HATP/EHDA: A Robot Task Planner Anticipating and Eliciting Human Decisions and Actions

Guilhem Buisan 1 , Anthony Favier 1,2 , Amandine Mayima 1 and Rachid Alami 1,2 * Abstract-The variety and complexity of tasks autonomous robots can tackle is constantly increasing, yet we seldom see robots collaborating with humans. Indeed, humans are either requested for punctual help or are given the lead on the whole task. We propose a human-aware task planning approach allowing the robot to plan for a task while also considering and emulating the human decision, action, and reaction processes. Our approach, named Human-Aware Task Planner with Emulation of Human Decisions and Actions (HATP/EHDA), is based on the exploration of multiple hierarchical tasks networks albeit differently whether the agent is considered to be controllable (the robot) or uncontrollable (the human). We present the rationale of our approach along with a formalization and show its potential on an illustrative example.

I. MOTIVATION

Imagine that you are working in a factory and order your robotic assistant to assemble a small piece of furniture (represented by a stack, Fig. 1(a)) including several components (represented by cubes, Fig. 1(b)). Some components are only accessible by one, others are reachable by both of you and still others are reachable by a another human, carrying her own task. Many ways of realizing this task are available for the robot: depending on how you formulated your request, it can assume that you will help it or not; it can try to perform it on its own, if you are busy doing something else, even if it takes longer; it can request punctual help from the other human, to more efficiently perform the task if verbal communications are feasible; finally, it can also share the entire task with this third agent, fully involving her in the assembly. All these solutions may or may not be feasible, and can be more or less efficient, depending on the world state, the goal, and more importantly the estimated decision and action processes of the surrounding humans.

To tackle these issues, we present a novel task planning approach dedicated to HRI which, by planning for both the human and the robot, tries to satisfy multiple objectives:

1) Plan with or without assuming a prior shared goal. The robot and the human are not always sharing a goal. Our planner can balance between integrating the sharing of a goal with a human (assumed to be collaborative) in the plan and making the robot do the task alone, or integrate the possibility to ask for punctual human help.

2) Model the human decision processes. When taking part in a task, a human (assumed willing to collaborate) will {guilhem.buisan, anthony.favier, amandine.mayima, rachid.alami}@laas.fr also plan to reach their (potentially shared) goal. Our robot must be able to account for this to provide plans that are expected by the human partner and explainable to them.

3) Help the human decision, but not compel it. By modeling the human decision processes and their potential effects, the planner will need to consider various courses of action, leaving more latitude to the human and avoiding replanning 4) Act and decide on the different agents' beliefs. It is important to be able to represent actions as having different effects on the beliefs of the robot or the human. Indeed, some robot actions are partially or not observable by the human. Therefore, when performing them, the human has no way of knowing the complete new world state. Moreover, these effects and their observability often depend on the current world state, which representation must be supported by the planner. Finally, decisions made while planning may require to reason on both the robot and the human beliefs (e.g. knowledge alignment communication actions, robot asking questions).

To do so, we took inspiration from previous work on human task modelling and human-aware task planning to build a task planner focusing on human-robot collaboration. Our planner is able to explore in a distinct manner the deliberation and plan elaboration processes of the robot and the human, in order to build robot plans and anticipate the decisions, actions and reactions of the human. Moreover, it maintains one belief base per agent (human or robot).Actions preconditions and effects can be expressed in any of these belief bases. It allows to represent situational or inherently non observable actions from agents, knowledge transfer actions, and to detect beliefs divergences and plan accordingly. Our scheme is designed to provide a suitable framework enabling the anticipation of the beliefs, potential decisions, reactions and contributions to a shared goal or to an interaction situation of both agents. This overall anticipation process takes place within the robot decisional activity.

In the sequel, we first discuss related work before presenting our approach, its intents and rationale. Then, we provide a formalization of our planner scheme. Finally, some examples are presented before concluding.

II. BACKGROUND

To plan for the human decisions and actions, we need to model the humans decision and action processes. Thus, we first present common ways of modelling human activity excerpted from human-computer interaction literature. Then, we review several contributions to elaborate shared humanrobot plans.

A. Human Task Modeling

Multiple approaches try to model the human activity. They are mainly used to design a system that integrates gracefully in human tasks, in order to improve their performance. These tasks can be seen as hierarchical, where abstract ones decompose into smaller, more concrete ones.

A common way of representing human activity and interaction with computer at high abstraction level is by using task models. The hierarchical structure of human activity was first exploited by Annett and Duncan [START_REF] Annett | Task analysis and training design[END_REF]. They state that tasks can be described at several levels of abstraction until a certain criterion is met. Each task can thus be refined into subtasks detailing the procedure followed by the human to achieve the higher level task.

Task modeling has then evolved to introduce interaction with systems, produced and needed information, potential errors and a wide variety of operators specifying how tasks interacts with each other during their execution. Task models are now commonly used in user-centered and user interface designing processes. Most advanced notations include Con-curTaskTrees [START_REF] Paternò | Concurtasktrees: an engineered notation for task models[END_REF] and HAMSTERS [START_REF] Martinie | Analysing and demonstrating tool-supported customizable task notations[END_REF].

These models are used to design or to evaluate interactive systems. They allow the designer to better understand the user task or to study the user workflow using their system. However, these models contain too little information for a system to be able to reason and take decision on them (either in planning or acting).

We drew inspiration from these models, sharing commonalities with Hierarchical Task Networks (HTNs), to represent human decision processes in HATP/EHDA.

B. Planning a Task for Both the Human and The Robot

While human activity modeling and autonomous planning have been studied separately for decades, there are still only few systems proposing to incorporate human activity into planning for intricate interactive tasks, leading to shared plans [START_REF] Grosz | Collaborative plans for complex group action[END_REF]. Planning for both a robotic agent and a human differs largely from multi-robot planning. Indeed, while the robotic agents are planning for itself and will surely execute the plan, the human is not directly controllable (making them follow the plan may require the robot to at least communicate and perhaps negotiate) and can also have their own plan they are trying to execute.

Most approaches to the so-called human-aware task planning problem assume a fully controllable human, willing to participate in the accomplishment of a common goal [START_REF] Torreño | Cooperative multi-agent planning: A survey[END_REF], [START_REF] Sebastiani | Dealing with on-line human-robot negotiations in hierarchical agent-based task planner[END_REF]. Then, information and plan sharing are done in a postprocessing step or at execution time [START_REF] Devin | An implemented theory of mind to improve human-robot shared plans execution[END_REF], [START_REF] Nikolaidis | Planning with verbal communication for human-robot collaboration[END_REF].

The Hierarchical Agent-based Task Planner (HATP) proposes a hierarchical approach to multi agents task planning [START_REF] Alili | A task planner for an autonomous social robot[END_REF], [START_REF] Lallement | Hatp: An htn planner for robotics[END_REF]. This HTN-based planner is able to elaborate a multi-agents plan based on a single HTN tree. Moreover, it maintains one beliefs base per agent allowing to write task decomposition rules and actions preconditions and effects in any agent beliefs base. Finally, HATP also computes costs for the plans found based on action costs and predefined social rules. However, HATP assumes that a shared goal has been established between the human and the robot prior to the planning process and that the generated plan will be shared with the human before the execution [START_REF] Milliez | Using human knowledge awareness to adapt collaborative plan generation, explanation and monitoring[END_REF]. Indeed, HATP does not represent the human as an agent having a separate decision process that may lead to diverging plans without robot communication.

Other approaches are explicitly considering an external human model, which can be used to predict future human actions, and plan accordingly. Hoffman and Breazeal present an approach where the robot anticipates human actions to provide efficient support [START_REF] Hoffman | Effects of anticipatory action on human-robot teamwork efficiency, fluency, and perception of team[END_REF]. The environment is represented as a first-order Markov process (implying that the human can be represented as an hidden Markov model acting upon the, observable, environment). Buckingham et al. propose a planning scheme questioning humans mental models returning the effects of expected future humans actions [START_REF] Buckingham | Robot planning with mental models of co-present humans[END_REF]. The planner is then able to determine a robot policy influencing the humans actions. In this work, they show how this framework is able to cope with interactive tasks even without assuming that the human is collaborating. Similarly, Unhelkar et al. proposed a POMDP-based approach called CommPlan [START_REF] Unhelkar | Decision-making for bidirectional communication in sequential human-robot collaborative tasks[END_REF]. The POMDP is built using a user defined MDP (Markov Decision Process) representing the collaborative task and an AMM (Agent Markov Model) representing the human decision-making process. This POMDP is then solved to produce a robot policy which, inter alia, decides when the robot has to communicate about its beliefs, to question the human about theirs and to ask the human to perform an action. Besides, the human AMM is not only specified by the programmer but also refined during the interaction via learning. However, these approaches consider the human model as an oracle on which reasoning is hardly possible during the planning process. Moreover communication models and human decision processes are coarse and do not offer any insight for helping the robot planning process.

Additionally, to cope with the uncertainty of the human knowledge, Petrick and Foster propose to use conditional planning allowing to plan for incomplete information [START_REF] Petrick | Planning for social interaction in a robot bartender domain[END_REF]. By doing so, the planner elaborates a plan for the robot accounting for multiple possible human choices, and depending on the knowledge received the execution component can execute the right branch of the plan.

