Mario Selvaggio
email: mario.selvaggio@unina.it

Marco Cognetti

Stefanos Nikolaidis

Serena Ivaldi

Bruno Siciliano

Autonomy in Physical Human-Robot Interaction: a Brief Survey

Keywords: Physical Human-Robot Interaction, Human-Centered Robotics, Human-Robot Collaboration

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

I. INTRODUCTION

A FULLY autonomous robot is a machine that is able to carry out a task by sensing, planning, and acting into an environment without any human intervention. However, despite the great progress achieved by automation in the recent years, we are still far from providing robots with full autonomy, that would allow them to successfully deal with unpredictable events or unforeseen situations. Nowadays, in most robotic applications, it is customary to have robots that are operated or supervised by a human operator, who can provide superior situation awareness, logic, and problem-solving capability. Sometimes, this is enforced by safety regulations and/or ethical concerns (e.g., a robot is still fully operated by a doctor during surgical procedures). In other words, the interaction between humans and even the most autonomous robot, albeit minimal, is needed and often desirable.

In Human-Robot Interaction (HRI) applications, autonomy constitutes a means rather than the goal and its level varies widely from one application to another. Autonomy allows reducing the human operator's workload when performing a task that can be repetitive and/or requires skills, effort or precision levels that exceed those of a human.

In the past, several robot control architectures were designed for humans to interact with a (partially) autonomous robot. This design methodology was typically referred to as Shared Control (SC). In the last decade, the advancements of sensing, inference, modeling, and learning methods have extended SC capabilities and have widened its spectrum of applications. This gave rise to Shared Autonomy (SA) approaches where the robot is capable of seamless adaptation of its autonomy level based on its own understanding of the human actions/intentions and of the surrounding environment. Adaptation is the most desirable feature when the robot operates in dynamically changing environments, needs to accomplish diverse tasks and/or when the human behavior evolves over time. The autonomy level is typically adapted by opportunely arbitrating the user and the autonomous controller inputs. Until now, SC and SA expressions have been used interchangeably. In this survey, we make this distinction clearer: in SA the robotic system automatically adjusts its level of autonomy based on internal/external information, while in SC the human manually tunes it. The application determines the paradigm that needs to be adopted.

In both approaches, autonomy constitutes the key aspect to be properly designed. In the past, other papers tried to propose continuous or discrete classifications of autonomy levels in SC applications. However, these classifications are drawn for specific domains such as telerobotics [START_REF] Ferrell | Supervisory control of remote manipulation[END_REF], [START_REF] Sheridan | Human and computer control of undersea teleoperators[END_REF], autonomous vehicles [START_REF] Thrun | Toward robotic cars[END_REF], [START_REF]Taxonomy and definitions for terms related to on-road motor vehicle automated driving systems[END_REF], and surgical robotics [START_REF] Yang | Medical robotics-regulatory, ethical, and legal considerations for increasing levels of autonomy[END_REF], and are hard to be generalized. In general, it would be more appropriate to define a spectrum in place of discrete levels of autonomy for SA approaches, since the robot may continuously vary its autonomy level in function of external signals coming from the human, the task, and/or the environment.

In this survey, we review the use of autonomy in physical Human-Robot Interaction (pHRI). For us, the word physical comprises both proximal and remote (bilateral teleoperation) HRI scenarios. In the former, the human and the robot are in direct contact, which may be mediated by a third object (e.g., in cooperative manipulation scenarios). In the latter, the connection between the human, at the local site, and the robot, operating in a remote environment, is obtained by means of an appropriate force feedback action that is provided to the user. This survey provides the following contributions: (i) we review the role of autonomy in pHRI, highlighting the difference between SC and SA as design paradigms; This survey is not meant to be a comprehensive literature review, rather, we want to provide the reader with an overview of the different approaches. A recent literature review on intention detection and arbitration for pHRI is given in [START_REF] Losey | A Review of Intent Detection, Arbitration, and Communication Aspects of Shared Control for Physical Human-Robot Interaction[END_REF]. To the best of our knowledge, the considered work is the closest to this survey. However, it mostly focused on medical and rehabilitation fields while our focus comprises a broader range of systems and applications.

The rest of the paper is organized as shown in Fig. 1: Section II overviews the general concepts behind the use of autonomy in pHRI systems; Section III reviews the state-ofthe-art SC methods while Section IV overviews the latest SA methods. In addition, Section V discusses haptic-based communication methods in SC/SA while Section VI concludes the paper by discussing open challenges.

II. AUTONOMY IN PHYSICAL HUMAN-ROBOT

INTERACTION

In a very broad sense, autonomy can be integrated in a pHRI scenario as shown in Fig. 2. The evolution of the robotic system can be described by the following dynamics:

ẋ(t) = f (x(t), u(t)) u(t) = h θ (u h (t), u a (t); θ(t)),
where x is the robot/environment state, u is the control input. A (possibly non-linear) arbitration function h θ combines/modulates u a and u h , which are the autonomous control and the human inputs, respectively. Modulating the two inputs u h and u a , h θ determines the autonomy level of the robotic system. Here, θ models the robot understandings of the human and/or of the environment used by the arbitration function to modulate the two inputs. For example, θ may contain information about the human action/intention or the task completion status. In general, u h is a signal belonging to the following robot channels: configuration, inputs and/or task.

A SA system modifies the weight of the human and the autonomous control inputs based on θ. Conversely, in SC the arbitration function h θ reduces to h(u h , u a ), i.e., it does not depend on external variables other than the human/autonomous control inputs. This function is totally designed by the human -usually to be fixed during a task -resulting in a user-defined role/autonomy division between the user and the autonomous controller. As matter of fact, no system intelligence is involved, and the robot does not perform any adaptation when the human/environment evolve their behavior/status over time. To give an example, most of the times SC approaches are designed to implement a linear combination of the human and the autonomous controller signals, i.e., (in the scalar case)

h(u h , u a ) = α u h + (1 -α) u a (1)
where α ∈ [0, 1] is a weight allocating the control authority between the human and the autonomous controller. In a SC approach, the weight α, or more in general the arbitration function h, is designed by the human, which may also manually modify/tune it over time. In case α is automatically tuned, e.g., through inference of the human actions [START_REF] Jain | Probabilistic human intent recognition for shared autonomy in assistive robotics[END_REF], the same arbitration function can be used to realize a SA system.

III. SHARED CONTROL

In this section, we review SC approaches and classify them based on the type of interaction: proximate (Sec. III-A) and remote (Sec. III-B).

SC was primarily introduced as a control architecture for remotely operated robots where embedding some autonomy in the robot was essential to overcome large communication delays between the local and remote sites [START_REF] Niemeyer | Telerobotics. Cham[END_REF]. Classically, the architectures corresponding to different human interaction modalities have been grouped into three classes: 1) direct control, which implies no intelligence or autonomy in the system, all the degrees-of-freedoms (DoFs) of the robot are directly controlled by the user via local interfaces; 2) supervisory control, where the user commands and feedback occur at a higher level, the connection is looser and the robot has to rely on a stronger local autonomy to refine and execute tasks [START_REF] Park | Supervisory teleoperation control using computer graphics[END_REF], [START_REF] Blackmon | Model-based supervisory control in telerobotics[END_REF]; 3) shared control, comprehensive of all the intermediate levels in which the robot is controlled by a combination of direct user commands and autonomy [START_REF] Williams | Shared control of multiple-manipulator, sensorbased telerobotic systems[END_REF]. In this context, the most preeminent classification of autonomy levels was proposed in [START_REF] Sheridan | Humans and automation: System design and research issues[END_REF].

Generally, a SC architecture is conceived to provide motion commands correction/overlay or assume control of subtasks. For instance, motion overlay compensating beating hearth movements during robotic surgery gives the user the possibility of operating on a virtually stabilized patient [START_REF] Ortmaier | Motion estimation in beating heart surgery[END_REF]. Subtask control is used to maintain a stable grasp over long time periods relieving the user from constantly imposing the corresponding commands [START_REF] Griffin | Feedback strategies for telemanipulation with shared control of object handling forces[END_REF]. In general, SC paradigms are designed to combine the cognitive skills of the human and the robustness and precision abilities of robots.

This design paradigm evolved in the context of telerobotics and found numerous applications in diverse contexts, such as space/undersea exploration [START_REF] Douglas | Real-time shared control system for space telerobotics[END_REF], [START_REF] Brantner | Controlling ocean one: Human-robot collaboration for deep-sea manipulation[END_REF], wheelchairs control [START_REF] Nguyen | Shared control strategies for human-machine interface in an intelligent wheelchair[END_REF], autonomous driving [START_REF] Johns | Exploring shared control in automated driving[END_REF], humanoid teleoperation [START_REF] Penco | A multimode teleoperation framework for humanoid loco-manipulation: An application for the icub robot[END_REF], nuclear sites decommissioning [START_REF] Talha | Towards robotic decommissioning of legacy nuclear plant: Results of human-factors experiments with tele-robotic manipulation, and a discussion of challenges and approaches for decommissioning[END_REF], aerial robotics [START_REF] Lee | Semiautonomous haptic teleoperation control architecture of multiple unmanned aerial vehicles[END_REF], assistive robotics [START_REF] Argall | Autonomy in rehabilitation robotics: An intersection[END_REF], and surgical robotics [START_REF] Xiong | Shared control of a medical robot with haptic guidance[END_REF].

