Alexandre Chapoulie

Patrick Rives

David Filliat
email: david.filliat@ensta-paristech.fr

Topological segmentation of indoors/outdoors sequences of spherical views

Topological navigation consists for a robot in navigating in a topological graph which nodes are topological places. Either for indoor or outdoor environments, segmentation into topological places is a challenging issue. In this paper, we propose a common approach for indoor and outdoor environment segmentation without elaborating a complete topological navigation system. The approach is novel in that environment sensing is performed using spherical images. Environment structure estimation is performed by a global structure descriptor specially adapted to the spherical representation. This descriptor is processed by a custom designed algorithm which detects change-points defining the segmentation between topological places.

I. INTRODUCTION

Navigation is a challenging task allowing a mobile robot to move in its environment. Topological navigation consists in navigating in a topological graph in which topological places are linked by edges representing accessibility. Topological navigation is part of a larger hierarchical scene representation made up of: metric, topological and semantic. Metric and topological approaches are developed for example in [START_REF] Courbon | Autonomous navigation of vehicles from a visual memory using a generic camera model[END_REF] using perspective images visual memory. Recently, methods such as [START_REF] Meilland | Dense visual mapping of large scale environments for real-time localisation[END_REF] or Google Street View [START_REF] Vincent | Taking online maps down to street level[END_REF] use a more generic approach based on spherical images visual memory. Semantic level corresponds to place labelling as proposed by [START_REF] Ranganathan | PLISS: Detecting and Labeling Places Using Online Change-Point Detection[END_REF] and [START_REF] Wu | Visual place categorization: Problem, dataset, and algorithm[END_REF] for localization and labeling.

Topological mapping process aims to segment the environment creating topological places linked in the topological graph. First approaches were made using Hidden Markov Model (HMM) and Partially Observable Markov Decision Process (POMDP) based on the Baum-Welch algorithm. The authors in [START_REF] Koenig | Unsupervised learning of probabilistic models for robot navigation[END_REF] show good results in a simulated environment. In [START_REF] Shatkay | Learning topological maps with weak local odometric information[END_REF], odometry is used for environment sensing. Despite the consistent topological map produced, those algorithms present main limitations due to offline map computation and computation time rapidly increasing with the amount of data. The approach in [START_REF] Tapus | Incremental Robot Mapping with Fingerprints of Places[END_REF] uses POMDP for map update but comparison between places is done using an efficient fingerprinting system providing an online algorithm. An alternative to these greedy algorithms is the use of graph cuts based on the spectral clustering algorithm. The paradigm of graph cut based algorithms consists in creating basic graphs in which nodes will be clustered by cutting edges of minimal energies. O.Booij et al. [START_REF] Zivkovic | From images to rooms[END_REF] proposed an energy function based on the number of edges linked to each node. Cuts will be performed on narrow paths, like doors, which involves very specific environments. The authors in [START_REF] Blanco | Subjective local maps for hybrid metric-topological SLAM[END_REF] based their energy function on a novel concept: the sensed space overlap. The sensed space overlap are the features commonly viewed from various nodes. The more the features are seen by two nodes, the higher the edge weight between these two nodes. CovGraph is a quite similar concept used in [START_REF] Martín | Less-mapping: Online environment segmentation based on spectral mapping[END_REF]. In [START_REF] Zivkovic | Hierarchical map building using visual landmarks and geometric constraints[END_REF], edges weights are determined by a similarity measure between local features (SIFT features [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF]) extracted from images. While the methods do not depend any more on narrow paths for clustering, they depend on the robot ability to sense the environment and match features together. Change-point detection is a well known technique used in video segmentation for surprising event detection. This technique relies on various theories such as CUSUM used in [START_REF] Tsechpenakis | Robust online change-point detection in video sequences[END_REF] or the Shannon's information theory as in [START_REF] Itti | A principled approach to detecting surprising events in video[END_REF]. While having been used in video for many years it has only been recently applied to environment topological segmentation. Work is due to the authors in [START_REF] Ranganathan | PLISS: Detecting and Labeling Places Using Online Change-Point Detection[END_REF] and [START_REF] Ranganathan | Bayesian surprise and landmark detection[END_REF]. Changepoint detection paradigm is detecting surprising events in environments modelled by probability parameters or distributions. The brought up matter is the modelling of the environment probabilities. Proposed solution in those papers tackles the problem modelling the environment parameters with the multivariate polya model. It is included in a Bayes inferring system using survival analysis for change-point detection. Main purpose in [START_REF] Ranganathan | PLISS: Detecting and Labeling Places Using Online Change-Point Detection[END_REF] is not topological map construction but place recognition, which can be considered as loop closure detection without labelling. The algorithm is used to create topological maps in [START_REF] Ranganathan | Bayesian surprise and landmark detection[END_REF].

Despite the algorithm used for topological mapping, the way the space is sensed and represented is of major importance. Various data from multiple sensors are used like odometry in [START_REF] Shatkay | Learning topological maps with weak local odometric information[END_REF], laser scans and vision in [START_REF] Tapus | Incremental Robot Mapping with Fingerprints of Places[END_REF] and [START_REF] Ranganathan | Bayesian surprise and landmark detection[END_REF] or purely vision in [START_REF] Zivkovic | Hierarchical map building using visual landmarks and geometric constraints[END_REF]. Vision presents the advantage over all other sensors to be very informative. Topological mapping based on images allows segmentation taking into account a great amount of information about the environment. Spherical representation is even richer than perspective representation. Spherical images allow information capture from the whole surrounding environment and then produce information independent from the orientation of the robot.

[10] and [START_REF] Vincent | Taking online maps down to street level[END_REF] are some papers illustrating the effectiveness of the representation.

Contributions

All previously presented algorithms are designed for indoor topological mapping exploiting various type of data extracted from the environment. We seek for a generic approach of topological mapping in indoor and outdoor environments. In this paper, we aim to give an appropriate and generic definition of a topological place. It is a place whose structure parameters do not vary too much. Then, while navigating in the same topological place, the structure parameters extracted from the perceived environment are almost constant. Environment structure parameters are textures, appearance frequency of straight lines, orientation of the straight lines, curvatures, repeated patterns. The main advantage of this definition is that it fits to indoor and outdoor environments. The commonly used definition of rooms and corridors only fits to indoor environments. Given this proper definition, we need to estimate environment structure parameters and detect changes in them. Structure parameters are estimated using an adapted global descriptor called GIST [START_REF] Oliva | Modeling the shape of the scene: A holistic representation of the spatial envelope[END_REF]. As we use spherical representation of the environment, we adapted GIST to spherical images. Given our definition, GIST is much more adapted than other local descriptors like SIFT used in [START_REF] Ranganathan | Bayesian surprise and landmark detection[END_REF] and [START_REF] Zivkovic | Hierarchical map building using visual landmarks and geometric constraints[END_REF]. Local descriptors do not relate the whole environment structure consistency but just a subset of the environment without consistency. As they are not related to each other, local features lose the consistency unless we add geometrical constraint for example. Environment structure changes related by GIST variations will then define the transitions between the topological places. Spherical images presenting the same structure parameters are clustered together in a topological place. GIST changes are detected using a change-point detection algorithm designed to run online and in constant time. The approach specificities lie on the use of the environment spherical representation, environment structure extraction descriptor GIST adapted to the spherical representation and Neyman-Pearson lemma based change-point detection algorithm. Due to the definition of topological places used here and hence the information extracted from images, a room can be composed of different places depending on the robot movement. Being in an open space and moving close to a cluttered space will lead to two topological places as a surprising event will rise from the variation of the perceived environment structure.