Likewise, Sanelli et al. ( [START_REF] Sanelli | Short-term human-robot interaction through conditional planning and execution[END_REF]) present an approach not only elaborating conditional plans for the robot depending on the possible human choices (e.g. the choice of activity the human wants to perform), but they are able to transform this conditional plan into a Petri net plan to handle its execution. This contribution is inspired by a previous work of Nardi and Iocchi ([17]) in which they present a method for transforming (linear) joint plan into a Petri net plan managing its execution. Interestingly, the human actions from the plan are changed into a part of the Petri net where the robot elicits the action (e.g. via a verbal communication) if the human does not perform it by themselves. However, these approaches only request the human to make single actions, instead of sharing a high level goal, which can become unpleasant if done repeatedly.

Finally, Chakraborti et al. use both the robot model and the estimation of the model the human has of the robot to improve plan explicability [START_REF] Chakraborti | Plan explanations as model reconciliation: Moving beyond explanation as soliloquy[END_REF]. Indeed, they propose a novel approach called model reconciliation which they present as a classical planning problem. In this problem, the goal is to make identical both the optimal plans generated via the robot model and the human estimation of the robot model. To do so, they define a list of operators on the models in order to modify them until the plans match. However, it only has been applied to robot plans and not to joint plans. Indeed, the generated plans contain only robot actions, and the robot and the human do not directly collaborate in the presented tasks.

III. DESCRIPTION A. Rationale

We separate the agents who may take part in a given task into two categories: the controllable agent (i.e. the robot) for which the planner needs to select the best course of actions to generate a plan; and the uncontrollable agent (i.e. the human) on whom the planner has no direct control but, still, has a representation of their decision, action and reaction models.

The two agent types are fundamentally different: 1) the robot is controllable since the process is run by the robot itself, 2) the human agent is not controllable since the process can only "speculate" on their decisions and actions, but can model that the robot actions can still influence them and that some of them are observable by the robot, 3) the two agents are not equivalent, the robot agent role is to help, assist and facilitate human and to synthesize pertinent, legible and acceptable behavior.

We want to devise a planner allowing the controllable agent to plan for its actions while anticipating the decisions, actions and reactions of the uncontrollable agent. Moreover, we want the planner to be able to generate plans where the robot actions elicit situations calling for human decision, action and reaction, thus creating and anticipating collaboration and interaction.

This problem may be seen as a classical non deterministic planning problem, but enriched with the ability of the robot to model the actions, beliefs and decision process of the human. Thus, we have to consider distinct action models, beliefs and execution streams for each of the agents involved. HTN approaches have already been shown to be suitable for HRI as they allow to communicate about the plan more easily [START_REF] Lallement | Hatp: An htn planner for robotics[END_REF]. Therefore, we chose to use HTN planning for both the controllable and uncontrollable agents. HTN planning aims at decomposing abstract tasks into atomic, primitive tasks by choosing from a list of available contextdependent refinements for each abstract task, ensuring that preconditions and effects of refined primitives tasks are satisfied throughout the created plan. Similarly to HATP [START_REF] Sebastiani | Dealing with on-line human-robot negotiations in hierarchical agent-based task planner[END_REF], our planner elaborates a plan with several streams of actions each assigned to an agent involved in the task. But while in HATP, all the streams are built starting from an initial root node corresponding to a shared goal between all agents, our planner starts from multiple initial root nodes corresponding to the first task of the initial agenda of each different agents.

B. Definitions

The main structure manipulated by our planner is the agent, more precisely two will be represented, the human and the robot. Each agent has their own beliefs, action model, agenda, plan and triggers. The planner has to use their action models and beliefs to decompose the tasks in their agenda into primitive tasks (actions) that are inserted in their plan. By doing so, it also has to update the beliefs of each agent and to model their reaction by executing the triggers.

a) Agents: First, we define an agent state as a tuple σ α = d α , π α , s α , with d α the agenda, π α the partial plan and s α the beliefs of the agent α (more details are presented in what follows). Then, we define an agent as being α = name α , σ α , Λ α , T r α , with name α the agent name, σ α the agent state, Λ α the action model and T r α the triggers of the agent α (detailed in what follows). Then we define two agents: the controllable one -the robot -; and the uncontrollable one -the human -. We have σ = σ robot , σ human representing an agents state, being the state of all the agents at a certain plan step. Let Σ be the set of all the possible agents states.

b) Beliefs: Let S be the set of all possible world states, we call beliefs of an agent α the state s α ∈ S in which this agent thinks the world is in. It is important to note that the state of the controllable agent (robot) is assumed to be the real world state estimation for the planner, as we consider the planner as being part of the controllable agent. c) Action models: We represent the action model of an agent α as Λ α = Op α , Ab α , M e α where Op α are the primitive tasks (i.e. operators, actions) that the agent α can perform, Ab α the set of abstract tasks and M e α are the methods (i.e. decompositions) describing how an agent α can perform an abstract task through a refinement process. It is important to note that while this representation makes a clear distinction between the robot and the human tasks, it does not prevent representing joint abstract tasks or tasks that can be either done by one or the other agent. Indeed, as we show later, complementary abstract tasks can be represented and some tasks can have the same operational model even if they are not in the same agent action model.

More precisely, the primitive tasks (operators) are defined as functions: Op o : Σ → Σ∪⊥ which produce new agents state, being the effect of the application of the primitive task, or false if the task is not applicable. We represent operators as being instantaneous (or all having the same duration) in their realization. With this definition of operators, we are able to represent action effecting the beliefs of any agents (e.g. depending on the observability of a robot action, the operator will or will not update the beliefs of the human). Moreover, we can represent actions whose only effects are knowledge sharing (e.g. verbal communication for belief alignment).

Then, methods are defined as tuple, containing an abstract task and a decomposition function: M e m = τ, δ with τ ∈ Ab and δ : Σ → (Op ∪ Ab) n ∪ () ∪ ⊥ with n ∈ N * , which, depending on agents state, decompose the abstract task returning a sequence of tasks (primitive or abstract), an empty sequence if the abstract task does not need to be decomposed, or false if the task cannot be decomposed in the current state. Multiple methods can address the same abstract task, the goal of the HTN planner is then to choose the right one to create a plan. d) Agents agendas and plans: An agenda d α and a plan π α (this agent only stream of actions) are defined for each agent α. The agenda d α is a sequence of tasks (abstract or primitive) having to be performed by the agent. The plan π α is a sequence of primitive tasks, built from the agenda, which the agent has to perform. The links of actions order between the two streams of actions (plans) are kept in each plan, allowing for coordination.

e) Agent triggers: Finally, we define for each agent α a set of so-called trigger functions T r α . These trigger functions aim at representing reactions of agents to certain situations (subsets of world states). They are useful to model event-driven behavior, as in PRS [START_REF] Ingrand | PRS: A high level supervision and control language for autonomous mobile robots[END_REF], when a specific world state triggers a reaction from an agent. Besides, these triggers can be used to represent social norms as defined in [START_REF] Carlucci | Explicit representation of social norms for social robots[END_REF], where the user can specify literals which, if true in the world state during the planning process, add some specific robot actions to the plan.

Trigger functions are defined as: T r t : Σ → (Op ∪ Ab) n ∪ () with n ∈ N * , returning a sequence of tasks to be inserted in an agent agenda as a reaction to specific agents state. For now, the tasks returned by a trigger function are added on top of the agenda, thus preempting any task that may have started to be decomposed. A considered solution is to support the flagging of some abstract tasks in the domain as being atomic. We can then prevent the tasks returned by a trigger to be inserted between any tasks resulting from the decomposition of an atomic task.

IV. THE PLANNING PROCESS

To start planning, HATP/EHDA must be given the two action models (the robot and the human HTNs), the initial beliefs of both agents (which can differ) and the initial agenda of both agents. The initial agenda of the robot represents the task to decompose, while the agenda of the human represents any task the human is estimated to be commited to. If a shared goal has been established prior to planning between the robot and the human (e.g. the human asking to perform a task with the robot), the agenda of both agent will be filled with the same task.

The planning process is done in three parts: (1) First, both HTNs are explored in a turn taking fashion, resulting in a valid joint plans tree. (2) Then, based on this tree, robot actions are selected according to action, plan-wide and social costs, resulting in a conditional plan, where at each step multiple human actions can be performed but only one robot action is set. (3) Finally, causal and threat links are added between actions of the conditional plan to ease its execution.

A. HTNs Exploration

The robot HTN exploration is a pretty standard depthfirst algorithm. The first task λ from its agenda d robot is popped, then if it is an abstract task λ ∈ Ab, all the applicable methods are applied, and their results are prepended to the agenda, thus giving new agents state (with the same beliefs as the previous ones but with the robot agenda updated) and branching our search space. We recursively iterate with the new task popped from the new robot agenda. Eventually, the popped task will be a primitive one λ ∈ Op, its function will then be applied to the currently explored agent states. If it returns false (⊥), the action is not applicable, and the exploration backtracks to another decomposition of an abstract task. However, if the action is applicable (returns a new agents state), the action is added to the robot plan and the triggers are run for each agent, updating their agenda if necessary. Then, the human HTN is queried to get their possible next actions from this new agents state. The possible actions found are added to the human plan, and, for each possible new agents state, we apply the triggers of each agent then we continue the robot HTN exploration. This exploration continues until the robot agenda is empty, or all the branches return false. The HTNs exploration process is summarized on Fig. 2.