In most of the above-mentioned contexts, the human usually interacts with a complex robotic system (e.g., having many DoFs) to accomplish one or more tasks simultaneously. SC is, thus, required to reduce the amount of user's workload that would be necessary to direct control the system. For example, controlling the rotational end-effector DoFs of a robotic arm contributes significantly more to decreased performance and increased difficulty than translational ones [START_REF] Young | Formalized task characterization for human-robot autonomy allocation[END_REF]. SC may be designed to reduce the effect of these difficult-to-control features on task performance [START_REF] Abi-Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF].

A. Proximate interaction

In the context of proximate pHRI, SC principles are leveraged to design collaborative [START_REF] Colgate | Cobots: robots for collaboration with human operators[END_REF] and cooperative robotic systems [START_REF] Haddadin | Physical Human-Robot Interaction[END_REF] integrating autonomy. For instance, SC methods are used to enable cooperative manipulation of long objects (grasped at the two ends by the human and the robot) constraining their motion as they were transported on a wheel [START_REF] Takubo | Human-robot cooperative manipulation using a virtual nonholonomic constraint[END_REF] or varying the task effort assignment via dynamic role exchange/sharing mechanisms [START_REF] Mörtl | The role of roles: Physical cooperation between humans and robots[END_REF]. In this case, SC can be implemented through classical or variable impedance/admittance control techniques [START_REF] Arnold | Variable impedance control for phri: Impact on stability, agility, and human effort in controlling a wearable ankle robot[END_REF], virtual constraints [START_REF] Bowyer | Active constraints/virtual fixtures: A survey[END_REF], or hybrid force/velocity control [START_REF] Magrini | Hybrid force/velocity control for physical humanrobot collaboration tasks[END_REF]. An admittance-based SC architecture for collaborative object transportation with dual-arm robot is developed in [START_REF] Tarbouriech | Admittance control for collaborative dual-arm manipulation[END_REF] to increase the productivity in manufacturing: estimating and compensating the object gravity is performed autonomously, while human applied force in the cooperative task space is used to move the object in the desired direction. Similarly, a group of mobile robots can transport an object in cooperation with a human by compensating its dynamics and orienting towards the user-preferred direction of motion acting as Caster-like wheels [START_REF] Hirata | Distributed robot helpers handling a single object in cooperation with a human[END_REF]. Outside industrial environments, cooperative object manipulation requires constraint avoidance algorithms and effort sharing policies [START_REF] Lawitzky | Load sharing in human-robot cooperative manipulation[END_REF]. Recent work is focusing on designing distributed multi-robot SC frameworks where a human operator physically interacts with an object manipulated by a multi-manipulator robotic system [START_REF] Lippi | Human multi-robot physical interaction: a distributed framework[END_REF].

Semi-autonomous driving, in which a user and an autonomous controller simultaneously control the vehicle, is another field in which proximate interaction SC is highly employed. Shared control of intelligent vehicles between a human driver and a lane-keeping and obstacle avoidance assisting system is addressed in [START_REF] Nguyen | Driver-automation cooperative approach for shared steering control under multiple system constraints: Design and experiments[END_REF]: the steering assistance actions are computed according to the driver's real-time driving activity. Finally, SC is leveraged for wheelchair control in tight environments in [START_REF] Alonso-Mora | Shared control of autonomous vehicles based on velocity space optimization[END_REF]: the driver commands a preferred velocity which is transformed into a collision-free smooth local motion that respects the actuator constraints. Although SC allows the human to always takeover in case of disagreement with autonomy, it lacks the additional intelligence that can be provided by estimation of human intentions, desires, and beliefs as in SA.

B. Remote interaction

In remote pHRI scenarios, the human and the robot are spatially separated, and the interaction is established through appropriately designed communication channels. SC methods are used to implement a taskor a trajectory-level interaction.

The former approach is used when accomplishing a task requires fulfilling several sub-tasks simultaneously. Thus, the accomplishment of some sub-tasks is carried out by the autonomous controller to facilitate the human operator. For instance, an autonomous control action makes the robot gripper always pointing in the direction of an object to facilitate its approaching and grasping during sort and segregation of nuclear waste activities [START_REF] Abi-Farraj | A visual-based shared control architecture for remote telemanipulation[END_REF]. Task prioritization and wholebody control architectures allows implementing a hierarchical division of roles between the human and the autonomy [START_REF] Selvaggio | Passive task-prioritized shared-control teleoperation with haptic guidance[END_REF]: this allows a humanoid robot to coordinately accomplish manipulation, locomotion and constraint avoiding tasks while accepting position goals issued by a human [START_REF] Brantner | Controlling ocean one: Human-robot collaboration for deep-sea manipulation[END_REF], [START_REF] Lentini | Alter-ego: A mobile robot with a functionally anthropomorphic upper body designed for physical interaction[END_REF].

The latter approach, allows the user to interact in real-time with a remote inspection robot at the trajectory level: the user can steer the reference path of an autonomous mobile robot (e.g., a UAV) by acting on path parameters that are simultaneously affected by an autonomous algorithm to ensure collision avoidance, path regularity, proximity to points of interest [START_REF] Masone | Shared planning and control for mobile robots with integral haptic feedback[END_REF] or maximize the collected environmental information [START_REF] Cognetti | Perception-aware human-assisted navigation of mobile robots on persistent trajectories[END_REF].

Besides, SC can be designed to improve the user's ability to remotely operate complex machines while simultaneously avoiding unsafe regions [START_REF] Alexander Broad | Highly parallelized data-driven mpc for minimal intervention shared control[END_REF]: to this end, obstacles avoidance can be performed by autonomously overriding the user's commands leveraging reactive techniques such as artificial potentials fields [START_REF] Brantner | Controlling ocean one: Human-robot collaboration for deep-sea manipulation[END_REF] or model predictive control [START_REF] Rubagotti | Semi-autonomous robot teleoperation with obstacle avoidance via model predictive control[END_REF].

Dual-arm robotic systems are typically employed to grasp and manipulate large objects: SC allows a human operator to specify the object motion while autonomy performs coordinated control of the arms to realize grasp stability in the remote space [START_REF] Hayati | Dual arm coordination and control[END_REF], [START_REF] Williams | Shared control of multiple-manipulator, sensorbased telerobotic systems[END_REF]. A framework to accomplish both coordinated bimanual grasping and asymmetric tasks is proposed in [START_REF] Laghi | Shared-autonomy control for intuitive bimanual telemanipulation[END_REF], while a SC architecture with a dynamic selection of the most suitable robot to be commanded by the user is presented in [START_REF] Hernansanz | A multi-robot cooperation strategy for dexterous task oriented teleoperation[END_REF]. Frequently, SC for dual-arm systems is designed with one arm remotely operated and the other completely autonomous and equipped with an eye-in-hand camera to provide visual feedback. In this case, a vision-based autonomous controller allows the execution of occlusion-free tasks [START_REF] Nicolis | Occlusion-free visual servoing for the shared autonomy teleoperation of dual-arm robots[END_REF], while avoiding self-collisions, joint limits, and singularities constraints [START_REF] Selvaggio | Haptic-based shared-control methods for a dualarm system[END_REF].

The benefits of SC on the human operator's workload are even more evident when a group of mobile robots (e.g., UAVs) need to be controlled by a user as in real-world search and rescue missions. SC architectures providing connectivity maintenance, formation control, and obstacle avoidance functionalities allow the user to control a semi-autonomous group of UAVs while redeeming from directly commanding single agents [START_REF] Franchi | Shared control: Balancing autonomy and human assistance with a group of quadrotor uavs[END_REF], [START_REF]Bilateral teleoperation of groups of mobile robots with timevarying topology[END_REF], [START_REF] Lee | Semiautonomous haptic teleoperation control architecture of multiple unmanned aerial vehicles[END_REF]. More recently, SC was used to perform cooperative grasping and transportation of an object with a group of aerial manipulations [START_REF] Gioioso | The flying hand: A formation of uavs for cooperative aerial tele-manipulation[END_REF], [START_REF] Mohammadi | Cooperative aerial tele-manipulation with haptic feedback[END_REF] or with heterogeneous robot teams [START_REF] Staub | The tele-magmas: An aerial-ground comanipulator system[END_REF] following the operator's commands. In a recent and comprehensive review on SC methodologies for human-robot team interaction, the autonomy level adaptation, e.g., based on the human confidence in performing certain tasks, is identified as a key step to be taken in the future [START_REF] Musić | Control sharing in human-robot team interaction[END_REF].

IV. SHARED AUTONOMY

As discussed above, in SC approaches the amount of autonomy, shared between the human and the robot, is either static or manually tuned by the human. However, as the physical interaction between the human and the robot has an evolving nature, autonomy adaptation approaches were started to be devised paving the way towards SA architectures. This enabled a human-robot interaction much closer to a human-human one where (mutual) adaptation is a predominant aspect.

