L Beaudoin
email: beaudoin@esiea.fr

L Avanthey

V Germain

A Gademer

J P Rudant

REAL TIME DETECTION OF FOREST FIRES AND VOLCANIC ERUPTIONS FROM METEOSAT SECONDE GENERATION IMAGES USING A NEURAL NETWORK

INTRODUCTION

One of the most important parameters in the estimation of the evolution of global warming is the gas composition of the atmosphere and its temporal variation. Amongst the various and complex processes that absorb or produce gases, the biomass burning has very important short and long term effects [START_REF] Levine | Biomass Burning and Global Change[END_REF]. Remote sensing plays a key role in monitoring these effects [START_REF] Prins | Global geostationary fire monitoring system[END_REF], but you have to make a compromise in temporal, spectral and spatial resolution [START_REF] Justice | Remote sensing of fire: potential and limitations[END_REF][START_REF] Kaufman | The effect of smoke particles on clouds and climate forcing[END_REF]. As burning savannas represents the main contribution to global biomass burning, monitoring Africa becomes a priority. Because of its near real time imaging capacities and its position over the African Continent, Meteosat Seconde Generation appears to be a very promising satellite to efficiently do this task.

In this article, co-written with undergraduate students, we start by describing the data used and the way to obtain them. Then we describe two different algorithms to perform the detection of near real time forest fires and volcanic eruptions detection on Meteosat Seconde Generation images.

THE METEOSAT SECONDE GENERATION DATABASE

The image database used has been obtained by a home-made receiving, processing and archiving stations developed in collaboration with our undergraduate students.

Our first attempts to receive images directly from satellites occurred in 2002 [START_REF] Beaudoin | Receiving images directly from meteorological satellites in an engineer'school: technical and pedagogical aspects[END_REF]. These stations were analogical stations and in 2004 we developed digital receiving stations [START_REF] Beaudoin | A Meteosat Second Generation receiving, processing and storing images system developed by engineer students[END_REF] to be able to receive the latest generation of meteorological satellites (Meteosat Second Generation). In recent years, we have extended the reception to other satellites like the polar ones. In this section, we present our latest recommandations in developping and managing this kind of receiving, processing and archiving stations.

The hardware part of the network

To avoid the whole chain stopping when a problem occurs, it is very important to dedicate one computer to each critical task like receiving, processing and archiving. Even if this leads to a more complex network, it is a very efficient way to isolate problems and to permit the rest of the chain to continue to work. Stations running on Linux Operating Systems seems to be more stable than Windows Operating Systems. The monitoring task of the whole chain can also be more easily done using Simple Network Management Protocol (SNMP).

New software solutions as a key of an efficient operational management

After testing different software architectures, the best results obtained are based on Ruby On Rails framework(RoR), which is an object oriented script language with Object Relational Mapping Methods. This architecture based on RoR is fully compatible with the SNMP monitoring and postgreSQL with PostGIS server, permits a very efficient access to huge databases (3 Tera-Octet/year only for MSG) and simplifies a lot the development of image processing algorithms.

The Meteosat Seconde Generation Images

The data used in this work are Meteosat Second Generation images. In table 1, you will find the main characteristics of the data [START_REF] Eumetsat | MSG system overview-TD07[END_REF]. Obviously, as Meteosat Second Generation (MSG) is a geostationary satellite, it is particularly well adapted for near real time applications.

FOREST FIRES AND VOLCANIC ERUPTION DETECTION

The physical phenomenon

First of all, in order to define these eruption detection algorithms, we start by describing the context and the physical properties that lead us to identify the most efficient spectral bands for hot spots detection. We pay attention particularly to important aspects that we have to take into account, like the solar influence for example.

An hybrid morphological and multispectral algorithm

The algorithm starts by filtering images with a tophat morphological filter. By doing this, i.e. making the difference between the original image with the opening mathematical morphological operator, we focus attention on patterns smaller than the morphological element used (a square for us). In this way, we obtain the potential fire areas. On these areas, we then use the multispectral difference between the 3.9 µm and the 10.8 µm channels. This difference is a good estimator because it grows up of fire [START_REF] Li | A review of avhrr-based fire active fire detection algorithm: Principles, limitations, and recommendations[END_REF] but false alarms remain.

An Artificial Neural Network to improve performances

Given the results we have obtained with this algorithm, we wanted to know if an artificial neural network (ANN) could improve the accuracy of the detection considering the time and its exactness (is it a real eruption or not?). In particular, we focus on the interest of a weighted sum of other channels than only the 3.9 and 10.8 ones. So we chose to use an ANN with supervised learning. Indeed, we have at our disposal a lot of data thanks to our images storage on our own ground station (gathered over many years) and to the ground data coming from the different volcano survey programs.

Results and validation

We complete this article with a comparison between the results we obtained with both algorithms, the hybrid one and the hybrid with neural network one and we highlight the strong and weak points of those two methods.

CONCLUSION

In this article, we have presented our solutions in receiving, processing and archiving images directly from satellites, dealing with the hardware and software aspects. We then have used the data acquired to work on real time detection of forest fires and volcanic eruptions. We have presented two algorithms, one based on a hybrid multi-spectral and morphological approach and the other one based on an adapted neural network approach and tested the performance of each algorithm.

In the undergraduate teaching world (university or engineering school), it is our responsability to find answers to fundamental questions like : how can we optimize the training of our students to be operational in the research or industrial worlds or how to create vocations for scientific careers. At our scale, we, a French Engineering School called ESIEA, have decided to emphasize very soon in the teaching the relationships between our undergraduate students and our research laboratories.

In this article, we have presented a concrete example of research activities co-developed with undergraduate students and the scientifical level of competences reached during this kind of cross-collaboration.

Table 1 .

 1 Thanks to EUMETSAT agency for the autorization of receiving satellite images. Main characteristics of the MSG data (HRV channel for High Resolution Visible channel)

	spectral channel (µm)	0.6, 0.8, 1.6, 3.9, 6.2, 7.3, 8.7, 9.7, 10.8, 12.0, 13.4
	sampling distance (km) 1×1 (HRV channel) 3×3 otherwhise
	radiometry depth	10 bits per pixel
	image size	11136×5568 (HRV channel), 3712×3712 otherwise
	time sampling	15 minutes


Laurent Beaudoin
email: beaudoin@esiea.frgademer@esiea.fr

Antoine Gademer

Loica Avanthey

Vincent Germain

ESIEA Vincent Vittori

Potential Threats of UAS Swarms and the Countermeasure's Need

Keywords: unmanned aerial system, swarms, countermeasure, terrorism

The rising capabilities and growing accessibility of recent Unmanned Aerial Systems (UAS) widen the risks of success of a terrorists attack through the current aerial defence systems. We will examine first the complexity of the threats from a single unmanned vehicle, to a team of unmanned vehicles and finally to a swarm of unmanned vehicles (and any other association of these three combinations). Then, from an operational point of view, we will see that early detection of danger -a critical stage in the development of counter-attacks -has become very difficult because small unmanned vehicles like UASs precisely possess the ability to take off directly within the sphere of attack. The next stage, equally critical, consists in elaborating the response that best fits the attack. We distinguish three general categories of active and passive countermeasures: destruction, incapacitation and jamming of the enemy UASs. We will then study several possible countermeasures appropriate to the type of attack (enemy's formation: isolated drone, team, swarm; weapon type: bomb, kamikaze, bacteriological etc.). We first present countermeasures that are rather conventional (they usually come from air defense systems) and others specific to the UAS case. We will finish by a case study in which we will tackle the use of simplified physical models for calculating positions in real time in an optimized way in a UAS swarm under constraints.

Introduction

We previously presented the risks presented by the use of single micro-UAS by terrorist groups given the current flaws in the aerial defence systems (Beaudoin & Gademer, 2010). This scenario is nowadays more than conceivable considering the rising capabilities of recent UASs and their growing accessibility. This perspective thus opens new breaches, even more dangerous than the previous ones, and renders obsolete most of the existing solutions.

This article deals with the potential threats related to the use of micro UASs, which weigh less than 5 kilograms, for terrorist purposes in two ways: the increasing level of automation of these systems and their new capacity for collaboration. In a second step, we will discuss the current counter measures to prevent or fight such situations. Then we will widen the debate with a case study that includes the prospects offered by collaborative systems in terms of counter-measures.

Technological abilities for new threats 2.1 Unmanned Vehicle Systems (UVSs) and level of automation

Automated unmanned vehicles are robots of different sizes [START_REF] Abatti | Small power: the role of micro and small UAVs in the future[END_REF], carrying no human on board, but designed to fulfil various types of missions known as the three "Ds" (Dull, Dirty or Dangerous). They can be remotely controlled or follow a predetermined plan or react to their environment, or even use a combination of the three previous situations. In the literature [START_REF] Christ | The Rov Manual : a user guide for observation-class remotely operated vehicles[END_REF][START_REF] Singer | Wired for War : the robotics revolution and conflict in the 21 st century[END_REF], robots are often spoken about, and you can find a lot of autonomy scales. But more than the autonomy (which is a bit anthropomorphic) we prefer to define an automation scale.

We will distinguish several levels of automation:

Level 1: Slave (assisted piloting, disturbance compensation) Level 2: Automated (maintains its orders and takes high level orders) Level 3: Automatic Navigation (a priori mission plan) Level 4: Response from contextual data (dodging) without human intervention Level 5: Decision-maker (expert system) from contextual data (navigation in unknown environment, realization of complex missions, coordination) Levels 1 and 2 require the intervention of a pilot during the mission and therefore a continuous communication link between himself and the UVS during the attack.