The human HTN exploration differs from classical HTN planner as the goal is not to produce a complete plan, but rather to list all the actions the human is likely to perform in a given agents state. We recursively decompose the first task of the human agenda d human with every applicable method, until we reach an applicable operator. All the operators from all the applicable decompositions are returned to the robot HTN exploration and applied. Two special cases are handled during the exploration. If the human agenda is empty whereas the robot one is not, the exploration returns a default action IDLE for the human (which does not modify agents beliefs nor agendas). This action represents the non-involvement of the human in a task. Besides, if no applicable action is found for the human a default action WAIT is returned (which does not modify agents nor agendas). This action represents the impossibility of the human to act in the current situation, making them wait for the robot to proceed. This default action can also be used in a domain to represent the human decision to wait for the robot to act.

Once the robot agenda is emptied, the agents state is set as a success, the plan is added to the valid plans tree and the search can be continued until no decomposition is left for any task.

B. Conditional Plan Selection

Once this exhaustive search has been done, the result is a valid plans tree of alternating robot and human feasible actions along with their current beliefs leading to a task completion. The goal of this second planning step is to select robot actions such as each human action in the plan has only one robot action as a child. To do so, we define a cost function cost : σ × Op → R + representing the cost of an action in a specific state. The data structure is now similar to a two players game tree. However, MinMax approaches are not suitable here, as we are not in an adversarial setup but more into a collaborative one. Indeed, trying to minimize the maximal possible cost is assuming that the human will always do the actions leading to the worst plan. This defensive behavior could lead to non optimal plans. We thus propose to explore this tree differently.

Moreover, like in HATP we allow to define social costs functions. These functions take a complete human and robot sequence of actions (π r and π h ) and return a cost (R + ) which is added to the cost of the plan previously determined. By doing so, we can penalize non acceptable sequence of robot actions (e.g. serving a meal just after taking out the trash) or non satisfactory human required contribution (e.g. the robot requesting the human to perform small tasks multiple times instead of giving the big picture of the real task to perform).

The approach we propose for plan selection is to minimize the average cost. It represents the human potentially selecting any course of actions in their stream (while still respecting the action model defined in their HTN). The algorithm is given the root action of the task network previously generated and returns the cost of the conditional plan selected while having selected the robot actions in the task network minimizing the average cost of plans. Finally, causal and threats links are computed on the conditional plan, to help the supervision in its execution.

V. EXAMPLES

To highlight the potential of our approach we present as example a cube stacking scene. The scene is depicted in four different scenarios on Fig. 3. The goal consists in stacking the colored cubes on the empty marks to match the colors of Fig. 1(a). All cubes placed in the middle of the table are reachable from anywhere. However, when close to one side a cube is only reachable from this specific side.

The partial robot and human actions models, as well as their exploration are presented in Fig. 4.

Each scenario is commented below with their corresponding selected plan shown in TABLE I.

a) H1 and R act together: First, the human sets a shared goal by asking the robot to stack cubes with him. Since H1 requests the robot to achieve the goal, it is not a shared goal, the robot agenda is filled with the task to achieve and the agenda of H2 starts empty.

Since it is a shared goal, Both human and robot agendas are initialized with the "Stack" task. Thus, the robot anticipates that the human will pick the unreachable second red cube by querying the human action model. The selected plan to collaboratively stack can be seen in TABLE I(a).

b) Robot acts alone: This time the human asks the robot to stack the cubes but then leaves the scene, the robot must act alone. Hence, the only applicable method to make the second red cube reachable is to move to the other side even though the movement action is expensive (we can imagine a table way longer than shown on the figure).

c) Robot asks punctual help: The first human acts the same way but another one is present, not involved in the task. The robot starts exploring its HTN and, thanks to the presence of the other human, a new method is applicable allowing the robot to ask for help. It can either ask for punctual help or involve completely the other human in the task. Of course, just asking help for one cube is less costly than asking to build the whole stack together. However, asking help to someone not already involved in a common task is still expensive since they have to put themselves in the context of the task. Yet, this punctual help is actually less costly for the robot than moving to the other side so the robot chooses to ask for punctual help. Note that we model the that after being asked to punctually help, the human can either stack the cube herself or just make it reachable to the robot by placing it in the middle. Only the first branch is shown in TABLE I(c) but the selected plan is in fact conditional with two branches as depicted in Fig. 4.

d) Robot invites Human2 to share a goal: Same initial setup but now two cubes are out of reach. Asking for punctual help is still less costly than moving around the table. Nevertheless, this disturbs the human so each new punctual request becomes more expensive than before. Thus, this time setting a shared goal becomes less costly for the robot than asking twice for punctual help.

Using HATP/EHDA on a real collaborative setting HATP/EHDA has been integrated into a complete robotic architecture dedicated to human-robot collaboration [START_REF] Sarthou | The director task: a psychology-inspired task to assess cognitive and interactive robot architectures[END_REF],

inspired by [START_REF] Lemaignan | Artificial cognition for social human-robot interaction: An implementation[END_REF]. Besides HATP/EHDA, the architecture embeds a situation assessment component [START_REF] Sallami | Simulation-based physics reasoning for consistent scene estimation in an hri context[END_REF] together with a semantic knowledge management [START_REF] Sarthou | Ontologenius: A long-term semantic memory for robotic agents[END_REF] to assess the state of the environment and estimate human beliefs. When the supervision decides of a task to perform and if this task corresponds to a human-robot shared goal or an individual robot goal, it invokes HATP/EHDA. Then, it controls the execution of the obtained plans. Their structure allows the controller to determine in which condition it has to simply wait for the human to choose or to act, or if it has to ask them to make a decision. An attached video illustrates several situations where it is shown that the human can make a choice or another in the case of a shared goal (Fig. 1). It also shows the case where the robot decides how and when to involve a human in the realization of a task.

VI. CONCLUSION

HATP/EHDA is a task planning approach allowing a robot to plan its actions while accounting for human decision, action and reaction, resulting in a conditional joint plan. To do so, a robot HTN is explored and human HTN models are queried (corresponding to human task modeling) to retrieve the possible human decisions, and actions. In fact, both human and robot action effects and preconditions can be expressed in either agent beliefs, allowing to predict, maintain or realign any belief divergence during the task planning process. We claim that HATP/EHDA planning framework is well suited and can be tuned to cover most of the humanrobot planning problems and schemes previously envisaged in the literature: planning for human-robot while assuming a shared goal ( [START_REF] Lallement | Hatp: An htn planner for robotics[END_REF], [START_REF] Unhelkar | Decision-making for bidirectional communication in sequential human-robot collaborative tasks[END_REF], [START_REF] Nardi | Representation and execution of social plans through human-robot collaboration[END_REF]), planning in conditions where the robot can help and facilitate known human activities ( [START_REF] Hoffman | Effects of anticipatory action on human-robot teamwork efficiency, fluency, and perception of team[END_REF]), planning for the robot alone and deciding when and in which conditions it can request help from human ( [START_REF] Tellex | Asking for help using inverse semantics[END_REF]), integration of communication acts in the plans ( [START_REF] Buisan | Human aware task planning using verbal communication feasibility and costs[END_REF], [START_REF] Devin | An implemented theory of mind to improve human-robot shared plans execution[END_REF], [START_REF] Belhassein | A horizontal approach to communication for human-robot joint action: Towards situated and sustainable robotics[END_REF]), incremental human-robot plan negotiation ( [START_REF] Milliez | Using human knowledge awareness to adapt collaborative plan generation, explanation and monitoring[END_REF], [START_REF] Chakraborti | Plan explanations as model reconciliation: Moving beyond explanation as soliloquy[END_REF]) and determining which decision should be better postponed to leave more latitude to the human partner ( [START_REF] Devin | About decisions during humanrobot shared plan achievement: Who should act and how?[END_REF]).

Fig. 1 .

 1 Fig. 1. (a) A robot and a human assembling a (b) cube stack. The robot environment estimation is depicted on top. For the best efficiency, the robot must plan for and adapt to the human possible decision and action processes.

Fig. 2 .

 2 Fig. 2. The HTNs exploration, as explained in IV-A, consists in iterative loops of four steps : (1) Get possible robot actions from the robot HTN, add them in the plan and apply their specific effects on the H & R beliefs, (2) Check Triggers and add the reactions in the corresponding agendas, (3) Get possible human actions based on his/her updated (estimated) beliefs, add them in the plan and apply their effects on the H & R beliefs, (4) Check Triggers again and add the reactions in the corresponding agendas.

Fig. 3 .

 3 Fig. 3. Cube stacking scene: A different plan is selected for each scenario, involving nearby humans in the less disturbing way possible.

  (a) R and H1 build the stack together as a shared goal requested by H1. (b) H1 requests to stack the cubes and R acts alone.

Fig. 4 .

 4 Fig.4. Illustration of the incremental exploration of various courses of actions corresponding to scenarios depicted in Fig.3(b), (c) and (d). Since H1 requests the robot to achieve the goal, it is not a shared goal, the robot agenda is filled with the task to achieve and the agenda of H2 starts empty.

TABLE I EXECUTION

 I TRACE OF A SELECTED PLAN FOR EACH SCENARIO.