The transition from the SC to the SA paradigm was smooth. Some works preliminary introduced human-robot cooperative control with different autonomy levels leveraging features such as active constraints, machine learning, and automated movements in the context of robotic surgery [START_REF] Berthet-Rayne | Hubot: A three state human-robot collaborative framework for bimanual surgical tasks based on learned models[END_REF]. On this line, platforms able to deal with different autonomy levels for human-robot coexistence and collaboration in manufacturing applications were developed [START_REF] Pichler | Towards shared autonomy for robotic tasks in manufacturing[END_REF]. Besides surgical and industrial scenarios, several other fields envisioned the use of multilevel autonomy such as autonomous driving [START_REF] Johns | Exploring shared control in automated driving[END_REF], space [START_REF] Gao | Review on space robotics: Toward top-level science through space exploration[END_REF], and assistive robotics [START_REF] Argall | Autonomy in rehabilitation robotics: An intersection[END_REF].

As stated above, in the SA paradigm the autonomy level is dynamic and its adaptation is seamlessly performed by the robot during the task execution. This adaptation is usually performed leveraging information extracted from the human and/or from the environment (including the task). According to the source of information that triggers the autonomy adaptation, we list approaches that extract information from the human in Sec. IV-A and approaches that use environmental information in Sec. IV-B.

A. Human

In this section, we survey approaches that extract and use information from the human operator to adapt the autonomy. In the following, we consider human intentions (Sec. IV-A1), muscle activity (Sec. IV-A2), and skills (Sec. IV-A3).

1) Human intentions: A SA system may infer which is, in a probabilistic sense, the action that the human is performing. Based on this information, it can compute what action the robot must undertake, regulating its autonomy and/or providing assistance. Leveraging this concept, a human-robot mutual adaptation framework for collaborative object transportation tasks is presented in [START_REF] Nikolaidis | Human-robot mutual adaptation in shared autonomy[END_REF], [START_REF]Human-robot mutual adaptation in collaborative tasks: Models and experiments[END_REF]: a bounded memory adaptation model assumes that the human stochastically switches between a finite set of modal policies and a mixed-observability Markov decision process chooses the robot action, accordingly. A SA approach for assistive teleoperated robots that infers and predicts human intentions is proposed in [START_REF] Jain | Probabilistic human intent recognition for shared autonomy in assistive robotics[END_REF]: a recursive Bayesian filter fuses multiple observations to infer the human goal and alter the system autonomy level in function of its estimated uncertainty. On the same line, a framework based on policy blending is presented in [START_REF] Dragan | A policy-blending formalism for shared control[END_REF]: the robot assistance, during a teleoperated reach-to-grasp task execution, is provided as arbitration of two policies, namely, user's input and the robot's prediction of the user's intent.

Approaches based on SA can be used to assist humans with disabilities in object reaching and manipulation (e.g., slicing and scooping) tasks: a linear blending function with user-tunable parameters and a confidence metric estimating the human goal are used in [START_REF] Gopinath | Human-in-the-loop optimization of shared autonomy in assistive robotics[END_REF] to determine the arbitration between the autonomous controller and the human. Similarly, the human task is modelled as a Markov decision process in [START_REF] Jeon | Shared autonomy with learned latent actions[END_REF], which provides the autonomous controller with the human goal estimates using dimensionality reduction techniques. A SA teleoperation framework, which mimics the arm movements of an operator through a bimanual robotic system, is presented in [START_REF] Rakita | Shared control-based bimanual robot manipulation[END_REF]: the human is assisted on-the-fly in completing different bimanual tasks (e.g., object handover, container opening) by means of a recurrent neural network using the user motion information detected through a motion capture system. Gametheoretic approaches also can be used to build SA frameworks: the system assumes that the human is optimizing its objective function, while its latent intention is inferred from feedback errors to determine the parameters of a variable impedance controller during human-robot co-assembly tasks [START_REF] Li | Continuous role adaptation for human-robot shared control[END_REF], [START_REF]A framework of human-robot coordination based on game theory and policy iteration[END_REF].

2) Human muscle activity: Instead of inferring the human intentions, some papers focus on estimating a metric related to the human fatigue and take actions for minimizing it. A framework for proximal human-robot collaboration is presented in [START_REF] Peternel | Robot adaptation to human physical fatigue in human-robot co-manipulation[END_REF]: the robot implements a hybrid force/impedance controller and estimates the human muscle activity while performing the task thanks to wearable EMG electrodes. When the human muscle activity exceeds a threshold, the robot uses the learned skills (encoded as periodic dynamic motion primitives) for helping the human in reducing his/her fatigue. A similar idea is proposed in [START_REF]Caring about the human operator: Haptic shared control for enhanced user comfort in robotic telemanipulation[END_REF], where the 'rapid upper limb assessment' is used to estimate the human muscle activity during remote teleoperation tasks: based on this information, the robot adapts its trajectory to minimize it. An interesting emerging direction consists in estimating the human fatigue thanks to a continuous monitoring of the human activities [START_REF] Ji | A probabilistic framework for modeling and real-time monitoring human fatigue[END_REF].

3) Human skills: Attributing skills to humans allows defining distance metrics between the performances of expert and naive operators. The autonomy level can then be autonomously regulated according to these metrics. In surgical robotics, a SA teleoperation framework that adapts its cooperative properties to the estimated skill level of the operator is proposed in [START_REF] Enayati | Skill-based human-robot cooperation in teleoperated path tracking[END_REF]: skill profiles, captured as task performance measures, are exploited to modify the behavior of the assistive robotic system and enhance the user experience by preventing unnecessary restrictions for skilled users. On the same line, the assistanceas-needed paradigm provides the user with variable assistance during surgical training according to its current and past performances [START_REF] Enayati | Robotic assistance-as-needed for enhanced visuomotor learning in surgical robotics training: An experimental study[END_REF]. A partially observable Markov decision process is used to represent the expertise level of an operator during teleoperated navigation of a mobile robot [START_REF] Milliken | Modeling user expertise for choosing levels of shared autonomy[END_REF]: the SA framework uses the inferred user's expertise level and environmental observation to fuse the user's input with the appropriate autonomous controller.

In general, the correct interpretation of data and attribution of human mental states are crucial aspects in SA systems. Perspective-taking (i.e., the ability to take one another's perspective and reason from this alternative point of view) on robots would be a valuable asset for people working with them [START_REF] Trafton | Enabling effective human-robot interaction using perspective-taking in robots[END_REF]: interpreting data from a human perspective allows overcoming ambiguity and incompleteness that can often be present in human demonstrations [START_REF] Berlin | Perspective taking: An organizing principle for learning in human-robot interaction[END_REF] and communicate and interact naturally with humans [START_REF] Milliez | A framework for endowing an interactive robot with reasoning capabilities about perspective-taking and belief management[END_REF]. Theory of mind computational models allow attributing beliefs, goals, and desires to the human operator [START_REF] Scassellati | Theory of mind for a humanoid robot[END_REF], [START_REF] Devin | An implemented theory of mind to improve humanrobot shared plans execution[END_REF]. In this perspective, neural networks have shown to be capable of building models for agents' behavior predicting the main characteristics and mental states [START_REF] Rabinowitz | Machine theory of mind[END_REF]. However, the development of efficient computational models that predict the human behavior in realtime is still an open challenge as will be discussed in Sec. VI.

B. Environment

In this section, approaches that use information about the environment (rather than the human operator) to adapt the autonomy level are discussed. The most common method to retrieve environmental information is to focus on what the robot has to fulfill, i.e., the task, and extract information directly from it. In this perspective, Learning-from-Demonstration (LfD) has been proven to be an effective approach: the idea is to extract expert users' behavior while executing some tasks, and use this information to help non-expert users in accomplishing similar tasks. This paradigm is adopted in the context of a pick-and-place remote manipulation task in [START_REF] Abi-Farraj | A learning-based shared control architecture for interactive task execution[END_REF], where trajectories from expert users are captured through a haptic device, encoded into some distributions, and then used by an adaptive controller to determine the system autonomy. This way, naive operators are assisted during the task execution through haptic cues that point in the direction of the trajectories performed by the expert users.

Similarly, a task-parametrized Gaussian Mixture Model (GMM) is used to build a representation of a remotely executed scanning task in [START_REF] Havoutis | Learning assistive teleoperation behaviors from demonstration[END_REF]: datapoints from expert operators are collected to encode the task. This is used, together with the user input, inside a linear quadratic regulator that computes the robot stiffness and damping that determines the autonomy level of the teleoperated robot. A similar approach is presented in [START_REF]Supervisory teleoperation with online learning and optimal control[END_REF], where a Task-Parametrized Hidden Semi-Markov Model (TP-HSMM) is used together with an incremental online learning algorithm to encode models of a hot-stabbing task. A model predictive control, that uses the TP-HSMM predicted state evolution, allows anticipating and adapting the robot to future events. The approach is extended in [START_REF] Havoutis | Learning from demonstration for semi-autonomous teleoperation[END_REF], where the system is also able to automatically disambiguate between local and remote task parametrizations. LfD is used in [START_REF] Del Pulgar | Using learning from demonstration to generate real-time guidance for haptic shared control[END_REF] for encoding remotely performed peg-in-hole tasks: GMMs are used to extract information from demonstrations of expert operators, which is then used to generate forcebased haptic guidance trajectories that help non-expert users in fulfilling the insertion task. Similarly, LfD is used to create surgical task models in [START_REF] Berthet-Rayne | Hubot: A three state human-robot collaborative framework for bimanual surgical tasks based on learned models[END_REF]: the proposed framework collects demonstrations and segments the task based on tool-tissue or tool-tool interaction. The task is encoded as a continuous hidden Markov model which is used to regress a path among those captured during the demonstration, helping naive users through visual and haptic cues.

