In comparison with standard HMM (Hidden Markov Model) with forced alignment, this paper discusses two automatic segmentation algorithms from different points of view: the probabilities of insertion and omission, and the accuracy. The first algorithm, hereafter named the refined HMM algorithm, aims at refining the segmentation performed by standard HMM via a GMM (Gaussian Mixture Model) of each boundary. The second is the Brandt's GLR (Generalized Likelihood Ratio) method. Its goal is to detect signal discontinuities. Provided that the sequence of speech units is known, the experimental results presented in this paper suggest in combining the refined HMM algorithm with Brandt's GLR method and other algorithms adapted to the detection of boundaries between known acoustic classes.

BRANDT'S GLR METHOD & REFINED HMM SEGMENTATION FOR TTS SYNTHESIS APPLICATION

Safaa Jarifi*, Dominique Pastor*, Olivier Rosec**

INTRODUCTION

The objective of this paper is the segmentation of large acoustic databases for application to corpus-based speech synthesis. Segmenting spontaneous and continuous speech signals is still an issue. Because the sequence of speech units is known, automatic segmentation is usually performed by HMM's with forced alignment. This procedure shows reasonable results. However, in order to guarantee a good quality of a synthetic voice, the outcome of the segmentation stage must still be verified manually, which is a difficult task. Thus, it is still important to design a segmentation algorithm capable of providing segmentation marks close to handmade ones with the smallest possible number of errors.

With respect to the foregoing, the purpose of this paper is to analyze and compare the accuracies of three segmentation algorithms on a large French corpus. The first one is the standard HMM with forced alignment as described above. The second one is the refined HMM, originally proposed in [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF] for segmenting a Chinese corpus. These two methods lead to a number of segmentation marks that corresponds to the number of phonemes in the input speech unit sequence. Thus they do not yield omissions nor insertions. The third algorithm is Brandt's GLR method ( [START_REF] Obrecht | Automatic segmentation of continuous speech signals[END_REF]) which aims at detecting discontinuities of speech signals without any further knowledge upon the phonetic sequence. As this algorithm is linguistically unconstrained, it makes insertions and omissions.

From this comparison, we derive an approach aimed at improving the accuracy of the refined HMM so as to tend to some reasonable performance objective introduced below.

The paper is organized as follows. In the next two sections, we briefly present the refined HMM and Brandt's GLR THIS STUDY IS SUPPORTED BY THE R&D DIVISION OF FRANCE TELECOM. method. After introducing how performance measurements are computed, section 4 presents and discusses experimental results. On the basis of these results, we suggest in section 5 an approach for improving the refined HMM.

THE REFINED HMM ALGORITHM

The main idea of this method is to train a GMM model for each HMM boundary with super vectors that are extracted using frames around the boundaries ( [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF][START_REF] Sethy | Refined Speech Segmentation for Concatenative Speech Synthesis[END_REF]). This method is carried out in three steps: 1. Achieve an HMM segmentation with forced alignment.

Thus, the number of segmentation marks equals that of the handmade segmentation. 2. For a small database that is manually segmented, create a super vector for each boundary of this database. This vector is obtained by putting together acoustic vectors for frames near the boundary. In Fig. 1, we illustrate a super vector with (2N + 1) frames.

Each boundary B depends on the phoneme X to the left of it and on the phoneme Y to its right. We denote this boundary by X -B + Y as proposed in [START_REF] Young | The HTK Book for HTK V3.2.1[END_REF] (see Fig. 2).

If we model each possible pseudo triphone by a GMM, the models are badly trained. This is because the number of labeled data is limited in practice. Therefore, a classification and regression tree (CART) is used in order to cluster pseudo-triphones into a reduced number of classes; this cart is a recursive binary tree where each node corresponds to a phonemic or linguistic question. Then a GMM is trained for each leaf node on the CART. 3. Given a labeled sentence and its segmentation, try to refine each boundary of every segment. In this respect, for each frame in a certain vicinity of a given HMM boundary, compute the likelihood that this frame contains the actual boundary. The likelihood that the true boundary 1 We form a super vector centered on the current frame. Since this super vector is assumed to represent a pseudotriphone, we determine the corresponding leaf node in the CART. We then compute the likelihood of the GMM model associated with this leaf node. Finally, the optimal boundary is then assumed to be in the frame that has the maximum likelihood.

BRANDT'S GLR METHOD

The aim of this method is to detect discontinuities in speech signals. Speech signals are assumed to be sequences of homogeneous units. Each unit or window w is a finite sequence w = (y n ) of samples that are assumed to obey an AR model:

y n = ∑ p i=1 a i y n-i + e n .
In this equation, p is the model order, which is assumed to be constant for all units and e n is a zero mean white gaussian noise with variance equal to σ 2 . Such a unit is thus characterized by the parameter vector Θ = (a 1 , . . . , a p , σ ). Let w 0 be some window of n samples and Θ 0 the corresponding parameter vector. Brandt attempts in [START_REF] Obrecht | Automatic segmentation of continuous speech signals[END_REF] to decide whether w 0 should be split in two subsegments w 1 and w 2 or not. In fact, a possible splitting derives from the detection of some jump between the parameter vectors Θ 1 and Θ 2 of w 1 and w 2 respectively. Brandt's GLR method decides that such a jump has occurred by comparing: D n (r) = nlog σ0 -rlog σ1 -(n -r)log σ2 to a predefined threshold λ . Note that D n is merely the GLR. In the equation above, r is the size of the time interval covered by w 1 , whereas σ1 and σ2 are the noise standard deviation estimates of the models characterized respectively by the parameter vectors Θ 1 and Θ 2 . Thus, the change instant corresponds to arg(max r (D n (r)) ≥ λ ).

A direct implementation of this method is computationally expensive. Thus, we use the sub-optimal version recommended in [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF]. In particular, the length of w 2 is fixed to a predefined value L. For further details, the reader can refer to [START_REF] Obrecht | Automatic segmentation of continuous speech signals[END_REF][START_REF] Obrecht | A New Statistical Approach for the Automatic Segmentation of Continuous Speech Signals[END_REF].

EXPERIMENTAL RESULTS AND DISCUSSION

Our purpose is to analyze the behavior of the algorithms presented above. We do so by computing performance measurements on the basis of experiments. We start by describing the criteria used to evaluate the performance of each algorithm. These performance criteria are the probabilities of insertion and omission and the accuracy. On the basis of [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF], we then adjust the refined HMM parameters for application to a French corpus. For this tuning, only the accuracy is needed because the refined HMM yields no insertions and no omissions. For Brandt's GLR method, we compute the probabilities of insertion and omission. The last subsection compares the accuracies of the refined HMM, the standard HMM and Brandt's GLR method.

Probabilities of insertion and omission, accuracies

The quantities described in this section allow us to measure the performance of any segmentation algorithm. We propose the subsequent definitions especially in order to take into account insertions and omissions of algorithms such as Brandt's GLR method.

We start by briefly describing how to locate insertions and omissions of a segmentation algorithm so as to compute the probabilities of insertion and omission of this same algorithm.

Let U = {U 1 ,U 2 , . . . ,U n } and V = {V 1 ,V 2 , . . . ,V p } be the time instants of the segmentation marks obtained respectively by an automatic algorithm and by a manual procedure (hereon referred to as the reference segmentation). For each U j , a correspondence is done with the reference segmentation by determining the time instant V k j which is closest to U j . This way, a sequence V U = {V k 1 , . . . ,V k n } is built in order to compare both segmentation.

The reader can easily verify the following facts: the omissions are the marks V , ∈ {1, . . . , p}, that are not in the list V U ; if V U contains m times the same mark, the number of insertions n i equals m -1. In the latter case, if V is the mark contained m times in the list V U , the nearest mark to V in U is considered as a non-insertion and, thence, the m -1 other marks are regarded as insertions.

We define the ratios P i = n i p+n i and P o = n o n+n o . The former can be regarded as the probability of insertion of the segmentation algorithm, whereas the latter can be considered as the probability of omission of this algorithm. Note that n + n o = p + n i .