 [START_REF] Paternò | Concurtasktrees: an engineered notation for task models[END_REF]This work was partially supported by the Artificial and Natural Intelligence Toulouse Institute (ANITI) under grant agreement No: ANR-19-PI3A-0004.


Xavier Torrent
email: xavier.torrent@eagrof.udl.cat

Eduard Gregorio

Jean-Paul Paul Douzals

Cyril Tinet

Joan R Rosell Polo

Santiago Planas

Joan R Rosell-Polo

Assessment of spray drift potential reduction for hollow-cone nozzles: Part 1. Classification using indirect methods

Keywords: Pesticide, spray, drift, drift potential, droplet size, nozzle classification. Nomenclature

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

Introduction

Spray drift is one of the main pollution sources identified when pesticides (also known as plant protection products, PPP) are applied on crops. Harmful effects of pesticides on humans and the environment are known for years. The potential adverse consequences of PPP usage can be significantly dispersed along time and space. As a result, the effects of pesticides on living beings, including humans, may emerge far away from the place where the treatment was performed and often after a long time. Field spray treatments can cause exposure to humans by several ways such as inhalation and dermal contact with the PPP spray drift during the application or with the PPP volatilised fraction some time after the treatment [START_REF] Butler Ellis | Bystander exposure to pesticide spray drift: new data for model development and validation[END_REF]2018;Damalas, C. A. 2015). The spray drift of PPP can be evaluated with a variety of methodologies. These can be divided into two types: those applied in field with the aim of measuring actual drift under reallife conditions (direct methods); and those which attempt to estimate drift potential (DP) under controlled conditions (indirect methods).

In field trials, the use of passive collectors continues to be the most popular methodology for the evaluation of drift during an application [START_REF] Mcartney | Comparative performance of air-induction and conventional nozzles on an axial fan sprayer in medium density apple orchards[END_REF][START_REF] Garcerá | Spray pesticide applications in Mediterranean citrus orchards: Canopy deposition and off-target losses[END_REF]Torrent et al., 2017;[START_REF] Kasner | Spray drift from a conventional axial fan airblast sprayer in a modern Orchard work environment[END_REF], even though the process required is time-consuming and labour-intensive. Other authors, with the aim of simplifying the process, have developed spray drift models, based on many spray drift trials carried out in field conditions, to predict this phenomenon [START_REF] Holterman | An empirical model based on phenological growth stage for predicting pesticide spray drift in pome fruit orchards[END_REF]. In recent years, the application of light detection and ranging (LiDAR) systems [START_REF] Hiscox | Dispersion of Fine Spray from Aerial Applications in Stable Atmospheric Conditions[END_REF][START_REF] Gregorio | LIDAR as an alternative to passive collectors to measure pesticide spray drift[END_REF][START_REF] Gregorio | Measurement of spray drift with a specifically designed lidar system[END_REF] for the field measurement of spray drift has been proposed. These systems have important advantages over passive collectors, both in terms of sensor performance (range and time-resolved measurements)

and lower labour requirements.

The aim of the so-called indirect methods is to determine DP, defined as the fraction of the spray, as a percentage of the output of a spray generator, that is displaced downwind as airborne spray (ISO 22856:2008). The main advantage of indirect methods is their capacity to delimit the complexity and large number of variables that intervene in the drift phenomenon, as the tests are performed under controlled and reproducible conditions. Dimensional analyses of droplet populations are key to interpreting spray drift, with V 100 the droplet size parameter most related to drift prone situations, as reported by [START_REF] Bouse | Effect of spray mixture on droplet size[END_REF] and [START_REF] Arvidsson | Spray drift as influenced by meteorological and technical factors[END_REF]. For this reason, numerous studies have been performed with characterisations of nozzle-generated droplet populations. In the vast majority of these studies, fan-type nozzles have been tested [START_REF] Nuyttens | Drift from field crop sprayers: The influence of spray application technology determined using indirect and direct drift assessment means[END_REF], which are normally used in the treatment of field crops (2D crops). However, it is also of interest to evaluate hollow-cone nozzles. These are used in tree crop treatments (3D crops),

where larger amounts of PPP tend to be used and where DP may be augmented because of the use of air-assistance in the treatment. One of the few studies to undertake a classification of this type of nozzle was that of Van de Zande et al. (2008), using a phase Doppler particle analyser (PDPA), as was also the case in subsequent studies by [START_REF] Holterman | Effects of PDA sampling techniques on spectruml characteristics of agricultural sprays[END_REF][START_REF] Holterman | Comparison of 1D PDA sampling methods to obtain drop size and velocity distributions inside a spray cone of agricultural nozzles[END_REF]. In these latter studies, an analysis was made of the effects of different variables (minimum number of droplets, scanning typology, nozzle height with respect to the measuring point) on droplet sizing. Good correlations have been found in comparative studies of different techniques (PDPA, laser diffraction analysis and particle/droplet imaging analysis (PDIA) (Herbst (2001a;[START_REF] Nuyttens | Effect of nozzle type, size and pressure on spray droplet characteristics[END_REF].

However, with so many techniques (phase Doppler particle analysis (Tuck et al., 1997), laser diffraction analysis [START_REF] Derksen | Droplet spectrum and wind tunnel evaluation of Venturi and pre-orifice nozzles[END_REF], particle measuring system (PMS) [START_REF] Teske | Modeling finer droplet aerial spray drift and deposition[END_REF], and particle droplet imaging analysis [START_REF] Kashdan | A digital image analysis technique for quantitative characterization of high-speed sprays[END_REF]) available to characterise nozzlegenerated droplet populations, the results can vary. In this sense, to harmonize the results obtained through the different methodologies, the ISO 25358:2018 proposes a methodology based on a set of standard nozzles for the definition of droplet size class boundaries.

The wind tunnel is currently the most commonly used indirect method to study and classify nozzles according to their DP. Following this method, [START_REF] Taylor | An Attempt to Relate Drop Size to Drift Risk[END_REF] determined the DP of ASAE reference nozzles for different wind speeds and nozzle heights. [START_REF] Guler | Wind tunnel evaluation of drift reduction potential and spray characteristics with drift retardants at high operating pressure[END_REF][START_REF] Guler | Spray characteristics and drift reduction potential with air induction and conventional flat-fan nozzles[END_REF] and [START_REF] Ferguson | Determining the uniformity and consistency of droplet size across spray drift reducing nozzles in a wind tunnel[END_REF][START_REF] Ferguson | Determining the drift potential of venturi nozzles compared with standard nozzles across three insecticide spray solutions in a wind tunnel[END_REF] evaluated drift potential reduction (DPR), comparing standard and drift reduction flat-fan nozzles. In addition to the effect of nozzle type, evaluation has also been made of the effect of nozzle size [START_REF] Nuyttens | Influence of nozzle type and size on drift potential by means of different wind tunnel evaluation methods[END_REF]. Studies have also been made of the correlation between wind tunnel recorded data and field measured data in order to extrapolate the drift reduction values to field conditions [START_REF] Butler Ellis | Wind tunnel measurements and model predictions for estimating spray drift reduction under field conditions[END_REF]Torrent et al., 2017). [START_REF] Douzals | Spray deposition in a wind tunnel: a kinetic approach of the wind speed effects[END_REF][START_REF] Douzals | In situ droplet size measurements in a wind tunnel[END_REF] measured droplet size in a wind tunnel using different flat-fan nozzles, heights, orientations and wind speeds, defining new DP indicators such as drift ratio (DR) and time-offlight (ToF). Another methodology to evaluate DP for different operating conditions is based on the use of a test bench [START_REF] Balsari | A test bench for the classification of boom sprayers according to drift risk[END_REF], which allows assessment of working parameters [START_REF] Miranda-Fuentes | Developing strategies to reduce spray drift in pneumatic spraying in vineyards: Assessment of the parameters affecting droplet size in pneumatic spraying[END_REF] and classification of different application equipment according to their potential drift reduction [START_REF] Gil | Determination of drift potential of different flat fan nozzles on a boom sprayer using a test bench[END_REF][START_REF] Grella | Toward a new method to classify the airblast sprayers according to their potential drift reduction: comparison of direct and new indirect measurement method[END_REF].

Most of the previously cited studies reporting indirect drift assessments focused on flat-fan nozzles, being these the most used in field crops. The amount of spray drift generated by hollowcone nozzles used in tree crops is significantly higher. Therefore, the main aim of the present study is to classify for the first time hollow-cone nozzles used in tree crops (3D crops). A second objective is to compare three indirect methodologies for DPR determination: PDPA, ISO wind tunnel (WT1) (discrete collection) and volumetric wind tunnel (WT2) (whole collection) to provide guidelines for drafting a harmonized methodology for testing hollow-cone nozzles.

Materials and methods

Droplet size characterization using a PDPA

The droplet size spectrum was characterized using a phase Doppler particle analyser device The flow rate of ten nozzles of each model was measured, and the nozzle which most closely approximated the nominal flow rate (with a deviation from the nominal flow rate in all cases below 5%) was the one chosen for testing. When coinciding, the same units of the nozzle models selected in this case were also used in the WT1 and WT2 tests (see sections 2.2 and 2.3).

