integrated every 0.1 s.

The simulation process of our tree search is detailed in Fig. 1. The tree is initialized with a single root node representing the current context. Each tree node stores 3 values: Q the expected return, P the action prior and N the number of visits. The nodes are built and evaluated iteratively through the following steps:

• Selection: We follow the PUCTS [START_REF] Silver | Mastering the game of go with deep neural networks and tree search[END_REF] formula to select the next action following a trade-off between the exploitation of Q and the exploration of unvisited nodes with low N . At a node state S the action A is chosen using the following formula:

A t = argmax A Q(S, A) + c puct P (S, A) B N (S, B) 1 + N (S, A) (1)
with c puct an hyper-parameter balancing the trade-off between exploration and exploitation. We found c puct = 2 to perform the best in our experiments.

• Expansion: We expand leaf nodes by all physically possible actions from the state of the leaf node, following a prior P and some continuity constraints. These constraints ensure both comfort and physical feasibility of successive actions. Prior design and continuity constraints are described in Section III-D. • Evaluation: We consider that driving rewards are rather short term (crash or not, exit road or not within the next 6 or 8 seconds). Therefore they do not need to be bootstrapped by a learned value network, but rather can be evaluated at the current simulation step by checking for them directly. Our computed reward r t at state s t is made of these main components:

-Progress: distance advanced since the last node, normalized by maximum allowed speed limit ([0, 1]), -Collision: penalty for collision with car and pedestrian (-5) or object (-2), -Route: -0.5 if the vehicle is not on the expected road, -Drivable area: -1 if the vehicle is not on the drivable area, -Center of the road:

* -sin(θ)/2 where θ is the angle difference between the ego heading and the closest centerline heading, * -d/2 where d is the distance between the ego position and the closest centerline.

• Back up: We update the Q values using the cumulative reward as in MuZero [START_REF] Schrittwieser | Mastering atari, go, chess and shogi by planning with a learned model[END_REF]:

G k = l-1-k τ =0 γ τ r k+1+τ Q s k-1 , a k := N s k-1 , a k × Q s k-1 , a k + G k N (s k-1 , a k ) + 1 N s k-1 , a k := N s k-1 , a k + 1
(2) We use a discount factor γ of 1.

D. Prior and continuity constraints

An efficient MCTS exploration process can be achieved by leveraging two approaches.

Firstly, providing the MCTS an intuition over actions to explore to prioritize the more probable ones. This issue is tackled using a prior over the distribution of actions for each node. This prior is usually learned and inferred for every node [START_REF] Schrittwieser | Mastering atari, go, chess and shogi by planning with a learned model[END_REF], which is computationally expensive, or handcrafted. Secondly, to further streamline the exploration process, we narrowed down the action space, thereby reducing the overall actions that need to be explored to the most critical ones. To achieve this, we integrated continuity constraints into the MCTS to ensure not only the physical feasibility of the actions explored but also to enhance comfort and to reduce the exploration time.

1) The prior: We designed a prior which relies on both handcrafted rules and learned rules, all without incurring any additional computational overhead.

The prior function is made of two parts:

• The handcrafted prior P h prioritizes exploration around the constant speed with null steering angle, • The learned prior P l is obtained by deriving the prediction of the ego trajectory by the NN into consecutive actions. This prior advantages the possibility of following NN actions for the first T time steps of the internal simulation of the MCTS. We found T = 1 s to perform the best in our experiments. Both P l and P h are Gaussians centered on the chosen action. The Gaussian are parametrized with a very high variance (σ 2 = 100) to encourage an almost uniform exploration.

The designed prior can be written:

P t = P t h + P t l if t ≤ T P t h if t > T (3)
2) Continuity constraints: To ensure the output trajectory is physically feasible and to minimize the total number of actions to explore, we implemented continuity constraints in the MCTS.

These constraints are two folded:

• The Tree Constraint: At a given step t of the real-world vehicle movement, the root node of the novel tree will be constrained to explore neighboring accelerations and steering angles relatively to the actions taken at time t -1 by the previous tree. This constraint favors a behavior continuity between successive time-steps and corresponding MCTS. • The Node Constraint: During the MCTS internal expansion phase, exploration only focuses on neighboring accelerations and steering angle values relatively to the actions of his parent node. This constraint favors a behavior continuity during the expansion phase of a given MCTS. We formulate both continuity constraints as restricting the following action (a t+1 , δ t+1 ) to be within a range of a t ±0.15 m.s -2 for the acceleration and δ t ±π/240 rad for the steering angle with (a t , δ t ) the action at the previous time-step.

IV. EXPERIMENTAL RESULTS

Dataset:

We show results on the nuPlan dataset. It encompasses 1300 hours worth of real vehicle motion data along with its corresponding simulator. Within the nuPlan framework, we chose to assess the performance of planners on closed-loop non-reactive agents benchmark. We focus on this benchmark, as evaluations conducted in closed-loop more effectively assess an agent's driving capabilities without the need to compare them to a flawed 'ideal' behavior as typically seen in open-loop assessments. Additionally, we chose non-reactive agents for our study, as preliminary experiments and other performance benchmarks [START_REF] Dauner | Parting with misconceptions about learningbased vehicle motion planning[END_REF], [START_REF] Caesar | Nuplan: A closedloop ml-based planning benchmark for autonomous vehicles[END_REF] have demonstrated that outcomes are largely consistent between reactive and non-reactive agents. All simulations are ran on 100 scenarios of each of the 14 scenarios types (totaling 1,118 scenarios in practice, as all 14 types do not have 100 available scenarios) of the nuPlan challenge, following the Val14 benchmark validation set [START_REF] Dauner | Parting with misconceptions about learningbased vehicle motion planning[END_REF].