At level 3, the system is independent of the pilot and knows how to place itself in its environment. For this, it relies on passive sensors (AHRS, GPS, clock…) and blindly follows the mission plan that has been given to it beforehand. This involves a detailed knowledge of the place in which the mission will take place to make sure everything goes smoothly.

At level 4, the system has a minimum knowledge of its surrounding environment and can react to events such as performing collision avoidance. To do this it uses a number of active sensors (distance measurement, short range communications, etc.), but the establishment of an accurate mission plan beforehand remains a fundamental element.

Level 5 introduces concepts of artificial intelligence and decision-making that require significant computing power. To take full advantage of these new features, many perceptive sensors are usually added, as well as a large storage capacity that allows the robot to make inferences from the state of its environment, both in space and time. These robots are able to realize complex missions in unexplored environments, to interact with them in a meaningful way, or to reschedule an ongoing mission because of encountered events.

The higher the level of automation is, the more the human cost and risk is minimized from the point of view of the attacker and the greater the probability of an unexpected attack increases (because fewer staff are involved upstream and on field). The impact on the financial cost is more complex to measure, because it is much more influenced by the material cost of the device (due to the payload and the number of sensors) than by the embedded intelligence (software part). In what follows, we will apply the previous scale to micro-UASs. Given the current technological breakthroughs available at a lower cost, micro UASs represent new threats. Moreover, the multiplication of supply depots all over the world makes it impossible to survey or to detect suspicious individuals or groups. If you look at what exists today on the market for micro-UASs (less than 5 kg category) and given what we just described, we can distinguish three cases: Levels 1 and 2 which are relatively common, with reasonable prices. We find material for flying model aircraft (<500 €) or the first micro-UAS (<1 000 €) as the AR. Drone Parrot, Quad Flyer GAUI or first models from Mikrokopter.

Level 3 is the standard micro-UAS premium (~ 10 000 €) as the models from Draganfly Innovations Inc.., Microdrone Gmbh or Fly-n-Sense. Note that the models from Mikrokopter offer this capability for less than 2 000€, but need to be assembled by an engineer. Levels 4 and 5 are for now confined to laboratories (Valenti et al. 2007(Valenti et al. , 2007b)).

Unmanned Aerial Systems (UASs) and level of collaboration

After having established the automation scale of UAS, let's talk now about the collaboration scale of UAS among themselves. We will examine the definitions by increasing complexity from the isolated individual, a group of individuals, a team and to finish, a swarm. Through these concepts (see figure 1), we will take the opportunity to note the strengths and weaknesses of these different formations.

Figure 1: Different levels of collaboration in operation

Isolated individuals

The most basic case is about the isolated individual (Beaudoin & Gademer, 2010). The UAS can be piloted or autonomous and has a specific mission to perform. Small in size, easy to assemble, affordable to fly, some models can even embed a light payload. They have all the assets to be used for terrorists operations in the close future. However, if the pilot or the UAS is stopped, disabled or destroyed, the threat is removed.

A group of individuals

A group of UASs is composed of several isolated individuals, each with their own mission without coordination. Their sphere of action does not necessarily lie on the same location and each unit can be considered as the case described in the previous paragraph. But by increasing the number of individuals, we multiply the probability of a successful attack by trying to saturate the defense's capabilities. The main advantage of the group is that it does not need any collaboration among the individuals and thus does not need advanced collaborative capacity.

Team of UASs

A team of UASs can be seen as a group in which all members are assigned specialized tasks and are usually coordinated by a chief. Team formation is particularly effective: the objectives are divided and each member can focus on achieving its task. With UASs on the third level (automatic navigation) of the automation scale, you will have synchronized action but no possibility to update the mission plan according to what happens on the field. The fourth level (without human intervention) will give you reaction to the surroundings but may lead to a fatal loss of synchronization between the team members, which quickly leads to using UASs of the fifth level. At this step, all members are communicating with each other and the leader chooses what to do next. So the action is fast and has things in common with a commando operation.

The missions that a team can perform could be far more complex than the one in the previous case. The team strength is also its weakness: the more each member is highly specialized, the more the destruction of a key element can jeopardize the whole mission (coordinator UAS, UAS with the lethal load, UAS dedicated to the collection of information...). Survival of team-members is therefore critical and fundamental to the proper performing of the mission.

The enemy can also try to predict the behaviour of a team, in a certain way, because it usually works following a logical reasoning, and so it is possible for him to act accordingly.

Swarm of UASs

A swarm, unlike a team, is made of a uniform mass of undifferentiated individuals [START_REF] Clough | UAV swarming? So what are those swarms, what are the implications, and how do we handle them?[END_REF]. The robots forming a swarm are at least of the fourth level on the automation scale. The swarm has no "chief" or "organization". Its efficiency is based on the emergent behaviors related to the large number of individuals and their interactions, that's why they cannot be controlled and need to be automated. The intelligence is decentralized [START_REF] Frantz | Swarm Intelligence for Autonomous UAV Control[END_REF]: each individual interacts with others on the same basis of simple rules describing the reactions of individuals to their local environment (like a shoal of fish). This decentralization, combined with the large number of individuals, allows the swarm to be a highly resistant form (Chaumette et al., 2010). If some individuals disappear, it will have little influence on the conduct of the mission. The resulting action is certainly less efficient, but the mission can still succeed. Similarly, the swarm is resistant to local disturbances or to the addition of new individuals into the system, the overall behaviour is the only one taken into account.

However, the behaviour of the swarm is only based on individuals' reactions. So it is not deterministic [START_REF] Lamont | UAV Swarm Mission Planning Development Using Evolutionary Algorithms-Part I[END_REF][START_REF] Lamont | UAV Swarm Mission Planning Development Using Evolutionary Algorithms and Parallel Simulation-Part II[END_REF]. Then, we can only estimate a probability of success, even in a favourable situation, which is far removed from the optimum way of the team work. The main strength of a swarm, its distributed intelligence and its lack of hierarchical bonds, is also its main weakness, which is its lack of strategic global view.

Finally, the apparence of the swarm itself can fulfil another objective in psychological warfare. Indeed, it can inspire both fear and powerlessness into the collective unconscious as for example in "The Birds" of Hitchcock, or like the killer bees from South America, the ants in Indiana Jones, or grasshopper clouds.

The vulnerability of existing defense systems and counter measures

Vulnerability of present defense systems and attacks by micro-UASs

In practice, defense systems in simplified can be viewed as the achievement of two critical phases: detection and identification of the danger and counteraction through appropriate response while restricting collateral damage.

The traditional tools of detection used by air defence systems can be categorized into two families:

Active radar surveillance: they generate waves and use the rebound of the echoes on potential flying objects to locate them. From there, it is possible to estimate their distance, their speed of approach, the penetration vector, and even have an idea about their trajectory (at least in the short term) and their size.

Monitoring by passive observation of the electromagnetic spectrum, either in the visible or thermal infrared or by listening to the radio waves on the common communication channels.

In practice, the data fusion of multiple sensors allows to reduce noise and false alarms to the maximum while maintaining reliability. Except unusual cases, the bigger the device is, the easier it is to notice. Usually the defence systems are optimized to detect aircraft or missiles. They both move at a rather high altitude and reach substantial speeds during the approach stage of the target.

The main problem posed by micro-UASs is that the approach stage can be practically non-existent, because their small size allows them to be launched into action very close by the target [START_REF] Carnu | The new face of air oriented terrorism and air defence systems vulnerabilities[END_REF][START_REF] Miasnikov | Threat of Terrorism Using Unmanned Aerial Vehicles: Technical Aspects[END_REF][START_REF] Gademer | A low cost spying quadrotor for global security applications using hacked digital cameras[END_REF][START_REF] Gademer | Réalité Terrain Étendue : une nouvelle approche pour l'extraction de paramètres de surface biophysiques et géophysiques à l'échelle des individus[END_REF]Gademer, , 2010a) ) . This cancels the long range defensive strategies and raises the problem of reactivity from the decision line. Reactivity that has to be all the quicker as we are near the target. Their slow flight at a very low altitude is an aggravating factor that increases the probability of non-detection. Moreover, their electric motors do not leave a thermal signature, which makes their detection extremely difficult.

Finally, the topography of the theatre of war can also be an additional factor of complexity, as in the case of an urban environment. Here, the sphere of attack is limited. Therefore the interception stage inevitably takes place near the target, so probably within the urban environment itself. Thus the risk of collateral damage is much higher.

Counter-measures against these new threats

Once the danger is detected, it is then necessary to determine according to the context the best adapted countermeasure. There are two big families of countermeasures [START_REF] Mirkarimi | Countering the tactical UAV Threat[END_REF][START_REF] Haulman | US unmanned aerial vehicles in combat, 1991-2003[END_REF]. The first family, the active one, tries to incapacitate or to destroy the threat in a direct way (systems of airto-ground defence for example). The second, the passive one, tries to protect from the danger in an indirect way (physical protections around the target, the use of decoys, organized by systems of communications or of jamming of the sensors of the aggressor as will be detailed in the practical case part).