Section 2 presents the redesigned image processing algorithm for the GIST computation. Section 3 describes our change-point detection algorithm. Experimental results for indoor and outdoor environments are provided in section 4. The proposed method is discussed in section 5.

II. ENVIRONMENT DATA EXTRACTION

Images are acquired by an omnidirectional camera for the indoor environment and a multi camera system [START_REF] Meilland | A Spherical Robot-Centered Representation for Urban Navigation[END_REF] for the outdoor environment. They are an approximation of a spherical imaging system. Spherical images allow a registration of the whole surrounding environment. Information extracted from the image are independent from the robot orientation. Our omnidirectional camera however is not a spherical imaging system and our images are mostly half spheres. The approximation is sufficient for mobile robots which evolve on ground and rotate only around the upward axis.

A. A Scene Global Descriptor: GIST

Proposed by A. Oliva and A. Torralba in [START_REF] Oliva | Modeling the shape of the scene: A holistic representation of the spatial envelope[END_REF] and [START_REF] Oliva | Building the gist of a scene: the role of global image features in recognition[END_REF], the GIST is a global descriptor of a scene depicted by an image. Given the observation that humans are able to classify images at a glance under properties of openness, expansion, naturalness and roughness [START_REF] Oliva | Building the gist of a scene: the role of global image features in recognition[END_REF], they analyse how images are understood by humans in order to create an automatic classifier. The study reveals that humans are receptive to what they call the spatial envelope of the scene. The spatial envelope is the set of spatial frequencies the image is made up of. The 2D Fast Fourier Transform (FFT) is applied to the images to obtain the spatial frequencies. As expected, similar places present an equivalent 2D FFT amplitude pattern, i.e same frequencies and orientations. The GIST is simply a registration of the frequencies and orientations of the downsampled image FFT amplitude pattern into a vector. Frequencies and orientations registration is performed by applying Gabor filters. Dimension reduction is sometimes performed using Principal Component Analysis (PCA).

While they are able to create a machine learning based automatic classifier along the dimensions they definedopenness, expansion, naturalness and roughness-, we are mostly interested by the property of the spatial envelope which is a descriptor of the scene structure. So, a topological place change while navigating will result in a spatial envelope change. Our algorithm is based on this observation and tries to detect those variations in the spatial envelope along the path followed by a robot.

B. GIST on Spherical Images

Our images are projected onto panoramic images for an easiest computation and visualisation but they still are considered as spherical images and they offer more properties than panoramic images. On spherical images there exists spatial periodicity from any point onto the sphere and in any direction. With panoramic images, we lost a part of the periodicity but we preserve horizontal spatial periodicity. It is enough for the sphere approximation used in this study. Original GIST was designed to be computed on perspective images and are here applied to panoramic images. 2D FFT is then computed on the panoramic images. A solution to overcome those drawbacks is to use a better spherical representation with FFT adapted to the representation as presented in [START_REF] Górski | Healpix: A framework for highresolution discretization and fast analysis of data distributed on the sphere[END_REF]. As FFT automatically consider periodic signals, the original GIST computation is done by zero-padding the image to eliminate periodicity consideration along each dimension. In our case, we removed the zero-padding system along the image horizontal axis but keep it along the vertical one because of horizontal spatial periodicity conservation. The 2D FFT amplitude pattern of the panoramic image is multiplied by the 2D FFT amplitude patterns of Gabor filters extracting the structure of the environment under the frequencies and orientations studied. Then, we need to establish the frequencies and orientations of interest to detect spatial envelope variations. Given the various 2D FFT amplitude patterns of our images, we choose to study 3 frequency scales -low, medium and high-along 6 orientations -0 • to 150 • by step of 30 • -. The Gabor filters 2D FFT amplitude patterns used are shown in Figure 1. The original GIST computation system registers the 2D FFT image amplitude pattern response to each Gabor filter by downsampling the response and stacking each value into a vector. This leads to a descriptor size S D = N f .N o .N c .N s with N f the number of frequencies, N o the number of orientations, N c the number of color channels and N s the size of the downsampled 2D FFT filtered image amplitude pattern. The size of the descriptor is of a few hundreds dimensions. For spatial envelope variation detection, a very downsized version of the descriptor is far enough. Instead of downsampling the 2D FFT filtered image amplitude pattern and stacking each value, we integrate all the values over the 2D FFT amplitude pattern size. We only get one response value per Gabor filter. Moreover, we work with grayscale images which reduce the descriptor size by a factor 3. The resulting size of our GIST descriptor is S D = N f .N o . In our case, the descriptor size is 18 and is sufficient to detect environment structure changes.

III. CHANGE-POINT DETECTION ALGORITHM

A. Change-point Detection Theory

Change-point detection is based on hypothesis testing. Assertions are made about parameters of the process we want to observe. Null hypothesis H 0 is the normal situation in which the observed parameters stick to the assertions. Alternate hypothesis H 1 is the abnormal situation where parameters vary from the assertions. Change-point detection algorithm evaluates the monitored parameters and determines when there is a switch from hypothesis H 0 to hypothesis H 1 . For online implementations, it is important to detect precisely the instant when the change-point occurs. For offline processes, the whole signal can be treated to detect change-points. For online processes, data are presented serially and its harder to detect exact change-point instants. The raised alarm instant is the moment when the monitoring process raises an alarm indicating a switch from hypothesis H 0 . The alarm instant is greater than the change-point instant. The change-point is then applied at the alarm instant because the delay between the two instants is unknown.