Tap water was used as spray liquid for all nozzles. The temperature of the spray liquid was 20±1 o C and the liquid pressure was 500, 700 or 1000 kPa depending on the nozzle model tested (Table 1). All measurements were performed in an air conditioned room at 20±1 o C at 70-80% of relative humidity. Three repetitions for each nozzle model were carried out. Each repetition was performed with a different single nozzle unit, so three different units were tested for each model.

In all tests, the nozzle position was 0.15 m above the measuring point for all hollow-cone nozzles and 0.30 m for the flat-fan nozzles due to the fan length. To sample the whole cone section, the scan trajectory for the hollow-cone nozzles consisted of a continuous scan of the spray along 7 parallel lines 300 mm long with a separation of 36 mm (Fig. 1a). In the case of the FF-type nozzles, line length was 800 mm and line separation 15 mm (Fig. 1b). All measurements were carried out along the long axis of the spray cloud with a linear displacement of the nozzle at a constant speed of 3 mm s -1 during 780 s and 1860 s for the cone-type and FF-type nozzles, respectively.

Measurement acquisition was performed with the software BSA Flow v.

ISO wind tunnel (WT1) tests

A detailed explanation is provided in this section of the methodology employed in the WT1 wind tunnel, situated in Maqcentre -Parc Científic i Tecnològic Agroalimentari de Lleida (PCiTAL, Lleida, Spain). The tunnel characteristics meet those of the International Standard ISO 22856:2008. The tunnel is 2.0 m wide, 1.0 m high and has an operating length of 7.0 m (Fig. 2).

Test conditions in the tunnel interior were 2±0.1 m s -1 for air flow, with turbulences below 8%, and local speed variations below 5%.

A total of 38 nozzles were tested of different manufacturers: 19 HC-STN nozzles, 9 HC-DRN nozzles, 1 FC-STN nozzle, 6 FF-STN nozzles and 3 FF-DRN nozzles. Included in this list are the 28 most representative nozzle models and sizes used on tree crops in Spain. Ten additional nozzles used on field crops were also included to enable comparison with tests made in other laboratories.

Test pressure for the HC nozzles was 500, 700 and 1000 kPa, for the FC nozzle was 1000 kPa and for the FF nozzles 200, 250, 300, 500 and 700 kPa depending on the nozzle tested (Table 2).

In all tests, a mixture of a water-soluble fluorescent tracer, brilliant sulfoflavine (BSF) yellow (CI 56205) (Biovalley, Marne La Vallee, France), was sprayed at a concentration of 0.3 g L -1 , with a total of 3 repetitions per tested nozzle, following the methodology described by Torrent et al.

(2017).

Volumetric wind tunnel (WT2) tests

The WT2 tunnel is located at the facilities of the Information & Technologies for Agricultural Processes Joint Research Unit (IRSTEA, Montpellier, France). This tunnel was designed based on a criterion different to ISO 22856:2008. The tunnel is 3.0 m wide, 2.0 m high and has an operating length of 9.0 m, with a total of 180 grooves along the floor of the tunnel which are 50 mm wide and 100 mm deep (Fig. 3). The fluid is collected using 60 collecting tubes, making it necessary to position the set of tubes in three consecutive sections to cover the whole tunnel. The tunnel is comprised of a closed circuit in which air flow is generated by 6 air fans. Air temperature and humidity are automatically controlled. The most important distinguishing feature of the WT2 tunnel is that, unlike the WT1 tunnel that uses droplet collectors to determine sedimenting and airborne drift, a distribution test bench composed of slightly inclined grooved channels are situated on the tunnel floor to collect the sedimented droplets. The liquid deposited in each groove travels towards a measuring tube system where the flow of each groove is measured individually using load cells [START_REF] Douzals | How spray characteristics and orientation may influence spray drift in a wind tunnel[END_REF].

The sprayed fluid was tap water at a temperature of 20±1ºC. Ambient conditions in the tunnel interior were 20±1ºC and 70-80% relative humidity. Air flow speed was 2.0±0.1 mꞏs -1 .

The selected nozzle units were those whose flow rate closest to the nominal, as explained in section 2.1. As can be seen in Table 3, a total of 4 Albuz hollow cone nozzles were tested, two of which were STN type (ATR 80 Lilac and ATR 80 Grey) and two DRN (TVI 80025 Purple and tested at 1000 kPa to facilitate a comparison with the WT1 tests. Pressure was set with a 5 kPa precision and automatically corrected with a frequency of 3 Hz.

Each nozzle was tested in both vertical position, as in the WT1 (position for field crops), and in horizontal position (position for tree crops). The nozzles were situated 1.25 m from the start of the collection area. As shown in Fig. 2, the collection area considered for deposition evaluation was between grooves g i and g f , positioned at 2.00 m and 7.70 m downwind from the tested nozzle, respectively. In addition, tests were conducted with the ATR 80 Grey and TVI 8003 Blue nozzles spraying vertically and horizontally, using two units at the same time situated on a bar and separated from each other by a distance of 1.50 m.

Data analysis

Details are provided in this section of the post-processing of the results obtained for each of the test methodologies (PDPA, WT1 and WT2).

Statistical analysis

For the case in which a comparative analysis was made of the PDPA, WT1 and WT2 methodologies, the results shown in the tables and figures correspond to the mean value of the 3 replicate tests made in each case.

To study the effect of nozzle type, size and working pressure from the results obtained, a one-way analysis of variance (ANOVA) with Fisher's least significant difference (LSD) test was performed for each effect. Previously, the normality and homogeneity of variance of the studied variables were verified with the Shapiro-Wilk test and Levene's test, respectively. A confidence level of 95% was considered in all tests. Statistical analyses were done using JMP® Pro 13 (SAS Institute Inc., Cary, NC, 1989-2007 for Windows).

Spray drift potential reduction

In the first methodology tested, droplet size characterisation using PDPA, the characteristic parameters D V50 , V 100 and V 200 were used as DP indicators.

For the case of WT1, the DP of each nozzle was calculated in accordance with ISO 22856:2008, based on the following expressions:

𝐷𝑃 𝑊𝑇1 ∑ 𝑉 (1) 𝐷𝑃 𝑊𝑇1 ∑ 𝐻 (2)
where DP V (WT1) and DP H (WT1) represent the total airborne and the total sedimenting DP for the WT1, respectively. V T(i) is the airborne DP at the vertical collector line i (%) (there were 5 vertical collector lines); while H T(j) is the sedimenting DP at the collector line j (%) (there were 6 horizontal collector lines), according to the following expressions:

𝑉 𝑜𝑟 𝐻 / ⁄ 100 (3)
where: v (i/j) is the volume deposited in the collector line i or j (L), given by Eq. ( 4); d C , the distance between collectors (0.1 m for vertical collectors and 1.0 m for horizontal collectors); D C , the collector diameter (0.002 m); q N , the nozzle flow rate (L min -1 ); and t S , the spraying time (s).

𝑣 / (4)

where: v D is the sample dilution volume (L); F, the fluorimeter reading (µg BSF L -1 ); and C D , the BSF concentration (g BSF L -1 ).

For the case of WT2, only the DP H was determined. This was calculated as the global fraction of the sprayed liquid transported by the grooved channels along the tunnel, from a distance 2.00 m downwind from the nozzle position to 7.70 m. Finally, DP H was calculated using the following expression:

𝐷𝑃 𝑊𝑇2 ∑ 𝐻 (5)
where: gi and gf are the grooves at 2.00 and 7.70 m downwind from the tested nozzle, respectively;

and H T(g) is the sedimenting spray mass at groove g (%), according to the following expression:

𝐻 (6)
where: 𝑊 is the collected liquid mass (kg); t C is the collection time (s); and q N is the nozzle flow rate (L min -1 ).

From the corresponding DP values obtained for each methodology and nozzle, the DPR was then calculated. The DPR was determined by relating the value of the DP of the candidate nozzle (C)

with the DP value of the reference nozzle (R), in all cases the Albuz ATR 80 Lilac at 700 kPa, using the following expression:

𝐷𝑃𝑅 1 𝐷𝑃 𝐷𝑃 ⁄ 100 (7)
where: DP C is the drift potential of the candidate nozzle (%); and DP R is the drift potential of the reference nozzle (%). When considering the V 100 values (Table 4), significant differences were found between Albuz STN and DRN nozzles of similar flow rate (ATR 80 Yellow-TVI 80015 Green, ATR 80 Orange-TVI 8002 Yellow and ATR 80 Red-TVI 80025 Purple at 700 kPa; ATR 80 Grey-TVI 8003 Blue at 1000 kPa). Also, as nozzle size increased, the V 100 value decreased for the STN nozzles and significant differences between different sizes were observed (ATR 80 Lilac-ATR 80 Yellow-ATR 80 Orange-ATR 80 Red at 700 kPa). However, no significant differences between nozzle size were observed for the DRN nozzles, with a V 100 value even being obtained with the largest tested hollow-cone nozzle size (TVI 8003 Blue) which was higher than the other values. A similar trend was observed in the V 200 , D V10 , D V50 and D V90 parameters.

Results

Droplet size characterization using a PDPA

The effect of pressure was analysed for an STN (ATR 80 Grey) and DRN (TVI 8003 Blue) nozzle, at 700 and 1000 kPa. In the case of the STN, significantly higher V 100 and V 200 values, and lower droplet size values, were obtained at 1000 kPa. In contrast, no significant differences were observed in any of the characteristic parameters for the DRN nozzle. a, b, c, d Threshold nozzles corresponding to 25%, 50%, 75%, 95% and 99% drift reduction classes, respectively.