Besides the task, environmental constraints can be used to trigger the system adaptation. An adaptive authority framework handling target occlusions is presented in [START_REF] Balachandran | Adaptive authority allocation in shared control of robots using bayesian filters[END_REF]: the control allocation between the human and the autonomous controller is adapted based on target measurements uncertainty of an adaptive Bayesian filter. This estimates the pose of the target based on visual measurements and its covariance matrix is used to linearly weight the contribution of the human and the autonomous controller.

It is worth to note that the use of human/environment sources of information is not mutually exclusive. A challenge in the design of effective SA frameworks is to understand how to properly combine and, possibly, prioritize information gathered from multiple sources, as will be discussed in Sec. VI.

V. HAPTIC COMMUNICATION

In both remote and proximate pHRI scenarios, haptic communication between the human and the robot is always inherently present. In some SC/SA approaches the autonomous controller inputs, opportunely arbitrated, are provided to the users as haptic signals [START_REF] Abi-Farraj | A learning-based shared control architecture for interactive task execution[END_REF]. Control of the robotic system is thus shared, since user's movements are influenced by haptic signals generated exploiting knowledge of the environment and the task [START_REF] O'malley | Shared Control in Haptic Systems for Performance Enhancement and Training[END_REF]. In this way, the potentially variable autonomy is reflected to the user, the system becomes more legible/transparent, while the operator retains its full control.

The exchange of forces helps to increase the human situation awareness providing useful information about, e.g., the current system status, proximity to constraints [START_REF] Selvaggio | Passive task-prioritized shared-control teleoperation with haptic guidance[END_REF], environmental obstacles [START_REF] Luo | A teleoperation framework for mobile robots based on shared control[END_REF], etc. Haptic signals integrated in SC/SA systems can be equivalently seen as virtual fixtures, that help the human to operate into restricted regions and/or to move along desired paths [START_REF] Rosenberg | Virtual fixtures: Perceptual tools for telerobotic manipulation[END_REF], [START_REF] Bowyer | Active constraints/virtual fixtures: A survey[END_REF]. Haptic displays realize the cobotic behaviour of the robotic device [START_REF] Colgate | Cobots: robots for collaboration with human operators[END_REF] making it potentially well-suited to safety-critical tasks (e.g., surgery) [START_REF] Munawar | A surgical robot teleoperation framework for providing haptic feedback incorporating virtual environment-based guidance[END_REF]. However, their effective integration is subject to the stability and the safety certification of the interactive robotic system. Haptic-based SC/SA frameworks have been developed to guide the user towards grasp poses that maximize manipulation capabilities [START_REF] Ghalamzan | Human-in-the-loop optimisation: Mixed initiative grasping for optimally facilitating post-grasp manipulative actions[END_REF], [START_REF] Parsa | Haptic-guided shared control grasping: collision-free manipulation[END_REF], or avoid incurring into the system constraints along post-grasping trajectories [START_REF] Selvaggio | Haptic-guided shared control for needle grasping optimization in minimally invasive robotic surgery[END_REF]. At a larger scale, whole-body haptic teleoperation interfaces are currently being developed for bipedal robots to provide the user with a sense of the robot's executed motion [START_REF] Ramos | Dynamic locomotion synchronization of bipedal robot and human operator via bilateral feedback teleoperation[END_REF].

Contextualized haptic assistance can be provided to the operator in a structured manner exploiting models of the task learned from demonstration [START_REF] Havoutis | Learning from demonstration for semi-autonomous teleoperation[END_REF], [START_REF] Berthet-Rayne | Hubot: A three state human-robot collaborative framework for bimanual surgical tasks based on learned models[END_REF]. The level of autonomy, adjusted exploiting the confidence into human and autonomous control, is reflected to the user through haptic guidance [START_REF] Zeestraten | Programming by demonstration for shared control with an application in teleoperation[END_REF], [START_REF] Havoutis | Learning assistive teleoperation behaviors from demonstration[END_REF]. Exploiting the online estimated probability of following a certain trajectory, mechanisms for automatic regulation of haptic assistance have been developed [START_REF] Aarno | Adaptive virtual fixtures for machine-assisted teleoperation tasks[END_REF], [START_REF] Ekvall | Online task recognition and real-time adaptive assistance for computer-aided machine control[END_REF]. However, the haptic feedback provided to the human operator may be in conflict with other sensory signals (e.g., audio or visual). The conflict may be caused by a low confidence estimation of human goals performed by the autonomous control. This results in low or wrong assistance causing a decrease of trust in automation by the human operator [START_REF] Javdani | Shared autonomy via hindsight optimization for teleoperation and teaming[END_REF], [START_REF] Chen | Trust-aware decision making for human-robot collaboration: Model learning and planning[END_REF]. Accounting for this in the design of SA frameworks can potentially lead to reduced user's workload and higher trust in automation [START_REF] Luo | A workload adaptive haptic shared control scheme for semi-autonomous driving[END_REF] as discussed in the next section.

VI. CONCLUSIONS AND DISCUSSION

In this letter, we briefly surveyed the use of autonomy in pHRI, discussing SC and SA as implementation paradigms. The autonomy level is manually designed and tuned by the human in SC while it is automatically adapted by the system in SA exploiting the robot understanding of the human and/or the task/environment.

In this view, SC still constitutes a powerful paradigm for combining human decision-making and robot precision capabilities. Indeed, it provides assistance through commands overlay and subtasks control while leaving the human operator the ultimate authority over the system. The common trend behind the design of SC architectures is the leverage of task models and model-based control. However, while this is advantageous for stability and safety certification, it makes SC strategies specific to the application domain and to the task to be performed. As no autonomy adaptation is envisioned in this paradigm, any change in the task requires substantial strategy modifications leading to tedious interruptions and setting up times. This constitutes the main limiting factor, as the level of the robot autonomy is desirable to change according to the human/environment evolving behavior.

Determining the level of autonomy that a human wants a robotic system to have is a very complex problem. There are cases in which users appreciate that the robotic system guides them [START_REF] Welfare | Consider the human work experience when integrating robotics in the workplace[END_REF]. However, there are also cases where the user wants that the autonomy is limited and the robotic system does not take invasive actions, (see, e.g., the surgical domain). Since pHRI embraces a wide range of applications, we believe there is no unique answer to this open problem but it requires the development of a case-by-case solution.

Contrarily, SA approaches provide this favorable autonomy level adaptation feature that leverages inference of the human intentions or the task progress. However, other environmental information are typically ignored. Thus, some of the open questions are: how does this information increase the versatility of the robots in performing everyday tasks? How to combine the information coming from multiple sources in a unified framework? Our intuition is that the SA framework should be able to dynamically understand the importance of each source and appropriately choose its autonomy level.

As advanced SA techniques are being developed, using various adaptation mechanisms and haptic communication means, these require novel control methodologies that assure a safe interaction between the human and the robotic system. The enhanced flexibility of SA systems, that are capable of providing contextual or personalized assistance and seamless adaption of the autonomy level, is a desirable trend that raises new challenges for safety and stability certification [START_REF] Lasota | A survey of methods for safe human-robot interaction[END_REF]. A possible approach is to use passivity-based control techniques as largely done for SC scenarios [START_REF] Giordano | A passivity-based decentralized strategy for generalized connectivity maintenance[END_REF].

As discussed in Sec. IV, most of the SA approaches use user's goals inference within a predict-then-act paradigm. However, when the user's goals cannot be predicted with high confidence, SA methods may not assist the user or give little assistance [START_REF] Javdani | Shared autonomy via hindsight optimization for teleoperation and teaming[END_REF]. Developing reliable inference methods to effectively regulate assistance is still an open research field. Moreover, SA approaches that require task/environment inference are challenged by unstructured environments with ill-defined tasks. This issue may be mitigated by developing approaches that render robots capable of online learning, updating in real-time their understandings of the user's goals and of the task/environment. To this end, reinforcement learning and deep learning techniques are capable of learning autonomy/assistive policies directly, instead of optimizing them. In particular, deep reinforcement learning allows implementing model-free SA but this typically requires lots of training data, which can be burdensome for human users operating physical robots [START_REF] Reddy | Shared autonomy via deep reinforcement learning[END_REF].