The accuracy of any given segmentation is computed as follows. First, locate the insertions as described above and remove them from the list U. For each mark U j of the resulting list of non-insertions, consider the closest reference mark V k j . If the distance |V k j -U j | is less than or equal to a given tolerance value ε, the mark segmentation U j is said to be correct. Otherwise, it is called an error. The accuracy is then defined as the ratio in percentage of the number of correct marks to p + n i :

accuracy = 100 p + n i n ∑ j=1 I [0,ε] (|V k j -U j |)
where I [0,ε] (x) equals 1 if x ∈ [0, ε] and 0 otherwise. The accuracy depends on the number of insertions, the number of omissions and ε. Therefore, an accurate segmentation must make a good compromise between these three parameters.

For instance, a segmentation with many insertions will clearly be characterized by a P i close to 1 and an accuracy close to 0; similarly, in the case of many omissions, P o is close to 1 and the accuracy remains small; in contrast with the foregoing, an accurate segmentation is such that P o and P i are small and the accuracy is close to 1. Further mathematical details regarding these criteria will be given in a forthcoming work.

Application of the refined HMM algorithm to a French corpus

As mentioned in [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF], the method "makes no inherent assumptions for the language or speaker type". So, our purpose is to validate the parameter values exhibited in [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF] when we apply the method to a French corpus containing 7350 sentences. We also adjust some parameters in addition to the reference. We proceed by using HTK toolkits [START_REF] Young | The HTK Book for HTK V3.2.1[END_REF]. Note that the notion of accuracy used in [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF] is a particular case of that employed in this present paper to measure the performance of segmentation algorithms.

The training parameters of this algorithm are: the training size, the number of frames (2N + 1), the frame step e, the frame size (set to 20 ms), the number of GMM components (equal to 1, see [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF] for details), the acoustic vector dimension N c (set to 39 : 12 MFCCs+ energy+ 13 first order deviations+ 13 secondary deviations), the stopping criteria of the CART. These are the minimum number of leaf node instances, denoted by MT I, and the value T of the log likelihood to exceed, in order to consider a question as an actual node of the CART. For every HMM mark of the database, the refined HMM boundary is searched within a 60 ms interval centered on this mark with a search step fixed to 5 ms. The accuracies presented below are calculated for ε equal to 5, 10, 20 and 30 ms. They must be compared to those obtained by standard HMM and given in table 1.

In table 2, we point out a suitable pair (T, MT I) that yields a good level of accuracy when the tolerance varies. The results of table 2 are obtained by following [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF] and thus fixing the pair (N, e) to (2, 30) and the training size to 300. We observe that T hardly influences the accuracy. We fix T to 100. The results also show that the smaller the MT I, the better the accuracy.

Table 3 illustrates the contribution of the training database size. We again fix the pair (N, e) to (2, 30). The pair (T, MT I) is set to (100, 10) according to the foregoing. On the basis of these results, we choose a size of 300 sentences in order to limit the number of manually labeled boundaries. This value is close to that obtained for a Chinese corpus in [START_REF] Wang | Refining Segmental Boundaries for TTS Database Using Fine Contextual-Dependent Boudary Models[END_REF] With table 4, we verify that (N, e) = (2, 30) still remains a suitable choice for dealing with our French corpus. In fact, this choice seems to be a reasonable trade-off between the following two facts. On the one hand, the total duration corresponding to the super vector must be long enough to involve as much information as possible concerning the transition between the two phonemes around the boundary. On the other hand, if this duration is too long, the super vector will take into account information not directly linked to the boundary itself.

Summarizing, the refined HMM algorithm performs well when applied to a French corpus (6% accuracy gain when the tolerance is 10 ms) with MT I = 10, N = 2, e = 30 ms and a training size equal to 300.

Insertions and omissions with Brandt's GLR method

For Brandt's GLR method, the model order p and the window length L are chosen equal to 16 and 20 ms respectively. The threshold λ is set to 30 as in [START_REF] Obrecht | A New Statistical Approach for the Automatic Segmentation of Continuous Speech Signals[END_REF].

We found that the probabilities of insertion and omission are equal to 0.6 and 0.1 respectively. This high insertion probability is explained by the oscillatory behavior of the GLR function. Note that the insertion probability is divided by two when the Brandt'GLR method is merged with a silence/speech detection [START_REF] Jarifi | Jump and silence/speech detection for automatic continuous speech segmentation[END_REF]. Indeed, many insertions are located in silences (see Figure 3).

Comparing the accuracies of the refined HMM and Brandt's GLR methods

The results presented in this section are obtained by averaging the accuracies using a cross-validation procedure where each test set contains 1200 sentences. For the refined HMM, the training set contains 300 sentences for each test. Figure 4 depicts the results obtained with the three methods. Note that for Brandt's GLR method three curves are plotted. The "Brandt's GLR" curve represents the accuracies of this algorithm taking into account its insertions and omissions; the "Brandt's GLR and speech/silence detection" curve displays the accuracies when Brandt's GLR method is merged with the speech/silence detection algorithm already used in [START_REF] Jarifi | Jump and silence/speech detection for automatic continuous speech segmentation[END_REF]; the "ideal Brandt's GLR" curve is obtained by computing accuracies after removing the insertions and omissions via the procedure of subsection 4.1.

According to the results illustrated by these curves, we can make the following remarks: the refined HMM is more accurate than the standard HMM segmentation; the Brandt's GLR method is not accurate because of its large number of insertions even when this number of insertions is significantly reduced; the accuracy of the "ideal" Brandt segmentation is itself significantly better than that of the refined HMM. Therefore, the marks produced by Brandt's GLR method that are not insertions are more accurate than those of the refined HMM.

SUGGESTIONS FOR IMPROVING THE REFINED HMM

As mentioned above, Brandt's GLR method is not accurate with respect to the accuracy measure given in this paper. It is however worth noticing that our assessment is too strict regarding Brandt's GLR method because the definition of accuracy does not take into account the distribution of segmentation marks. In fact, insertions of Brandt's GLR method remain located in silence regions and in the vicinity of handmade marks. It also turns out that high values of the GLR correspond to actual discontinuities of speech signals.

Hence, we suggest to improve the accuracy of the refined HMM by proceeding as follows.

Given a segmentation mark performed by the refined HMM algorithm, compute the GLR of this initial mark. If the GLR exceeds some threshold (to define), keep this mark. Otherwise, consider that neither the refined HMM nor Brandt's GLR method are reliable. Therefore, choose a segmentation algorithm adapted to the acoustic classes of the segments to identify. These classes are known thanks to the sequence of speech units we have. Basic examples of such algorithms are speech/silence detection and voiced/unvoiced detection. More sophisticated techniques are described in the literature on the topic (see for instance [START_REF] Toledano | Automatic Phonetic Segmentation[END_REF]). Since Brandt's algorithm segmentation marks that are not insertions are accurate, it can easily be thought up that a reasonable performance objective for the approach described above is to achieve accuracies better than those of the refined HMM and closer to those of the "ideal" Brandt segmentation.

CONCLUSION

This paper analyzed the performance measurements of two automatic segmentation algorithms: the refined HMM algorithm and Brandt's GLR method. To carry out our assessment, we used three performance criteria, namely, the probability of insertion, the probability of omission and the accuracy. From the experimental results, we derived an approach for improving the refined HMM segmentation algorithm as well as a reasonable performance target (the accuracy of the "ideal" Brandt's GLR method). With respect to the contents of this paper, the purpose of our forthcoming work will be twofold. On the one hand, we will complete our analysis concerning the performance criteria. In particular, we will study how the distribution of marks can be taken into account or merged with the criteria employed in this paper. On the other hand, we will detail, implement and test the method proposed Figure 4: Segmentation accuracy for 900 sentences in the foregoing section. Our intention is to approach the accuracy of the "ideal" Brandt segmentation.

Figure 1 :

 1 Figure 1: Example of a super vector for a particular boundary

Figure 2 :

 2 Figure 2: Examples of pseudo-triphones lies within a given frame is then computed as follows.We form a super vector centered on the current frame. Since this super vector is assumed to represent a pseudotriphone, we determine the corresponding leaf node in the CART. We then compute the likelihood of the GMM model associated with this leaf node. Finally, the optimal boundary is then assumed to be in the frame that has the maximum likelihood.