1) Neyman-Pearson Lemma:

Assume that the input observations X 1 , ..., X τ -1 are independent random variables with a probability density function f 0 (X i ), while the observations X τ , ... are independent random variables with a probability density function f 1 (X i ). Let's assume that f 0 is the probability density function under hypothesis H 0 and f 1 under H 1 . Suppose we have X 1 , ..., X n observations up to an instance n and we test the above hypotheses for these observations. The likelihood ratio (equation 1) indicates whether the value X i mostly belongs to f 1 or f 0 .

s i = ln f 1 (X i ) f 0 (X i ) (1)
The Neyman-Pearson lemma conducting a simple hypothesis test define the uniformly most powerful test as the one rejecting the null hypothesis H 0 whenever:

S n τ = n j=τ ln f 1 (X i ) f 0 (X i ) = n j=τ s j > ν (2)
The above equation yields to the simple hypothesis test:

T c = min{n : max 0≤τ ≤n n j=τ ln f 1 (X i ) f 0 (X i ) > ν} (3)
where T c is the instant at which the change-point is detected and ν the threshold controlling the detection sensitivity. The lower the threshold, the greater detected change-points number. max 0≤τ ≤n n j=τ ln f1(Xi) f0(Xi) > ν gives the instant τ giving the maximum of dissimilarity between f 0 and f 1 . n being the current instant, T c will be either n leading to no change-point detection or τ which is the exact change-point instant. This algorithm gives the exact change-point instants whereas it needs a delay to evaluate the probability density function f 1 . The computation time is very low for a small n but increases rapidly with the number of observations. No assertions are done concerning H 0 and the probability density functions f 0 and f 1 always need to be estimated for all the change-point τ tested over all observations.

2) CUSUM approach: The CUSUM approach can be considered as a slight derivation of the Neyman-Pearson. The new equation

D n = max{0 : D n-1 + ln f 1 (X i ) f 0 (X i ) } with D 0 = 0 (4)
presents the advantage to be evaluated iteratively and in constant time. Detecting if a change-point occurs is simply done by comparing the current value to the defined threshold:

D n > ν (5)
The main drawback of this approach is when the value is above the threshold, we get the alarm instant and there is no way to get the exact change-point instant. As we want to detect structure changes while we are navigating in an environment, we cannot afford this inaccuracy.

B. Kalman Filtering and Neyman-Pearson Lemma in an Online Detection Algorithm

1) Data Observations and Assumptions:

The algorithm is applied on multidimensional data as each of the 18 dimensions of the GIST vector are treated individually. Sample signals are shown in Figure 2. Main variations observed should correspond to significant changes in the structure of the environment. In order to treat those signals, we need to establish an evolution model. We assume that the data follow a normal distribution. This means that the value of the data in each dimension is represented by the mean and a standard deviation representing the signal noise. Moreover, the signals are assumed to be independent. Assume that µ 0 is the mean of X 1 , ..., X τ and µ 1 the mean of X τ +1 , ..., X n . µ 0 describes the topological place we are leaving while µ 1 describes the topological place we are entering. τ is the instant and location of the topological place change. Considering the normal distribution of f 0 and f 1 with a constant measure noise σ, the uniformly most powerful test becomes

S n τ = (n -τ + 1)(µ 1 -µ 0 ) 2 2σ 2 (6)
This equation mainly describes the detection of a mean shift (µ 1µ 0 ) 2 as almost the remaining terms are constants. τ has no real importance in the equation as the tested τ defines the observations on which µ 0 and µ 1 are estimated. Given this observation, the described algorithm aims to detect the mean shifts characterizing the topological place changes.

2) GIST variation detection: State estimation is performed using a very simple discrete Kalman model with no control input. The state is measured in a sliding window and modelled as

x n = [µ 0,1 , ..., µ 0,18 , µ 1,1 , ..., µ 1,18 ] t (7)
where µ 0,i are the mean computed along each dimension in the first half of the sliding window and µ 1,i the mean in the second half. The Kalman model of the system is:

x n = x n-1 + w y n = x n + v (8)
k i is simply the difference between the two means computed as k i = µ 0,iµ 1,i and is the expression of the mean shift. While navigating in the same topological place, the parameters are not supposed to change. µ 0,i and µ 1,i should remain constant. The transition state model is then defined with the identity matrix. w is the model error described by a Gaussian noise of null mean. w only comprises the standard deviation in each dimension. We use the value of 0.2 for all µ. v is the measure error described by a Gaussian noise of null mean. v contains the noise standard deviations. Experimentation and observations led to the conclusion that the standard deviations vary between the frequency domains. The values are 2.4 for the low frequencies, 3.2 for medium frequencies and 3.6 for high frequencies and the thus for µ 0 , µ 1 . All noise standard deviations (w and v) are empirically estimated on a representative sample of signals. y n corresponds to the observed signals at time n and is the measured state with measure noise added. Kalman filtering (feedback with Kalman gain) is applied on the Kalman model to extract an estimated state xn with a minimum of variance. This system leads to two smoothed curved representing µ 0 and µ 1 . The two curves are finally simply the mean estimate spaced out by half of the sliding window size. As shown in Figure 3, the curves are mixed up when there is no changepoint and let appear a delay otherwise. k being the difference between the two curves let appear a peak proportional to the mean shift when there is a change-point. These peaks are then detected and compared with a threshold ν. If the value is greater than ν the peak defines structure change in the environment. The threshold directly impact the sensitivity of the algorithm and so the number of change-points detected.

The presented algorithm has the advantage to give the precise

IV. EXPERIMENTAL RESULTS

In the following experiments, the sliding window comprises 20 images and the threshold ν was set to 0.35.

As the algorithm is designed to run online, computation time is an important information about the process. All the algorithm is not optimally coded with Matlab. The GIST vector requires around 80ms to be computed. The changepoint detection takes less than 10ms most of the time, some peaks to 15ms are observed. The whole process takes around 100ms to detect change-points in the environment. Images can then be processed up to 10Hz which is sufficient for slowly moving robot because there will not be large displacements at high frame rates. An implementation in C++ will lead to a very effective real-time computation allowing online environment segmentation even on fast moving robot with a higher camera frame rate.