The first active countermeasures to fight against micro-UASs are inspired by classic anti-aircraft defences. However, if the latter showed their ability on "classic" targets, their efficiency against smaller and more reactive targets is much more mitigated, especially in urban zones with the public at risk. These methods are also difficult to apply against enemies attacking simultaneously on multiple fronts, even if we increase the ability of the defence system to react and make its saturation limit recede. The team mode of operation should besides allow implementing operational strategies (decoys, shields, rams) which complicates at the same time the stage of detection and interception. The swarm, on the other hand, should be easier to detect globally because it is not evident to mask the arrival of a cloud of robot craft, but it should show itself on the other hand much tougher to neutralize.

The passive countermeasures based on the physical protection of the target (installation of nets for example) are last resort solutions. However, within the context of attack by micro-UAS, these solutions can be effective because of the small size of the robots. The use of decoys supposes that we know a priori the sensors used by the drone to make his kamikaze attack and how this information is used particularly in the final phase. The jamming of communication would appear to be effective against drones of level 1 or 2 which require the control of a pilot. It can also prove interesting to perturb the interdrones communication required for a team or a swarm. The jamming of the sensors (false GPS information, camera dazzling, magnetic disturbance of the heading sensor) can also be an effective approach, whatever the level of automation.

Case study of a UAS swarm

Operational context

As we have seen previously, there can be a high operational interest to locally jam GPS cover. But a loss of the signal can easily be detected by the attacker who can then activate a ploy like estimating the course, the ground-speed and a timer in order to nonetheless reach the area of the target. More interesting is the case in which we only slightly modify the GPS signal to give false positions to the attackers in order to lure them into a chosen area. For the attacker, this strategy of defence is much more difficult to detect. In every case, this strategy can be complicated to apply on an area with fixed facilities, furthermore if the perimeter of the area to protect is mobile. A possible solution could be to use a swarm of UAS, each of them having an action (eventually mobile) of locally jamming. In this hypothesis, we use the swarm in a situation of defence. As for the aggressor, a solution could be to perform a kamikaze attack in order to create a breach in the defence system in position. In our next section, we will show an example an innovating demonstrator to test scenarios of swarm-based attack and defence in a given operational context.

Operational modelling of a swarm in defense

To continue working, the swarm will have to respond to the suicide bomber attack. The maneuver that is least costly in human resources will be a dodge to avoid contact with the bomber, but also with other UASs of the swarm. However, in order to have an operational interest, we will have at the same time to minimize the deformation of the network of the UAS swarm. Finally, to check the operational feasibility of these solutions, we want to be able to perform the associated calculations locally and almost instantly, which excludes conventional solutions such as those based on numerical modeling of virtual reality. To accommodate the constraints, we propose to develop a demonstrator adapting a physical library (Chipmunk) mainly used in video games on smart-phones. This pragmatic approach allows us to leverage for our problem all the improvements and developments made by the video game industry for which resource constraints and time calculations are close to what we want. The problem then is to find how to model our problem in the range of tools available in the library. The modelling solution that we propose for the demonstrator is: Avoidance of UAS done through a repulsive force like the Coulomb one so as 1 / r ², where r is the distance between the UASs.

Minimizing deformation of the mesh done by linking the UASs with their neighbours in eight connexions by restoring forces in the manner of a spring where the coefficient of stiffness and length at rest reflect the physical reality (UAS's reactivity and inter-UAS distance respectively).

Figure 2 shows the physical network of the modelization. The big square is the attack UAS, and the small ones the defend UAS. The images shows different position of the attack UAS and the re-organized response of the defend UAS. The real-time constraints can be totally satisfied on architectures with limited computing power, and therefore be available in operation.

The modelling shows that it is virtually impossible for the attacker to destroy or disrupt the defender's swarm effectively, unless he develops abilities to move very much faster than those of the defenders.

Collaboration among UASs in attack

From the perspective of the attacker, since a single attack is not enough, we have explored different scenarios of attacks of the defensive swarm by another offensive group using the demonstrator indicated above.

Among the initial findings, it appears that an attack from a team of UASs that begins by encircling the defensive swarm to limit the operating space increases dramatically the effectiveness of a direct attack, but needs strong coordination to have a maximum effect.

We can reverse the demonstration and say that a UAS swarm in attack would be practically unstoppable unless the defender demonstrates strong collaboration. If we describe a cloud of UAS as graph, we think it will be possible to use graph matching techniques to distort an attacking swarm with amazing efficiency over the defensive swarm.

We can conclude this part by saying that countering a swarm (in defence or attack) is very expensive because it seems necessary to have high level collaboration on the defence group side. Costs are an additional vulnerability factor for aerial security against a collaborative UAS attack.

Conclusion

We started this article by defining the new levels of automation and collaboration that the current UAS technology can offer. We then presented how these new capacities could increase the potential menace of a terrorist attack using simple short-range flying robots and why it seems necessary to start thinking about appropriate responses to this particular problem. In the last part we have shown with a simplified demonstrator that some basic rules could give a UAS swarm a strong endurance to kamikaze attack, which can be used in a defensive way to maintain a local jamming on an area or in an offensive way to overwhelm the enemy. Against collaborative UASs, it seems that the only solution would be smarter and more numerous UASs. To conclude, our numerical approach has shown its value to estimate the behaviour and interactions of an UAS swarm. Nevertheless these results should be consolidated by practical tests; which will need to integrate the physical constraints of the robots and their sensors, as the reacting time, the measurements errors including the positioning error, the processing and synchronization capacities. Another way of extending this work could be 3D simulations, with remarkable increase in complexity with both attack and defence strategies.

Figure 2 :

 2 Figure 2: Modelization

Figure 3

 3 Figure3shows screen shots of the demonstrator. This reacts in near real time. The modeling approach shows the desired behavior (deformation of the mesh of the swarm optimized and UAS-UAS avoidance made).

Figure 3 :

 3 Figure 3: Demonstrator From this demonstrator, we can draw two initial conclusions:


L Beaudoin

L Avanthey

A Gademer

V Vittori

L Dupessey

J.-P Rudant

AQUATIS AND RYUJIN PROJECTS: FIRST STEPS TO REMOTE SENSING OF THE SEA BOTTOM BY SMALL HOMEMADE AUTONOMOUS UNDERWATER VEHICLES

INTRODUCTION

For many applications such as pipeline surveys, environmental, archeological or security studies, precise information on the sea bottom can be critical. But because of the difficulties of underwater exploration, even coastal areas are mostly unsurveyed. The main issues are due to the hostility of the sea environment: pressure, salinity, and a limited visibility (less than 15 meters most of the time). It is also very difficult to get a precise localisation: there is a huge drift and it is impossible to use such device as the GPS data for live geo-positionning. For all these reasons, it takes a lot of time to cover an area undersea, and the use of divers may be too dangerous or expensive. That is why the use of underwater robots is considered as an efficient solution: it allows deeper and longer diving as well as the use of optimized payloads.

In a divide and conquer approach, using a team of robots allows to decrease the time needed to cover the area of interest.

The main hindrance to such development is the cost (> 10,000 euros) and the size (manipulation, transportation, etc.) of the robots. That is why we present in this article two small low cost homemade underwater robots. These robots are called Aquatis and Ryujin and benefited from the experience earned on our previous aerial robotic work [?, ?, ?]. A first section summarize the technical aspects of the robots (mechanical and electronic designs, software developments). Then we present the first operational results obtained during pool tests and also during an international student contest dedicated to autonomous underwater robotics. This section ends with pedagogical return of experience.

OVERVIEW OF THE ROBOTS

Two robots, two approaches

The AQUATIS robot is quite conventional in its structure. Its goal is to educate the students in how to build an underwater vehicle (about 8,000 euros) and to increase their awareness of the harsh conditions of this environment. This being done, they can rapidly learn the basis of programming Autonomous Underwater Vehicles (AUVs). Then they can concentrate on high level development and try to innovate in this area. The robot is dedicated to perform automated mission.

When we discovered the SeaPerch [?] in the summer of 2010, we decided to do some research on an advanced design.

It gave birth to the RYUJIN robot that stands as an alternative to the AQUATIS AUV. Its structure is radically different from ⇤ Thanks to Fischer connectors Society for sponsoring us and Charenton-le-Pont city for diving and simming pools access. robots of the same category. Its key features: small size, easy to build and low cost (about 1,000 euros). Its goals: to achieve automated missions with the same efficiency as the other robots and serve as a learning platform for students working in the laboratory.

Designing an underwater robot implies combining knowledge in various domains but we can group them under three main functions: sealing the hull, connecting sensors and electronics, and low and high level algorithmics.

Hardware and mechanics

AQUATIS

Basically, the hull of the AQUATIS robot is mainly composed of two aluminum alloy tubes of 25 cm and 55 cm long and 21 cm in diameter and an external cubic frame. The long component contains all the embedded hardware and the other the NiMH batteries. So, it is relatively easy to replace flat batteries without opening the robot for long time mission. The purpose of two separate compartments is to prevent interference from the IMU.The external frame serves to hold the tubes, and thrusters; and carry all sensors. The movements of the robot are performed by four thrusters, two on vertical and two on horizontal planes.

For that we use BTD 150 thrusters from Seabotix associated with Graupner Navy V15R speed controllers. The overall structure is 75 cm long, 51 cm wide and 57 cm height (figure ??, left), for 39 kg weight [?].

RYUJIN

First of all, the mechanic parts were assembled with the simplest tools we could use such as saws, drilling machine, screw drivers and a CNC machine for the caps. The robot is made of a unique tubular housing in PVC where the electronic is housed.