Figure 3 :

 3 Figure 3: Brandt's GLR segmentation

Table 1 :

 1

		HMM segmentation accuracies
	ε	5	10	20	30
	accuracy 33.54 59.77 85.24 92.83

Table 2 :

 2 Accuracy vs (T, MT I)

	T	ε	MT I = 10 MT I = 20 MT I = 40 MT I = 100
		5	38.49	38.08	37.48	35.13
	20 10	64.55	64.29	62.94	60.13
		20	87.91	87.74	87.05	85.16
		30	94.46	94.44	93.93	93.45
		5	38.55	38.12	37.48	35.13
	100 10	64.63	64.28	62.94	60.13
		20	87.98	87.73	87.04	85.16
		30	94.50	94.46	93.93	93.45
		5	38.38	37.90	37.49	35.13
	350 10	64.32	64.01	62.94	60.13
		20	87.93	87.51	87.11	85.16
		30	94.35	94.42	93.93	93.45

Table 3 :

 3 Accuracy vs training set size Training size ε = 5 ε = 10 ε = 20 ε

	= 30

Table 4 :

 4 Accuracies for different values of (N, e) e N ε = 5 ε = 10 ε = 20 ε

	= 30


Titouan Verdu

Gautier Hattenberger

Simon Lacroix

Flight patterns for clouds exploration with a fleet of UAVs

Modeling the cloud microphysics processes is essential to improve our understanding in climate changes and reduce the uncertainties in weather predictions. Aircrafts, remote sensing and ground-based infrastructures provide either sparse or coarse spatial measurements that are not sufficient to develop fine cloud models. UAVs have shown their ability to collect relevant cloud in-situ measures, and can be even more efficient when deployed in fleets. However, collecting relevant cloud data call for specific trajectories: this paper introduces a series of flight patterns dedicated to cloud exploration by a fleet of UAVs. The patterns definition comprise both a priori geometric information and real-time reactions to collected data. Results in simulated clouds assess their relevance for cloud in situ data collection.

I. Introduction

The precise understanding of the clouds micro-physical properties is still a challenge for atmosphere scientists. The complexity of the involved physical processes calls for thorough models, whose relevance and adequacy require dense and precise data to be assessed. For this purpose, ground-based and satellite measurements can be complemented by in-situ measurements provided by instrumented research aircrafts. Yet, the observations collected by aircraft are localized in space and time [START_REF] Rauber | Rain in shallow cumulus over the ocean: The rico campaign[END_REF], which limits the understanding of clouds evolution.

The use of UAVs is now significantly spreading within the atmosphere scientists community. For instance, recent experimental campaigns have been conducted to analyze air-sea interactions [START_REF] Reineman | The use of ship-launched fixed-wing UAVs for measuring the marine atmospheric boundary layer and ocean surface processes[END_REF], to track and estimate gaseous pollution plumes [3], [START_REF] Egorova | Estimation of gaseous plume concentration with an unmanned aerial vehicle[END_REF], or to compare measures of cloud extinction profiles with air parcel models [START_REF] Sanchez | Top-down and bottom-up aerosol-cloud closure: towards understanding sources of uncertainty in deriving cloud shortwave radiative flux[END_REF]. Large UAVs are also used to collect data in the upper atmosphere [START_REF] Li | The nasa high-altitude imaging wind and rain airborne profiler[END_REF].

Yet, dense data are required to precisely assess the physical phenomena that take place in the atmosphere. For this purpose, the use of a fleet of UAVs is very relevant [START_REF] Corrigan | Capturing vertical profiles of aerosols and black carbon over the Indian Ocean using autonomous unmanned aerial vehicles[END_REF]: a fleet can acquire synchronous data over large extents of space, allowing for instance the assessment of fluxes, which no single measurement system can provide. Moreover, intelligent fleet control strategies can be developed so as to optimize the data collection, while autonomously adapting to the situation at hand. This paper presents on-going work on the development of a fleet of UAVs to explore clouds, in the context of the NEPHELAE project, whose purpose is to develop and actually deploy a fleet of autonomous UAV to collect data within and around cumulus clouds. The project involves atmosphere scientists from the Meteo France 1 ENAC, Université de Toulouse, Toulouse, France 2 LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France research lab GAME, the drone team of ENAC, and roboticists from LAAS/CNRS, and builds upon prior exploratory work [START_REF] Renzaglia | Monitoring the evolution of clouds with UAVs[END_REF]. Various axes of work are carried out, that span from the conception of a dedicated UAV and the development of on-board atmospheric sensors, to the definition of individual UAV flight control laws and overall adaptive fleet control schemes. We focus on the two latter points, and depict in details the specific flight patterns developed to achieve adaptive data collection.

Outline: The next section presents the overall approach retained for the fleet operations, which relies on the assembly of sequences of dedicated flight patterns. Section III depicts the defined flight patterns, which are evaluated in section IV, and the paper concludes with a roadmap of developments towards actual flight experiments.

II. Problem statement and approach

A. Mission definition

Numerous discussions have been conducted with atmosphere scientists in order to understand their needs. Thanks to intensive atmosphere microphysics simulations, they have established a first conceptual (macroscopic) cloud model for continental cumulus clouds, that links key meteorological parameters (e.g. updraft, entrainment) to basic cloud geometry (e.g. width, height, aspect ratio) [START_REF] Lamraoui | In-cloud icing and supercooled cloud microphysics: from reanalysis to mesoscale modeling[END_REF]. For instsance they assessed linear relationships between the cloud base diameter, the cloud height and vertical fluxes. On the basis of these observations, they defined basic data collection needs to assess the model validity. The variable of interest to collect are:

-The pressure, temperature and humidity -The wind field and turbulences -The liquid water content (LWC), which represents the mass of liquid water in a cloud for a specified amount of dry air, an essential information in cloud microphysics [START_REF] Wallace | Atmospheric Science: An Introductory Survey: Second Edition[END_REF]. The atmosphere scientists have defined a series of information to collect so as to track and monitor the various stages of a cumulus cloud life, from cloud formation (dominated by updraft air flows) to dissipation (dominated by entrainment at the cloud borders). These information define zones to be mapped by the UAVs, that are illustrated in the Fig. 1.

The information to gather in these zones are the following:

• At the basis of the cloud (purple), the information to gather are the shape of the cloud contour, and the distribution of the LWC and the vertical wind at the elevation of the basis. The latter information in particular define the "center" (or core) of the cloud, where the updraft is the higher.

• Cumulus clouds exhibit a column where updrafts take place (blue), which can be coarsely described as a slanted truncated cone. The main interest of gathering information within this zone is to follow the evolution of the vertical wind during the life of the cloud.

• By mapping vertical winds on thick sections of the cloud (green), the scientists can estimate air fluxes.

• And finally, measuring the vertical wind, turbulences and the evolution of the LWC at the borders of the clouds frontier (red) is essential. Once the zone to gather data have been defined, the life span of the cloud will determine the frequency of exploration of each part. The cumulus clouds life extent is of the order of 30 minutes, which imposes constraints on energetic autonomy, attainable horizontal and vertical speeds, weight of the UAV, ... Cloud exploration is a highly constrained problem, that actually requiress the development of specific UAVs (see chapter V).

B. Approach to fleet control

The UAV fleet is to be tasked by high level commands such as "assess the entrainment at the cloud edge" or "quantify the updraft at the cloud base". This calls for deliberative approach that explicitly models (maps) the environment on the basis of in-situ measurements and that builds actions plans (trajectories) based on aircraft performance models and sensing capacities.

But instead of directly planning trajectories in space and time, the deliberative layer assembles trajectories defined as a sequence of specific flight patterns, each pattern being adapted to the acquisition of one of the information listed above. The flight patterns can partly be parameterized geometrically (e.g. specifying at which elevation a horizontal section of the cloud is to be mapped), but are also defined as adaptive trajectories which execution is servoed on acquired data (e.g. the perceived LWC can be used to detect the cloud boundaries when mapping a cloud section).

The specification and development of the overall planner is still under way. A centralized architecture will be used: all UAVs transmitting their data down to the ground station, where data are processed to build cloud maps using Gaussian Processes regression techniques [START_REF] Reymann | Adaptive sampling of cumulus clouds with UAVs[END_REF], and where the task allocation and primitive assembling processes are also executed. Such a centralized architecture can be easily disturbed by loss of communication and does not scale up with the number of UAVs. Evolving towards a distributed architecture can balance these issues and is on our research agenda -and is actually also a reason why we chose to specify flight plans as sequence of patterns, thus easing the decision processes.

Finally, note that initial information on the cloud can help the scientist to specify the task to be achieved, and the central planner to decompose the tasks into sequences of primitive patterns. For instance [START_REF] Lauda | All-sky camera network to track clouds and calculate their spatial dimensions[END_REF] have developed a method to assess coarse geometric parameters of a cloud using a network of all-sky cameras, such as its base height, size and horizontal velocity. Atmospheric Lidars and radar can also provide similar data to initialize the sampling strategy of the UAV fleet.