The concept of human trust in autonomy is another essential aspect to be considered when developing effective humanrobot collaboration techniques. Trust favors the adoption of semi-autonomous systems such as robot assistants [START_REF] Chen | Trust-aware decision making for human-robot collaboration: Model learning and planning[END_REF]. SA paradigms integrating the notion of trust require the definition of its computational model, which is a research question per se. The trust towards a robotic system depends on many factors such as the context, the application, and several individual factors such as user's attitude and experience. It also evolves over time, which can be anchored in specific features of the robot, and can be influenced by the user experience and the robot behavior [START_REF] Gaudiello | Trust as indicator of robot functional and social acceptance. an experimental study on user conformation to icub answers[END_REF]. Developing sophisticated predictive models integrating trust into the robot decision-making in a principled way, while maintaining computational tractability, is an exciting area for future work [START_REF]Human-robot mutual adaptation in collaborative tasks: Models and experiments[END_REF]. This opens interesting questions: how much autonomy should the system have? How does this affect users' trust and their willingness to use the system? Transparency and explainability of the system behavior, intended as the human understanding of what the system is doing, why, and what it will do next is another important aspect to consider [START_REF] Alonso | System transparency in shared autonomy: A mini review[END_REF]. In this context, haptics may be used to increase system legibility and the situational awareness of the human, which may increase trust towards the system.

Ultimately, the evaluation of SA systems is highly subjective, users generally may prefer more assistance when performing difficult tasks, as this might allow a more efficient task completion. In our opinion, SA approaches require the development of contextualized benchmarking and validation methods for their objective evaluation. These validations in simulated and/or real-world scenarios may speed up the deployment of robots in our every-day life [START_REF] Fontaine | A quality diversity approach to automatically generating human-robot interaction scenarios in shared autonomy[END_REF].

Solving the above-mentioned open issues will bring to a significant advancement in the field of pHRI. We believe that SA will be a fundamental paradigm in the next future, especially for helping non-experts and people with disabilities in performing everyday tasks, thanks to its nature to adapt to the user's requirements.

Fig. 1 .

 1 Fig. 1. Categorization of approaches considered in this brief survey.

Fig. 2 .

 2 Fig. 2. A general architecture integrating autonomy in a pHRI scenario. Symbols are explained in Sec. II. Arbitration (h θ ) of the control signals (u h , ua) is either tuned by the human operator -shared control (SC) -or by the autonomous control through inference -shared autonomy (SA).

This paper was recommended for publication by Editor Jee-Hwan Ryu upon evaluation of the Associate Editor and Reviewers' comments. This work was supported by the European Union's Horizon 2020 research and innovation programme under grant agreement No 101017008. 1 M. Selvaggio and B.


D V Antonov

R S Volkov

R M Fedorenko

P A Strizhak

Guillaume Castanet

S S Sazhin
email: s.sazhin@brighton.ac.uk

Temperature measurements in a string of three closely spaced

Keywords:

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

Introduction

Adding water into fuel droplets is known to lead to their puffing (swelling of droplets and their disintegration into a relatively small number of smaller droplets) and/or micro-explosion (disintegration of droplets leading to the formation of a cloud of aerosols). Practical engineering applications of these processes, including those in Diesel engines, are well known [START_REF] Ogunkoya | Performance, combustion, and emissions in a diesel engine operated with fuel-in-water emulsions based on lignin[END_REF] . These processes have been extensively studied experimentally. Among numerous papers focused on this topic we can mention [START_REF] Morozumi | Effect of physical properties on microexplosion occurrence in water-in-oil emulsion droplets[END_REF] , where the effects of various physical properties on the occurrence of micro-explosions are described, and [START_REF] Cen | Experimental investigation on the sputtering and micro-explosion of emulsion fuel droplets during impact on a heated surfaceInt[END_REF][START_REF] Antonov | Comparison of the characteristics of micro-explosion and ignition of two-fluid water-based droplets, emulsions and suspensions, moving in the high-temperature oxidizer medium[END_REF] , where the results of investigation of the effects of ambient temperatures on micro-explosions are presented. The authors of [START_REF] Avulapati | Puffing and micro-explosion of diesel-biodiesel-ethanol blends[END_REF][START_REF] Antonov | Breakup and explosion of droplets of two immiscible fluids and emulsions[END_REF] described the results of their experimental investigation of fuel composition on puffing and micro-explosion. As follows from the parametric study of the occurrence of microexplosions in water-in-oil emulsions presented in [START_REF] Moussa | Parametric study of the microexplosion occurrence of w/o emulsions[END_REF] , this phenomenon is more likely to occur in larger droplets (with diameters above 20 μm) than in smaller droplets. The effects of coalescence of the dispersed water droplets on the occurrence of micro-explosions were investigated experimentally by the authors of [START_REF] Suzuki | Visualization of aggregation process of dispersed water droplets and the effect of aggregation on secondary atomization of emulsified fuel droplets[END_REF][START_REF] Califano | Experimental evaluation of the effect of emulsion stability on micro-explosion phenomena for water-in-oil emulsions[END_REF] .

The most advanced models of puffing and micro-explosion developed so far are based on Direct Numerical Simulation [START_REF] Shinjo | Modeling temperature distribution inside an emulsion fuel droplet under convective heating: a key to predicting microexplosion and puffing[END_REF][START_REF] Shinjo | Physics of puffing and microexplosion of emulsion fuel droplets[END_REF][START_REF] Fostiropoulos | Numerical investigation of heavy fuel oil droplet breakup enhancement with water emulsions[END_REF] . These were complemented by several simplified models of the phenomena [START_REF] Girin | Dynamics of the emulsified fuel droplet micro-explosion[END_REF][START_REF] Sazhin | A simple model for puffing/micro-explosions in water-fuel emul-sion droplets[END_REF][START_REF] Fostiropoulos | A simple model for breakup time prediction of water-heavy fuel oil emulsion droplets[END_REF][START_REF] Antonov | Modeling the micro-explosion of miscible and immiscible liquid droplets[END_REF][START_REF] Sazhin | A new approach to modelling micro-explosions in composite droplets[END_REF] . The latter model and its recent modifications (e.g. [START_REF] Antonov | Puffing/micro-explosion in rapeseed oil/water droplets: The effects of coal micro-particles in water[END_REF] ) has proven to be effective for the analysis of various observations of puffing and micro-explosion. It will be used in the present analysis.

In our previous paper [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] , we presented the results of the experimental and theoretical investigations of the mutual effect of

Nomenclature B M(T )

Spalding mass (heat) transfer number [ Water-fuel interface 0 Initial ∞ Ambient conditions droplets on their puffing/micro-explosion in a flow, using an example of two closely spaced composite rapeseed oil/water droplets in tandem. This paper is focused on the generalisation of the results of [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] in the following three directions. Firstly, in contrast to [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] we consider not two but three droplets, one behind the other. Secondly, we consider not rapeseed oil/water but Diesel fuel/water droplets in a wide range of fuel and water volume fractions. Thirdly, the focus of our analysis is not only on finding the time instant when puffing/micro-explosion starts, but also on the investigation of time evolution of temperature at the fuel-water interface before the development of puffing/micro-explosion. The analysis of three droplets instead of two will allow us to perform more realistic investigation of the effects of surrounding droplets on any particular droplet in a spray. In this case, we will be able to consider not only the influence of the droplet in front of a given droplet but also the one behind it at the same time (cf. the results of a similar investigation presented in [START_REF] Chiang | Interacting, convecting, vaporizing fuel droplets with variable properties[END_REF][START_REF] Chiang | Asymmetric calculation of three droplet interactions[END_REF] ).

The following volume fractions of Diesel fuel and water were used in the experiments: 90% Diesel fuel/10% water and 10% Diesel fuel/90% water, although most attention is focused on the former case. Droplets with high volume fractions of Diesel fuel are widely used in various spray combustion devices [START_REF] Ayhan | Experimental investigation on using emulsified fuels with different biofuel additives in a DI diesel engine for performance and emissions[END_REF][START_REF] Gad | Experimental study of diesel fuel atomization performance of air blast atomizer, exp[END_REF] , while those with low volume fractions of Diesel fuel are used for thermal and fire purification of liquids [START_REF] Shannon | Science and technology for water purification in the coming decades[END_REF][START_REF] Romero | Optimal water purification using low grade waste heat in an absorption heat transformer[END_REF] . In both cases, a water sub-droplet is located inside a Diesel fuel droplet.

The main features of the experimental setup and procedure used in our analysis are summarised in Section 2 . The new experi-mental results are presented in Section 3 . In Section 4 an overview of the model used in the analysis is presented. This includes a summary of the model developed in [START_REF] Sazhin | A new approach to modelling micro-explosions in composite droplets[END_REF] and the results of investigation of the mutual effects of three droplets, one behind the other, on the values of Nusselt ( Nu ) and Sherwood ( Sh ) numbers. The model described in Section 4 is used for the analysis of experimental data presented in Section 3 . The results are presented in Section 5 . In Section 6 the key results of the paper are summarised.

Experimental setup and procedure

The experimental setup and methodology used in our analysis are essentially the same as described in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] except that an opening was drilled in the metal cylinder to allow droplet illumination by a laser beam. The temperature profiles in the droplets were obtained using the Planar Laser Induced Fluorescence (PLIF) method following the methodology described in [START_REF] Strizhak | Heating and evaporation of suspended water droplets: experimental studies and modelling[END_REF] . In contrast to [START_REF] Strizhak | Heating and evaporation of suspended water droplets: experimental studies and modelling[END_REF] , the PLIF measurements in our experiments were performed using a Phantom MIRO M310 video camera (monochromic images with maximal resolution 1280 pixels × 800 pixels, 6 . 5 × 10 5 fps, 12 bit depth) and continuous DPSS laser KLM-V532/h-10 0 0 0 (wave length 532 nm; width of the spectral line 0.1 nm; maximal power 10 W with fluctuations not exceeding 5%; aperture beam diameter 3 mm).