A. Indoor Environments

Indoor environments present a great advantage for topological places computation. Places are well defined by rooms and corridors and structure changes are then defined by doors. We tested our algorithm in an indoor environment to validate our approach. Found change-points are easy to compare with doors location. The indoor environment is the Kahn building in the INRIA Sophia-Antipolis research center. The ground plane is shown on Figure 4. The trajectory followed by our robot is overlaid in red on the ground plane. The trajectory starts at the bottom on the right and ends at the bottom on the left. The crosses are the change-points detected by the presented algorithm. Topological places are then defined between two crosses. The first cross is not a real change-point. The detection is due to movements very close to the camera during the robot initialization. Interestingly, we notice that none of the change-points are located at the door locations but are instead detected before and after door locations. This can be seen on images (406, 751) and (2446, 2731) on Figure 4. From the algorithm side, the door locations themselves are considered as topological places. While not intuitive at first sight, it is very meaningful because they are transitions and are very dissimilar with the environments of both sides. At the door locations, the images are mainly composed of the door uprights and the door itself. A small part comprises the environments from both sides. In terms of orientations and frequencies, the more significant components are orientations of 0 • , representing vertical edges, in the domain of high frequencies, relating strong edges (door uprights). The door itself is related by low frequencies in any orientation as they are texture-less in our experimentations. Before and after the door location, these orientations and frequencies are less significant because the doorstep represent a small part of the image. Before and after images are then characterized by orientations and frequencies peculiar to each environment type. Images (2731, 3421) and (4561, 5356) on Figure 4 shows that when the robot comes back on its path, change-points are detected on the same location. Here are examples when the robot enter offices, about-turns and leaves the offices. Moreover, images (2446, 4246) are very spatially close and look very similar. They correspond to images before entering the first office and after leaving it. These images demonstrate the stability of the detected change-points in the environment. Whatever the path followed by the robot, the change-points are detected on very close locations. Change-points are detected all along the path and some do not correspond to door locations. They are true change-points due to important variations in the perceived environment. Such change-points are illustrated by images 7636 and 7951 on Figure 4. In both images, we can see the same environment. However, the first image seems to describe a place with a lot of space available. The topological place defined between these two change-points is mostly related to this open space. Te second change-points describes a more cluttered place. While the same objects as in the previous change-point are present, we are closer to them. They are of more importance in the perceived environment and have a greater influence in the GIST vector. We then switch from an open space to a cluttered space. This demonstrate that the structure in the perceived environment is an important parameter for environment segmentation. Such kind of segmentation relates the closeness parameter and allows to describe how far away we are from some place. We had some illumination problems at the bottom on the left of the trajectory resulting in strong intensity variations in the images and even in unexploitable images. Finally, this seems to have a small impact on the topological places detection. The effects are additional change-points and change-points without exact location around the doors. Image 13201 on Figure 4 is an example of this kind of illumination issue. Disappearance of change-points is due to allowing true change-point detection if at least 6 dimensions converge to change-point detection. For each dimension taken separately, it is impossible to have change-point location variation due to threshold choice. Change-points are well localised in each signal and following the peak value compared to the threshold, they are considered as change-points or not. During the 6 dimensions convergence step, we impose a half sliding window distance between two detected change-points in order to avoid over segmentation and noise sensitivity. If a change-point is detected by lowering the threshold and its distance to the next detected change-point with a higher threshold is inferior to the half sliding window distance, the detected change-point with the higher threshold then disappears. Hopefully, we observe on Figure 5 that there is always black crosses close to the red crosses. This means that disappearing change-points with threshold 0.35 are replaced by very close change-points with threshold 0.25.

B. Outdoor Environments

The algorithm was also tested on outdoor environments to prove the validity of our topological place definition. Conversely to indoor environments, change-points are not as well defined as doors. The outdoor environment is the INRIA Sophia-Antipolis campus. A satellite view of the campus is shown in Figure 6. Like for the indoor environment, the trajectory followed by the robot is overlaid in red and the crosses are the detected change-points. The trajectory starts at the bottom and ends at the top of the image.

Images 109, 173 and 205 on Figure 6 show change-point detection while passing in front of a building. Image 109 is while entering the place in front of the building and image 205 is while leaving the place. We could think of a topological place defined between this two images but there is a change-point detected between them and represented by image 173. Determining topological places in outdoor environments is harder than in indoor environments. Nevertheless, this change-point is determined by structure change in the environment. In the first image, the place is mainly composed with the building, the small walls and vegetation. In the second image, the wall disappears and let just appear road. In terms of orientations and frequencies, the small wall is made of orientations of 90 • , representing horizontal edges, of high frequencies due to strong edges. The road corresponds to low frequencies in any orientation. The rest of the scene is unchanged. This switch of orientations and frequencies defines this change-point. Images 347 and 409 represents change-points while entering and leaving a parking. It can be seen from the satellite image that there is a lot of vegetation. Coming back to the purpose of GIST defined by A. Oliva and A. Torralba in [START_REF] Oliva | Modeling the shape of the scene: A holistic representation of the spatial envelope[END_REF], there is a switch from naturalness to human made environment for the first change-point and the inverse for the second one. The parking is a human made environment and it is surrounded by nature. The accessing roads are a small part of the environment in the places before and after the parking. Images 805 and 847 are detected change-points before and after passing under a bridge. While presenting different orientations, this example is very similar to the doorstep case in indoor environments. The images relate very dissimilar environments before and after the bridge. During this experimentation, strong glares -due to a low altitude of the sun in the sky-generate important vertical lines of light in the images. Examples are shown in images 409, 631 and 1049 on Figure 6. They sometimes enforce changepoint probability of occurrence by adding evidence to weak change-point detections, i.e. change-points detected in less than 6 dimensions. While this adds high vertical frequencies in the image, their impact on the detected change-points is hard to evaluate. In outdoor environments, it is very hard to evaluate the detected change-points correctness. While some seem to be intuitive like the bridge case or when passing in front of a building, other are very hard to justify. Images 631 and 651 are two detected change-points in front of a building. The first change-point is easy to explain as we are entering the zone in front of the building. The second change-point is hard to justify. We encountered strong glares in this part of the trajectory but we cannot advance that they are responsible of the change-point. Whereas not showed, the next changepoint is also hard to justify. We cannot say at first glance why there are change-points at these locations.