It is surrounded by a submerged frame of PVC pipe that maintains it as well as the sensors and the motors. This has many advantages. On the one hand, the low cost of PVC makes the material very accessible, which fits very well with our desire to design a low-cost robot. On the other hand it allows multiple assemblies which gives us the opportunity to build the form we want and change it at will. The small size of the robot makes it easier to test and to transport.

The main challenge in designing this robot was to overcome the technical hindrance of the propulsion system. Most underwater propulsion systems on the shelf are relatively big (more than 10 cm long), which dictates the size of the robot.

Therefore we chose to modify small motors in order that they can run in salt water and under pressure. It was quite a bet but it works very well. The final fully-equipped robot weighs under 10 Kg and measures 30 cm x 20 cm x 20 cm (figure ??, right).

Electronics design and Sensors

AQUATIS

The brain of the robot is an embedded computer. The communication with the different sensors is done via a pyramidal architecture. On the top, all the entries of the computer are in USB mode. Some sensors are USB native, but others not. So, the next level of the pyramid is dedicated to the conversion of different communication and control protocols in USB. To do that, we use a Controller Area Network or CAN that is connected to homemade multifunction boards. The gateway between the high level computer and the multifunction boards is an Ethernet/CAN module. On the other, different protocols (analog, RS232, RS485, PWM) are converted into CAN signal. These conversions are done by the same homemade board which reduces logistic constraints. The CAN allows use giving each item of data an id, and priority handling.

RYUJIN

The electronics of the RYUJIN robot had to be as small as possible in order to fit in the small housing. As we had gained experience on working with UAVs in the laboratory (it is one of our lines of research), we designed electronics that not only fits the recommendation for the application but also our learning approach for our students. Indeed, it is very similar to our other projects, which are all based on our homemade learning card, called ULC. This way, students can jump from one project to another, either aerial or underwater, without many changes in the electronics. Moreover, each enhancement on either of the projects can be transferred to the other ones. We have built a frame that slides out of the pipe when you want to reach the electronic cards. This frame is fixed to the rear plug with 4 screws and allows us to plug on it the following devices: the power supply board, the 4 electronic drives, the batteries, the sensor card, the motherboard and the internal camera.

Sensors

We put in both robots the conventional sensors like temperature and pressure sensors to compute the depth at which the robot is navigating, and even a humidity sensor to detect leaks inside the watertight chamber. Both robots have IMU to estimate their attitude To help navigation and collect data we also put a Sonar on the AQUATIS robot and underwater video cameras with spotlights on both. We are currently developing some applications and algorithms with video and sonar put together.

FIRST RESULTS

Pool tests

The first tests have been made in a diving pool (upto 15m deep) to validate the waterproofness of the structures and sensors.

Then, we developed command, control, auto-piloting and vision algorithms in a swimming pool. This kind of environment is particularly favorable: very clear water, about 30 degree celsius temperature, no waves and no current. Obviously, in real operational environments, the problem is much more complicated. The first campaigns in sea water were made during the student contest called SAUC-E.

The SAUC-E contest

The Student Autonomous Underwater Vehicle Challenge Europe (SAUC-E) aims to stimulate innovation and technology, and encourage young people to pursue careers in engineering and underwater related areas. The event was organized by the NATO Undersea Research Centre (NURC) in La Spezia (Italy). Students were asked to design and build AUVs capable of performing real missions tasks like following a prescribed route, finding and passing through validation gates, finding and following a pipeline, surveying a wall of a dock, finding a mid-water target and cutting the rope that fixes it to the bottom, performing tracking of a moving surface target and going to a predetermined surfacing zone.

It is the second year that we have participated in this contest. In 2010, we presented the Aquatis robot, after one academic year of work from the student team, and in 2011, we presented the newly created RYUJIN robot at AQUATISs side. This year, we managed to participate in the final run with the RYUJIN AUV and ranked 5th in the contest. Unfortunately, for some mechanical problems, AQUATIS could not make it in time for the qualification runs. The ESIEA robots received two awards "Best use of resources" award for the team RYUJIN and "Perseverance and tenacity" award to the team AQUATIS.

PEDAGOGICAL ASPECTS

These two research projects are closely related to the work of students in our engineering school. It is a will of our laboratory to encourage the creativity of our students and to work within the constraints imposed by their workloads. In fact for most of those who participate in these research programs, their work on these projects is graded. Thus they participate in some pieces of the UAV to make it more competitive or efficient in a predefined task.

We accept students from the second year of their course upto PhD students. Concretely, the 2011 AQUATIS students team were between their second and fourth year of studies and the RYUJINs team was essentially composed of students between fourth year and PhD. That experience allows them to see what the research world is like and it gives them the opportunity to work in challenging and innovating projects in collaboration with researchers.

CONCLUSION

We have presented in this article two research and pedagogical projects which aim to develop low-cost light AUV for collaborative mapping. Both are designed for operational missions and teaching of computer science and electronics with a focus on localisation sensors for AQUATIS and advanced design for RYUJIN. We plan to use a sonar coupled with video to build visual odometry and be able to make Simultaneous Localisation And Mapping (SLAM) with 3D reconstruction of the scene the robots are moving in.

Besides, on our work on the UAV, we use LIDAR sensors. We want to test them in an underwater environment to compare the acquired data with those of the Sonar and to get more information of distance and environment. Eventually, we want to be able to merge those data with the other information we already have from the other sensors.

Finally, we plan to multiply the number of AUVs to be more prepared at an operational point of view and also to develop swarms of cheap AUVs in order to have more efficient mapping and work for other purpose like rescue, surveying, etc.

Fig. 1 .

 1 Fig. 1. The AQUATIS (left) and RYUJIN (right) robots.


Alireza Farhadi
email: afarhadi@sharif.edu

Jonathan Dumon
email: jonathan.dumon@gipsa-lab.grenoble-inp.fr

Carlos Canudas

Carlos Canudas-De-Wit
email: carlos.canudas-de-wit@gipsa-lab.fr

A Supervisory Control Policy Over an Acoustic Communication Network

Keywords: Networked control system, multi-agent system, supervisory control

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I. INTRODUCTION

A. Motivation and Background

There are advantages in using a fleet of simple autonomous agents instead of one sophisticated complex agent, in terms of quality of the gathered information, robustness against unexpected events, scalability, etc. The fleet system is scalable, the number of agents forming the fleet can be adapted to a given task and its constraints, and the redundancy of a multi-agent system increases the operational reliability. Moreover, distributed sampling for spatial analysis and complementary information gathered by different sensor packages on different agents results in the realization of tasks by a fleet system that cannot be easily achieved by single agent systems.

In addition, in some applications, such as the extremum source seeking via the non-modelbased gradient estimation method, single agent systems cannot arbitrarily maneuver in all directions while simultaneously estimating the gradient. However, the center of the fleet system in a circular formation can arbitrarily maneuver in all direction while agents simultaneously estimate the gradient. This is a required assumption to solve the extremum source seeking problem via the non-model-based gradient estimation method.

Hence, in recent years, fleets of autonomous agents have been in the sharp attention of research as well as industry communities . Existing multi-agent algorithms for coordinating fleets of autonomous agents (e.g., [1] - [4]) are distributed algorithms. However, there is an increasing interest in supervisory multi-agent algorithms for coordinating fleets of autonomous agents. A supervisory multi-agent policy enables on board planning, monitoring, and intervention in case of error/emergency. Consequently, our national research center partner, Ifremer [START_REF] Brinon Arranz | Translation control of a fleet circular formation of AUVs under finite communication range[END_REF] , is interested in developing a fleet of Autonomous Underwater Vehicles (AUVs) supervised by an Autonomous Surface Vessel (ASV) to localize an underwater flow source (e.g., source of fresh water, chemical pollution, etc.) with unknown location (see Fig. 1). Our contributions to this problem so far are algorithms presented in [1], [2] that form a circular formation of mobile autonomous agents with a time varying center; and other algorithms presented in [3], [4] that move the center of formation in the direction of the gradient of concentration flow intensity. In particular, in [3] the authors presented a two-loop control policy that localizes the unknown underwater flow source when concentration flow intensity has elliptical level sets. Note that [3] is not concerned with

Autonomous Surface Vessel (ASV)

Fig. 1. Two-loop control strategy with inner and outer control loops for a fleet of AUVs supervised by an Autonomous Surface Vessel (ASV). Inner control loop: AUVs use a distributed control law that forms a uniformly distributed circular formation of AUVs with a time varying center. Outer control loop: AUVi, i ∈ {1, 2, ..., n}, sends its sampled concentration data yi and rotational angle θi via a wireless link subject to transmission delay and random packet dropout with erasure probability α = 0 to a remote ASV that produces accordingly the control input u to be used to update the position of the center of formation.

communication imperfections.

B. Paper Contribution

Underwater communication is usually wireless and via acoustic modems, in which this type of communication is generally subject to transmission noise. Using classical error detection techniques such as Checksum algorithm, the underwater acoustic channel can be modeled as a packet erasure channel with erasure probability α. That is, with probability α, a received packet of data (containing information about measurements, etc.) that has been corrupted by noise cannot be recovered and is erased.