The three droplets were mounted as shown in Fig. 1 . The droplets shown in this figure are illuminated by the laser beam which leads to yellow light emission around them generated by Rhodamine B dye. Ambient gas temperature and velocity used in the experiments were in the range 589-629 K, and 0.1 m/s, respectively. The systematic errors of the measurement of these parameters were ±3 K and ±0 . 05 m/s, respectively.

Droplet initial radii and the distances between droplets were determined with systematic errors not exceeding ±0 . 025 mm and ±0 . 05 mm, respectively.

The results of calibration of fluoroform Rhodamine B emission intensity versus droplet temperature (measured using a thermocouple) are presented in Fig. 2 . These results were approximated by the calibration curve: Intensity = aT The time instant when puffing/micro-explosion started was determined by analysing video frames of the process and identifying the frame in which the first fragment separated from the main droplet. Thus, the systematic error of determining the time to puffing was equal to the time interval between frames which was 1 ms in our experiments. The analysis of images was carried out following the scheme presented in Fig. 3 , using algorithm DaVis v. 10.0.5.42579. Firstly, the smoothing of images using the linear filter was performed in areas of 3 pixels × 3 pixels. The difference in the intensity of the laser beam at its centre and at the periphery was taken into account based on an analysis of the emission intensity in a cuvette filled with Rhodamine B solution. The background was removed using a procedure called 'add algorithmic mask'. Finally, the temperature field was obtained using the calibration curve shown in Fig. 2 .

Pixels with unwanted fluorescence values were set to zero intensity in all the video frames (algorithmic masks), as in our previous papers [START_REF] Tkachenko | Experimental study of miscibility of liquids in binary droplet collisions[END_REF][START_REF] Strizhak | Application of the laser induced phosphorescence method to the analysis of temperature distribution in heated and evaporating droplets[END_REF] . The mean fluorescence intensity of water sub-droplets was determined in the selected recording area within 10 to 15 frames. The mean fluorescence intensity of water subdroplets containing Rhodamine B was between 3 and 50 counts. The background fluorescence intensity ranged from 0 to 2 counts depending on the frame region.

A resolution of 384 pixels × 800 pixels was used in the experiments. This resolution remained unchanged during the filtration process.

The error bars shown in the figures are the sums of systematic and random errors. Random errors r were determined as:

r = t(α c , n ) S,
where t(α c , n ) is the Student's coefficient, depending on the number of measurements n and confidence level α c , assumed equal to 0.95; S is the root squared deviation for a series of measurements.

Experimental results

Typical examples of the distribution of temperature inside the three droplets for various input parameters are shown in Figs. [START_REF] Antonov | Comparison of the characteristics of micro-explosion and ignition of two-fluid water-based droplets, emulsions and suspensions, moving in the high-temperature oxidizer medium[END_REF] (for droplets of 90% Diesel fuel) and 5 (for droplets of 10% Diesel fuel). Note that Rhodamine B dissolves well in water but does not dissolve in hydrocarbon fuels, including Diesel fuel. Thus the distribution of temperature inside the droplet could only be obtained in the water sub-droplet using the PLIF method. This is well illustrated by Figs. 4 and5 .

As can be seen in Figs. 4 and5 , in all cases the lead droplet heats up faster than the middle one and the middle one heats up faster than the downstream one. The lead droplet disintegrates first, followed by the disintegration of the middle and downstream droplets. This behaviour is similar to that described in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] for two droplets in tandem.

As follows from the analysis described in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] , the temperature which is the most important for the development of puffing and micro-explosion is the temperature at the fuel-water interface. The plots of this temperature versus time for droplets similar to those presented in Fig. 4 are shown in Fig. 6 . Stars in this figure show the time instants when the puffing/micro-explosion started. The temperatures at the fuel-water interface were measured at 7 to 10 points in each time instant. The scatter of these measurements did not exceed 15 K.

As follows from Fig. 6 , the lead droplet is the first to heat up, followed by the middle droplet and then the downstream droplet. This is consistent with the observed times to puffing/microexplosion discussed later in this section.

Plots similar to those shown in Fig. 6 were obtained for droplets of 10% Diesel fuel and 90% water. The general shapes of the curves were similar to those shown in Fig. 6 . The main difference between the results is that in the case of 10% Diesel fuel, the interface boundary heats up faster due to the thinner fuel film. For identical cases, but different compositions, the difference in time to puffing can reach 1 s. At the same time instants for the same initial condition but different compositions of droplets, differences in temperature at the fuel-water interface can reach 20 K.

Assuming, following [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] , that puffing/micro-explosion starts when the temperature at the fuel-water interface reaches the water nucleation temperature, we calculated the degree of superheating (difference between the water nucleation and boiling temperatures:

T SH = T N -T B ) versus heating rate d T /d t ≡ ˙ T at the fuel/water interface of composite droplets of 90% Diesel fuel and 10% water (lead, middle and downstream). The results are shown in Fig. 7 . As follows from this figure, an increase in T SH agrees well with the correlation suggested in [START_REF] Sazhin | A new approach to modelling micro-explosions in composite droplets[END_REF] :

T N = T B + 12 × tanh ( ˙ T / 50) ; 0 ≤ ˙ T ≤ 300 K / s . ( 1
)
This correlation is shown as the solid curve in Fig. 7 . 1), experiments described in [START_REF] Sazhin | A new approach to modelling micro-explosions in composite droplets[END_REF] (2) and experiments described in [START_REF] Su | Transient boiling of water under exponentially escalating heat inputs, Part I: Pool boiling[END_REF] (3). The solid curve shows the correlation predicted by Expression (1) .

Results similar to those shown in Fig. 7 for droplets of 90% Diesel fuel and 10% water were obtained for droplets of 10% Diesel fuel and 90% water. These results were also shown to be well approximated by Expression [START_REF] Ogunkoya | Performance, combustion, and emissions in a diesel engine operated with fuel-in-water emulsions based on lignin[END_REF] .

Plots of time to puffing/micro-explosion ( τ p ) for the lead, middle and downstream droplets of 90% Diesel fuel and 10% water versus ambient gas temperature are shown in Fig. 8 . As follows from this figure, for all three droplets, τ p decreases with temperature as in the case of isolated droplets or two droplets in tandem [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] . τ p for the lead droplet is always shorter than it is for the middle and downstream droplets for the whole range of temperatures under consideration.

Plots similar to those shown in Fig. 8 were obtained for droplets of 10% Diesel fuel and 90% water. The main difference between these plots and those shown in Fig. 8 lies in their smaller values of τ p (in almost all cases). This difference can be as much as 25%.

The higher the temperature, the smaller the difference.

Plots of time to puffing/micro-explosion ( τ p ) for the same lead, middle and downstream droplets as in Fig. 8 versus the distance between droplets ( L ) are shown in Fig. 9 . As follows from this figure, for all three droplets τ p decreases with increasing L as in the case of two droplets in tandem [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] . This decrease is hardly visible for the case of the lead droplet, but fast for the middle and downstream droplets, especially for small L .

Plots similar to those shown in Fig. 9 were obtained for droplets of 10% Diesel fuel and 90% water. The main difference between these plots and those shown in Fig. 9 lies in their smaller values of τ p . This difference could be as much as 20% for the lead droplet and 15% for the middle and downstream droplets. A more pronounced decrease in τ p with increasing L for the lead droplet of 10% Diesel fuel and 90% water, compared with that for droplets of 90% Diesel fuel and 10% water, was observed (not shown).

An overview of the model

Initiation of puffing/micro-explosion

As in our previous paper [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] , we assumed that puffing/microexplosion is initiated when the temperature at the fuel-water interface reaches the water nucleation temperature that is estimated based on Expression (1) . As in [START_REF] Antonov | Puffing/micro-explosion in rapeseed oil/water droplets: The effects of coal micro-particles in water[END_REF] , the effects of external gas flow on the values of Nusselt ( Nu ) and Sherwood ( Sh ) numbers are taken into account but not the effects of this flow on the recirculation inside the droplets. The effect on the puffing/micro-explosion of three droplets in a flow was also attributed to the impact of the external gas flow on the values of Nu and Sh . The latter effect was inferred from the analysis of the heat/mass transfer processes during the flow of air around three droplets positioned one behind the other, as described in the following section.

The effect of thermal radiation on puffing/micro-explosion is expected to be insignificant for the range of gas temperatures typical for our experiments (587-629 K) and is ignored in our analysis [29] . As in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] the effect of support on puffing/micro-explosion is taken into account using the approach suggested in [START_REF] Strizhak | Heating and evaporation of suspended water droplets: experimental studies and modelling[END_REF] .

Flow around three droplets, one behind the other

We carried out a numerical study of the heating and evaporation of three droplets, one behind the other, placed in a flow of air at atmospheric pressure. Our analysis was based on the approach developed in [START_REF] Castanet | Evaporation of closely-spaced interacting droplets arranged in a single row[END_REF] to evaluate heat and mass transfer in a line of evenly spaced droplets and applied in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] to the analysis of two droplets in tandem.