Score and metrics: We use the nuPlan official score, which measures driving quality between 0 and 100 through a combination of 16 normalized driving metrics related to infraction rate, ego comfort, or progress toward the goal. We decided to put a special emphasis on the metrics of collision rate (CR), driving area non-compliance (DA) and ego progress (EP) in our experiments, as they are key elements for a safe and efficient autonomous driving system.

Implementation details: For ablations studies, the number of simulation steps is limited to 256 in each MCTS. In our setup (Intel Core i7-9700K CPU @ 3.60GHz) the whole pipeline inference time is ∼ 0.15 seconds for this setup, including input pre-processing, prediction model, MCTS and post-processing. The pipeline runs on CPU only. For inference speed purposes, we only expand new possible actions every 1 s. We observed no drop of performance.

A. Ablation study over the prior

An ablation study over the choice of prior is presented table I. Continuity constraints are the one described section III-D. We can see from results of Table I that MCTS without prior is inefficient. Exploration being unguided, the expansion phase does not create node leading to a good reward a priori. Following P l for the first steps of the simulation allowed to significantly improve the exploration phase by guiding the MCTS to stay within the driving area. Indeed, thanks to continuity constraints, a good beginning of the trajectory allows to stay on the road and reach acceptable metrics. Interestingly, leveraging only P l leads to an increase of the collision rate: if the MCTS first actions differ from the prior's, there will be a mismatch between the guidance it provides and the actual scenes which can lead to collisions.

Prior Metrics Learned Crafted CR ↓ DA ↓ EP ↑ Score ↑ - - 6% 4% 31% 26% ✓ - 11% 3% 88% 65% - ✓ 6% 4% 95% 82% ✓ ✓ 5% 2% 96% 86%
Leveraging P h allows the MCTS to prioritize exploration of the most common behavior on average (staying at around the same velocity with a null steering angle), therefore minimizing collisions and optimizing overall progress. Notably, using only this naive prior without any kind of learning already yields very good performance, highlighting the power of guided exploration in the MBAPPE method. Finally, leveraging P h + P l allows to prioritize this kind of behavior while starting with a better heads up and leads to best results on this set of experiments.

B. Ablation study over continuity constraints

An ablation study over the choice of continuity constraints is presented Table II. For these experiments, prior is P h +P l .

It becomes apparent that when applied separately, continuity constraints offer only marginal improvements to our method. A possible explanation is that the handcrafted identity prior already directs the MCTS towards a form of constrained exploration similar to what is achieved through node constraints. However, utilizing both node and tree constraints independently does enhance the exploration process. Importantly, the combined effects of these constraints not only substantially increase performance but also ensure a consistent selection of actions, both within a single tree and across multiple trees that correspond to sequential planning steps.

C. Comparison with state-of-the-art methods

We compare MBAPPE's performance with other stateof-the-art method on the validation scenario of the Val14 benchmark [START_REF] Dauner | Parting with misconceptions about learningbased vehicle motion planning[END_REF]. See Table III.

Baselines: Urban Driver [START_REF] Scheel | Urban driver: Learning to drive from real-world demonstrations using policy gradients[END_REF] utilizes PointNet [START_REF] Qi | Pointnet: Deep learning on point sets for 3d classification and segmentation[END_REF] layers to process polyline and employs a MLP following a multi-head attention block to forecast the ego trajectory. GameFormer Planner [START_REF] Huang | Gameformer: Gametheoretic modeling and learning of transformer-based interactive prediction and planning for autonomous driving[END_REF] exploits a Transformer to predict all agents trajectories before refining ego planning via non-linear optimization. PlanCNN [START_REF] Renz | Plant: Explainable planning transformers via object-level representations[END_REF] leverages a CNN on rasterized inputs to predicts the ego trajectory. PDM [START_REF] Dauner | Parting with misconceptions about learningbased vehicle motion planning[END_REF] leverages an improved IDM [START_REF] Treiber | Congested traffic states in empirical observations and microscopic simulations[END_REF] model combined with a simple MLP to generate several trajectories which are then scored to return the optimal one. GC-PGP [START_REF] Hallgarten | From prediction to planning with goal conditioned lane graph traversals[END_REF] categorizes proposed plans according to their traversal of a route-constrained lane graph, and then identifies the most probable cluster center. For this comparison, we extended Urban Driver to predict trajectories of all other agents in the scene in addition to the ego's. We name this updated version Urban Driver Multi-Agent (Urban Driver MA). Then, we evaluated two versions of MBAPPE. One leverages Urban Driver MA as prediction and prior model (c.f. Figure 2), and the other a GameFormer model. Other components of those systems are identical.

In our experiments, we found that enhancing a prediction model with MBAPPE consistently results in improved planning. Specifically, when integrated with GameFormer, MBAPPE yields a substantial improvement in key metrics Fig. 4. A subset of a decision tree obtained with MCTS exploration. Nodes are colored according to their Q-value. The root node correspond to the present state of the vehicle in the nuPlan simulator. We observe that the orange left branch exploration leads to the ego leaving the expected route, hence the low Q-value. The red middle branch exploration leads to a collision, thus explaining the low Q-value. The green right branch exploration presents the expected behavior and therefore has the highest Q-value. The explored planning can also be observed in Figure 1.

compared to using non-linear optimization techniques as done with the GameFormer Planner.

Thus, MBAPPE not only delivers state-of-the-art performance, but is also an explainable and interpretable operator when applied to predictive models. This dual benefit both refines decision-making policies and provides added adaptability.