For inter -AUV communication if the distance between underwater vehicles is small (which is the case in this paper), then transmission is subject to small attenuation resulting in a communication with large signal to noise ratio particularly as in deep water the noise mainly comes from AUV itself (which produces low level acoustic noise). But, as the distance between the fleet and the ASV is very often large; and in particular, as receiver noise level at the ASV is very often high due to waves, reflections on the surface and other boats noise, communication from AUVs to the ASV is subject to packet dropout with erasure probability α ∈ [0.1, 0.5].

Nevertheless, in communication from the ASV to AUVs, signal to noise ratio can be large as the ASV can broadcast with its maximum power and receiver noise level at AUVs is low. Hence, in the supervisory control architecture of Fig. 1, communication between AUVs and from the ASV to AUVs is assumed lossless, while communication from each AUV to the ASV can be subject to packet dropout with erasure probability α = 0. Therefore, the supervisory control architecture of Fig. 1 is an example of the combined control-communication problem [5]- [13].

This paper presents an emerging example for the combined control-communication problem, which is described by the supervisory control architecture of Fig. 1. It extends the results of [3] to cases with more realistic representation for concentration flow intensity and illustrates that in the presence of severe random packet dropout, the two-loop control policy presented in [3] is not able to locate the unknown location of the underwater flow source without compensation of the effects of severe random packet dropout. However, this policy equipped with a coding strategy that provides a good quality of communication with a relatively low transmission delay locates the unknown location of the underwater flow source even in the presence of sever random packet dropout. The combined control-communication policy involves a tuning parameter that affects the quality of control, quality of communication and transmission delay. Hence, it can be tuned such that the interactions between control, quality of communication and transmission delay are balanced so that the best performance is achieved. A lower bound for tuning this parameter is presented and a simulator is developed and used to evaluate the trade-offs between quality of communication, transmission delay and control for a fleet of AUVs equipped with this combined control -communication policy. Using this simulator, the interactions between quality of communication, transmission delay and control are balanced for the condition simulated so that the best performance is achieved. It is illustrated that the performance of the best strategy in the presence of severe packet dropout is quite close to the performance of the ideal case of no dropout.

C. Paper Organization

The paper is organized as follows. In Section II, the problem formulation is presented. Then, Section III presents a supervisory multi-agent control policy over an acoustic communication network subject to imperfections. Subsequently, in Section IV, the interactions between quality of communication, transmission delay and control are balanced for the condition simulated to have the best performance for a fleet of Ifremer's AsterX AUVs. Section V summarizes the contributions of the paper.

II. PROBLEM FORMULATION

A. The Fleet of AUVs

This paper is concerned with a supervisory multi-agent control policy consisting of a fleet of Ifremer's medium size AsterX AUVs with n ∈ {4, 6, 8, 10} vehicles and an ASV, as shown in Fig. 1 that are used for localization of an underwater flow source with unknown location at the bottom of the ocean. Each AUV has a torpedo shape with the following specifications: Each AUV is equipped with sophisticated sensors. Therefore, in this study we ignore the effect of measurement noise. In the presence of high level measurement noise, appropriate filters can be used.

The fleet is supervised by an ASV. For communication between vehicles two different types of acoustic modems are used: AUVi Fig. 2. A fleet of AUVs in a circular formation in the reference coordinate system. θi: rotational angle, φi: heading angle, vi:

forward velocity, c: the center of formation vector, ri: position vector, and R0: the radius of the circular formation.

• Type 1-Acoustic modems for communication between each AUV and the ASV are Sercel MATS 300 with the settings as given in Table II. Both type 1 and type 2 modems use Binary Phase Shift Keying (BPKS) modulation and maximum likelihood de-modulation schemes with ternary outputs: 0, 1, idle.

The dynamics of each AUV is described by a 6 degrees of freedom model, which is subject to marine perturbations. However, the vehicles dynamics are handled by local control loops which are implemented within each vehicle. They result in a kinematic unicycle model for the fleet in a plane parallel to the ocean surface level, as follows:

ṙi = v i e(φ i ), φi = u i , e(φ) = cos φ sin φ , i ∈ {1, 2, ..., n}, (1)
where r i is the position vector, φ i the heading angle, and the control inputs are the vehicle forward velocity v i > 0 and the turning rate u i (see Fig. 2) [START_REF] Brinon Arranz | Elastic formation control based on affine transformations[END_REF] .

Throughout the paper, it is assumed that the source of concentration flow is located at the bottom of the ocean and the distribution of concentration flow intensity in the plane, where the fleet is located, is described by an unknown positive mapping ρ; and agent i measures the local concentration flow intensity as y i = ρ(r i ).

B. Formation Control (Inner Control Loop)

In [1] an inner feedback control law that asymptotically stabilizes AUVs to a circular formation around a dynamic center point c(t) with uniformly distributed formation3 was proposed for n(≥ 2) AUVs. With a desired forward velocity of v 0 and a desired rotational velocity of ω 0 , the feedback control law of [1] is given as follows:

v i = ||v 0 e(ψ i ) + ċ||, u i = (1 - < ṙi , ċ > < ṙi , ṙi > ) - ṙ i T (π/2)c < ṙi , ṙi > , T (φ) = cos φ -sin φ sin φ cos φ , ψi = w 0 (1 -κ < r i -c, v 0 e(ψ i ) >) - ∂U ∂ψ i , i = 1, 2, ..., n,
2 For each AUV a local control loop implements a feedback linearization technique that replaces the vehicle nonlinear dynamics with a pseudo linear dynamics. Then, H∞ controllers are used to compensate the effects of model inaccuracy and perturbations, including marine perturbations, and force the vehicle parameters ṙi and φi to follow the desired set points vie(φi) and ui, respectively [14].

U (ψ) = - K n n/2 m=1 1 2m 2 <             e(ψ 1 ) . . . e(ψ n )             , L             e(ψ 1 ) . . . e(ψ n )             > . (2)
Here κ > 0, ψ i (t) has the following initial condition:

ψ i (0) = tan -1 ( Im( ṙi (0)-ċ(0))
Re( ṙi (0)-ċ(0)) + i π) where i = 0 if Re(ṙ i (0) -ċ(0)) ≥ 0 and 1 otherwise, and L =L ⊗ I 2 , where L is the Laplacian matrix associated with the communication network of AUVs, ⊗ denotes the Kronecker product and I 2 is the 2 × 2 identity matrix.

Assuming that c(t) is twice differentiable, has bounded first and second time derivatives, and satisfies the following condition: sup t≥0 | ċ(t)| < v 0 , then, as shown in [1], the control inputs, as given above, steer AUVs to trajectories that lie on the circle with radius R 0 = v 0 /|w 0 | and time varying center c(t). Moreover, if K > 0 and the communication network between AUVs is complete, then AUVs are uniformly distributed on that circle. Remark 2.1: i) Throughout the paper it is assumed that the communication network between AUVs is complete. That is, every AUV talks to every other AUV; and hence, every AUV is connected to every other AUV.

ii) To form a uniformly distributed circular formation of AUVs with center c, parameters ψ i , i ∈ {1, 2, ..., n}, must be exchanged between AUVs.

iii) Parameters κ and K change the convergence rate to a circular formation and a uniform distribution of AUVs on the circular formation, respectively.

III. SUPERVISORY MULTI-AGENT CONTROL POLICY OVER ACOUSTIC COMMUNICATION NETWORK (OUTER CONTROL LOOP)

In this section, by implementing the inner control loop (2) we are given a stable uniformly distributed circular formation of n AUVs in a plane that is described by a center point c, radius R 0 , and an angle θ i (see Fig. 2). In this circular formation, the position of each AUVi is described by the following equation: r i = c + R 0 e(θ i ). The objective of this section is to provide an outer control loop policy located at the ASV equipped with a coding strategy for real-time reliable communication that moves the center of formation c towards the source of concentration flow in the plane where AUVs are located. This objective is fulfilled by updating ċ in (2), as follows:

ċ = u, (3)
where the control signal u is generated from the received rotational angles θ i , i ∈ {1, 2, ..., n}, and sampled local concentration flow intensity y i , i ∈ {1, 2, ..., n}, taken by individual AUVs, which are transmitted to the ASV over an acoustic wireless communication network subject to packet dropout.

The outer control loop policy considered in this paper uses the output of a repetition coding strategy as its input. The repetition coding strategy can be easily implemented and for this reason it is used in this study. In the repetition coding strategy considered in this paper instead of sending one packet of data corresponding to each pair of measurements (y i , θ i ), M identical packets of data are transmitted. Consequently, using this coding strategy the possibility of not recovering a pair of measurements at the ASV is reduced to

α M .
In what follows the outer control loop policy is described and then the coding strategy in more detail.

A. Outer Control Loop Design

In this section, it is assumed that the outer control loop action is updated at the ASV, as follows:

u(t) =      n i=1 ρ(r i (t))e(θ i (t))
if all transmitted pairs to the ASV are recovered

n i=1 ρ(r i (t -))e(θ i (t -)) Otherwise (4)
where θ(t -) denotes the previous update when all transmissions are successful. This is to say that when transmission to the ASV is not reliable, then u(t) is chosen to be equal to the previous outer control loop action that has been updated based on all successfully recovered transmitted pairs to the ASV.

In the following theorem borrowed from [3], it is shown that in the absence of communication imperfections when the concentration flow intensity has elliptical level sets, updating ċ = u, as suggested by ( 4), moves the center of formation towards the location of the unknown flow source. In the following theorem it is assumed that for some positive definite matrix A, ρ is a continuously differential mapping and satisfies the following property:

(z 1 -c * ) A(z 1 -c * ) < (z 2 -c * ) A(z 2 -c * ) ⇒ ρ(z 1 ) > ρ(z 2 ), z 1 , z 2 , c * ∈ R 2 . ( 5
)
This is to say that the signal strength has a unique maximum at a point c * (the unknown fixed location of the source) and has compact elliptical level sets in the plane where the fleet is located.