V. CONCLUSION

While indoor environments are studied in [START_REF] Koenig | Unsupervised learning of probabilistic models for robot navigation[END_REF], [START_REF] Shatkay | Learning topological maps with weak local odometric information[END_REF], [START_REF] Tapus | Incremental Robot Mapping with Fingerprints of Places[END_REF], [START_REF] Zivkovic | From images to rooms[END_REF], [START_REF] Blanco | Subjective local maps for hybrid metric-topological SLAM[END_REF], [START_REF] Martín | Less-mapping: Online environment segmentation based on spectral mapping[END_REF], [START_REF] Zivkovic | Hierarchical map building using visual landmarks and geometric constraints[END_REF] and [START_REF] Ranganathan | Bayesian surprise and landmark detection[END_REF], segmentation on outdoor environments has rarely been studied. Nevertheless, methods like [START_REF] Blanco | Subjective local maps for hybrid metric-topological SLAM[END_REF] and [START_REF] Martín | Less-mapping: Online environment segmentation based on spectral mapping[END_REF] do not restrict their algorithms to indoor environments and could be applied to outdoor environments if the sensed information can be employed. Structure parameters described by the GIST are a valuable representation used in a common approach for indoor and outdoor environments. One drawback of this approach is some sensitivity to illumination changes between the images. Normalisation steps are used and reduce the effects but they are still an issue which consequences are hard to evaluate. In terms of obtained topological maps, the closest results are presented in [START_REF] Martín | Less-mapping: Online environment segmentation based on spectral mapping[END_REF] while their method is based on the graph cuts. The approach described in this paper allows online environment segmentation into topological places using very low dimensional data. Approaches using features like SIFT ( [START_REF] Ranganathan | Bayesian surprise and landmark detection[END_REF], [START_REF] Zivkovic | Hierarchical map building using visual landmarks and geometric constraints[END_REF]) require more computation time due to an higher number of features of higher dimension. The presented approach is very efficient using a low dimensional GIST in an simple change-point detection algorithm. It can be easily enhanced to be used at higher frame rates for fast moving robots. Future work will focus on place labelling as GIST was originally designed to categorize environments using machine learning based algorithm. We will study how places are distinguishable and categorizable using our low dimensional GIST. It will allow to determine which orientations and which frequencies are characteristic of which kind of places. Considering possible labelling process and the change-point location robustness of our algorithm, we aim to integrate it in a larger framework of hierarchical SLAM. Metric level will be performed using [START_REF] Meilland | A Spherical Robot-Centered Representation for Urban Navigation[END_REF]. Topological navigation will be a combination of the presented work combined with [START_REF] Chapoulie | A spherical representation for efficient visual loop closing[END_REF]. Environment segmentation will allow loop closure detection on topological places instead of being performed on images. Loop closure detection will enhance the segmentation process performing place recognition. Already seen places will be inserted in the estimation process of change-point detection improving the change-point location accuracy when coming back to previous places. Semantic level will be based on the labelling ability of this work.

Fig. 1 .

 1 Fig. 1. The figure shows the 18 superimposed Fourier Transform amplitudes of the Gabor filters: 3 frequency scales and 6 orientations. The red colors are for the highest values while the blue colors are for the lowest ones.

Fig. 2 .

 2 Fig. 2. Sample signal at the top is of high frequency along orientation 0 • . Sample signal in the middle is of middle frequency along orientation 0 • . Sample signal at the bottom is of low frequency along orientation 30 • .

Fig. 3 .

 3 Fig. 3. Top graphic shows the sample signal of middle frequency in orientation 0 • in blue. The green curve is the state estimation in the first half of the sliding window. The red curve is the state estimation in the second half of the sliding window. The vertical lines are detected change-points. Bottom graphic shows the mean shift k. The red lines are the threshold used. Vertical lines are still the detected change-points when a peak is detected under or over the threshold.

Fig. 4 .

 4 Fig. 4. Kahn building -Indoor environment.

Figure 5

 5 Figure 5 shows the algorithm robustness to the threshold ν choice and change-points dependence only on environment structure. The tested thresholds are 0.6, 0.35 and 0.25. Blue crosses are detected change-points for the three thresholds. Green crosses are detected change-points for threshold 0.35

Fig. 5 .

 5 Fig. 5. Change-points stability over threshold ν.

Fig. 6 .

 6 Fig. 6. INRIA Campus -Outdoor environment.


Abdelhak Chatty
email: abdelhakchatty@ieee.org

Philippe Gaussier
email: gaussier@ensea.fr

Ilhem Kallel
email: ilhem.kallel@ieee.org

Philipe Laroque
email: laroque@u-cergy.fr

Adel M Alimi
email: adel.alimi@ieee.org

Adaptation Capability of Cognitive Map Improves Behaviors of Social Robots

In this paper, we study the impact of the cognitive map's adaptation in the context of multi-robot system. This map governs the emergence of non-trivial behaviors and structures at both individual and social levels. In particular, we show that adding a simple imitation and deposit behavior allows the cognitive robots to adapt themselves in unknown environment to solve different navigation tasks. We show that in our architecture the individual discoveries in each robot (i.e., goals) can have an effect at the population level, which induce then a new learning at the individual level and reciprocally, from the individual to the population level. We performed a series of experimentations with robots and simulated agents to validate our system.

I. INTRODUCTION

Emergent behavior is one of the main topics of research in the field of social robotics. For instance, in an unknown environment, interaction between robots can be based on stigmergy [START_REF] Holland | Stigmergy, self-organization, and sorting in collective robotics[END_REF] which means indirectly communicating through the environment changes. In this kind of environment, the memory is the environment itself, however we believe that the use of a cognitive map in each robot is essential when the robot cannot leave a physical trace. Therefore, our aim is to put on light the adaptive capability of a cognitive map to solve at the same time a navigation task and to solve a deposit problem. The cognitive map can help to lead the emergence of non-trivial structures and behaviors in a Cognitive multi-robot system (CMRS). Many models based on reactive agents/robots were proposed in this area. For example [START_REF] Deneubourg | The dynamics of collective sorting robot-like ants and ant-like robots[END_REF] has proposed a model relying on biologically plausible assumptions to account for the phenomenon of dead body deposit in ants. [START_REF] Gaussier | Avoiding the world model trap: An acting robot does not need to be so smart![END_REF] shows that acting on objects simplifies the reasoning needed by multi-robot systems and allows deposit of scattered objects. In [START_REF] Beckers | From local actions to global tasks: Stigmergy and collective robotics[END_REF] the authors studied the deposit system and sorting of colored frisbees by a multi-robot system. In [START_REF] Martinoli | Collective and cooperative group behaviours: Biologically inspired experiments in robotics[END_REF] the author studied the deposit of small cylinders by a group of agents. In comparison to these previous works, we propose a solution which is use of cognitive maps and local rules to allow our robots to develop different emergent behaviors. The remainder of this paper is organized as follows: section 2, describes the bio-inspired architecture of our cognitive map. Section 3 depicts the structure, building and the adaptive capability of the cognitive map. Section 4 describes the building of the emergent deposit system. We analyze in seection 5 how the robots self-organize in emergent structures. The last section concludes the paper.