HC-STN: Hollow-cone standard nozzle; HC-DRN: Hollow-cone drift reduction nozzle; FC-STN: Full-cone standard nozzle; FF-STN:

Flat-fan standard nozzle; FF-DRN: Flat-fan drift reduction nozzle.

ISO wind tunnel (WT1) tests

Table 6 shows the results obtained in sedimenting and airborne drift potential reduction (DPR H and DPR V , respectively) for the 38 tested nozzles. Using these results, a classification of the nozzles was made based on the DPR H , determining their spray drift reduction class according to the thresholds of 25%, 50%, 75%, 90% and 95% (Table 6). In general, it can be seen that the both parameters. It can also be seen that, for nozzles with a reduction greater than 90%, the DPR H 323 takes slightly higher values than the DPR V . 324 325 (ATR) nozzles, with the exception of the ATR 80 Grey for the DPR H which is at the upper limit, 335 are below the 90% reduction threshold. In contrast, all the DRN (TVI) nozzles are above this 336 threshold.

Volumetric wind tunnel (WT2) tests

In the WT2 tests, four different spray configurations were studied, with the nozzles oriented vertically and horizontally and using in each case one or two nozzles simultaneously. In most of the deposition curves (Fig. 5), two peaks can be observed, each corresponding to the two extremes of the hollow cone generated by the nozzle. Also apparent is the similarity between the DRNgenerated curves, with no nozzle size effect observable as also seen in the WT1 tests (Fig. 5). In the single-nozzle tests, there are clear differences in the deposition curves generated from the vertical (Fig. 5a) and horizontal (Fig. 5b) nozzle positions. In the vertical spray, the deposition peaks are higher, though shorter distances are attained of up to 1.5-2 m for the DRN and 4 m for the STN nozzles. In contrast, with horizontal spraying, the distances increase to 3-4 m for the DRN and 6 m for the STN nozzles, due to the respective droplet sizes. In the double-nozzle tests, similar results were obtained, after normalising for the spray flow rate, to those of the singlenozzle tests (Fig. 5c,5d).

Methods comparison

Shown in Table 7 is Class G is also defined for reductions below 25%.

The different models are ordered from highest to lowest DPR V100 value.

The other parameters evaluated also followed a decreasing reduction class order. However, two exceptions were observed: TVI 8002 Yellow at 700 kPa tested in WT1 (DPR H and DPR V ) and ATR 80 Grey at 1000 kPa also tested in WT1 (DPR H ). In the first case, the TVI 8002 Yellow nozzle should be in the same drift reduction class as the other DRN models. It can be seen in Table 6 that the DPR values for this nozzle obtained in WT1 are very close to the limit of classes B and C, and so, in effect, it could be considered equivalent to the other DRN models. With respect to the second exception, ATR 80 Grey, this appears in Table 7 in the position following ATR80 Red due to its higher, though very close, V 100 value (Table 4). If this nozzle had been tested at the same pressure as the other STN models (700 kPa), the respective positions of these two nozzles would very probably have been inverted, with which the class C would be justified.

In fact, the DPR H values of both nozzles were very similar and very close to the limit between classes C and D (Table 6). The DPR values of WT2 (V-1N) are comparable to those obtained in WT1, both for the STN model and the two DRN models. For the set of 3 nozzles, the same considerations can also be maintained as established for Table 7, with values of different order of magnitude observed between WT and PDPA for the STN model and of the same order for the DRN models. In order to identify the characteristic parameter of the droplet size spectrum which best fits the results obtained with WT1, 6 simple linear regressions were performed. In these regressions, the DPR values calculated using PDPA (DPR V100 , DPR V200 and DPR DV50 ) and those obtained with WT1 (DPR H and DPR V ) were correlated for the hollow-cone nozzles common to both methodologies (STN: ATR 80 Yellow, Orange and Red at 700 kPa, ATR 80 Grey at 1000 kPa;

and DRN: TVI 8002 Yellow, 80015 Green, 80025 Purple at 700 kPa and TVI 8003 Blue at 1000 kPa).

The results of this study revealed that the characteristic parameter which best fits the DPR obtained with WT1 was the V 100 , with coefficients of determination R 2 =0.771 and R 2 =0.948 corresponding to the DPR H -DPR V100 and DPR V -DPR V100 correlations, respectively. This was followed by the D V50 (R 2 =0.674 and R 2 =0.895, respectively) and V 200 (R 2 =0.612 and R 2 =0.854, respectively).

Discussion

The droplet size measured for the hollow-cone nozzles using a PDPA showed that DRN nozzles produced larger droplets than the STN nozzles. This effect has been observed in previous research on flat-fan nozzles [START_REF] Nuyttens | Effect of nozzle type, size and pressure on spray droplet characteristics[END_REF][START_REF] Guler | Spray characteristics and drift reduction potential with air induction and conventional flat-fan nozzles[END_REF]. These results were compared with those reported by van de Zande et al. ( 2008), and it was seen that the D V10 , D V50 and D V90 values obtained in our study were lower for the STN and higher for the DRN nozzles. With respect to the V 100 and V 200 parameters, in our study higher values were obtained for the STN and lower values for the DRN nozzles. The differences between the results obtained in these two laboratories can be attributed to the characteristics and calibration of the equipment used and the actual nozzle units employed, as was previously indicated by [START_REF] Nuyttens | Drift from field crop sprayers: The influence of spray application technology determined using indirect and direct drift assessment means[END_REF]. Regarding the nozzle classification based on DPR values (Table 5), the DPR V100 and DPR V200 allow a similar classification only for DRN nozzles, while the DPR DV50 classifies in a different way all types of nozzles.

Regarding the nozzle size, for the STN nozzles, the V 100 value decreased when nozzle size increased and significant differences between different sizes were observed. For DRN nozzles, no significant differences were obtained. In flat-fan nozzles, [START_REF] Nuyttens | Influence of nozzle type and size on drift potential by means of different wind tunnel evaluation methods[END_REF] also observed the importance of the effect of nozzle type (STN and DRN) and that the effect of nozzle size was more important in the case of STN than DRN nozzles.

For both type of nozzles (STN and DRN) evaluated in WT1, equivalent DPR H and DPR V values were observed, obtaining similar classification for each nozzle. This similarity between sedimenting and airborne deposition results was also observed in FF-type nozzles tested by [START_REF] Taylor | An Attempt to Relate Drop Size to Drift Risk[END_REF]. However, for the risk assessment both measurements must be taken into account. In general, the DPR of the STN models (ATR 80 Yellow, Orange, Red and Grey) increases with nozzle size, as expected. In contrast, this behaviour has not been observed for DRN nozzles.

In WT2 vertical and horizontal nozzle positions were studied. In the case of vertical spraying, the deposition did not reach the final section of the tunnel (Fig. 5a). For nozzle classification in the horizontal configuration (Fig. 6) is preferable to consider depositions at distances further than 3 m instead of 2 m to avoid misinterpretations (e.g., parabolic droplet path). Moreover, in order to reduce the testing time, two nozzles could be used (Fig. 5c,d), as the deposition collected in both cases was almost proportional to the sprayed volume.

Methods comparison shows that the wind tunnel WT1 presents less capacity to discriminate between nozzle types (DRN, STN) than the PDPA (Table 7). This may be explained by the interaction of other factors in the tunnel other than droplet size (e.g. air-droplet fluid dynamics, which can be variable). Regarding the correlation between DPR values based on PDPA and WT1 measurements, the V 100 was the best indicator of sedimenting (R 2 =0.771) and airborne (R 2 =0.948) deposition. The results showed that both wind tunnels (WT1 and WT2) classify in a similar way (Fig. 7) despite the different nozzle position (vertical and horizontal in WT1 and WT2, respectively).

To establish consistent comparisons between assessment methods it would be necessary to dispose of wider results with additional nozzle types. The results presented have been obtained by applying indirect methods under controlled conditions. However, in order to determine which of these methods best approaches the reality, the results obtained in this work should be contrasted with field drift measurements.

Conclusions

Different hollow-cone nozzle models were classified according to their drift potential reduction Finally, it should be verified that the balance of DRN in terms of environmental and efficacy against pests is favorable.

  potential reduction based on sedimenting deposition in wind tunnel (%) DPR V drift potential reduction based on airborne deposition in wind tunnel (%) DPR DVx drift potential reduction based on D Vx (%) DPR Vx drift potential reduction based on V x (%) D Vx volume diameter, indicating that the x (% of spray volume) is in smaller droplets fraction of droplets smaller than x µm in diameter (%)

  4.50 (PDPA, DantecDynamics A/S. Skovlunde, Denmark) and only spherical droplets were considered (the percentage of non-spherical droplets was below 10% for all tested nozzles). For each nozzle several parameters were determined from the cumulative volumetric droplet size distribution and the following percentile characteristics calculated: i) D V10 , D V50 , and D V90 , representing the diameter below which smaller droplets constitute 10%, 50% and 90% of the total volume, respectively; and ii) the proportional characteristics V 100 and V 200 , representing the percentage of volume of drops having a diameter smaller than 100 μm and 200 μm, respectively.