III. Flight patterns

This section presents the concepts of the flight pattern primitives that have been developed to gather efficiently atmospheric data. The idea is to create several flight plans that are easily executable for the UAV with limited processing power. The computational complexity of these algorithms is limited by the possibility to embed them on a dedicated electronic card such as a Raspberry Pi. The implemented solution is not an optimal path planning method driven by an utility criterion but rather a set of adaptive shapes triggered by sensor readings in real-time.

Schematic illustrations are shown for a better understanding of the patterns. The shape of the cloud is displayed in black, the UAV is represented in orange, the theoretical trajectory in green, the calculated points and circles in blue and finally, in red, the parameters.

Observation: The basic parameters are directly given by the design of the UAV. That's the case of the cruise speed, the max roll angle and the minimum curvature radius deduced from the first two parameters with the following equation :

R min = V 2 g tan(roll max ) + R margin (1)
where R min corresponds to the minimum radius, V the cruise speed, g the gravitational constant, roll max the maximum roll angle and R margin a margin to warrant the execution of the curve even in harsh condition.

A. The lace

The lace pattern is inspired by [13] that develops a method to estimate the boundaries of an dynamic environment with a team of robots. They prove that with a swarm of several agents it is possible to collect data, communicate them to the others and perform the required calculations to estimate the frontier. The interesting part of their work is that they succeed to distribute all the processing part and to deploy their team of robots in a cooperative way.

In our case, the UAVs use LWC data as the information to detect the cloud boundary. This boundaries being not sharp, a wider space around it has to be covered to ensure its detection: the chosen pattern is adapted to cover enough distance each time a threshold on the LWC data is crossed. EstimateBorder(ListBorderP oint) 22: end procedure Table I depicts the algorithm that achieves this pat-tern. Every time the UAV crosses the cloud border based on LWC threshold, it exploits its position and heading (purple arrows on Fig. 2) to compute the center of the next circle that it will track, depending on the minimum turning radius R min and an angle set to ± π 2 (in grey). The aim is to collect as much points of the border as possible to better estimate the outer shape of the cloud.

B. The rosette

This pattern is designed for multiple purposes. As the lace pattern, it can be used to estimate the cloud border, but its role is to mainly collect information in the core of the cloud by crossing several times its central part. This provides valuable information for measuring the air mass flow when flying two UAVs at two different altitudes.

Table II presents the associated algorithm. The only parameter required to initialize the path is a 3D position inside the cloud. After reaching this point along a straight line, the UAV will continue until the border is crossed. Once outside the cloud it will initiate a turn around according to the minimum radius and estimate a new center point from the data gathered during the last segment inside the cloud. This operation is repeated as many times as required to complete the map of the data with a satisfying coverage.

C. The conic spiral

The main goal of the conic spiral pattern is to gather data from the cloud's core, which is where the updraft is at its maximum intensity. Starting from the cloud base, it can expend to the top of the cloud or even a bit higher. For the time being, the parameters are based on the geometry determined by other patterns like rosette at different altitudes. The resulting trajectory looks like a spiral along a slanted cone as see on Fig. 4.

D. The Zamboni

The name of this pattern is coming from a manufacturer of ice rink resurfacer, who defined a geometric path to efficiently cover an area with strong constraints on the turn radius. This pattern offers a simple and fast way to cover a rectangle defined by geometrical parameters and for a large range of cloud sizes. Additionally, the coverage is more regular than the rosette pattern, which might be a mission requirement in some cases. This pattern is not driven by sensors measurements.

E. Other basic patterns

In addition to the specific flight patterns that have been designed with meteorological data acquisition in mind, some standard basic patterns are also available. They can be used by the mission planing system to join the different patterns or during non measurement flight phases.

GoTo Reaching a 3D waypoint. Path Follow a sequence of straight lines between waypoints. Circle Hold a position while flying in circle. Flower A simplified purely geometric form of the rosette pattern.

IV. Implementation and simulations

This project is developed based on the Open-Source autopilot project Paparazzi 1 . The simulations are based on the flight dynamic model JSBSIM 2 for a better realism. A preliminary work from atmospheric scientists have built a high-fidelity model of the clouds based on Large-Eddy-Simulations (LES). The results are stored in Meso-NH files 3 containing all micro-physical properties of the atmosphere, including the LWC. This last information is used to feed the UAV simulation and to test the sensor-based patterns. On this preliminary work, the data are coming from a static environment, later work will introduce horizontal wind and temporal evolution to the clouds. The first path plan implemented and tested is the Lace pattern. It has been created to detect the border of the cloud at a given altitude, so with a zero vertical speed. The Fig. 7 displays the LWC points above 0 from the Meso-NH file (in red). The blue points corresponding to the estimated border (yellow points in Fig. 6) are correctly matching with the shape of the cloud.

The final evaluation of the different patterns in regards of the mission objectives will be done by the atmosphere scientists. The criteria will be the feasibility to reconstruct the cloud micro and macro physical characteristics from sparse local measurements. This will be done by considering the flight time, the energy consumption and the coverage density compared to systematic survey that is traditionally used in such missions.

The PPRZ autopilot allows the creation of a simulation with multiple aircraft. The aim being to use each UAV with a particular pattern, a fleet of three UAV has been created to confirm the possibility to gather different data in several zone of the cloud. Two UAV execute the rosette pattern, based on GPS position, at different altitude and center. The last one, uses the lace pattern, with a positive vertical speed between the two 2D horizontal plan created by the others UAV. The Fig. 8 shows the result getting in Google Earth with the KML path of the two first UAV. The blue path corresponds to the trajectory of the rosette pattern deploy in the base of the cloud and in green, at the top of the cloud. The first picture of the Fig. 9 shows, in red, the lace pattern used to scan the border of the cloud and the second picture display a 2D view of all the trajectories of the fleet.

The Fig. 10 reveals a 3D view of the different KML path of the UAV. The rosette pattern allows the collect of data all over a 2D horizontal plan whereas the lace pattern gather data all around the frontier of the cloud in 3D.

V. Conclusion and future work

This work proposes a new approach for the exploration of clouds. The main objective is to design trajectories that will efficiently collect measures depending of the requirements of the scientists processing these data. This goal is achieved by creating adaptive flight patterns reacting to sensors in real-time.

Each pattern have been described and implemented into a realistic simulation framework, including the flight dynamic of the UAVs and the clouds modeling. The comparison of the boundary points obtained during the simulation with the reference environment proves the validity of the pattern approach.

The next step of this work will be to run the simulation over a dynamic cloud environment in order to assess the adaptability of the patterns to moving boundaries. The actual UAVs that will be used in the project are under development and will allow, once ready, to perform hybrid simulation mixing a real flight with simulated sensors. A flight management and mission planing system will be build on top of these flight patterns in order to control the fleet and perform task allocation from high level operator inputs.

Finally the atmosphere scientists involved in the project will evaluate the overall efficiency of the performed trajectories with regards to their objectives of cloud modeling.

Appendix: Development of a UAV dedicated to clouds exploration

The UAV used to explore a cloud have to answer specific constraints required to collect data over a satisfactory coverage. Here is a list of the constraints : Speed High flight speed to follow the horizontal motion of the cloud even in the presence of wind. Autonomy Enough flight time to execute the mission and collect data during the complete life time of a cumuls cloud.

Weight

Light to be easily operable (take off and land) and transportable. Once the constraints of the plane were well defined, an optimization method has been used to define the UAV conceptual design. The picture Fig. 11 shows the first prototype of the UAV and the Table. III exposes its noticeable features. This UAV is equipped with the autopilot Paparazzi (PPRZ). This Open-Source system developed at ENAC [START_REF] Hattenberger | Using the Paparazzi UAV System for Scientific Research[END_REF] has been used worldwide on hundreds of airframes. PPRZ's unique flight plan language allows the execution of complex procedures, navigation patterns, and eventbased actions, which are not readily available in other systems. In particular, it has already been used in atmospheric studies [START_REF] Reymann | Adaptive sampling of cumulus clouds with UAVs[END_REF].