II. THE BIO-INSPIRED ARCHITECTURE

Each robot in our cognitive multi-robot system is able to learn and to create its own cognitive map online, whose structure depends on their own experience and discovery of the environment in which they live, based on bio-inspired architecture. Starting from neurobiological hypotheses on the role of hippocampus in the spatial navigation, [START_REF] Muller | The hippocampus as a cognitive graph[END_REF] form a model of the cognitive map in the hippocampus representing the entire environment and not only the shortest paths to a given goal. The model proposed by [START_REF] Hasselmo | Hippocampal mechanisms for the context-dependent retrieval of episodes[END_REF] provides a complete neural architecture of the learning process and use of a cognitive map and the association with a mechanism of action selection. [START_REF] Martinet | Spatial Learning and Action Planning in a Prefrontal Cortical Network Model[END_REF] also propose a model of cognitive map in the prefrontal cortex, which is based on cortical columns. in the same ideas biologically inspired, several works [START_REF] O'keefe | The hippocampus as a cognitive map / John O'Keefe and Lynn Nadel[END_REF], [START_REF] Milford | Mapping a suburb with a single camera using a biologically inspired slam system[END_REF] brought to light special cells in the rats hippocampus that fire when the animal is at a precise location. These neurons have been called place cells (PC). We do not directly use them to navigate, plan or construct a map, we rather use neurons called transition cells (TC) [START_REF] Gaussier | From view cells and place cells to cognitive map learning: processing stages of the hippocampal system[END_REF]. This kind of cells are inspired by a neurobiological model of temporal sequences learning in the hippocampus [START_REF] Alvernhe | Different CA1 and CA3 representations of novel routes in a shortcut situation[END_REF], [START_REF] Lubenov | Hippocampal theta oscillations are travelling waves[END_REF], [START_REF] Smith | Hippocampal place cells, context, and episodic memory[END_REF]. A transition cell codes for a transition between two PCs successively winning the competition, respectively at time t and δt. The model [START_REF] Banquet | Spacetime, order and hierarchy in fronto-hippocamal system : A neural basis of personality[END_REF], which presents the role of the hippocampus, shows us the architectures grounding using the transitions between locations. The entorhinal cortex (EC) receives signals from associative cortical ranges and then it filters and merges this multimodal information in order to transfer it, on one hand to pyramidal cells (CA3), and on the other to the dentate gyrus (DG). The DG operates an eminence between the signals and puts together a temporal hierarchy which later on is retransmitted on CA3 cells. This temporal hierarchy allows CA3 to be aware of past events and put them in correspondence with present events, therefore behaving like an associative memory through stocking possible transitions between these events. The recognition of the ongoing sequence happens at the level of CA1 using EC and CA3 information. This information is then sent to the Subiculum to be processed, independently from the robots orientation, through the heads executive cells. It also departs to the prefrontal cortex (PRC) to serve the higher levels of cognitive processes.

III. THE COGNITIVE MULTI-ROBOT SYSTEM

Our interpretation of the bio-inspired model is presented in figure 1: the signals provided by EC are solely spatial and consistent with spatial cells activities. Spatial cells activities are calculated from visual information then submitted to a Winner-Take-All competition in order to only select the cell with the strongest response at a specific location. We will subsequently be speaking about the current location by indicating the spatial cell which has the highest activity at a given location. The temporal function at the level of DG is reduced to the mere memorization of past location. The acquired association at the level of CA3 is then the transition from a location to another aside from all information concerning the time put to carry out this transition. Once the association from the past location and the new one is learned, every new entry will reactivate the corresponding memory in the DG. During exploration of the environment, the cognitive map is gradually created when the robot moves from one place to another. The equations governing learning in the cognitive map are 1:

dW CC ij (t) dt = T (t).((γ-W CC ij ).X C i (t).X C j (t)-W CC ij (t).(λ1.X C j (t)-λ2)) (1)
T (t) is a binary signal (0 or 1) active when a transition is made (moving from one place to another). This signal controls the learning of recurrent connections W CC . γ is a parameter less than 1 regulating the distribution of motivation activity in the map. λ1 and λ2 are parameters of active and passive oblivion respectively on the recurrent connections. S(t) is a signal marking the satisfaction of a goal (for exemple the resources discovery). This signal controls the learning of synaptic connections between neurons in W M C motivations activity X M and neurons of the cognitive map of activity X C , where the equation is dW M C ij (t)/dt = S(t), f or i, j = arg max k,l (X C l (t).X M K (t)). After having explored the environment, the robots now are in a position to predict in each situation the locations directly reachable. During a change in winning locations, a neuromodulation signal is transmitted to point out that a transition has just taken place. The achieved transitions activity then resets back towards the PFC. In order to show the robustness of the cognitive map, we try to study initialy, the behavior of a cognitive multi-robot system, based on the same model, capable of learning several goals in unknown environment. Figure 2 presents the initial environment, which is composed by 2 sources (R1 and R2), 2 obstacles(O1 and O2) and 2 identical robots with a threshold of vigilance equal to 0.65 and a duration of the learning equal to 30 minutes. To create the PC, the robot takes, at each moment in time, a visual panorama of the surrounding environment. A monodirectional camera mounted on a pan system allows to make several shots. The views are processed to extract visual landmarks. After learning these landmarks, a visual code is created by combining all the landmarks of a panorama with their azimuth. This configuration serves as a code to PCs. Figure 3 shows that our cognitive robots are able to avoid the stable and dynamic obstacles, to navigate, to learn and to construct on-line and at the same time, their own cognitive map in a unknown environment. The shape of the cognitive map in figure 3, proves that its construction is related to the robot's own perception, that is why the different robots also learn the position of the 2 sources in different manner, and the number of the PCs is not the same (7 for the first robot, and 9 for the second with the same threshold of vigilance). The change in the environment (the moving obstacles and the increasing the size of the environment) allows us to show the adaptive capability of the cognitive map. Figure 4a shows the new environment.

Using previously parameters, figure 4b andc prove that the robots were able to adapt their own cognitive maps to learn the new environment throught adding a new PCs and TCs. This validates the robustness of the cognitive map because the change in the environment has not disturb the robots from learning about the new environment.

A. The selection of the shortest path

When discovering a source (food or water), the motivation associated with it (thirst or hunger) is associated with the cognitive map at the location where it was found. This motivation then spreads to the graph, indicating the shortest path to reach the source from whichever location known. We can therefore merge these motivation activities with the transition prediction activities coming from the hippocampus. The level of prediction of different transitions from the hippocampus is substantially the same. The activity derived from the cognitive map comes then to predetermine the transition choice among those that have been predicted, through selecting thereby the transition leading the fastest towards the target. A field of neurons gathers the information on the robots direction during its entire passage of a location. It provides therefore, at the exit of a location, the direction and the length of the trajectory performed at the location. This direction is considered to be the one which is required to perform the transition. During the selection of a particular transition in order to reach the target, we can replicate, in terms of direction, the motion associated which has already been learned during the discovery of the environment. Thus, the robots are able to reset from transition to another by taking the shortest path in order to reach its target. In practice, when the need for a given source arises, the drive triggers the activation of the appropriate goals and throught the cognitive map the appropriate TCs whose destination is the goal location. Figure 5 shows the difusion of the motivation activity of the two robots along the cognitive map combining transition prediction and motivation gives the recognized transition, and the action corresponding to this transition is selected until the TC whose origin codes the robots' actual location. The figure also shows the nearest path (dark blue) selected by the robots. Thus, we prove that the cognitive map aims to teach new positions of sources to the robots and evolve in a unknown environment. It allows robots to avoid planning problems before complete exploration of the environment. Moreover, it gives the same results as an ant algorithm [START_REF] Dorigo | Ant algorithms and stigmergy[END_REF] without the need to leave physical trace in the environment.