V. AN EXPLICIT AND EXPLAINABLE METHOD

A key benefit of this technique is its simplicity: it requires only basic high-level directives in the form of a reward function (e.g., move ahead, avoid collisions, stick to the route, and remain on the road). Despite its vague prior, the method yields highly effective and realistic planning. This eliminates the need for specific, hard-to-generalize rules, like basing decisions on the road's curvature or the speed of the car ahead, as well as the use of hardly interpretable neural networks. As a result, our approach is highly flexible, adaptable, and explainable.

Indeed, decisions of the MCTS are explainable and the internal process that led to those decisions can be easily observed and analyzed. Figure 4 provides an example of a decision tree of the MCTS in which we can observe several exploration branches and their consequences on the tree expansion. In particular, we observe on the green right branch that internal exploration leading to desirable behavior yields the highest Q-value and further exploration of that branch. When exploration leads to collisions or to the ego leaving its expected route, the Q-value is low and exploration stops, as shown in the red middle and orange left branches. Figure 4 shows that MCTS decisions-making process is transparent and explainable, thus leading to an explicit and safe planning.

VI. CONCLUSION

This paper presents MBAPPE, a novel approach extending MCTS for planning within a partially learned environment in the context of autonomous driving. Through ablation studies, we highlighted the advantages of incorporating the designed priors and continuity constraints into the MCTS tree. Comparative analysis using a benchmark on the nuPlan simulator revealed that MBAPPE is an effective refinement operator for planning models, consistently outperforming vanilla models across all evaluation metrics. Finally, we emphasize the interpretability provided by this technique, a critical attribute for ensuring the safety and reliability of autonomous vehicles.

In terms of future work, as MBAPPE improves planning model capabilities, one could fine-tune the prior network similarly to the approach used in AlphaGo [START_REF] Silver | Mastering the game of go with deep neural networks and tree search[END_REF]. This would enable the network to better emulate the MCTS output, thereby refining its priors and initiating a cycle of selfimprovement. Better results could also be achieved with a more complex learned prior inferred for each node [START_REF] Schrittwieser | Mastering atari, go, chess and shogi by planning with a learned model[END_REF], [START_REF] Chen | Driving maneuvers prediction based autonomous driving control by deep monte carlo tree search[END_REF], as well as learning a bootstrapped value network to estimate node expected returns in addition to the current reward. However this would require more network inferences and could harm the execution time.

Fig. 2 .

 2 Fig. 2. MBAPPE pipeline A prediction model infers future trajectories of other agents in the scene. This information is fed to the MCTS which outputs a sequence of consecutive actions. Those are integrated to form an improved trajectory planning for the ego.

Acknowledgments Thank you to Valentin Charraut for his fruitful help on implementation and optimization. We are also thankful to Thibault Buhet and Dzmitry Tsishkou for their insights, revisions and relevant comments.

//github.com/


Béatrice Gervais-Bergeron1
email: beatrice.gervais-bergeron@umontreal.ca

Adrian L D Paul1

Pierre-Luc Chagnon2

Alan J M Baker3

Antony Van Der Ent3

Michel-Pierre Faucon6

Celestino Quintela-Sabarís7

Michel Labrecque1

Trace element hyperaccumulator plant traits: a call for trait data collection

Keywords: CSR strategies, Functional traits, Hyperaccumulation, Metallophytes, Plant functions, Synthesis analysis

Background and aims Hyperaccumulator plants exhibit extreme ecophysiological characteristics, which make them suited for phytoremediation and phytomining applications. Understanding their ecological strategies might help identify the species and functions to be favored in phytoremediation, phytomining, restoration and conservation projects for metalliferous sites.

2 Methods Here, we identified the hyperaccumulator species in the worldwide plant trait database TRY, and cross-referenced these trait syndromes associated with the ability of plants to concentrate metals. This allows us to link trace element hyperaccumulation with broader plant ecological strategies.

Results Hyperaccumulators tend to have smaller leaves and poor competitive ability compared to non-hyperaccumulator species. Contrary to expectations, we found no indication of hyperaccumulators being more resource-conservative on the leaf economics spectrum. However, these data remain fragmentary as only 2.7% of hyperaccumulators have their traits published in the TRY database.

Conclusion

The recent development of trait-based models to construct plant communities providing optimal ecosystem services (e.g., phytoremediation, restoration) requires further research to identify predictable trait-service relationships. We thus call for an international collaborative sampling effort to measure traits in more hyperaccumulator species.

Introduction

Mining activities are major sources of pollution directly tied to human and environmental health issues worldwide. These activities severely threaten metalliferous ecosystems characterized by extreme environmental conditions (e.g., high metal concentrations, low resource availability), endangering some of the world's most biodiverse and endemic-rich communities [START_REF] Myers | Biodiversity hotspots for conservation priorities[END_REF][START_REF] Baker | Metallophytes: the unique biological resource, its ecology and conservational status in Europe, central Africa and Latin America[END_REF][START_REF] Ibanez | Twenty years after Jaffré et al. (1998), is the system of protected areas now adequate in New Caledonia?[END_REF]. These ecosystems harbor a pool of species (i.e., metallophytes) with high ecological value and for use in contaminated land rehabilitation, phytomining, as well as metalliferous site restoration, and conservation [START_REF] Whiting | Research priorities for conservation of metallophyte biodiversity and their potential for restoration and site remediation[END_REF][START_REF] Wójcik | Metallophytes of serpentine and calamine soils -their unique ecophysiology and potential for phytoremediation[END_REF][START_REF] Chaney | The long road to developing agromining/phytomining[END_REF][START_REF] Quintela-Sabarís | Plant functional traits on tropical ultramafic habitats affected by fire and mining: insights for reclamation[END_REF]. Some metallophytes, called hyperaccumulators, are of particular interest because of their unique and extreme ability to accumulate trace elements (i.e., >100 times higher concentrations than most metallophytes) (van der [START_REF] Van Der Ent | Hyperaccumulators of metal and metalloid trace elements: facts and fiction[END_REF].