In order to collect the desired data, the UAV embed a group of specific sensors developed by the meteorologist. The payload is composed of a humidity and temperature sensors, a 3D Pitot probe which can collect static and differential pressure and is useful to determine the airspeed (vertical and horizontal) and finally a LWC sensors based on the reflection of the light on a droplet. This set of sensors will supply all the local and punctual information useful to guide the UAV in the cloud and to construct its model.

Fig. 1 .

 1 Fig. 1. The different zones in which UAVs will gather data: the cloud base (purple), its body (green), the internal updraft (blue) and the cloud borders (red).

Fig. 2 .

 2 Fig. 2. The lace patternThe Fig.2illustrates the path followed by the UAV in a 2D horizontal plane. It only needs a 3D starting waypoint (in red) which is inside the cloud. To extend the exploration to the 3D volume of the cloud, an extra vertical speed can be specified.

Fig. 3

 3 Fig.3illustrates the path of the UAV at different times when following the rosette pattern. The red point corresponds to the point to go through and in the final picture, the purple zone is the estimation of the cloud center. A future improvement will consist in incorporating the measured updraft winds in the definition of the cloud center point by the updraft.

Fig. 3 .

 3 Fig. 3. Rosette path

Fig. 4 .

 4 Fig. 4. Conic spiral path A sensor based version is currently under development. It will integrate information from the vertical wind component and the UAV energy consumption to adapt the center of the spiral in real-time similarly to glider's pilots.

Fig. 5 .

 5 Fig. 5. Zamboni pathThe Fig.5illustrates the execution of this pattern. Required parameters are:-A 3D point corresponding to an estimation of the center of the cloud, -Two distances which are the length of the cloud sides, -A distance between two pathways.

Fig. 6 .

 6 Fig. 6. Screenshot of the Paparazzi simulation of a lace pattern The Fig. 6 shows the result of a flight simulation with sensor feedback in real-time. The plain line corresponds to the actual UAV path while the green circle corresponds to the current desired trajectory. Each yellow point is associated to a detection of the border of the cloud. With this aircraft model, the flight speed is around 18m/s, with a turn radius of 90 meters and it takes 20 minutes to get the presented result after around 7 laps.

Fig. 7 .

 7 Fig. 7. Screenshot of the cloud display software

Fig. 8 .

 8 Fig. 8. View in 2D of the KML path of the two UAV using the rosette pattern

Fig. 9 .

 9 Fig. 9. View in 2D of the KML path of the UAV using the lace pattern

Fig. 10 .

 10 Fig. 10. View in 3D of the KML path of the fleet

Fig. 11 .

 11 Fig. 11. Picture of the UAV designed for the NEPHELAE project (without the payload)

  TABLE III Features of the NEPHELAE UAVs

	Features	Values
	Cruise speed	15 to 25 meters per second
	Autonomy	electrical battery to fly
		during 2 to 3 hours
	Desired altitude	1000 to 3000 meters
	Curve radius	80 to 100 meters
	Wingspan	1,6 meters
	Payload weight	around 800 gramms
	Battery weight	around 900 gramms
	UAV and autopilot weight	around 800 grams
	Total weight	2 to 4 kilogramms
	Take off	Bungee
	Landing	Net

http://paparazziuav.org

http://jsbsim.sourceforge.net/

http://mesonh.aero.obs-mip.fr/mesonh54

Acknowledgments

The authors would like to thank the members of the NEPHELAE project and in particular Aurélien Cabarbaye for the UAV design and Nicolas Maury for the cloud modeling and patterns evaluation.


A Model of Cooperative Agent Based on Imitation and Maslow's Pyramid of needs

Le Guen Herve and Moga Sorin

Abstract-Recent works have addressed the problem of imitation in the framework of the interactions between two agents, whether humans or robots. We develop a model aiming at improving the self-organization of population of robots by relying on imitation. Imitations between the robots are regulated by a very simple model of emotional expression. The model is tested in the context of a simple task for the robots: to explore their environment to localize sources needed for their survival. Following a biology-inspired approach, imitation has been introduced within a population of autonomous agents, as bidirectional social needs, in line with the Maslow's Pyramid of needs [START_REF] Maslow | A theory of human motivation[END_REF]. In our model, imitation is integrated into a global architecture based on artificial neural networks. Running our simple and scalable model resulted in a significant increase of the population's survival rate and a decrease of the global amount of the average necessary movements of each agent.

I. INTRODUCTION

This paper presents our most recent results on the influence of imitation within a population of autonomous robots. More precisely, we attempt to find the minimum elements that can produce an efficient self-organization. Since the beginning of artificial intelligence, the role played by intrinsic individual intelligence has steadily decreased. Parallel research, in various fields, was aimed at proving the large amount of knowledge derived from others in individual intelligence. In psychology, the most famous experiments were conducted by Baldwin and Piaget cited by [START_REF] Nadel | Imiter pour dcouvrir l'humain[END_REF], [START_REF] Moga | Apprendre par imitation: une nouvelle voie d'apprentissage pour les robots autonomes[END_REF], who showed the importance of imitation in infant development. In ethology, the collective intelligence of the ant, bee or primate is well known. A computational point of view emphasizes the obvious superiority of a distributed exploration of the set of possible states [START_REF] Ferber | Les Systèmes multi-agents: Vers une intelligence collective[END_REF]. This can be a first step towards an efficient collective intelligence. The next question to solve is then the sharing of distributed knowledge. The fact that imitation is the possible root of communication and social learning [START_REF] Gallese | A unifying view of the basis of social cognition[END_REF], [START_REF] Arbib | The Mirror System, Imitation, and the Evolution of Language[END_REF], [START_REF] Rizzolatti | Language within our grasp[END_REF] is well accepted now, as is shown by the amount of recent research in this area. One crucial reason for this growing interest by neuroscientists is probably the discovery of mirror neurons in primates [START_REF] Rizzolatti | Language within our grasp[END_REF]. The mirror neurons also fire when an action is performed, or when the same action, performed by a peer, is perceived. Indeed, the fact that the smallest functional component of the brain can behave in an imitative way constitutes a strong argument in favor of the role of imitation as the root of social abilities. Furthermore, mirror neurons are located in the equivalent of Broca's area in Le Guen Herve and Moga Sorin are with the Institut TELECOM ; TELECOM Bretagne ;UMR CNRS 3192 Lab-STICC LUSSI, Technople Brest Iroise CS 83818 29238 Brest Cedex 3 FRANCE (email: {herve.leguen, sorin.moga}@telecom-bretagne.eu).

This work was supported by the french ministry of research Grants the human brain, which contains the neurons most involved in language formulation. We therefore chose to consider in the present work that self-organization relies on imitation. By studying the role of imitation in self-organization, we aim to supplement recent research on the various problems raised by imitation for robotics. Most of this research deals with the correspondence problem ( [START_REF] Alissandrakis | Imitation with alice: learning to imitate corresponding actions across dissimilar embodiments[END_REF], [START_REF] Alissandrakis | Correspondence mapping induced state and action metrics for robotic imitation[END_REF], [START_REF] Rajesh | Towards a real-time bayesian imitation system for a humanoid robot[END_REF], [START_REF] Alissandrakis | Synchrony and perception in robotic imitation across embodiments[END_REF], [START_REF] Elshaw | An associator network approach to robot learning by imitation through vision, motor control and language[END_REF], [START_REF]Imitation in animals and artifacts[END_REF], [START_REF] Moga | Apprendre par imitation: une nouvelle voie d'apprentissage pour les robots autonomes[END_REF] ): how can one get a humanoid robot to learn a sequence of actions by imitation and to succeed in linking the different body parts it observes with its own body components. In line with the analysis presented in [START_REF]Imitation in animals and artifacts[END_REF], deal with the "how to imitate" problem. Other works [START_REF] Jansen | A model for inferring the intention in imitation tasks[END_REF], [START_REF] Jansen | A model for inferring the intention in imitation tasks. Robot and Human Interactive Communication[END_REF] were focused on how the intention can be perceived by the robot in order to guide the imitation. In other words, how the robot can infer the goal of the perceived action and how this goal can be used to select which part of an action is the most important.

Conversely, the present paper focuses on the "when to imitate" and "what to imitate" problems, thus implying a basic perception of intention. We assume that the correspondence problem (i.e the capacity of each robot to associate its own body components to body part it perceives) is solved. We propose a way to integrate a controlled imitation behavior within a population of autonomous robots. It is to a certain extent a holistic approach. Thus we solved two kinds of problems: first, how to integrate the imitation into the behavioral architecture of a robot or agent and, second, how to integrate it at the population level, i.e. how imitation needs to be adjusted to other basic behaviors (obstacle avoidance, random exploration, etc.) , and how the target of imitation can be selected among a large number of possibilities. Finally, it should be noted that the context of the study is deliberately limited to a simple exploratory task: each robot has to localize a source corresponding to each of its vital needs in order to survive.