Theorem 3.1: [3] Suppose that even number of n AUVs are given, the concentration flow intensity ρ is a continuously differentiable mapping satisfying the property (5) and communication is free from imperfections. Suppose also that by implementing the inner control loop the n AUVs form a stable uniformly distributed circular formation. Then, under the outer control loop action (4), the point c = c * is an asymptotically stable equilibrium of (3).

In reality the level sets of concentration flow intensity has more complex shape than elliptical shape considered in [3]. In fact, level sets that are resulted from the summation of a few elliptical sets (as shown in Fig. 5) are better representation for the level sets of concentration flow intensity.

Therefore, in the following theorem we extend the results of [3] to the cases with more realistic representation for concentration flow intensity.

Theorem 3.2: Suppose that n ∈ {4, 6, 8, 10, ...} AUVs are given, communication is free from imperfections, by implementing the inner control loop the fleet system forms a stable uniformly distributed circular formation and the fleet system is under the action of the outer control loop policy (4). Then, the point c = c * is an asymptotically stable equilibrium of (3) for the concentration flow intensity of the following form

ρ(z) = β 1 e -α 1 (z-c * ) A 1 (z-c * ) + ... + β p e -αp(z-c * ) Ap(z-c * ) , α 1 , ..., α p > 0, β 1 , ..., β p ≥ 0, A 1 , ..., A p > 0. (6)
Proof: The proof follows from a Lyapunov stability argument involving the Lyapunov function

L(c) = ρ(c * )-ρ(c)
, numbering those AUVs that have a non-negative projection along the signal gradient from 1 to n 2 (i.e., for AUVi, i = 1, 2, ..., n 2 , ∇ρ (c)e(θ i ) ≥ 0), the fact that as n is even and AUVs are uniformly distributed (see Fig. 2), r i , c and r i+ n 2 all lie along the same line, and the projection of the quadratic function (z -c * ) A j (z -c * ), j = 1, 2, ..., p, evaluated along this line is a parabola with its minimum corresponding to a point in the direction of r i from c.

The detail of the proof is as follows: For each A j > 0, j = 1, 2, ..., p, the quadratic function q j (z) =(z -c * ) A j (z -c * ) evaluated along the line that connects r i , c and r i+ n 2 is a parabola with its minimum corresponding to a point in the direction of r i from c. Due to the symmetry of this parabola and as r i is closer to its minimum, it is the case that

(r i -c * ) A j (r i -c * ) ≤ (r i+ n 2 -c * ) A j (r i+ n 2 -c * ), in which from (6) it implies that ρ(r i ) ≥ ρ(r i+ n 2 ). Consequently, L(c) = - n 2 i=1 ρ(r i ) -ρ(r i+ n
2 ) ∇ρ (c)e(θ i ) ≤ 0. The only situation in which L(c) = 0 for c = c * is the case when n = 2 and the AUVs displacement vectors from the center of formation are orthogonal to ∇ρ(c). As we excluded the case of n = 2, then L(c) < 0 for n ∈ {4, 6, 8, 10, ...} AUVs considered in this theorem. Hence, under the outer control loop action (4), the point c = c * is an asymptotically stable equilibrium of (3) for the concentration flow intensity of the form (6).

B. Coding Design

As mentioned earlier, underwater transmission via acoustic modems is subject to random packet dropout in communication from AUVs to the ASV with erasure probability α. If the underwater condition does not significantly change during search mission, the erasure probability α can be assumed fixed and it can be measured by transmitting test signals. Therefore, throughout it is assumed that the erasure probability is known a priori.

To compensate the effects of random packet dropout and improve the quality of communication from AUVs to the ASV, a repetition coding strategy is used. According to this strategy corresponding to each pair of measurements (y i , θ i ), instead of sending just one packet of data, M identical packets of data are sent. Therefore, using this strategy, the probability of not recovering a pair of measurements at the ASV is reduced to α M .

In addition of the random packet dropout underwater transmission via acoustic modems is also subject to the following major communication imperfections:

• long sound travel time T di in communication between AUVi and the ASV, which is due to the slow propagation of underwater sound waves [START_REF] Brinon Arranz | Collaborative estimation of gradient direction by a formation of AUVs under communication constraints[END_REF] . As this delay can be measured using test signals, throughout it is assumed that the sound travel time T di is known a priori.

• limited communication bandwidth: The bit rate of the type 1 modems is D 1 = 100 bits/s and the bit rate of the type 2 modems is D 2 = 480 bits/s. These limited communication bandwidths result in a long packets transmission time in communication of long packets of data [START_REF] Elia | When bode meets Shannon: control-oriented feedback communication schemes[END_REF] .

To avoid collision of transmitted information, a Time Division Multiple Access (TDMA) scheme [15] is used (see Fig. 3) [START_REF] Elia | Limitations of linear control over packet drop networks[END_REF] . The type 1 modems are used to transmit pairs (y i ,θ i ), i ∈ {1, 2, ..., n}, from AUVs to the ASV, and control signal u from the ASV to AUVs. The type [ 1] 2 modems are also used to exchange ψ i , i ∈ {1, 2, ..., n}, between AUVs.

) (time t data Sampled ( ) T M ] [ ] [ 1 1 k k y θ ] [ ] [ 2 2 k k y θ ] [ ] [ k k y n n θ }} / { max , max{ 2 2 s i i s v v d v d D N + } / { max s i i v d ] [ 1 k ψ ] [ 2 k ψ ] [k n ψ 1 1 D N M 1 1 D N 1 1 D N M s v v d D N + 2 2 } , max{ 2 2 s s v T v d D N + 1 [ ] ( [ ]), [ ],
n i i i y k e k if transmission is reliable u k otherwise u k θ =  ∑  + =   
As mentioned above to compensate the effects of packet dropout and have a reliable communication from each AUV to the ASV, a repetition coding strategy is used. That is, corresponding to each pair of measurements (y i , θ i ), instead of sending just one packet of data with length For a given fleet of AUVs, the trade-off between quality of communication that is presented in terms of the possibility of not recovering a pair of measurements at the ASV, i.e., 100α M percent, and M for a given α, is geometric, while the trade-off between M and C(M ) = M N 1 D 1 Fig. 4. A fleet of AUVs supervised by the ASV. h: operating depth, R0: the radius of the circular formation, and q: the distance between the ASV and the projection of the center of formation on the surface.

for N 1 = 60 bits and D 1 = 100 bits/s is linear. Hence, for a large α (e.g., α = 0.5) an excellent quality of communication demands a large transmission delay relative to the case of M = 1.

As AUV and the ASV use embedded programming, the supervisory multi-agent control policy must be applied on discrete time domain. To avoid collision in transmission of information between vehicles, the sampling period T (M ) for updating outer control loop action is defined as follows (see Fig. 3):

T (M ) = nM N 1 D 1 + (n -1) max{ N 2 D 2 + d v v s , T s } + max N 2 D 2 + d v v s , max i { d i v s } + N 1 D 1 + max i d i v s , (7)
where N 2 is the length of packet corresponding to each ψ i (N 2 = 30 bits), d v is the maximum distance between AUVs 7 , v s = 1500m/s is the speed of underwater sound waves, T s is the security time to be defined shortly, and d i is the distance between AUVi and the ASV. Note that when the fleet operates at a high depth, then d i ≈ h, where h is the operating depth of the fleet, provided the ASV follows the projection of the center of formation on the surface (see Fig. 4).

Remark 3.3: If the ASV moves exactly above the center of formation, transmission time delay from all AUVs to the ASV is the same. But, in reality this is not the case; and the ASV that follows the projection of the center of formation on the surface, can just be very close to it (see Fig. 4). In this case, as shown in Fig. 4, packets transmitted by AUVi are received by the ASV later than expected, while packets transmitted by AUVj are received earlier than expected. This [START_REF] Martins | Feedback stabilization of uncertain systems in the presence of a direct link[END_REF] When the formation is perfect, i.e., it is circular, dv = 2R0. But, as the formation may be disturbed during search mission due to perturbations, etc., dv is chosen to be 3R0.

may result in collision of data at the ASV. Therefore, to avoid this collision, the security time,

T s = max i,j (|d i -d j |) v s = (q + R 0 2 ) 2 + h 2 -(q -R 0 2 ) 2 + h 2 v s ,
is added to T (M ) to compensate the time differences in propagation of packets from different AUVs.

If the sampling period T (M ) is sufficiently small, then a simple way to approximate the value of the center of formation in discrete time domain c[k] is as follows:

c[k] = c[k -1]+T (M )u[k].
Similarly, its first and second derivatives can be approximated, as follows:

ċ[k] = u[k],
and

c[k] = u[k]-u[k-1] T (M )
, respectively. Remark 3.4: i) When a pair of measurements (y i ,θ i ) is not recovered at the ASV, the control input u[k] is updated with the last value:

u[k] = u[k -1].
ii) The angle of the outer control loop signal, i. As each AUV has a limited life time, it is essential that the fleet locates the source of concentration flow as soon as possible. Therefore, the performance of the fleet is described by the time period between starting a mission and the time that the fleet finds the source. This time period is denoted by T total . Obviously, a fleet with smaller T total has a better performance.