Although over 700 hyperaccumulator species have so far been identified (van der Ent et al. 2015b;[START_REF] Reeves | A global database for plants that hyperaccumulate metal and metalloid trace elements[END_REF], many questions concerning their ecological functions and potential applications remain unanswered [START_REF] Lange | Copper and cobalt accumulation in plants: a critical assessment of the current state of knowledge[END_REF], making it challenging to incorporate them in any rehabilitation schemes [START_REF] Reeves | Tropical hyperaccumulators of metals and their potential for phytoextraction[END_REF][START_REF] Kazakou | Hypotheses, mechanisms and trade-offs of tolerance and adaptation to serpentine soils: from species to ecosystem level[END_REF][START_REF] Kidd | Agronomic practices for improving gentle remediation of trace element-contaminated soils[END_REF]. Developing an approach to identify species and functions that can meet restoration or rehabilitation goals is, therefore, imperative. In this regard, a trait-based approach linking trace element accumulation strategies to plant morphology is a promising research avenue, given the wide array of plant traits that can be measured rapidly and the broad ecological processes it can tackle (e.g., environmental filters, biogeochemical processes) [START_REF] Laughlin | Applying trait-based models to achieve functional targets for theory-driven ecological restoration[END_REF][START_REF] Lange | Copper and cobalt accumulation in plants: a critical assessment of the current state of knowledge[END_REF].

Metallophytes, including hyperaccumulators, often share common characteristics (morpho-physio-phenological traits), allowing for survival under the adverse conditions encountered on metalliferous sites [START_REF] Violle | Let the concept of trait be functional![END_REF][START_REF] Baker | Metallophytes: the unique biological resource, its ecology and conservational status in Europe, central Africa and Latin America[END_REF]. As a result, many generalizations have been made on their ecological traits and strategies, including (i) slow growth rates; (ii) investment in defense and secondary metabolites; (ii) multiple stress tolerances; (iv) extensive root system development; (v) high nutrient use efficiency (resource conservation strategy); (vi) investment in microbial nutritional symbioses (e.g., mycorrhizae or nitrogen-fixing bacteria); (vii) intolerance to shade and (viii) xeromorphic characteristics [START_REF] Ernst | Evolution of metal tolerance in higher plants[END_REF][START_REF] Kazakou | Hypotheses, mechanisms and trade-offs of tolerance and adaptation to serpentine soils: from species to ecosystem level[END_REF][START_REF] Baker | Metallophytes: the unique biological resource, its ecology and conservational status in Europe, central Africa and Latin America[END_REF][START_REF] Quintela-Sabarís | Plant functional traits on tropical ultramafic habitats affected by fire and mining: insights for reclamation[END_REF][START_REF] Paul | Stocks and biogeochemical cycling of soil-derived nutrients in an ultramafic rain forest in New Caledonia[END_REF]. Moreover, because metalliferous soils are typically harsh environments with low vegetation cover and thus little competition over resources [START_REF] Kazakou | Hypotheses, mechanisms and trade-offs of tolerance and adaptation to serpentine soils: from species to ecosystem level[END_REF][START_REF] Novakovskiy | Long-term dynamics of plant communities after biological remediation of oil-contaminated soils in far north[END_REF], metallophytes are generally categorized as stress-tolerators (sensu [START_REF] Grime | The C-S-R model of primary plant strategies -origins, implications and tests[END_REF] with poor competitive ability and high capacity to conserve acquired resources [START_REF] Wright | The worldwide leaf economics spectrum[END_REF][START_REF] Ernst | Evolution of metal tolerance in higher plants[END_REF][START_REF] Baker | Metallophytes: the unique biological resource, its ecology and conservational status in Europe, central Africa and Latin America[END_REF][START_REF] Maestri | Metal tolerance and hyperaccumulation: costs and trade-offs between traits and environment[END_REF][START_REF] Reich | The world-wide 'fast-slow' plant economics spectrum: a traits manifesto[END_REF][START_REF] Lazzaro | Intraspecific trait variability and genetic diversity in the adaptive strategies of serpentine and non-serpentine populations of Silene paradoxa L[END_REF]). These characteristics stand in contrast to fast resource-acquisitive species that invest in low-cost biomass to acquire resources rapidly but constantly invest in biomass replenishment, as more resources are lost to litter, predation, or parasitism [START_REF] Reich | The world-wide 'fast-slow' plant economics spectrum: a traits manifesto[END_REF][START_REF] Wright | The worldwide leaf economics spectrum[END_REF]. As stress-tolerant species, hyperaccumulators are also expected to have smaller leaves and modest overall development [START_REF] Pierce | A global method for calculating plant CSR ecological strategies applied across biomes world wide[END_REF]. Local studies have confirmed some of these trends with species, populations or ecotypes exposed to trace elements in soils [START_REF] Kazakou | Species adaptation in serpentine soils in Lesbos Island (Greece): metal hyperaccumulation and tolerance[END_REF][START_REF] Adamidis | Species adaptive strategies and leaf economic relationships across serpentine and non-serpentine habitats on Lesbos, Eastern Mediterranean[END_REF][START_REF] Lazzaro | Intraspecific trait variability and genetic diversity in the adaptive strategies of serpentine and non-serpentine populations of Silene paradoxa L[END_REF], as environmental factors may induce around 30% of intraspecific variability in traits [START_REF] Albert | A multi-trait approach reveals the structure and the relative importance of intra-vs. interspecific variability in plant traits: Intra-vs. interspecific variability in plant traits[END_REF]). Nevertheless, it remains unknown whether these relationships hold at the global scale between hyperaccumulator and non-hyperaccumulator species. Although, at this large scale it might be difficult to distinguish hyperaccumulator species form closely related non-hyperaccumulator species, traits-interspecific variability is generally high enough to distinguish broad tendencies.