The first part of the paper presents the main phenomena concerning or relating to imitation. We have tried to determine a minimum set of low-level properties that leads to an efficient self-organization. This has been achieved in a large extent by studying an infant's abilities to imitate. These abilities include facial imitation [START_REF] Nadel | Imiter pour dcouvrir l'humain[END_REF], perception by the infant that he or she is being imitated [START_REF] Nadel | Imiter pour dcouvrir l'humain[END_REF], and empathy [START_REF] Decety | A social-neuroscience perspective on empathy[END_REF], [START_REF] Arbib | Emotions: from brain to robot[END_REF], [START_REF] Decety | The power of simulation: Imagining one's own and other's behavior[END_REF], [START_REF] Singer | The neuronal basis and ontogeny of empathy and mind reading: Review of literature and implications for future research[END_REF], [START_REF] Jabbi | Empathy for positive and negative emotions in the gustatory cortex[END_REF]. The interest in empathy sprung directly from the innate ability to imitate facial expressions and induced the study of emotions. Finally, the study of emotions was linked to the study of social needs as modeled by the Maslow's pyramid of motivations [START_REF] Maslow | A theory of human motivation[END_REF]. In a second part, we describe how each imitation phenomenon is modelled within an overall presentation of the robotic architecture and its implementation. The third part presents simulation results and compare them with the initial architecture.

II. IMITATION

Research of the minimal properties that an agent needs to possess in order to obtain efficient interactions leads naturally to consider what is innate or universal in human beings. Below are some observed phenomena related to imitation that present fall into these two categories.

A. Innate imitation abilities

According to Piaget, cited by [START_REF] Moga | Apprendre par imitation: une nouvelle voie d'apprentissage pour les robots autonomes[END_REF], imitation is a sensorymotor learning process that leads to intelligence building. Earlier research focused on on delayed imitation, considered as a witness of representation appearance. But the studies undertaken by Meltzoff and Moore emphasized the innate ability to imitate. At least in the case of facial expression and simple gestures of tongue, mouth and fingers, the existence of natural mechanisms that facilitate imitation seems to be well-accepted now. Years of experiments led Meltzoff to the active intermodal mapping theory. This theory explains the phenomenon through the detection of similarities between the internal representations of, firstly, the visual perception of the demonstrator's face, and secondly, the internal representation of sensory motor perceptions. These representations, in the form of a map, could facilitate such detection. Although this mechanism is not yetfully understood, it constitute evidence of innate imitation abilities. In addition, it provides a clue to the strong implication of emotions in imitation phenomena. Moreover, the global linkage seems to be very complete and sharp: according to Meltzoff [START_REF] Nadel | Imiter pour dcouvrir l'humain[END_REF], the evolution of imitation is strongly linked to the development of all the personal aspects of self-knowledge. The more a baby or young infant learns about himself (motor abilities, goal-oriented actions, emotions, etc.), the more imitation enables him to make the association: "if it works this way for me, it must be the same for others". This process leads the infant to perceive very early that the actions of others may express intentions since he has intentions himself.

B. The perception of the fact of being imitated

An infant is very early able to perceive the fact that an adult or another infant is imitating him. Studies conducted by Meltzoff [START_REF] Nadel | Imiter pour dcouvrir l'humain[END_REF] produced some very informative results. Fourteen month-old babies were more interested by adults imitating them than by adults imitating video pictures of another baby. The two aspects of this perception of the fact of being imitated were separated into, firstly, synchrony between the baby's actions and the adult's actions and, secondly, the fact that these actions were identical. Experiments demonstrated that babies were more attracted by imitation than by merely synchronized actions. Moreover, they also tested the adults concerned in order to verify that they were really imitating.

C. Empathy

Although there was little interest in empathy a decade ago, its definition is hardly a subject of controversy. The common meaning given to the term is very similar to the basic definition used by scientists. Decety [START_REF] Decety | A social-neuroscience perspective on empathy[END_REF] suggests a basic definition: "an interaction between any two individuals, with one experiencing and sharing the feelings of the other." . Recent progress in neuroimaging permits a very precise description of the neural mechanisms involved in empathy. It is impossible here to describe all these mechanisms in full, but a superficial summary could be as follows: the activation of the same zones, except the primary sensory cortical area, involved in the same real experience with an intensity depending on each person's own regulation, and thanks to a top-down cognitive analysis of the other, and a bottom-up perception of the other person's emotional expression, both processes taking place at the same time. This last point is of particular interest to us, owing to its direct link with the innate spontaneous facial imitation phenomenon. In other words, the perception of facial expression influences the cognitive process. Most psychologists or neuroscientists agree that empathy generates a matching spontaneous facial expression. But studies of imitation, specially the ones by Meltzoff and Moore, demonstrate that this matching is already present in the newborn child. So the fact that the simple perception of facial expression plays a role in a very internal experience suggests that imitation cannot be studied without taking emotional expression in account. Section III will describe how this emotional interaction has been modelled. An explicit description of the chosen viewpoint regarding the emotions will be first given below.

D. Emotions

The role played by the expression of emotion in facial expressions has been outlined in the previous part through the empathy mechanisms and the imitation of facial expressions. Many studies have been carried out on the subject of human emotions which, owing to the great complexity of this phenomenon, and represent many different schools of thought (see [START_REF] Belzung | Biologie des emotions[END_REF] for a review). One point that does not provoke discussion is the almost universal nature of emotional expression. Studies [START_REF] Belzung | Biologie des emotions[END_REF] show a very low variability in the perception of facial expressions whatever the population concerned. In contrast to empathy, nobody has succeeded in giving a definition of emotions that achieves consensus even within a single disciplinary field. Nevertheless the results displayed by Rolls [START_REF] Rolls | Memory systems in the brain[END_REF], which are based on recent technological advances in neuroimaging, are very informative and are in line with other parts of our paper. Rolls proposes that emotions are not only elicited by rewards and punishments arising from the current situation but are also influenced by situations that are expected. For instance, relief can be produced by the termination or non-appearance of a punishment. In the same logic, frustration, anger or sadness are the outcomes of the disappearance or mistaken expectation of a reward. Motivation is thus the expectation of reward and can be steered toward a secondary rewarding stimulus that becomes the goal for action. The model presented in this paper only focuses on the reward mechanisms and the emotions used are thus only related to motivation and reward, with the lack of satisfaction being considered as pain. So the findings on empathic response to pain have also been used for this case. Following the same reasoning as in the previous parts and linked to them, if emotions constitute an appraisal of the current situation and if those emotions are expressed in a universal manner, then the emotional expression will present characteristics well suited to serve as a criterion in target selection for imitation. Therefore, the fact that, firstly, new born children are able to perceive which facial expression is being made before them and, secondly, that young infants are very early able to make the hypothesis that their own internal state associated with such acts could be identical to that of another person doing the same thing, leads us to consider that these mechanisms are involved in communication modulation.

E. Maslow's pyramid of needs

We have presented above the phenomena involved in imitation that we have chosen to model. The problem is to integrate all these processes into a global architecture. As there exist no neurobiological data, we turned towards psychology and a well established model, namely Maslow's pyramid of needs [START_REF] Maslow | A theory of human motivation[END_REF]. This model has been used successfully many times and, despite the date of its publication, it is still used in numerous domains. According to this model, a human being's motivations follow a hierarchy (Fig. 1). Although the influence of each particular need varies from one person to another the principle is the same. There are two main classes of needs. The most important needs are called primary needs. Put briefly, they are made up of the physiological needs such as eating, breathing, maintaining the bodily temperature, escaping predators, and so on. According to the theory, if a deeper need is not satisfied, needs higher up in the hierarchy cannot be a source of motivation for an individual [START_REF] Maslow | A theory of human motivation[END_REF]. The second class of needs are called secondary needs. They constitute the social aspect of human motivation. First there is the gregarious instinct of human beings: the need to belong. Human beings need friendship, love, social relationships. This need is the need to belong to a social group, an association, or any kind of social network. Next is the need for esteem. This need is in fact bidirectional: human beings need first of all to feel esteem for others, but also to receive esteem from others. These two needs have been interpreted, in our context, as the need to imitate, and the need to be imitated. They are based, firstly, on the decision process of the agents(explained in next section) and, secondly, on the two different kinds of satisfaction, presented with their properties in the previous section. The fact that rewards may be shared thanks to an empathic response implies that a reward must be expected after some social interchange. Consequently, as the fact of being imitated is perceived by the agent concerned and as imitation is likely to induce empathic satisfaction, it seems logical to model them as needs, that is to say, as expected rewards. Finally, it can be added that implementing imitation as a social need is facilitated by the architecture of the initial model [START_REF] Ph | Impact of imitation on the dynamics of animat populations in a spatial cognition task[END_REF], which is based on a subsumption architecture [START_REF] Brooks | A robust layered control system for a mobile robot[END_REF]. This is also a hierarchical architecture composed of basic behaviors. The implementation of these needs will be described in greater detail in the next section.