The following corollary extends the results of Theorem 3.2 by presenting a condition on the number of packet repetitions M for localization of the source in the presence of communication packet dropout. Corollary 3.6: Suppose that n ∈ {4, 6, 8, 10} AUVs are given, the concentration flow intensity ρ is a continuously differentiable mapping described by (6) and communication from AUVs to the ASV is subject to packet dropout, as described earlier. Suppose also that by implementing the inner control loop the n AUVs form a stable uniformly distributed circular formation and the repetition coding strategy as described above is used. Then, under the outer control loop action, the source is located if the number of packet repetitions M satisfies the following condition:

(1 -(1 -α M ) n ) J(M ) < T a T 0 , J(M ) = T a T (M ) , T a = r 0 V max . ( 8
)
Proof: When transmission to the ASV is not reliable (i.e., some of transmitted measurements are not recovered), from the description of the outer control loop policy (and in particular as the outer control loop action is not updated when packet dropout occurs and hence the center of formation continues moving along the previous direction) it follows that in most cases the time derivative of the Lyapunov function used in the proof of Theorem 3.2 at the center point

c[k], i.e., L(c[k]) ≈ ∆L(c[k]) T (M ) = L(c[k])-L(c[k-1]) T (M )
, will be still negative; and hence, the center of formation c continues moving towards c * . However, after entering the center of formation c into the ball with center c * and radius r 0 , if transmission to the ASV is not reliable while the center c reaches to c * , then the gradient signal ∇ρ(c[k]) will be in the opposite direction

of ċ[k] = n i=1 ρ(r i [k])e(θ i [k]); and therefore, L(c[k])(≈ ∆L(c[k]) T (M ) ) = -∇ρ (c[k])ċ[k]
will be positive. Consequently, c is getting away from c * and exits the ball if during the time period

T a = r 0
Vmax that the center c moves away from c * with a constant speed of V max all transmissions to the ASV are unsuccessful. Note that in this situation the function

L(c[k]) = ρ(c * ) -ρ(c[k])
is an increasing function of time, in which from the description (6) for the concentration flow intensity ρ it follows that the center of formation c is getting away from c * . To avoid such situations, the probability that all transmissions to the ASV are unsuccessful within the time period of T a second, i.e., (1 ) , where J(M ) = Ta T (M ) , must be small, e.g., less than Ta T 0 . This results in the condition (8) for M . Extensive simulation study of the next section for different values of α illustrates that the above condition on the size of M guarantees that the center of formation c enters to the ball with center c * and stays there for enough time so that the source c * is located.

-(1 -α M ) n ) J(M
As discussed earlier, a larger M results in a better quality of communication but as clear from Fig. 3 it also results in a larger packets transmission delay and therefore a longer time latency between making measurements and applying the control actions, which obviously damages the performance of both inner and outer control loops. Note that as the improvement in the quality of communication increases geometrically with M ; while time latency increases linearly with M , a small increase in M results in a significant improvement in the quality of communication; but a small increase in the time latency between making measurements and applying the control actions.

As shown in Corollary 3.6, in the presence of severe packet dropout, a small M may not results in localization of the unknown underwater flow source. On the other hand, from Fig. 3 it follows that by increasing M , while the quality of communication improves significantly, the time latency between making measurements and applying the control actions on the fleet increases (linearly), which obviously damages the performance of the fleet system and results in a larger mission time T total such that for a very large M the mission time may be larger than the AUVs life time. Therefore, in one extreme, small M will not stabilize the fleet system particularly in the presence of severe random packet dropout, while for a bit larger M , the quality of communication is much better and hence localization of the underwater flow source with a relatively small time latency is achieved. But in other extreme, a very large M results in a very long time latency and hence a large mission time that will be larger than AUVs life time, while for a smaller M , a search mission with smaller mission time is achieved. Hence, there exist an optimal M * between these two extremes that results in a good quality of communication with small time latency and therefore the smallest T total . Simulation study of the next section for different values of α illustrates that for α = 0.5, α = 0.3 and α = 0.1, there exists a M * .

IV. SIMULATION RESULTS

As shown in the previous sections, the supervisory multi-agent control policy of Fig. 1 is subject to two main communication imperfections: packet dropout in communication from AUVs to the ASV and transmission delay in communication between AUVs and the ASV. But, the effects of these drawbacks can be compensated by a proper adjustment of the number of packet repetitions M so that the best performance in terms of the smallest mission time is achieved. This result is illustrated in the following section.

In this section for the purpose of illustration, the proposed supervisory multi-agent control policy over the acoustic communication network subject to packet dropout and transmission delay is applied to a fleet of Ifremer's medium size AsterX AUVs via MASim simulator developed in our research team in GIPSA-Lab. MASim is a MATLAB/SIMULINK simulator that simulates the behavior of fleets of Ifremer's AsterX AUVs in the actual environment. The fleet considered in the simulation study has the following specifications: n = 4, R 0 = 50m, w 0 = 0.02rad/sec, v 0 = 1m/s and h = 1500m. It is assumed that the concentration flow intensity at the horizontal plane parallel to the water surface level at the depth h = 1500m (where the unknown source is located) is described as follows (note that AUVs are unaware of the concentration flow intensity description): Considering the transmission power level of type 1 and type 2 modems and the maximum distance between AUVs and the ASV, communication in the presence of low level noise (e.g., in deep water, where the noise mainly comes from AUV itself) can be considered almost lossless. Therefore, in the following simulations, just 5 percent packet loss is assumed to model communication between AUVs and from the ASV to AUVs. However, in the case of communication from AUVs to the ASV as the receiver is no longer in deep water and it is very close to the surface, it is subject to other sources of noise (e.g., waves, reflections on the surface and other boats noise) that dramatically degrades communication performance. Therefore, for communication from AUVs to the ASV much more packet loss, e.g., 50 percent packet loss (i.e., α = 0.5) is assumed. Moreover, it is assumed that there is a marine perturbation of 30 newton at the 50 degree angle with respect to the X-axis of the reference coordinate system (see Fig. 2). Note that MASim simulator also include the effects of 6 degrees of freedom dynamics model of AUVs, local control loops and inner control loop in search mission.

ρ(z) = β 1 e -10 -3 (z-c * ) A 1 (z-c * ) + β 2 e -10 -3 (z-c * ) A 2 (z-c * ) + β 3 e -10 -3 (z-c * ) A 3 (z-c * ) , (9)
To coordinate the fleet of AUVs towards the unknown location of the source in the presence of the above severe packet dropout in transmission from the fleet to the ASV, the supervisory multi-agent control policy of Section III is used. Table IV summarizes the parameters used for simulations [START_REF] Minero | Data rate theorem for stabilization over time-varying feedback channels[END_REF] . In each simulation the fleet first forms a stable circular formation with center at c(0) via the inner control loop. It then starts the search mission by implementing the outer control loop. In each simulation T total is the time duration between the starting search mission at c(0) and the first time that the center of formation enters into the ball with center c * and radius r 0 = 20m and stays in this ball for at least T 0 = 10T a second. to the two-loop control policy of [3]. As clear from Fig. 5, the trajectory of the case with dropout but without repetition in coding is non-smooth and has a trend to be unstable [START_REF] Minero | Stabilization over Markov feedback channels: the general case[END_REF] , while for the case without dropout the source is located in T total = 4262 second. As clear from Fig. 5, without repetition in coding, localization of the unknown underwater flow source is not achieved.

As discussed in Section III, a larger M results in a better quality of communication but larger packets transmission delay (and therefore, longer time latency) that both affect the performance of the fleet T total in the opposite direction: As clear from Fig. 5 for the case of α = 0, an excellent quality of communication results in a smooth search trajectory for the fleet under [START_REF] Minero | Data rate theorem for stabilization over time-varying feedback channels[END_REF] To model a typical underwater search mission, the parameters used in simulations, such as the description for concentration flow intensity, v0, R0, etc., were chosen following several technical discussions with our colleagues from Ifremer who have many years of practical experience in operational exploration with AUVs. [START_REF] Minero | Stabilization over Markov feedback channels: the general case[END_REF] For this case, after the center of formation enters into the ball with center c * and radius r0, the center of formation shortly exits the ball. control. On the other hand, as pointed out in the previous section, a large M results in a large packets transmission delay; and therefore, a long time latency in the outer control loop and a long sampling period T (M ). As will be illustrated shortly, this will result in a non-smooth search trajectory and therefore a large T total . Hence, the interactions between quality of communication, transmission delay and control must be balanced via a proper selection of the number of packet repetitions M so that the best performance (which corresponds to the smallest T total ) is achieved.

To find the proper number of packet repetitions M * for the condition simulated, the simulations are repeated 20 times for each number of packet repetitions: M = 1, 2, 3, 4, 5, 6, 7, 8. For M = 1, it is observed that in most cases the source cannot be located and the trajectory of the center of formation has a trend to be unstable [START_REF] Nair | Topological feedback entropy and nonlinear stabilization[END_REF] . This result is expected from the formula (8) as this formula for α = 0.5 is not satisfied for M = 1. For other cases (i.e., M ≥ 2), it is observed that in all simulations, the search is concluded, as expected from the formula (8), within the life time of AUVs which is 5 hour. Table V summarizes the obtained empirical values for the mission time [START_REF] Nair | Stabilizability of stochastic linear systems with finite feedback data rates[END_REF] for different M ; and Fig. 6 illustrates the trade-off between empirical T total and M . Fig. 7 also illustrates trajectories of the center of formation c for M = 1, 4, 8.