Moreover, since different metalliferous soils (e.g., serpentine, calamine, seleniferous, and Cu-Co rich soils) have distinct limiting factors (e.g., fertility, climates) [START_REF] Delhaye | Plant community assembly along a natural metal gradient in central Africa: Functional and phylogenetic approach[END_REF][START_REF] Garnica-Díaz | Global plant ecology of tropical ultramafic ecosystems[END_REF]) and since luxuriant tropical forests and fast-growing ruderals can develop on metalliferous sites [START_REF] Baker | Metallophytes: the unique biological resource, its ecology and conservational status in Europe, central Africa and Latin America[END_REF][START_REF] Delhaye | Community variation in plant traits along copper and cobalt gradients[END_REF][START_REF] Galey | Ultramafic geoecology of South and Southeast Asia[END_REF], it remains unclear whether these environments select for stress tolerators or whether alternative strategies could allow functionally distinct species to establish in these environments. Focusing on a global scale means that resolution at the species or population levels would be limited, but it is an essential step to evaluate the generalizability and predictability of a trait-based approach.

To identify one or many hyperaccumulation strategies within a worldwide trait spectrum, we systematically evaluate linkages between leaf traits/ecological strategies and trace element hyperaccumulation by cross-referencing the plant trait database TRY [START_REF] Kattge | TRY plant trait database -enhanced coverage and open access[END_REF] and the global hyperaccumulator database [START_REF] Reeves | A global database for plants that hyperaccumulate metal and metalloid trace elements[END_REF].

Material and Methods

Using the global plant trait database TRY (comprising data from> 200,000 species), we gathered data on leaf area (LA -area of one leaf), specific leaf area (SLA -leaf surface area/dry mass ratio), and leaf dry matter content (LDMC -leaf dry mass*leaf fresh mass-1) [START_REF] Kattge | TRY plant trait database -enhanced coverage and open access[END_REF]). These traits were selected to ensure broad species coverage (i.e., widely measured traits) while capturing essential components of plant strategies [START_REF] Pierce | A global method for calculating plant CSR ecological strategies applied across biomes world wide[END_REF]. They are key traits on the economic spectrum strategies [START_REF] Wright | The worldwide leaf economics spectrum[END_REF][START_REF] Reich | The world-wide 'fast-slow' plant economics spectrum: a traits manifesto[END_REF] and identify the CSR strategies: Competitive (C), Stress-tolerant (S), and Ruderal (sensu [START_REF] Grime | The C-S-R model of primary plant strategies -origins, implications and tests[END_REF]. Moreover, traits related to nutrient acquisition, such as SLA and LDMC, might be associated with trace element accumulation [START_REF] Lange | Copper and cobalt accumulation in plants: a critical assessment of the current state of knowledge[END_REF].

Species life forms were also obtained from the TRY database or the literature and subsequently categorized according to [START_REF] Pierce | Allocating CSR plant functional types: the use of leaf economics and size traits to classify woody and herbaceous vascular plants[END_REF]: trees, shrubs, forbs, graminoids, hydrophytes, and others (e.g., succulents, moss, and lichens). We further separated woody species (trees and shrubs) from non-woody species, as the presence of lignified tissues strongly covaries with the position of a plant along the resource acquisition-conservation spectrum [START_REF] Pierce | Allocating CSR plant functional types: the use of leaf economics and size traits to classify woody and herbaceous vascular plants[END_REF][START_REF] Díaz | The global spectrum of plant form and function[END_REF]. Potential hyperaccumulator species were first identified using the maximum concentrations of trace elements in leaves from the Global Hyperaccumulator Database [START_REF] Reeves | A global database for plants that hyperaccumulate metal and metalloid trace elements[END_REF]. The sources were validated to omit (i) non-peer-reviewed sources, (ii) data from hydroponic and spiked soil experiments (van der Ent et al. 2015a), and (iii) records of foliar trace element concentrations below the hyperaccumulation thresholds (van der Ent et al. 2021). All species names were verified with the Taxonomic Names Resolution Service (TNRS) as recommended in TRY [START_REF] Boyle | The taxonomic name resolution service: an online tool for automated standardization of plant names[END_REF][START_REF] Kattge | TRY plant trait database -enhanced coverage and open access[END_REF]. All traits were averaged to species level, as mostly done in global trait analysis [START_REF] Díaz | The global spectrum of plant form and function[END_REF], and outliers were checked for possible data entry errors [START_REF] Pérez-Harguindeguy | Corrigendum to: New handbook for standardised measurement of plant functional traits worldwide[END_REF]. The final database contained 4523 species, of which 19 were hyperaccumulators (Table 1). The CSR strategies were calculated using the 'StrateFy' program based on LA, SLA, and LDMC species mean values (Pierce et al.

2017).

Generalized linear mixed models (GLM) with binomial distributions were used to link hyperaccumulation to leaf traits (LA, SLA, LDMC) and plant strategies (i.e., Grime's C, S, and R scores). Model selection was based on AIC and pseudo-R2 values and further validated with a likelihood ratio test. Traits were normalized before analysis: LA and SLA were log-transformed and LDMC logit-transformed. All analyses were performed in R (version 4.2.0) with the "stats" package (R Core Team 2020) and the 'AICcmodavg' package [START_REF] Mazerolle | AICcmodavg: model selection and multimodel inference based on (Q)AIC(c)[END_REF].