Fig. 1 .

 1 Fig. 1. Scanning path during PDPA droplet size characterization corresponding to the following nozzles: (a) HC-STN, FC-STN and HC-DRN; (b) FF-STN and FF-DRN.

Fig. 2 .

 2 Fig. 2. Inside view setup of the WT1. Dimensions and position of the collectors (horizontals: H1-H6, verticals: V1-V5). Figure adapted from Torrent et al. (2017).

Fig. 3 .

 3 Fig. 3. Inside view setup of the WT2. Dimensions, nozzle and collection area positions.

330

  HC-STN: Hollow-cone standard nozzle; HC-DRN: Hollow-cone drift reduction nozzle; FC-STN: Full-cone standard nozzle; FF-STN: 331 Flat-fan standard nozzle; FF-DRN: Flat-fan drift reduction nozzle. 332 333 Classification of the Albuz nozzles, shown in Fig. 4, is based on the DPR H and DPR V . The STN 334

Fig. 4 .

 4 Fig. 4. Nozzle classification based on DPRH and DPRV measured with WT1. Reference nozzle: Albuz ATR Lilac at 700 kPa.

Fig. 5 .

 5 Fig. 5. Deposition curves corresponding to four different spraying arrangements using WT2. (a) Vertical spraying with 1 nozzle; (b) Horizontal spraying with 1 nozzle; (c) Vertical spraying with 2 nozzles; (d) Horizontal spraying with 2 nozzles.

Fig. 6 .

 6 Fig. 6. Nozzle classification based on DPRH measured with WT2. HS-1N (>2m) and HS-1N (>3m): a single nozzle spraying in horizontal position, considering depositions at distances further than 2 m and 3 m, respectively. VS-1N (>2m): a single nozzle spraying in vertical position, considering depositions at distances further than 2 m. Reference nozzle: ATR Lilac at 700 kPa.

  a comparison of the drift reduction classes established on the basis of the parameters evaluated with the PDPA (V 100 , V 200 , D V50 ) and the WT1 (sedimenting and airborne depositions), for the 8 hollow-cone nozzle models tested with both methodologies and 2 more tested only with the PDPA at a different pressure. Based on the DPR values determined in sections 3.1 and 3.2 and in accordance with ISO 22369-1:2006, the following drift reduction classes are presented: A (99%), B (95≤99%), C (90≤95%), D (75≤90%), E (50≤75%) and F (25≤50%).

Table 7 .

 7 Drift reduction classes determined from PDPA and WT1 evaluated parameters. Classes are defined according to the following DPR values: A (99%), B (95≤99%), C (90≤95%), D (75≤90%), E (50≤75%), F (25≤50%) and G (≤25%). Nozzles are sorted by DPRV100. : Hollow-cone standard nozzle; HC-DRN: Hollow-cone drift reduction nozzle.kPa, TVI 8003 Blue at 1000 kPa, and TVI 80025 Purple at 700 kPa) which were evaluated with all three methodologies used in this study. For each methodology, the DPR is expressed considering the following parameters: PDPA (D V50 , V 100 and V 200 ), WT1 (sedimenting and airborne deposition), and WT2 (sedimenting deposition with vertically positioned nozzle).

Fig. 7 .

 7 Fig. 7. Comparison between DPR values based on the following parameters: PDPA (DV50, V100 and V200), WT1 (V and H) and WT2 (SV-1N). Reference nozzle: ATR 80 Lilac at 700 kPa.

(

  DPR) using three indirect methods: PDPA, ISO wind tunnel (WT1), and volumetric wind tunnel (WT2). To the authors' knowledge, this is the first undertaken classification of hollow-cone nozzles with a wind tunnel, following ISO 22856:2008. The three indirect methods have shown that the DRN nozzles have DPR values greater than 90% in comparison with the STN. The use of this type of nozzles should be promoted with the aim of reducing the bystanders and residents' exposure, and the environment contamination.The findings of this work show that an equally valid initial hollow-cone nozzle classification can be obtained with either the V 100 or the DPR V . Comparted to the wind tunnel, the PDPA allows a simplified and faster classification methodology. However, the wind tunnel cannot be overlooked when trying to evaluate sedimenting drift (DPR H ) for risk prevention of surface waters, soils and non-target areas in general.The WT2 results point to the horizontal position of the tested nozzle as an interesting methodology for testing hollow-cone nozzles. Further studies are required to establish a new indirect methodology to classify cone nozzles, where the test conditions can be approximated to real working conditions in the field (droplet orientation and air-assistance).Progress should be made in the development of new simplified methods for nozzle assessment under real operation conditions, an issue that is addressed in Part 2 of this work. Further studies are needed for a global evaluation of hollow-cone DRN. Neither the beneficial effect for environment and human risk mitigation nor the efficacy of the DRN have not yet been assessed.

Table 1 .

 1 Nozzles characterized with the PDPA.

	(PDPA, Dantec Dynamics A/S. Skovlunde, Denmark) at the Information and Technologies for
	Agricultural Processes Joint Research Unit (IRSTEA, Montpellier, France). A total of 16 nozzles
	were tested, including 12 hollow-cone types (HC), of which 7 were standard STN and 5 drift
	reduction (DRN models, 3 flat-fan (FF) and 1 full-cone (FC). The models of the hollow cone

Pressure (kPa) Nominal flow rate (L min -1 ) PDPA measurement point height (m) Model Type

	ATR 80 Lilac *		700	0.42
	ATR 80 Brown		700	0.56
	ATR 80 Yellow		700	0.86
	ATR 80 Orange	HC-STN	700	1.17	0.15
	ATR 80 Red		700	1.62
	ATR 80 Grey		700/1000	1.76/2.08
	ATR 80 Green		700	2.00
	TVI 8001 Orange		700	0.61
	TVI 80015 Green		700	0.92
	TVI 8002 Yellow	HC-DRN	700	1.22	0.15
	TVI 80025 Purple		700	1.53
	TVI 8003 Blue		700/1000	1.83/2.19
	AVI 80015 Green		700	0.92
		FF-DRN			0.30
	ID 9001C Orange		500	0.51
	DG 8002 Yellow	FF-STN	700	1.21	0.30
	D3DC35 Brown	FC-STN	1000	2.00	0.15
	HC-STN: Hollow-cone standard nozzle; HC-DRN: Hollow-cone drift reduction nozzle; FC-STN: Full-cone standard nozzle; FF-STN:
	Flat-fan standard nozzle; FF-DRN: Flat-fan drift reduction nozzle. * Reference nozzle.

Table 2 .

 2 Nozzles tested using WT1.

	187
		Nozzle		Pressure	Flow rate
	Manufacturer	Model	Type	(kPa)	(L min -1 )
		AG 1030.015 Green		700	0.92
	Abba	AG 1030.02 Yellow	HC-STN	700	1.22
		AG 1030.025 Lilac		700	1.53
	Agrotop	Air Mix HC 80.025 Lilac	FF-DRN	500	0.60
		ATI 60.015 Green		700	0.92
		ATI 60.025 Lilac		700	1.53
		ATR 60 Red		700	1.62
		ATR 60 Yellow		700	0.86
		ATR 80 Grey	HC-STN	1000	2.08
		ATR 80 Lilac*		700	0.42
		ATR 80 Orange		700	1.17
	Albuz	ATR 80 Red		700	1.62
		ATR 80 Yellow		700	0.86
		AVI 80015 Green	FF-DRN	700	0.92
		TVI 80015 Green		700	0.92
		TVI 8002 Yellow		700	1.22
			HC-DRN
		TVI 80025 Purple		700	1.53
		TVI 8003 Blue		1000	2.19
		1553-14		1000	0.60
			HC-STN
	Hardi	1553-18		1000	1.10
		F110.03 Blue	FF-STN	300	1.20
		ID 9001C Orange	FF-DRN	500/700	0.51/0.60
		ITR 8001 Orange		700	0.60
		ITR 80015 Green	HC-DRN	700	0.90
		ITR 8002 Yellow		700	1.22
	Lechler
		LU 120.06 Grey	FF-STN	700	0.60
		TR 80015 Green		700	0.90
		TR 8002 Yellow	HC-STN	700	1.22
		TR 8003 Blue		700	1.81
		F11003 Blue	FF-STN	300	1.18
	Lurmark	HCX 10 Black		500	0.86
			HC-STN
		HCX 12 Yellow		500	1.03
	Teejet	D3DC35 Brown	FC-STN	1000	2.00

Table 3 .

 3 Nozzles tested using WT2.

	Nozzle		Pressure	Flow rate	VS-1N	HS-1N	VS-2N	HS-2N
	Model	Type	(kPa)	(L min -1 )
	ATR 80 Lilac *		700	0.42	X	X	-	-
		HC-STN
	ATR 80 Grey		700/1000	1.76/2.08	X	X	X	X
	TVI 80025 Purple		700	1.53	X	X	-	-
		HC-DRN
	TVI 8003 Blue		700/1000	1.83/2.19	X	X	X/-	X
	HC-STN: Hollow-cone standard nozzle; HC-DRN: Hollow-cone drift reduction nozzle
	VS-1N: Vertical spraying with 1 nozzle; HS-1N: Horizontal spraying with 1 nozzle; VS-2N: Vertical spraying with 2 nozzles; HS-2N:
	Horizontal spraying with 2 nozzles. * Reference nozzle.