B. Imitation and cognitive map

We believe that several benefits can be expected from imitation capability, among which the possibility to share partial knowledge of the environment, source locations and so on. In particular, [START_REF] Laroque | Cognitive map plasticity and imitation strategies to improve individual and social behaviors of autonomous agents[END_REF] showed that adding an imitation capability can dramatically enhance the survival rate of a multi-agent system. To study the influence of the imitation, we add in our cognitive multi-robot system, a reactive robot which uses an imitation strategy based on the azimuth: if a single robot is visible, it becomes the chosen imitation target; if several robots are visible, then the chosen target is the one that is closest to the direction of the robot who trying to imitate. It is important to mention that the imitated robot is never aware of being imitated. Figure 6a shows the reactive robot (RR) tries to follow one of the cognitive robots (CR1,CR2) which are in navigation task. In the same figure, we see that the reactive robot is able to see the two robots and decides to follow the robot which is the nearest to its own direction. Figure 6b show that the reactive robot succeeded to found the first source with following CR2 and after CR1 (the trajectory of robots given by Figure 6 allows to explain more the individual and the population behavior of robots). Finally, figures 6c, d,e and f also prove that the imitation strategy allows the reactive robot to find the second source with the help of only CR2. In emergent collective systems, the behavior of an agent is important for the emergence of other behaviors that will help the whole system to solve a specific task. With the use of an imitation strategy we show that it is the system, which is based on the building of a cognitive map, that can help an agent to satisfy its motivations. Thus, adding a simple imitation strategy, to our cognitive architecture, allows the system of multi-robot to help the individual robot. Fig. 6. The influence of the imitation behavior in multi-robot system. The experiment is done with three robots in the same environment as in figure 2. RR: reactif robot, CR1 and CR2 the cognitive robots, R1 and R2 are the two resources. The figure is presented with chronological order. The trajectory of the robot shows that RR is able to find the two resources by imitating the trajectory of CR1 and CR2 (the dashed arrows in the trajectory of CR1 and CR2 present the imitated trajectory). The video is available in http://perso-etis.ensea.fr/neurocyber/Videos/Cognitive Multi-Robot System/Imitation CRs-RR

IV. THE BULDING OF EMERGENT DEPOSIT SYSTEM

To show the adaptive capability of our cognitive map, we add a simple behavior of deposit to our agents. In this part we will use a simulated cognitive multi-agent system (CMAS). The CMAS use the same architecture, rules of learning and the same cognitive properties as the cognitive multi-robot system. The CMAS are motivated by the simulation of three types of needs (hunger, thirst and stress). Each need can be satisfied by a corresponding source, namely food, water and nest, that can be found in the environment. The level of each type of need is internally represented by an essential variable, ei(t) whose value is in [0; 1] and varies with time as de i /dt = -α n e i (t) where, α n represents the decreasing rate of the essential variable. When a satisfaction level e i (t) falls bellow a given ST, the corresponding motivation is trigged so that the agent has to reach a sources allowing to satisfy his needs using their cognitive map. Thus, changing its value has an impact on the frequency of the visits to the sources: the higher α n , the more frequent the visits. If no sources of the corresponding type have been found by the agent, the level decreases to 0 and the agent dies. To maintain the satisfaction level of our CMAS, instead of navigation between the threeoriginal sources it is interesting if the accumulation of individual decisions gives birth of the creation of relevant resources. The localisation of resources is important because when agents achieve them easily, they can increase their average satisfaction level and optimize the planning time looking for satisfaction of their motivations. In situated cognition context we believe that stigmergy based on local rules can lead to create emergent structures allowing creation of relevant resources. For this reason, we describe generic local rules where there is a relationship between the number of taken and deposits of resources according to the number of agents perceived. The agent can indeed, tend to favour the location that contain other agents rather than empty regions to create new resources. Thus, the perception of local agents will control the rules of taken and deposits. The condition of taking is computed by P r (T aken) = exp -λN A : the agent wants different types of resources in the environment. Indeed, the probability that an agent wants to take some resources goods increase when he perceives that the source is less used by other agents. So, the more agents are near a source, the more the probability of taking decreases and vice versa. Where N A is the number of agents in the neighborhood, λ is a constant. Equation of deposits P r (Deposits) = (1 -exp -αNA ) * (1 -exp -βt ) describes the condition for deposits as follows: the agent wants more to deposit more when the place is frequented by other agents and when he is far from the original source conducted the transaction of taking, this favors the relevance of the location of resources deposited. The deposit operation is built on the concept of refueling : the agent puts in the resources that already exist. Where α, β are environmental factors, N A is the number of agents in the neighborhood and t is the time since the take

V. ANALYSIS OF EMERGENT STRUCTURES

We use the environment as shown in figure 7a at t= 0 where the original sources are scattered. The agents start to move randomly in the environment, with a limited range visual of perception that can restrict the ability of agents to perceive the environment (see figure7b). When passing on sources (Water, Nest and Food) an agent increases his level of satisfaction and executes the local rule of taking and transport a quantity from the associated product. The probability of taking increases when the agent does not detect other agents next to the sources. If the decision to transport some products is taken, the agent continues his travel. The probability of deposits increases when the agent detects other agents and he moves away from the original sources. This means that the locations chosen for deposit are often common to several agents. Once deposited, goods constitute a new resources (Depot water, Depot nest and Depot food) allowing others to increase their satisfaction level. Agents also have the possibility of refueling resources by adding products to them. This allows stability resources in relevant locations close to several agents to fight against loss, since during the refuelling the available products in the resources will increase. However, resources which are abandoned or poorly visited will eventually disappear since the amount of goods available will decrease rapidly. Figures 7c,d ande show the disappearance of isolated resources. When a planning agent tries to reach a previously known ressource and realizes that this ressource has disappeared, two things happen (see figure 8): (i) the agent dissociates the current PC from the formerlycorresponding resource, and (ii) it resets the motivation to 0. Since the PC does not fire any more when the agent feels the need for this resource, there are chances that the use of transitions leading to this place be progressively forgotten. Similarly, when a new, matching resource is discovered, the paths leading to the resource are rapidly reinforced, making the cognitive map evolve synchronously with the environment.