Results

The best predictors for hyperaccumulation were LA and LDMC, although the full model (LA + SLA + LDMC) performed equally well (no statistical difference between AIC). Both models explained only 5.7% of the variance (d.f. = 4,522) and identified hyperaccumulators as having smaller leaves (LA, P <0.05) (Fig. 1a). However, this was not observed in hyperaccumulating woody taxa specifically (n = 4) (Table S1), although this may simply result from low statistical power. Regarding the position of hyperaccumulators along the leaf economics spectrum (mostly SLA-LDMC trade-offs), we found no evidence for a conservative strategy with thicker leaves (i.e., higher LDMC) (Fig. 1a).

Hyperaccumulators also had significantly lower competitive ability (%C) (P <0.05), which was the only predictor retained through model selection for all hyperaccumulators and nonwoody hyperaccumulators. Nevertheless, the model explained minimal variance (i.e., 3.1% for all hyperaccumulators and 3.4% for non-woody hyperaccumulators). Furthermore, no model could distinguish woody hyperaccumulator traits due to the small sample size (n = 4) and large dispersion. Overall, hyperaccumulators remained scattered across the CSR ternary plot and were poorly associated with any specific strategy (Fig. 1b). Finally, the CSR classification through leaf traits alone might be questionable for some species such as Gutierrezia microcephala, which is classified as a 100% R strategist, despite being usually described as a successional perennial species from desert habitats [START_REF] Parker | Association with mature plants protects seedlings from predation in an arid grassland shrub, Gutierrezia microcephala[END_REF].

Polygonaceae

Rumex acetosa forbs 1,510 29.1 0.15 Cu 1100 [START_REF] Tang | The uptake of copper by plants dominantly growing on copper mining spoils along the Yangtze River, the People's Republic of China[END_REF] Zn 11,000 [START_REF] Johnston | A comparative study of metal levels in plants from two contrasting lead-mine sites[END_REF] Pb 5540 [START_REF] Johnston | A comparative study of metal levels in plants from two contrasting lead-mine sites[END_REF] Rubiaceae

Discussion

Our preliminary results confirmed a weak trend for hyperaccumulators to have smaller leaves, a trait often observed in flora from 'harsh' environments, such as metalliferous soils [START_REF] Adamidis | Species adaptive strategies and leaf economic relationships across serpentine and non-serpentine habitats on Lesbos, Eastern Mediterranean[END_REF][START_REF] Lazzaro | Intraspecific trait variability and genetic diversity in the adaptive strategies of serpentine and non-serpentine populations of Silene paradoxa L[END_REF][START_REF] Sharma | Bridging the gap: linking morpho-functional traits' plasticity with hyperaccumulation[END_REF]. Hyperaccumulators were also relatively poor competitors with more S and R strategies (e.g., shade-intolerant) [START_REF] Ernst | Evolution of metal tolerance in higher plants[END_REF][START_REF] Baker | Metallophytes: the unique biological resource, its ecology and conservational status in Europe, central Africa and Latin America[END_REF]. This is in line with the underrepresentation of competitive broadleaf species from hyperaccumulators. However, contrary to expectations [START_REF] Kazakou | Hypotheses, mechanisms and trade-offs of tolerance and adaptation to serpentine soils: from species to ecosystem level[END_REF][START_REF] Adamidis | Species adaptive strategies and leaf economic relationships across serpentine and non-serpentine habitats on Lesbos, Eastern Mediterranean[END_REF], they were not consistently associated with the resource conservation end of the leaf economics spectrum. Nevertheless, it should be kept in mind that all models performed poorly, which can be caused by a weak ecological signal at a global scale but also, potentially (and maybe primarily), by a lack of quality data on traits and strategies of hyperaccumulators.

The high variability in hyperaccumulator traits/strategies could also suggest that many alternative strategies have convergently evolved to promote trace element accumulation through various pathways. The accumulation strategy may change according to the metalliferous biogeochemical systems (i.e., ultramafic soil with Ni and Co or calamine soils with Zn, Pb, and Cd) or even the trace element accumulated. For example, co-occurring Ni and Co may be stored in different tissues and cell parts (i.e., vacuolar or exocellular sequestration) [START_REF] Tappero | Hyperaccumulator Alyssum murale relies on a different metal storage mechanism for cobalt than for nickel[END_REF][START_REF] Rue | Uptake, translocation and accumulation of nickel and cobalt in Berkheya coddii, a 'metal crop' from South Africa[END_REF]Paul et al. 2020b) or one specific trace element may accumulate in different tissues depending on the species and interactions with other trace elements [START_REF] Broadhurst | Interaction of nickel and manganese in accumulation and localization in leaves of the Ni hyperaccumulators Alyssum murale and Alyssum corsicum[END_REF]Paul et al. 2020a).

This may translate into alternative strategies of hyperaccumulation, relying on distinct plant traits/strategies. Detecting such alternative strategies at a global scale will require many more points than the 19 hyperaccumulator species from which we could gather reliable data in this study.

Collecting more data on hyperaccumulator species is also necessary to address the non-independency between species and include some factors in further analysis (e.g., climate, phylogeny, habitat, life cycle, soil fertility) [START_REF] Broadley | Phylogenetic variation in heavy metal accumulation in angiosperms[END_REF][START_REF] Cappa | Evolutionary aspects of elemental hyperaccumulation[END_REF][START_REF] Joswig | Climatic and soil factors explain the twodimensional spectrum of global plant trait variation[END_REF].