The average values of Nu and Sh were obtained for the lead, middle and downstream droplets for the values of parameters used in the experiments ( Re in the range 5.8 to 6.3, B M in the range 0.05 to 0.28, B T in the range 0 to 0.16, Sc in the range 3. The results of calculations of the correction factors for these numbers, N u/N u iso and Sh/Sh iso , where Nu iso and Sh iso are Nusselt and Sherwood numbers for isolated droplets, are presented in Fig. 10 . Following [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF][START_REF] Castanet | Evaporation of closely-spaced interacting droplets arranged in a single row[END_REF] , the following formulae were used for estimation of Nu iso and Sh iso :

Nu iso = 1 + ( 1 + αRe P r ) γ • ( 1 + δRe ) β
(2)

Sh iso = 1 + ( 1 + αRe Sc ) γ • ( 1 + δRe ) β , ( 3
)
where α = 1 . 0024 , γ = 0 . 3419 , β = 0 . 0989 and δ = 0 . 2046 . Note that a deviation of a few per cent could be observed for both Nu and Sh between the results of the numerical simulations and those predicted by the classical models [29] .

As follows from Fig. 10 , the correction factors are less than 1 and increase with increasing C in all cases. The minimal values for all correction factors are predicted for the downstream droplets. For C ≥ 3 the correction factors for the lead droplet are indistinguishable from 1 on the plots.

The correction factors shown in Fig. 10 are used in the next section for the analysis of heating/evaporation of composite droplets and the development within them of puffing/micro-explosions.

Experimental results versus modelling

In this section the results of the application of the model described in Section 4 to the analysis of the experimental results described in Section 3 , and the comparison between the simulated and experimental results are presented. The thermodynamic and transport properties of Diesel fuel and distilled water were taken from [START_REF] Yaws | Yaws handbook of thermodynamic and physical properties of chemical compounds[END_REF] .

In contrast to previous analysis of puffing/micro-explosion, including the one presented in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] , our work focuses not only on the time to puffing/micro-explosion, but also on the time evolution of the temperature at the fuel-water interface before the start of puffing/micro-explosion. The results of our experimental observation of the latter temperature are shown in Fig. 6 .

In Fig. 11 we reproduced the experimental results presented in Fig. 6 (without error bars) and added the predicted values of this temperature using the model described in Section 4 . As follows from Fig. 11 , the general trends of the time evolution of T w observed experimentally and predicted by the model are similar for all three values of C. These include almost linear increase in T w with time for most of the heating period and smaller rates of increase in T w for the middle and downstream droplets compared with the lead droplets. This difference between the rates of increase in T w increases when C decreases.

Although the difference between observed and predicted values of T w lies within the experimental error bars in most cases, the observed T w tend to be larger than those predicted by simulations. This is attributed to the main assumption of the model that a water sub-droplet is located exactly in the centre of the fuel droplet. If we take into account a possible shifting of the water sub-droplet from this centre then we would expect quicker heating of the water-fuel interface in agreement with experimental observations.

In Fig. 12 we reproduced the experimental results presented in Fig. 8 and added the predicted values of this time to puffing/microexplosion using the model described in Section 4 . As follows from Fig. 12 , the general trends of the dependence of τ p on T gas observed experimentally and predicted by the model are similar for all three droplets. The shortest τ p is observed and predicted for the lead droplet. Both experimentally observed and predicted values of τ p decrease with increasing T gas . Observed and predicted differences in τ p for the lead and middle droplets and for the middle and downstream droplets decrease with increasing T gas .

At the same time, the observed τ p tend to be shorter than the predicted ones. This result is compatible with the trends in T w shown in Fig. 11 and is attributed to the main assumption of the model that the water sub-droplet is located exactly in the centre of the fuel droplet. In Fig. 13 we reproduced the experimental results presented in Fig. 9 and added the predicted values of this time to puffing/microexplosion using the model described in Section 4 . As follows from Fig. 13 , the general trends of the dependence of τ p on the distance parameter C observed experimentally and predicted by the model are similar for all three droplets. The shortest τ p is observed and predicted for the lead droplet. Both experimentally observed and predicted values of τ p for the middle and downstream droplets decrease with increasing C. Observed and predicted differences in τ p for the lead and middle droplets and for the middle and downstream droplet decrease with increasing C. As in the cases shown in Figs. 11 and12 , the tendency for the observed τ p to be shorter than predicted is attributed to the main limitation of the model used in the analysis, that the water sub-droplet is located in the centre of the fuel droplet.

Conclusions

The results of experimental and theoretical investigation of the mutual effects of three composite Diesel fuel/water droplets, one behind the other, on their puffing/micro-explosion are presented. The volume fractions of Diesel fuel (water) in the range 10% to 90% (90% to 10%) are investigated although most attention is focused on the case when the volume fraction of Diesel fuel is equal to 90%. The focus of the analysis is not only on finding the time instant when puffing/micro-explosion starts, but also on the investigation of time evolution of temperature at the fuel-water interface before the development of puffing/micro-explosion.

The experimentally observed temperatures at the fuel-water interface are shown to increase almost linearly with time for the lead, middle and downstream droplets. These temperatures were measured at 7 to 10 points in each time instant. The scatter of these measurements did not exceed 15 K. The lead droplet is shown to be the first to heat up, followed by the middle and then the downstream droplet, as expected.

Assuming that puffing/micro-explosion starts when the temperature at the fuel-water interface reaches the water nucleation temperature, the values of the latter temperature as a function of the heating rate are found from the experimental data. The results are shown to be consistent with the earlier suggested correlation for this temperature for all three droplets.

In agreement with the previous results for two droplets in tandem it is found that time to puffing/micro-explosion decreases with increasing gas temperature. It is shown that this time for the lead droplet is always shorter than that of the middle and downstream droplets, and the difference between them decreases as the distance between droplets increases.

The experimental results are interpreted in terms of the previously developed model of fuel/water droplet puffing/microexplosion, based on the assumptions that the water sub-droplet is located exactly in the centre of the Diesel fuel droplet and that this process is triggered when the temperature at the fuel-water interface reaches the water nucleation temperature. The effect of interaction between lead, middle and downstream droplets is taken into account via modifications to the Nusselt ( Nu ) and Sherwood ( Sh ) numbers for these droplets.

The required modifications to these numbers are obtained based on numerical calculations of the flow and heat/mass transfer processes around three droplets, one behind the other. Using the results of these calculations the dependences of N u/N u iso and Sh/Sh iso on the distance parameter C are obtained, where the subscript iso refers to isolated droplets. It is shown that these ratios are weak functions of Re , B M , B T , P r and Sc in the range of values for these parameters typical for these experiments. This allows us to estimate N u/N u iso and Sh/Sh iso for the initial values of Re , B M , B T , P r and Sc.

The predicted temperatures at the fuel-water interface are shown to be close to those observed experimentally for all three droplets in the distance parameter range 2.02 to 5.60.

As in the previously studied cases of isolated droplets and two droplets in tandem, both experimentally observed and predicted values of the time to puffing/micro-explosion ( τ p ) are shown to decrease with increasing T gas . Both experimentally observed and predicted values of this time are longer for the middle and downstream droplets than for the lead droplet. The experimentally observed differences in this time for the lead, middle and downstream droplets are close to the predicted values. to the fact that Diesel fuel is very volatile and thermal expansion compensates for droplet evaporation during the heating phase.

2 d

 2 + bT d + c, where a = 5 . 86 × 10 -3 ; b = -4 . 6568 ; c = 9 . 2542 × 10 2 .

Fig. 1 .

 1 Fig. 1. An image of the group of three droplets used in our experiments.

Fig. 2 .

 2 Fig. 2. The results of calibration of fluoroform Rhodamine B emission intensity versus droplet temperature (symbols) and the approximation of these results (calibration curve; solid curve). Random error in plotting the calibration curve did not exceed 9 K.

Fig. 3 .

 3 Fig. 3. The analysis of images performed using DaVis software.

Fig. 4 .

 4 Fig. 4. Typical temperature fields in three droplets (volume fraction of Diesel fuel is 90%; volume fraction of water is 10%), one behind the other, for ambient gas temperature T gas = 604 ± 10 K, distance between droplets L = 3 . 55 ± 0 . 05 mm, and initial droplet radii R d0 = 0 . 88 ± 0 . 03 mm. The droplet boundaries are shown by the black contours.

Fig. 5 .

 5 Fig. 5. Typical temperature fields in three droplets (volume fraction of Diesel fuel is 10%; volume fraction of water is 90%), one behind the other, for ambient gas temperature T gas = 604 ± 10 K, distance between droplets L = 6 . 48 ± 0 . 06 mm, and initial droplet radii R d0 = 0 . 91 ± 0 . 02 mm. The droplet boundaries are shown by the black contours.

Fig. 6 .

 6 Fig. 6. The temperature at the fuel-water interface versus time for the lead (1), middle (2) and downstream (3) droplets of 90% Diesel fuel and 10% water. Top, L = 9 . 86 ± 0 . 06 mm and R d0 = 0 . 88 ± 0 . 04 mm; middle, L = 6 . 48 ± 0 . 04 mm and R d0 = 0 . 89 ± 0 . 02 mm; bottom, L = 3 . 55 ± 0 . 05 mm and R d0 = 0 . 88 ± 0 . 02 mm.