Figure 7e shows that the CMAS converges to a stable solution with a fixed number of resources in fixed places for more than 20000 time steps (see figure 7f). Here we note the emergence of stable large resources which in some cases emerge to create resources "villages" (narrow regions containing all 3 resources). Figure 9 shows that until 4500 steps of time, the number of resources is not stable. Obviously the average of the convergence time increases with the increase of the number of agents. The number of persistent resources varies between 0 and 8. However, from 40 agents, the average number of resources stabilized at 8 and the average of convergence time stabilized at 7500 time steps. For 10 agents, the emergent number of persistent resources is 0, this shows that the cooperation between agents is not successful in order to determine the relevant locations in the environment. The analysis of the agent's behavior was able to prove that a fixed number of resources can emerge in fixed positions while minimizing the number's resources and the convergence time. The adaptive cognitive map, allows the CMAS to create emerging resources in relevant places frequented by agents. Note that the agents were able to adapt their environment and created villages of resources, which consist of three types of resources (water Depot, nest Depot and food Depot). The average number of visits to resources (115) is more important than to the original sources (27), which shows that their location is more convaincing. The same behavior also allows to keep a fixed number of resources (here 6) and remove others located in irrelevant places without having to use thresholds to limit the number of resources nor to specify their locations. The adaptive capability of the cognitive map, allows cognitive agents to create an emergent structure which is the stable state for the whole multi-agent system allowing the optimization of planing. Based on the selection of the shortest path, table I shows that agents can optimize their planning time with the use of relevant resources. This leads to a higher average satisfaction level. We calculate the average satisfaction level (ASL) according to equation 2. These values show the performance of our CMAS to keep the agents in their comfort zone.

ASL = ( 1 3i ) * ∑ i=n i=1 (SL wateri + SL f oodi + SL nesti ) N ( 2
)
Where SL is the satisfaction level of sources, n is the number of iterations, N is the number of expiriments. It is important to note that the selection of the resources locations by agents is just an adaptive behavior that begins with an individual decision of an agent during the deposit operation and ends with the maintenance or deletion of this deposit by the entire population. In conclusion, we talk about an individual decisions leading to emerging collective structures. Based on adaptive cognitive map, this experiment allows our CMAS (i) to optimize the planning time of agents and the number of deposits thanks to the learning of the new places of resources, (ii) to improve the adaptive behavior and the level of satisfaction of agents and finally (iii) to leads a fixed number of deposits in fixed places by creation of relevant emergent structures.

VI. CONCLUSION

In this paper, we brought to light the adaptive capability of the cognitive map, based on bio-inspired model, that enables a multi-robot system to adapt in a unknown environment to solve the navigation task and the deposit problem. We suggested a set of experiments in real robots that show how each robot system is able to learn, adapt and create on-line a cognitive map and how this architecture allows the robots to learn various goals in unknown environments. We also show from experiments on real robots and on simulation that combining learning capabilities with simple rules of taking and deposits and a simple strategy of imitation has a positve feedback atindividual and population levels. As prospects, we are trying to develop the "awareness"of robots/agents in order to allow them to learn the emergent behaviors. In this case, the emergent behavior becomes a "voluntary" behavior. This means that agents could be aware of their own state in the environment. To achieve our goal, we are trying to use an internal observer (IO) [START_REF] Tani | An interpretation of the "self " from the dynamical systems perspective: A constructivist approach[END_REF] based on enactive approach [START_REF] Varela | Book review: The embodied mind: Cognitive science and human experience by f. varela, e. thompson and e. rosch[END_REF]. The IO should allow agents to detect, categorize and create new emergent rules.

Fig. 1 .

 1 Fig. 1. Model of hippocampo-cortical of the creation of the cognitive map

Fig. 2 .

 2 Fig. 2. The cognitive multi-robot system in unknown environment. The video is available in http://perso-etis.ensea.fr/neurocyber/Videos/Cognitive Multi-Robot System/CMRS

Fig. 3 .

 3 Fig. 3. Simplified view of the cognitive maps of the robots based on transition cells. (a) presents the cognitive map of the first robot and (b) presents the cognitive map of the second robot. The construction process is based on: place recognition using PCs, activation of one PC and delayed activation of another allows for transition prediction (green transition) and the need for sources (R1 and R2) triggers maximum motivation for a given goals.

Fig. 4 .

 4 Fig. 4. Cognitive map evolution induced by a changing environment where R1 and R2 are the sources.(a) presents the cognitive map of the first robot and (b) presents the cognitive map of the second robot.

Fig. 5 .

 5 Fig. 5. Diffusion of the motivation along the cognitive map. The robots were able to select the shorest path in order to reach their targets. A and b show how the first robot satisfy its motivations related respectively to the sources R1 and R2. C and d also show how the second robot satisfy its motivations related respectively to the same sources R1 and R2.

Fig. 7 .

 7 Fig. 7. The figure shows 3 sources Water,Nest and Food providing resources of 3 different kinds (W=Depot water, N=Depot nest and F=Depot food). The position of the original sources is fixed and they can't disappear from the environment. Through the individual deposit process of agents, resources emerge and become stable after a while. the video is available in http://persoetis.ensea.fr/neurocyber/Videos/Cognitive Multi-Robot System/CMAS

Fig. 8 .

 8 Fig. 8. The evolution of the cognitive map. The PC that encodes the warehouse through time is presented by a red circle and all the paths (TCs) frequented by the agent that lead to the warehouse are reinforced in the cognitive map. (a) The current PC and the TCs that encode and lead respectively to warehouse, (b) The disappearance of the warehouse leads to the dissociation of the PC and the motivation from the old warehouse place. After discovering a new warehouse, the agent acquires (learns) the new place (creation of a new PC) and the TCs that lead to this new place become reinforced. (c) The forgotten of the old place : After a while, the TCs, that lead to the old warehouse, disappear and the new ones become completely reniforced.

Fig. 9 .

 9 Fig. 9. The average of persistent resources and convergence time in our CMAS. We can see that the average number of resources and the average convergence time stabilized with 40 agents.

TABLE I OPTIMIZATION

 I OF PLANNING TIME UNTIL 20000 TIME STEPS

		Only 3 sources	sources+deposits
	Average Planning Time	1599.8 time steps	450 time steps
	Average Satisfaction Level	59.89	88.07

ACKNOWLEDGMENT

The authors would like to thank the financial support of the Tunisian General Direction of Scientific Research and Technological Renovation (DGRSRT), under the ARUB program 01/UR/11 02, the Institut Franc ¸ais de Tunisie, the INTERACT french project referenced ANR 09 CORD 014, the NEUROBOT french project referenced ANR-BLAN-SIMI2-L2-100617-13-01 and DIGITEO project AUTO EVAL.