III. MODEL

The model was based on an existing model of an autonomous robot with goal-oriented navigation and imitation capabilities [START_REF] Banquet | A hippocampal model of visually guided navigation as implemented by a mobile agent[END_REF], [START_REF] Banquet | Place cells, maps and navigation strategies: processing steps of the corticohippocampal system[END_REF], [START_REF] Banquet | Sequence learning and timing in hippocampus, prefrontal cortex, and accumbens. Neural Networks[END_REF]. Its goals are derived from internal variables that have to be maintained in a comfort area. The values of these variables decrease in time. The robot population's task is to explore an unknown environment and to localize sources corresponding to its different intrinsic needs. Its survival depends upon the satisfaction of these needs by discovering the different locations of the sources. In order to link them with Maslow's pyramid, these individual needs are called primary needs. In reality, we refer to a need when the corresponding internal variable falls below a certain threshold. More generally, this model is structured as a Brooks architecture [START_REF] Brooks | A robust layered control system for a mobile robot[END_REF] with a hierarchy of different behaviors. These behaviors are, in the first place, obstacle avoidance, secondly goal-oriented navigation, thirdly imitation, and lastly random exploration. And so, at each computation step, if a behavior is either unnecessary or impossible, then the next one is attempted (Fig. 3). To these four basic behaviors correspond four modules. The obstacle avoidance module relies on a Braitenberg-like mechanism. The goaloriented navigation module is based on a biologically inspired model that makes use of the studies by O'Keefe and Nadel [START_REF] O'keefe | The Hippocampus as a cognitive map[END_REF] on the hippocampus and cognitive maps. Thanks to this model, a representation of the environment in the form of a graph is memorized according to the novelty aspect of a location by comparing visual landmarks positions [START_REF] Banquet | A hippocampal model of visually guided navigation as implemented by a mobile agent[END_REF], [START_REF] Quoy | Dynamical neural networks for planning and low-level robot control[END_REF]. Such a graph allows goal-directed navigation by propagating motivation from a source corresponding to a real need and to the current location of the robot. The graph is in fact implemented as an artificial neural network. This network is composed of two different layers, one that can be seen as a sensory cortex is used for self-localization and the other to propagate the motivation. The neurone where global activation, that derives from both localization and motivation, is maximum, becomes the goal for next action. Robots can thus retrieve the source location by following the motivation gradient (Fig. 2). Obviously, this kind of behavior is only possible when a source location is known. If that is not the case, the robot switches to the next behavior module. The next module is the imitation module, implemented in this initial model as a simple following imitation behavior, i.e. the robot is able to follow a peer's displacement. This behavior was possible when other robots were present in the field of perception. Lastly, the exploratory module carries out a random exploration of the environment. For more explanation about this model, see [START_REF] Ph | Impact of imitation on the dynamics of animat populations in a spatial cognition task[END_REF], [START_REF] Quoy | Dynamical neural networks for planning and low-level robot control[END_REF]. In this paper we present modifications concerning the imitation module only. As stated earlier, the imitation behavior was divided into three new natural needs called secondary needs. To be more precise, they are the acceptance need, the esteem for others need and the esteem by others need. These needs induce three new internal variables that, if they are not satisfied, decrease in time by the following dynamic:

V i t+1 = V i t .(1 -α) (1)
Where V i is the i th secondary variable, and 0 < α < 1.

To each secondary variable corresponds a specific basic behavior hierarchically integrated into the overall architecture. As a result, they function at the same level as the others, such as obstacle avoidance or random exploration.

In addition, an external signature has been added in order to model emotional expression. This signal can be perceived by the others agents so as to modulate imitation events within the whole population by giving a new target selection criterion for imitation.

A. The emotional signature

As already explained, the emotional signature expresses the current state and the expected state of the agent. Therefore, the motivational state that constitutes the expected satisfaction is also expressed in this signature. An agent in its comfort area displays a neutral signature whereas an internal variable below a certain threshold induces pain. That pain will cause a potential empathic response that is likely to incite another agent to move toward a known source. On the other hand, a motivated agent is likely to provoke an attractive empathic response. Indeed, the fact that making a decision about the action to perform depends upon the motivation, renders attractive the perception of the motivation with empathy. Consequently, keeping a motivated agent in its own field of perception becomes a source of motivation. This kind of reasoning leads to the selection of the imitation target according to its motivated state. We posit here that a motivated agent is thus more attractive than a satisfied one and that an marked lack of satisfaction induces pain. This signature expresses the self-appraisal of an agent, according to the following rule:

S =            50 if ∀i, V i > s 50 * (1 + M α ) -(V 4 + V 5 )/4 si M > KB min i {V i } else (2)
Where S is the agent signature, 0 < M < 1 its motivation V i is the i th internal variable, KB a noise constant, and α serves only to enhance the contrast. To be more precise, when several source locations propagate motivation, the one with the lowest internal variable provokes the highest motivation. Consequently, it is the only one that influences the selection of the action.

B. The acceptance need

This natural inclination has been interpreted as a gregarious instinct. It can also be perceived as the outcome of a social learning process produced by the combination of past satisfaction obtained with the help of a peer or by the empathic propagation of another satisfaction. Indeed, the empathic response to the perception of obtaining a reward also induces satisfaction in the observer. In fact, we make here the hypothesis that an innate empathic capability can serve as a kind of catalyst of social attraction. Empathy induces an association between satisfaction and the presence of others. This presence is considered so necessary to social satisfaction that it could be modelled as a need in itself. The association between a pleasure and a location is a well known result. The conditioned place preference technique is commonly used in ethology to illustrate this mechanism. Therefore, the sources that increase the associated internal variable are locations where a high density of population is perceived. An agent can thus aim for these meeting places by using its goal-directed navigation capability. In other words, the learned meeting location also propagates motivation through the motivational neural layer in order to guide the action selection. Moreover, the variable is set at its highest level each time the number of agents perceived reaches a percentage (70%) of the expected number, as initially known when the meeting place was first learned.

C. The esteem for others need

Here our hypothesis is that an imitation event is only possible if the imitator's signature is lower than the demonstrator's one. When several agents have a higher signature, the one with the highest is chosen as demonstrator. This decision mechanism is consistent with the fact that the global action selection criterion is the level of motivation. Following the agent with the strongest motivation will produce the highest motivated state, induced by the empathic response of the imitator. In this case, using this criterion to make a decision is equivalent to considering the influence of empathy. The corresponding internal variable is increased when an imitation leads to satisfaction, i.e. when an agent reaches a source by following another during a fixed number of time step.

Lastly, the fact that the motivational state is perceived, can be related to the other studies mentioned in the introduction, where the motivation is a distance to the goal. This kind of perception does not constitute a perception of intention but the perception that an agent intends to do something and of how distant from its goal it is. Perceiving how far the demonstrator is from the goal will help to decrease the number of possible goals of an observed action.