As clear from these figures and the table, the best performance in the presence of random packet dropout and marine perturbation is achieved for M * = 4. This case corresponds to a communication with good quality (i.e., 100.α M * = 6 percent packet dropout in communication from AUVs to the ASV) with a acceptable packets transmission delay (C(M * ) =2.4 second), which results in the best performance, i.e., T * total = 5414 second. This performance is only 27 percent worse than the ideal case of no dropout (i.e., α = 0 and no packet dropout in inter-AUV communication as well as in communication from the ASV to AUVs), which is T total = 4262 [START_REF] Nair | Topological feedback entropy and nonlinear stabilization[END_REF] For this case, after the center of formation enters into the ball with center c * and radius r0, the center of formation shortly exits the ball. [START_REF] Nair | Stabilizability of stochastic linear systems with finite feedback data rates[END_REF] For each M , the empirical value of mission time (empirical T total ) is the average of the mission times obtained from simulations. second.

The case of M = 1 corresponds to a system with a poor quality of communication (i.e., 100.α 1 = 50 percent packet dropout) but a small packets transmission delay (C(1) =0.6 second), in which this poor quality of communication results in a very non-smooth search trajectory.

On the other hand, the case of M = 8 corresponds to a system with an excellent quality of communication (i.e., 100.α 8 ≈ 0 percent packet dropout) but large packets transmission delay (C(8) =4.8 second), which induces a large time latency of 22.2875 second in the outer control loop. As clear from Fig. 7, this long time latency also results in a non-smooth search trajectory.

Therefore, for these two cases the performance is not satisfactory.

For illustration, the simulations are repeated for α = 0.3 and α = 0.1. Table VI summarizes the trade-off between empirical mission time and M ; and Fig. 8 illustrates the trade-off between empirical T total and M . It is observed that for all M ∈ {1, 2, 3, ..., 8} the search is concluded, as expected by the formula (8). From this table and figure, it follows that when α is small (e.g., α ≤ 0.1) there is no need to use a coding strategy.

V. CONCLUSION

This paper presented an emerging example for the problem of combined control-communication.

A supervisory multi -agent control policy over a communication network subject to packet dropout and transmission delay was presented for localization of an underwater flow source with unknown location. It extended the results of [3] to the cases with more realistic representation for concentration flow intensity and illustrated that in the presence of sever random packet dropout the policy that does not consider and compensate the effects of communication imperfection (the policy presented in [3]), cannot stabilize the system (locate the underwater flow source).

However, the combined control-communication policy with a good quality of communication and relatively low transmission delay, locates the flow source. As illustrated, the proposed controlcommunication policy with a small number of packet repetitions M has a poor quality of communication, which results in a very non -smooth search trajectory. On the other hand, as illustrated, the proposed policy with a very large M , which corresponds to a large transmission delay but an excellent quality of communication, does not result in a satisfactory performance either as this case corresponds to a large time latency and a long sampling period for updating the outer control loop action. However, it was illustrated that for α = 0.5, α = 0.3 and α = 0.1 there is an optimum number of packet repetitions M * , which results in the smallest mission time.

For future it is interesting to develop theoretical results for finding M * analytically. A starting point to achieve this goal is the development of a theorem that provides an upper bound for M under which the mission time is smaller than the AUVs life time. This theorem combined with Corollary 3.6 determine a set that M * belongs to.

Fig. 3 .

 3 Fig. 3. A TDMA scheme used for exchanging information between the fleet of AUVs and the ASV without collision. N1: the length of packets of data representing pairs (yi, θi) and u, N2: the length of packets of data representing ψi, M : the number of packet repetitions, D1: the bit rate of communication links between the fleet and the ASV, D2: the bit rate of inter-AUV communication links, Ts: security time, dv: the maximum distance between AUVs, di: the distance between AUVi and the ASV and vs: the speed of underwater sound waves.

N 1 ,

 1 M identical packets of data are sent within an allocated time slot to each AUV, in which for each AUV the required time to transmit packets is C(M ) =M N 1 D 1 second, where D 1 is the communication bit rate. As it takes C(M ) second to transmit M identical packets of data, C(M ) contributes to transmission time delay from AUVs to the ASV. Throughout, C(M ) is referred as packets transmission delay.

Definition 3 . 5 :

 35 e., u[k], k ∈ N + , represents the direction towards the unknown location of underwater flow source from the center point c[k]. Therefore, to have the fastest convergence to the unknown source location, instead of using (3), AUVs can update ċ[k] as follows: ċ[k] = V max u[k], where V max is the maximum possible speed of moving the center of formation with the possibility of maneuvering in all directions while AUVs simultaneously estimate the gradient. Subsequently, the next center of formation c[k] and c[k] are approximated by c[k] = c[k -1] + T (M )V max u[k] and c[k] = Vmax( u[k]-u[k-1]) T (M ), respectively.iii) In very long search missions, clock drift between AUVs must be estimated and an extra security time must be added to each AUV's cycle to avoid losing TDMA synchronization. As an example two quartz clocks with ±30ppm precision lead to a drift of 1.08 second in every 5 hour (which is equal to the AUVs life time). At each kT (M ) second, define a ball with center c and sufficiently large radius r 0 . Then, it is said that the fleet system converges to c * (or locates the unknown location of the source) if and only if the center of formation stays in this ball for enough time of T 0 ≥ 10T a second after entering to this ball, where T a = r 0 Vmax second. In this case, c is an approximation for c * .

β 1

 1 = 5.6864, β 2 = 17.0591, β 3 = 57.2546,

Fig. 5

 5 illustrates the trajectory of the center of formation c subject to 50 percent packet dropout (i.e., α = 0.5) in communication from the fleet to the ASV and 5 percent packet dropout in inter-AUV communication as well as in communication from the ASV to AUVs. Fig. 5 also illustrates the trajectory of the center of formation c without dropout (i.e., α = 0 in communication from the fleet to the ASV and no packet dropout in inter-AUV communication as well as in communication from the ASV to AUVs). Both cases do not include any repetition in coding. That is, M = 1, which corresponds

Fig. 5 .T

 5 Fig. 5. The trajectory of the center of formation c subject to random packet dropout and no repetition in coding (the black trajectory) and the trajectory of the center of formation c in the absence of dropout (the green trajectory).

Fig. 6 .

 6 Fig.6. The trade-off between the mission time T total and M. From this trade-off it follows that M * = 4 is the optimum number of packet repetitions.

Fig. 7 .

 7 Fig. 7. The trajectories of the center of formation c subject to 50 percent packet dropout in communication from AUVs to the ASV and 5 percent packet dropout in inter-AUV communication as well as in communication from the ASV to AUVs.

TFig. 8 .

 8 Fig. 8. The trade-offs between the mission time T total and M. From these trade-offs it follows that M * = 3 is the optimum number of packet repetitions.

  the value of signal c at sampling instant k ∈ N + = {0, 1, 2, 3, ...}. Re(•) denotes the real part and Im(•) the imaginary part of a complex number. Vectors/matrices are denoted by bold letters, inner product is defined by < z 1 , z 2 > = Re{z * 1 z 2 } where the superscript * denotes the conjugate transpose, and the Euclidean norm is denoted by || • ||. a denotes the largest integer less than or equal to a scalar a, and for the simplicity of notation the dependency of signal c(t) to time index t is dropped whenever confusion does not occur. Transpose of a vector/matrix A is denoted by A and the time derivative of signal c(t) is denoted by ċ(t).

Throughout the paper certain conventions are used: " =" means "by definition equals", c(t) denotes the value of signal c at continuous time t and c[k] (= c(kT ), where T is the sampling period) is

2-Acoustic modems for inter -AUV communication are DSPComm with the settings as given in Table III.

	Frequency	Bit rate	Transducer	Operating range
		10kHz	100 bits/s Omni directional	maximum 3km
				TABLE II
	MODEM SETTINGS FOR COMMUNICATION BETWEEN EACH ASTERX AUV AND THE ASV.
	Frequency	Bit rate	Transducer	Bit error rate
	10kHz	480 bits/s Omni directional BER=10 -6 for the range of 150m

• Type

TABLE IV PARAMETERS

 IV USED FOR SIMULATIONS.

TABLE V THE

 V TRADE-OFF BETWEEN EMPIRICAL T total MEASURED IN SECOND AND M FOR α = 0.5. THE PAIR

(M * , T * total )= (4, 5414) IS THE OPTIMUM PAIR.

That is, AUVs are uniformly distributed along a circumference by 2π n radians each.

The speed of underwater sound waves is typically vs =1500 m/s; and therefore, if the distance between AUVi and the ASV is di, then T di = di/vs second.

To exchange information (measurements, control commands, etc.) between vehicles with negligible distortion, long packets of data are used. Note that distortion is due to the quantization of information.

Currently TDMA scheme is the only commercially available technique for underwater multiple accessing without collision.

ACKNOWLEDGMENT

This work is supported by the FeedNetBack European project, grant agreement no.: 223866.

The authors thank Lara Brinon Arranz, Alexandre Seuret, Sebastien Varrier, Alain Kibangou, Julien Minet, and colleagues from Ifremer (Jan Opderbecke and Romain Piasco) for many helpful technical discussions.