International Trait Data Collection

Our preliminary study does not provide conclusive evidence for trait syndromes associated with trace element hyperaccumulation. We believe this may be primarily due to the lack of statistical power, given the poor representation of hyperaccumulators in the TRY database. A systematic review is currently underway to increase the hyperaccumulator species list. However, hyperaccumulators remain underrepresented in trait databases, as they are often rare and localized species [START_REF] Violle | Trait databases: misuses and precautions[END_REF].

The lack of trait representation calls for a coordinated international effort to gather trait data on hyperaccumulators, particularly from locally endemic species. Non-hyperaccumulator metallophyte species should also be sampled to distinguish hyperaccumulation strategies and traits from those specifically involved in trace element tolerance. Future investigations could also focus on Ni hyperaccumulator species as they represent ~70% of identified hyperaccumulator species [START_REF] Reeves | A global database for plants that hyperaccumulate metal and metalloid trace elements[END_REF]) and would remove the noise associated with different metal accumulation.

Only a few leaves are necessary to inexpensively measure key leaf economic traits (LA, SLA, and LDMC). These leaves can be obtained from field specimens, gardens, or controlled experiments (if controls on metalliferous soil are available). Detailed protocols can be found in the New handbook for standardized measurement of plant functional traits worldwide [START_REF] Pérez-Harguindeguy | Corrigendum to: New handbook for standardised measurement of plant functional traits worldwide[END_REF]) and the TRY database (WEB cited protocols) [START_REF] Kattge | TRY plant trait database -enhanced coverage and open access[END_REF]. Ideally, this approach should include more traits (i.e., plant height, seed mass, and stem-specific density) and trace elements leaf concentrations [START_REF] Lange | Copper and cobalt accumulation in plants: a critical assessment of the current state of knowledge[END_REF]). In addition, root traits (e.g., dry matter content, diameter, depth) should also be considered to extend this approach, as they seem correlated with trace element accumulation and stress-tolerant strategies [START_REF] Gervais-Bergeron | Willow aboveground and belowground traits can predict phytoremediation services[END_REF]. To participate in this international sampling effort, we ask for measurements of metallophyte traits and their publication on the TRY database. To join this initiative or for further questions, contact the corresponding author.

Conclusion

This study is the first attempt to link plant traits to their ability to concentrate trace elements. Our results did not provide evidence for hyperaccumulators being necessarily characterized by a resource-conservative trait syndrome or a stress-tolerating strategy (according to Grime's framework and a classification based on leaf morphology alone). We believe that our inability to unravel trait syndromes among hyperaccumulators is rooted at least partly in a lack of reliable trait data. However, it may also well be that leaf morphology is a poor predictor of a plant's ability to concentrate trace elements at such a large scale (e.g., decoupled ecophysiological processes or limiting factors). Filling the gaps will be essential to guide applied land reclamation efforts and preserve metalliferous environments. We thus call for an international collaborative sampling effort to measure and share on TRY the traits of hyperaccumulator and metallophytes species.

Fig. 1

 1 Fig. 1 Representation of hyperaccumulators' traits (a) and CSR strategies (b). Comparing all non-hyperaccumulators (gray circle, n = 4,503), non-woody hyperaccumulators (blue circle, n = 15), and woody hyperaccumulators (red circle, n = 4) species available on TRY database. Abbreviations: leaf area (LA), specific leaf area (SLA), leaf dry matter content (LDMC), competitive (C), stress-tolerant (S), and ruderal (R).

Table 1 .

 1 List of the 19 hyperaccumulators found on the global database TRY, their life forms, functional traits values, and 162 hyperaccumulation elements. 163

	Family	Species	Life	LA	SLA	LDMC	Trace	Concentrations	Source
			form	(mm2)	(mm 2 g-	(mg g-1)	element	(mg kg-1)
					1)
	Apocynaceae	Carissa spinarum	shrubs	339	9.46	0.47	Cu	702	(Rajakaruna and Bohm 2002)
	Brassicaceae	Arabidopsis halleri	forbs	291	38.2	0.19	Zn	53,900	(Stein et al. 2017)
							Cd	3640
	Brassicaceae	Odontarrhena tortuosa	forbs	21.7	15.3	0.33	Ni	1790	(Teptina and Paukov 2015)
		(syn. Alyssum tortuosum)
	Brassicaceae	Noccaea caerulescens (syn. Thlaspi caerulescens)	forbs	114	30.3	0.15	Zn Ni	53,500 16,200	(Reeves et al. 2001; Schwartz et al. 2006)
							Cd	2890
	Brassicaceae	Noccaea montana	forbs	164	18.3	0.15	Ni	4300	(Boyd and Martens 1998)
		(syn Thlaspi montanum)
	Caryophyllaceae	Minuartia verna	forbs	3.66	22.5	0.29	Zn	3200	(Johnston and Proctor 1977)
							Zn	18,400	(Fellet et al. 2012)
							Tl	3630	(Fellet et al. 2012)
	Compositae	Dieteria canescens (syn. Machaeranthera canescens)	forbs	97.2	10.8	0.26	Se	740 1350	(Beath et al. 1941) (Rosenfeld and Beath 1964)
	Compositae	Gutierrezia microcephala	shrubs	19.6	69.5	0.10	Se	1290	(Beath et al. 1941)
	Compositae	Symphyotrichum ascendens	forbs	96.4	10.5	0.21	Se	4460	(Pfister et al. 2013)
	Compositae	Symphyotrichum ericoides	forbs	63.9	14.0	0.24	Se	3000	(El Mehdawi et al. 2014)
	Fabaceae	Anthyllis vulneraria	forbs	600	16.9	0.18	Zn	14,500	(Escarré et al. 2011)
	Lamiaceae	Stachys recta	forbs	739	28.1	0.22	Ni	2600	(Lisanti 1952)
	Fabaceae	Astragalus canadensis	forbs	675	15.6	0.27	Se	1110	(Byers 1938)
		(Syn. Astragalus carolinianus)
	Meliaceae	Walsura pinnata	trees	27.1	16.2	0.40	Ni	8000	(van der Ent et al. 2019)
	Plantaginaceae	Linaria alpina	forbs	15.0	22.7	0.17	Ni	1990	(Vergnano Gambi O and Gabrielli R 1979)
	Plumbaginaceae	Armeria maritima	forbs	95.1	15.0	0.19	Zn Cu	5500 4230	(Szarek-Łukaszewska et al. 2004) (Farago et al. 1980)