  Table4shows the characteristic parameters of the droplet population (D V10 , D V50 , D V90 , V 100 , V 200 ) obtained with the PDPA. As expected, the DRN nozzles produced larger droplets than the STN nozzles.

Table 4 .

 4 Droplet size spectrum characteristics of the tested nozzles arranged according to the V100 value.

	Nozzle		Pressure	DV10	DV50	DV90	V100	V200
	Model	Type	(kPa)	(µm)	(µm)	(µm)	(%)	(%)
	ATR 80 Lilac *	HC-STN	700	57.20	95.30	144.10	54.87	99.06
	ATR 80 Brown	HC-STN	700	61.70	105.93	158.10	44.34	97.66
	ATR 80 Yellow	HC-STN	700	62.30	113.93	181.40	38.10	93.56
	D3DC35 Brown	FC-STN	1000	68.47	126.63	237.30	30.19	83.66
	ATR 80 Orange	HC-STN	700	67.90	125.37	196.47	29.99	90.80
	ATR 80 Grey	HC-STN	1000	70.93	132.87	219.40	26.16	85.80
	ATR 80 Red	HC-STN	700	74.33	139.00	226.33	23.01	83.30
	ATR 80 Grey	HC-STN	700	75.17	144.20	240.80	21.91	79.40
	ATR 80 Green	HC-STN	700	79.27	151.50	253.97	18.97	75.71
	DG 8002 Yellow	FF-STN	700	105.27	222.10	408.33	8.72	41.25
	AVI 80015 Green	FF-DRN	700	190.23	414.37	853.90	1.44	11.54
	ID 9001C Orange	FF-DRN	500	287.87	589.63	842.43	0.34	3.30
	TVI 8003 Blue	HC-DRN	700	264.23	489.47	792.47	0.32	3.86
	TVI 8003 Blue	HC-DRN	1000	281.50	514.47	809.97	0.27	3.11
	TVI 8001 Orange	HC-DRN	700	279.33	552.57	841.47	0.25	3.43
	TVI 80015 Green	HC-DRN	700	273.03	513.63	821.03	0.25	3.38
	TVI 8002 Yellow	HC-DRN	700	287.60	534.47	813.20	0.24	2.94
	TVI 80025 Purple	HC-DRN	700	300.83	549.17	811.80	0.18	2.42

HC-STN: Hollow-cone standard nozzle; HC-DRN: Hollow-cone drift reduction nozzle; FC-STN: Full-cone standard nozzle; FF-STN:

Flat-fan standard nozzle; FF-DRN: Flat-fan drift reduction nozzle. * Reference nozzle.

Table 5

 5 shows the DPR results calculated on the basis of the V 100 , V 200 and D V50 parameters. Nozzle

	classification was established based on the DPR V100 according to ISO 22369-1:2006. Threshold
	nozzles corresponding to 25%, 50%, 75%, 95% and 99% drift reduction classes are ATR 80
	Yellow, ATR 80 Grey at 1000 kPa, DG 8002 Yellow at 700 kPa, AVI 80015 Green at 700 kPa

and ID 9001C Orange, respectively. For the V 100 parameter, it can be seen how all the DRN models are classified in the same drift reduction class of 99%, except for AVI 80015 Green. The DPR values determined based on V 200 and D V50 are lower than those calculated with the V 100 , with lower spray drift reduction classes being obtained.

Table 5 .

 5 DPR values of the tested nozzles based on three droplet size indicators (V100, V200 and DV50). Albuz ATR 80 Lilac is considered the reference nozzle. The threshold nozzles for drift reduction classes are in bold. The position number of each nozzle is given in brackets. Classification changes when considering DPRV200 or DPRDV50 instead of DPRV100 are highlighted in grey.

	Nozzle		Pressure	DPRV100	DPRV200	DPRDV50	Spray drift
	Model	Type	(kPa)	(%)	(%)	(%)	reduction class
	ATR 80 Lilac	HC-STN	700	0 (1)	0 (1)	0.00 (1)	Reference
	ATR 80 Brown	HC-STN	700	19.18 (2)	1.41 (2)	10.04 (2)	<25%
	ATR 80 Yellow	HC-STN	700	30.55 (3)	5.55 (3)	16.35 (3)
	D3DC35 Brown	FC-STN	1000	44.97 (4)	15.55 (6)	24.74 (5)	25%
	ATR 80 Orange	HC-STN	700	45.34 (5)	8.34 (4)	23.98 (4)
	ATR 80 Grey (a)	HC-STN	1000	52.32 (6)	13.39 (5)	28.27 (6)
	ATR 80 Red	HC-STN	700	58.06 (7)	15.91 (7)	31.44 (7)	50%
	ATR 80 Grey	HC-STN	700	60.07 (8)	19.85 (8)	33.91 (8)
	ATR 80 Green	HC-STN	700	65.43 (9)	23.57 (9)	37.10 (9)
	DG 8002 Yellow (b)	FF-STN	700	84.11 (10)	58.36 (10)	57.09 (10)	75%
	AVI 80015 Green (c)	FF-DRN	700	97.37 (11)	88.35 (11)	77.00 (11)	95%
	ID 9001C Orange (d)	FF-DRN	500	99.39 (12)	96.66 (15)	83.84 (18)
	TVI 8003 Blue	HC-DRN	700	99.41 (13)	96.10 (12)	80.53 (12)
	TVI 8003 Blue	HC-DRN	1000	99.51 (14)	96.86 (16)	81.48 (14)
	TVI 80015 Green	HC-DRN	700	99.54 (15)	96.59 (14)	81.45 (13)	99%
	TVI 8001 Orange	HC-DRN	700	99.54 (16)	96.54 (13)	82.75 (17)
	TVI 8002 Yellow	HC-DRN	700	99.56 (17)	97.03 (17)	82.17 (15)
	TVI 80025 Purple	HC-DRN	700	99.68 (18)	97.55 (18)	82.65 (16)

Table 6 .

 6 DPR values of the tested nozzles determined from WT1 measurements. Albuz ATR 80 Lilac is considered 326 the reference nozzle. The threshold nozzles for drift reduction classes are in bold. The position number of each nozzle 327 is given in brackets. Classification changes when considering DPRV instead of DPRH are highlighted in grey.

	328
	329
	Nozzle		Pressure	DPRH	DPRV	Spray drift
	Model	Type	(kPa)	(%)	(%)	reduction class
	ATR 80 Lilac	HC-STN	700	0 (1)	0 (1)	Reference
	1553-14	HC-STN	1000	9.5 (2)	39.49 (5)	<25%
	ATR 60 Yellow	HC-STN	700	27.73 (3)	36.83 (3)
	TR 80015 Green	HC-STN	700	31.34 (4)	35.14 (2)
	TXA 8002 VK Yellow	HC-DRN	700	32.18 (5)	39.43 (4)
	1553-18	HC-STN	1000	39.23 (6)	53.08 (9)	25%
	AG 1030.015 Green	HC-STN	700	41.91 (7)	58.81 (11)
	HCX 10 Black	HC-STN	500	46.06 (8)	49.41 (7)
	HCX 12 Yellow	HC-STN	500	46.43 (9)	46.76 (6)
	TR 8002 Yellow (a)	HC-STN	700	53.1 (10)	52.17 (8)
	ATI 60015 Green	HC-STN	700	55.1 (11)	60.04 (13)
	LU 12006 Grey	FF-STN	200	57.92 (12)	59.19 (12)
	TXA 8003 Blue	HC-DRN	700	60.44 (13)	58.55 (10)
	ATR 80 Yellow	HC-STN	700	63.56 (14)	66.45 (14)
	AG 1030.02 Yellow	HC-STN	700	67.76 (15)	69.50 (16)	50%
	DG 8002 Yellow	FF-STN	700	70.60 (16)	67.32 (15)
	F11003 Blue	FF-STN	300	71.47 (17)	77.72 (22)
	ATR 80 Orange	HC-STN	700	71.5 (18)	70.95 (17)
	TR 8003 Blue	HC-STN	700	74.34 (19)	73.18 (18)
	F11003 Blue	FF-STN	300	74.96 (20)	76.39 (21)
	ATR 60 Red (b)	HC-STN	700	75.81 (21)	74.68 (19)
	AG 1030.025 Lilac	HC-STN	700	78.67 (22)	75.57 (20)	75%
	Air Mix HC 80025 Lilac	FF-DRN	500	85.68 (23)	86.62 (25)
	ATR 80 Red	HC-STN	700	87.77 (24)	81.96 (23)

a, b, c, d Threshold nozzles corresponding to 25%, 50%, 75%, 90% and 95% drift reduction classes, respectively.

Acknowledgements

This work was partly funded by the Secretaria d'Universitats i Recerca del Departament d'Empresa i Coneixement de la Generalitat de Catalunya, the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF) under Grants 2017 SGR 646, AGL2007-66093-C04-03, AGL2010-22304-04-C03-03, and AGL2013-48297-C2-2-R. The authors also wish to thank Mr. Antonio Checa (Randex Iberica, S.L.) for giving us free Albuz nozzles for the spray tests. Universitat de Lleida is also thanked for Mr. X. Torrent's pre-doctoral fellowship.