D. The need for esteem by others

This need has been interpreted as the need to be imitated. As with the previous need, action selection follows motivation intensity through empathy. The pain or the need, felt by an observed agent, activates the observer's motivational neural layer with the result that it moves toward one of its known sources. That is to say, the lower the emotional signature, the more it impacts on the internal state of the others. This impact will generate the observer agent's motivation; therefore, the more an agent is in difficulty, the more it is attractive. In short, internal primary variables decrease by the difference between the neutral value and the value of the signature of the agent feeling pain. Consequently, the decrease in primary variables induces motivation for the observer. This primary motivation has priority in the hierarchy of needs, but only in the presence of the agent in pain. Should this agent disappear, the motivation falls and the move toward the source stops. The reduction of variables is modulated by a parameter that can be regarded as the self-regulation process of empathy described by Decety in [START_REF] Decety | A social-neuroscience perspective on empathy[END_REF]. An agent considers himself as imitated when another agent is behind him, that is to say, perceived with an azimuth higher than π/2, during a fixed number of consecutive time step. In order to reduce the average number of displacements, a new basic behaviour implanted in the robots is to wait. It is linked to the esteem by others need and is used when an agent is not attractive enough to be imitated by the agent in the field of perception. As for the dynamic aspect of the resource needed, an agent does not increase the probability of its meeting another agent by moving. Owing to the acceptance need, it is likely to be located at a meeting place. The likelihood of meeting is improved by his waiting there. This is a passive response to the need for esteem. Moreover, this passive response maintains the synchrony between the imitator and the demonstrator. If the imitator gets too far from the demonstrator it has to wait since its motivation falls immediately.

Lastly, the satisfaction of the esteem for others need occurs when a source is reached. But in this case, this satisfaction comes from the empathic response to the agent's reward. The demonstrator associates this empathic satisfaction with its perception of the fact that it has been imitated. In other words, this mechanism implies the perception of being imitated. This phenomenon must also be incorporated into the set of minimal properties for the implementation of such a model.

E. Conclusion

Expressing such behaviors in the form of needs presents many advantages. Although at this stage the implementation is very simple, it offers the possibility of evolving towards social learning by extending the current neural layers. Such an implementation could make the association between signals that are the most relevant for efficient social interactions. But here our main objective is to propose a global synthesis of recent neuroscientific research in the form of a minimal set of biology-inspired properties. Moreover, the aim of this paper is also to facilitate the global integration of these properties. The next part will show that it enhances the efficiency of exploration by a population of autonomous robots. Lastly it should be emphasised that all the changes presented here have little influence on the overall computational complexity. Indeed, to a large extent they make use of the existing navigation mechanisms.

IV. RESULTS AND COMPARISON WITH THE INITIAL MODEL

A. Simulations

The results presented here have been obtained by means of computer-generated simulations. The simulator used (Fig. 4) relies on a client server architecture. The server constitutes the environment and agents are clients. The server has been implemented in java whereas agents are C programs. They communicate thanks to tcp connections that allows simulations to run on a parallel architecture, in other words, the server and the agents can run on different computers. The most recent version of the simulator could enable simulations with at least thousands of agents in a reasonable time.

To give a more precise description, this a two dimensional environment divided into squares. A map can be endowed with sources, obstacles and landmarks. The size of the perception field of every agent is a parameter. They can thus perceive another agent or a source if they are located in their neighborhood contrary to landmarks. Landmarks are perceived from a large distance except if there is an obstacle between them and the agent. That the reason why the localization system relies on them. In a real robotic context, the visual process must be able to detect these landmarks on its own, but here we assume this is already performed. The architecture use a synchronous communication protocol. At each simulation time step, the java server send to every agent a message that contains the set of perceptions corresponding to its position. To enhance the simulation speed, these perceptions are calculated in advance for each square. They are composed of a set of perceived landmarks, obstacles and source associated each with the angle made with a virtual north used as a reference. These data are completed with the set of the others agents located in the perception scope, associated with their emotional signature and their angle with the north. These sets of localized informations are the only data used by the agents. As described in previous section, the azimuth of the landmarks are sufficient to generate a cognitive map of the environment in the shape of a graph. The global decision process produced an elected action that is sent back to the server. As this is a synchronous protocol, the server wait all the agents have sent their action message before sending next perceptions messages. Once the server received all the actions, it displays the new positions, computes the agents perceived from each position and then send the next perceptions.

To complete the description, it can be added that, first, dynamic sources are also managed by the server. A source can thus have a limited capacity and disappear once it is empty. The server then generate a new one at a randomly chosen location. This kind of simulations emphasizes how an organization already shaped can accomplish the exploration task, and how it adapts to the new locations. But, the results presented here are not concerned with this property. Second, it is also possible to view an agent cognitive map and its activity through a GUI.

The outcomes of a simulations are log files that allow to complete a visual appraisal of the global behavior of the population (individual motivational states are also displayed through agents color). These files contain the internal states of every agent at each simulation time step. The results presented here are based on the analyze of them.

The analysis of the simulations seeks to illustrate the reliability and adaptability of the model. Therefore, it only shows the survival rate and the amount of movement in different types of situation. These results are then compared with two other kinds of agent: reactive and initial. Reactive agents are endowed with navigation abilities but with no imitation behavior. Initial agents constitute the starting point of our study. Their imitation behavior is not a need but rather a basic behavior of integrated into a subsumption architecture. This basic behavior in particular enhanced the survival rate of a population of agents with great adaptability and scalability [START_REF] Ph | Impact of imitation on the dynamics of animat populations in a spatial cognition task[END_REF]. Agents following the model presented in this paper are called Maslow agents. In addition, the field of perception was given a very low value. Results presented here only aimed to validate the Maslow model, but don't constitute a detailed analysis of the resulting selforganization. However, they prove a real improvement in cooperation.

B. Survival rate

Maslow agents were tested with a different density of sources and a different density of populations. II) showed a real enhancement of the global survival rate even with a very small population of five agents wherein communications are not frequent. Conversely, a high density of agents isn't a problem despite the number of potential meeting locations become high. In fact, the number of meeting location and its dynamic will the point that we'll focuse on. It constitutes a crucial point concerning the global resulting organization shape. Simple modifications seem to produce an interesting variability in outcoming organization. At present, the model described here strives for a centralized organization, but a more precise study is in progress. Obviously reactive agents are not impacted by the population size since there is no interactions between them. A significant gain in average movement (table III and table IV) of between 20% and 40% depending on the situation was observed. In addition, the model showed good adaptation abilities since this gain increased with the population density. This is consistent with the fact that a smaller proportion of the population is needed to explore the environment. More precisely, the observed phennomenon is an increase of the number of waiting situations since the primary needs are quickly satisfied. Waitings produce clustering of agents and are the mechanism that contribute to keep a meeting point alive. Thus agents arriving in one of these locations have, first, a higher probability to learn this place as a meeting point, and second, are quickly teached by the waiting agents. The waiting basic behavior strongly impacts the organizational dynamic by reinforcing the locations where interactions have a high likelihood to happend. Moreover this behavior reduces the use of power in a robotic context.

C. Quantity of movements

D. Diffusion of information in terms of density of population

Lastly, the collective level of knowledge was taken into account. To this end, the percentage of the population that knew all the sources in the environment was measured and its evolution compared for different population densities.

Knowledge propagation increases with the density of population. Despite the impact of density, communication This frequency depends greatly on the social needs that are settable. Future study may lead to the optimisation of different social parameters depending on the situation, knowing that high communication frequency reduces exploration but increase the information diffusion.

V. CONCLUSIONS AND FUTURE WORKS

Based on a synthesis of different recent research projects dealing with the study of emotions and imitation, we have proposed a holistic approach to the implementation of imitation in autonomous agents. The tests we conducted show that our modelling approach, which uses recent advances in neuroscience, has successfully increased the robot cooperation efficiency. Our architecture permits a simple and scalable model of agent. These developments should prove usefull in applications such as swarm piloting, data mining or ad-hoc networks. Some organizational analysis is presently being carried out to determine the optimal parameters for a given situation and the different shapes of resulting organizations. A real robotic implementation is currently also in progress in order to validate the model's reliability in real constraints.

Fig. 1 .

 1 Fig. 1. Maslow's Pyramid of needs

Fig. 2 .

 2 Fig.2. The goal-oriented navigation model[START_REF] Quoy | Dynamical neural networks for planning and low-level robot control[END_REF]

Fig. 3 .

 3 Fig. 3. The behavioral architecture

Fig. 4 .

 4 Fig. 4. The simulator

Fig. 5 .

 5 Fig. 5. Diffusion of information function of density of population

TABLE III QUANTITY

 III OF MOVEMENTS IN AN ENVIRONMENT WITH 3 SOURCES(PIXELS PER TIME STEP)

	Type		Size of population
	of agents 5	10	30	100
	Ractives	355	365	369	399
	Initials	357	358	367	388
	Maslow	317	289	254	245