Acknowledgments

We acknowledge the essential contribution of researchers administering and contributing to the TRY database and the Global Hyperaccumulator Database. Your data sharing enables conducting of global analyses such as this.

Funding

We acknowledge financial support from the Quebec Research Fund Nature and Technology (FRQNT No. 211259), the Natural Sciences and Engineering Council of Canada (NSERC), [funding reference number CGS D -569322-2022], the Federation of Canadian Municipalities (FCM), under the grant 'Use of phytoremediation to revitalize former industrial sites in eastern Montreal' and the Economic Development Division of the City of Montreal.

Data availability

The data presented in this study are available on the repository of the University of Montreal, at doi.org/10.5683/SP3/QKNQ08.

Competing interest

The authors have no relevant financial or non-financial interests to disclose.

Author's contribution

Béatrice Gervais-Bergeron, Pierre-Luc Chagnon and Michel Labrecque conceived the ideas and designed methodology. Data were collected and analysed by Béatrice Gervais-Bergeron. The first draft of the manuscript was written by Béatrice Gervais-Bergeron, Adrian L.D. Paul, Pierre-Luc Chagnon and Michel Labrecque. All authors contributed critically to the drafts and gave final approval for publication.


Design and Characterization of an Optical 4H-SiC Bipolar Junction Transistor

Pierre Brosselard 1) , Dominique Planson 1) , Dominique Tournier 1) , Pascal Bevilacqua 1) , Camille Sonneville 1) , Luong Viet Phung 1) , Mihai Lazar 2) , Bertrand Vergne 3) , Sigo Scharnholz 3) and Hervé Morel 1) pierre.brosselard@insa-lyon.fr 1) Univ Lyon, INSA Lyon, Univ. Claude Bernard Lyon 1, Ecole Centrale Lyon, CNRS, Ampère, F-69621, France 2) Nanomaterials, Nanotechnologies, L2N, EMR CNRS7004, Université de Technologie de Troyes, 10300, Troyes, France 3) ISL, French-German Research Institute of Saint Louis, 5 rue Général Cassagnou, 68301 Saint Louis, France

SiC bipolar transistors and thyristors have been introduced in the literature and have shown to have a promising performance [1]- [START_REF] Dheilly | Pulse characterization of optically triggered SiC thyristors[END_REF]. Those applications include but not limited to flexible ac transmission systems (FACTS), high-voltage direct current (HVDC) and wind power [START_REF] Mojab | Low-leakage drive for optically-triggered high-power SiC emitter turn-off thyristors[END_REF]. In this paper, an optical 4H-SiC BJT have been designed and characterized at Ampere Lab and fabricated at L2N. The BJT was designed to withstand a voltage of 10kV. The BJT were fabricated on a 4H-SiC wafer using a 120 μm thick epilayer with a doping concentration of 8×10 14 cm -3 (Fig. 1). After electrical characterization, we obtain a breakdown voltage about 11 kV [START_REF] Ammar | Optimized Junction Termination Extension and Ring System for 11 kV 4H-SiC BJT[END_REF]. For the optical structures, there is no contact and metal on the base fingers. A pulsed (5 ns) laser emitting UV at 349 nm is used to generate electron-hole pairs into SiC. The frequency of the laser is 1 kHz. In order to enlarge the laser beam size, a beam expander is used. Fig. 3 presents the electrical circuit for the characterization of the BJT. Actually, we have fixed the RLoad at 4.7 . The role of the capacitor is to stabilize the input voltage when the BJT switches on.

First measurements have been performed on the structure without metal and P + implantation on the base. We have characterized for two different Powers of Laser and Input voltage. At a given input voltage, we see an impact on the current peak (see Fig. 4, 5 and 6). Regarding the impact of the input voltage, the switching time is the same.

The first goal of our work was to turn-on an optical BJT with a pulsed UV emitting laser and it has been obtained as it can be observed. Now, we need to optimize the PCB design regarding parasitic inductors and integrate the capacitor very closed to the die. Moreover, we need to add a shunt resistor to measure the current. As the pulse duration of the laser is short, an optimization of the voltage and current measurements through the device is mandatory.

In the final paper, we will present results for the different structures of the BJT using our new design of the PCB integrating the Load Resistor, Capacitor and shunt resistor.

  Four different structures have been implemented in the layout for the optical parameters see on Fig. 2. Three different Base and Emitter lengths have been implemented 10, 15 and 20 µm. The last implemented BJT has got a 20 µm length without Metal on the Base PAD (Fig 2) and no P + implantation on this structure.

Fig. 1 .Fig. 3 .Fig. 4 .

 134 Fig. 1. Cross-section of the optical 4H-SiC BJT Fig. 2 Picture of 4 selected optical BJT with key parameters (Base and Emitter length)