Fig. 7 .

 7 Fig.7. The degree of super-heating ( T SH ) versus heating rate at the water/fuel interface of droplets of 90% Diesel fuel and 10% water (lead, middle and downstream) inferred from our experiments (1), experiments described in[START_REF] Sazhin | A new approach to modelling micro-explosions in composite droplets[END_REF] (2) and experiments described in[START_REF] Su | Transient boiling of water under exponentially escalating heat inputs, Part I: Pool boiling[END_REF] (3). The solid curve shows the correlation predicted by Expression (1) .

Fig. 8 .

 8 Fig. 8. Time to puffing/micro-explosion ( τp ) versus ambient gas temperature for the lead (1), middle (2) and downstream (3) composite droplets (90% volume fraction of Diesel fuel; 10% volume fraction of water). The distances between droplets ( L ) were 9 . 86 ± 0 . 08 mm and the initial droplet radii R d0 were 0 . 89 ± 0 . 04 mm.

Fig. 9 .

 9 Fig. 9. Time to puffing/micro-explosion versus the distance between droplets ( L ) for the lead (1), middle (2) and downstream (3) composite droplets (90% volume fraction of Diesel fuel; 10% volume fraction of water). The ambient gas temperature was 604 ± 10 K and the initial droplet radii R d0 were 0 . 89 ± 0 . 04 mm.

5 to 3 ,

 3 P r in the range 0.77 to 0.76, the distance parameter C = L/ (2 R d0 ) in the range 2 to 8). The results of calculations are shown in Appendix 1. As follows from these results (see Appendix 1), the values of Nu and Sh are weak functions of Re , B M , B T , Sc and P r which allowed us to calculate Nu and Sh using the initial values of the input parameters: Re = 5 . 82 , B M = 0 . 05 , B T = 0 . 024 , Sc = 3 . 52 and P r = 0 . 7722 .

Fig. 10 .

 10 Fig. 10. Correction factors for Nusselt and Sherwood numbers, N u/N u iso and Sh/Sh iso , for the lead, middle and downstream droplets versus the distance parameter C.

Fig. 11 .

 11 Fig. 11. The temperature at the fuel-water interface ( T w ) observed experimentally (predicted by the simulation) versus time for the lead (LE(LS)), middle (ME(MS)) and downstream (DE(DS)) droplets of 90% Diesel fuel and 10% water. Top, L = 9 . 86 ± 0 . 06 mm and R d0 = 0 . 88 ± 0 . 04 mm ( C = 5 . 60 ); middle, L = 6 . 48 ± 0 . 04 mm and R d0 = 0 . 89 ± 0 . 02 mm ( C = 3 . 64 ); bottom, L = 3 . 55 ± 0 . 05 mm and R d0 = 0 . 88 ± 0 . 03 mm ( C = 2 . 02 ).

Fig. 12 .

 12 Fig. 12. Time to puffing/micro-explosion ( τp ) observed experimentally (predicted by the simulation) versus ambient gas temperature for the lead (LE(LS)), middle (ME(MS)) and downstream (DE(DS)) composite droplets (90% volume fraction of Diesel fuel; 10% volume fraction of water).The distance between droplets ( L ) was 9 . 86 ± 0 . 08 mm and the initial droplet radii R d0 were 0 . 89 ± 0 . 04 mm (the same as in Fig.8).

Fig. 13 .

 13 Fig. 13. Time to puffing/micro-explosion observed experimentally (predicted by the simulation) versus the distance parameter ( C) for the lead (LE(LS)), middle (ME(MS)) and downstream (DE(DS)) composite droplets (90% volume fraction of Diesel fuel; 10% volume fraction of water). The ambient gas temperature was 604 ± 10 K and the initial droplet radii R d0 were 0 . 89 ± 0 . 04 mm (the same as in Fig.9).

Fig. A2 .

 A2 Fig. A2. Evolutions of the Nusselt and Sherwood numbers of the string of three droplets at the beginning of the heating process (LI, MI, DI stand for the lead, middle and downstream droplets) and just before puffing or micro-explosion (LE, ME, DE stand for the lead, middle and downstream droplets). The initial conditions: Re = 5.8, Pr= 0.77, Sc= 3.52, B M = 0.05 and B T = 0.02. The conditions just before puffing/micro-explosion: Re = 6 . 3 , B M = 0 . 3 , B T = 0 . 16 , Pr = 0 . 76 and Sc = 2 . 9 .

Acknowledgements

The authors are grateful: to the National Research Tomsk Polytechnic University (project VIU-ISHFVP-60/2019) which supported P.A. Strizhak (who contributed to the formulation of the problem and analysis of the results) and R.S. Volkov (who contributed to the development of the experimental setup); for scholarships from the President of the Russian Federation (Grants SP-447.2021.1 and MN-7/2260) which supported D. Antonov and R. Fedorenko (who performed the experiments, applied the model to their analysis and prepared the first draft of the paper); to the Université de Lorraine and the Institut Carnot Icéel for the CALICO (Combustion d'Aérosols LIquides Complexes) grant which supported G. Castanet (who contributed to the development of the model, the simulations and preparation of the text of the paper), and to the Russian Science Foundation (Grant 21-19-00876), which supported S.S. Sazhin (who contributed to the development of the model, analysis of the results and preparation of the text of the paper).

Declaration of Competing Interest

The work described has not been published previously and it is not under consideration for publication elsewhere. Its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out. If accepted, it will not be published elsewhere in the same form, in English or in any other language, including electronically without the written consent of the copyright-holder.

CRediT

Appemdix A

The determination of the Nusselt and Sherwood numbers for the three droplets positioned one behind the other is based on the same approach as described in [START_REF] Castanet | Evaporation of closely-spaced interacting droplets arranged in a single row[END_REF] . The problem is simplified by considering heat and mass transfers within the gas phase only. The assumptions made are the same as used in the derivation of the d 2 -law for an isolated droplet. The steady state Navier-Stokes equations, the continuity equation for mass, the convection-diffusion equations for the vapour and heat transfers are solved assuming that the droplet arrangement is axisymmetric. The droplets are assumed to be rigid spheres. Only the normal velocity, corresponding to the Stefan flow, is considered even in the case when Diesel fuel is weakly volatile in the conditions of the experiments. The tangential velocity at the liquid surface is assumed equal to zero. Since only the mean values of the Nusselt and Sherwood numbers are sought from the simulations, other simplifications are also made. Both temperature and vapour concentration are assumed to be uniform over the droplet surface. The finite element method is applied for the numerical solution. It uses an unstructured triangular mesh of increased density near the surface of the droplets (typically, the half perimeter of the droplets is divided into 100 elements of equal size).

Even with the above approximations, a comprehensive study of three droplets in a row would be time-consuming, due to a large number of parameters related to the geometry, surface conditions and flow field. An example of a parametric study, where the distance between droplets, the droplet sizes and the surface conditions are modified, was recently presented in [START_REF] Antonov | Puffing/micro-explosion of two closely spaced composite droplets in tandem: experimental results and modelling[END_REF] , but for a more simple case of two droplets. In the present study, we used experimental results that refer to droplet evolution to limit the scope of investigations. The ranges of Re , C, P r, Sc, B M and B T were approximated to determine the influence of these dimensionless numbers on heat and mass transfer under the selected experimental conditions.

Fig. A1 shows the vapour and temperature distributions around the three droplets for C = 2 , C = 4 and C = 6 . These simulations were performed for values of the parameters relevant to the beginning of the experiments when the surface temperature was about 340 K: Re = 5.8, P r= 0.77, Sc= 3.52, B M = 0.05 and B T = 0.024. As can be seen in this figure, the spacing between the droplets clearly affects the temperature and vapour distribution around the middle and downstream droplets. Using these temperature and vapour concentration fields, Sherwood and Nusselt numbers were calculated as:

where R is the radial coordinate from the centre of the droplet under consideration.

To evaluate the effect of interaction between droplets on heat and mass transfer processes, the Nusselt and Sherwood numbers were averaged over the surface of the droplets and divided by their counterparts for an isolated droplet using Eqs. ( 2) and ( 3) . The evolution of N u/N u iso and Sh/Sh iso is presented in Fig. 10 . As expected, a stronger reduction in the heat and mass transfers is observed for the middle and downstream droplets. As the droplets are heated, the conditions at their surfaces change. The heating process was the fastest for the lead droplet, and was almost the same as for an isolated droplet.

A decrease in Nu and Sh of about 6% was observed as a result of heating and evaporation as demonstrated in Fig. A2 . The evolutions of Nu and Sh as functions of C follow the same trends at the beginning of the process and just before puffing/micro-explosion starts. Note that the reduced Sherwood and Nusselt numbers, Sh/Sh iso and N u/N u iso , are only slightly affected by the heating process with variations of less than 0.5%. Therefore, it can be concluded that Sh/Sh iso and N u/N u iso are weakly dependent on Re , B M , B T , P r and Sc in the present study. They can be considered as functions of the distance parameter C only. Also, changes in the sizes of the droplets during the experiments can be ignored. This is related