P Boonyasopon

Andreas Riel

Wilhelm Uys

Louis Louw

S Tichkiewitch

N Du Preez

Automatic knowledge extraction from manufacturing research publications

Keywords: Knowledge Management, Decision making, Document Retrieval Technique

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Modern information technology provides access to a rapidly increasing amount of information sources inside and outside of organisational boundaries. Both in industry and academia the task of turning the vast amount of structured and unstructured information into useful and sustainable knowledge has become one of the biggest challenges, as knowledge is considered as a key to success in any organization. To face this challenge, knowledge management processes and tools aim at capturing and capitalizing on implicit and explicit organization knowledge residing in internal information sources such as people, databases and exchanged documents, as well as in external sources, most notably the internet.

Researchers are confronted with a very similar problem. Their access to publications is increasingly facilitated by internet and dedicated on-line data vaults. Currently deployed document retrieval techniques in related environments are mostly based on full-text search and categorization by title, keywords, abstract, or other specific parts of the whole documents. This approach is very limited and fails to take into account the actual content [START_REF] Riel | A Knowledge Mining Approach to Document Classification (Keynote paper)[END_REF]. Moreover, the process of categorization is usually done manually, which is time-consuming and error-prone.

The target of the research underlying this paper is to propose and conceive a knowledge mining system based on text mining that facilitates and supports researchers in finding relevant papers based on their actual interests. This paper presents a completely new approach to this target by the combination of two fundamentally different tools and algorithms for text mining and automatic topic identification. Section 2 explains the target in greater detail, section 3 introduces a particular text mining tool for automatic topic identification. Section 4 introduces a Wikipedia-based keyword extraction tool. Section 5 proposes a new approach to relating research papers using a combination of the two tools introduced in the previous sections. Section 6 briefly reports about a case study which is entirely based on CIRP publications. Finally, section 7 concludes this paper with an outlook on the next steps.

Target Description

The target of this research is to conceive a knowledge mining system that helps researchers capitalise, in a very efficient way, on knowledge hidden in existing research papers. It should help them find publications which are relevant to a particular paper. The interest of such a system is manifold. Firstly, it can help authors cite papers that are indeed related to their works. Secondly, it can help them discover relevant papers which they normally would not have looked for (e.g. papers from another domain). Thirdly, it can help them increase citation indices of their papers (by means of putting their papers into the system, and thereby making them available to be proposed as relevant papers to other authors). Many more useful specific applications can be envisaged [START_REF] Riel | A Knowledge Mining Approach to Document Classification (Keynote paper)[END_REF], but the authors considered the three abovementioned ones to provide key added value.

The system should use text mining and automatic topic identification to enable users discover the essential semantic elements in papers without having to read those. It is important to mention that the authors are researchers in the manufacturing, modern product development and innovation domains, and therefore can look at this subject from the user"s perspective only. The very first step was thus to do an extensive investigation in this field [START_REF] Uys | A Framework for Exploiting Electronic Documentation in Support of Innovation Processes[END_REF], and to select and procure appropriate tools. In a second step, a reference document corpus was specified.

Categorization by Automatic Topic Identification

One fundamental element of relating documents and of giving a basic idea of what documents are about is their categorization according to a defined set of topics. The targeted system should be able to automatically identify such topics.

Overview of CAT

The text mining tool CAT (Content Analysis Toolkit [START_REF] Www | [END_REF]) by Indutech (Pty) Ltd in South Africa [4] has been used as a point of departure in this research. The major capabilities of CAT are information extraction, clustering, concept linkage, and information visualization from electronic text documents. In particular the tool can automatically analyze and categorize a huge number of documents into different topics.

To use CAT, the user has to specify the files to be analyzed, indicate the number of expected topics to be extracted from the pool of documents, and define the number of times a word has to appear in order to be considered in the analysis (the minimum word frequency). One or more so-called "stop-lists", which specify words that have little or no semantic value, can be further selected or created to exclude such words from the analysis. Based on these inputs, CAT is able to automatically analyze all the documents provided. At the end of this process, CAT comes up with a results visualization as well as an Excel file, which essentially allows for the following operations:  Visualization of word clouds associated with identified topics. Each topic is also specified by the three most significant words associated with it.  Mapping each document to related topics.  Clustering documents based on their similarities.  Visualization of relationships among documents and topics.

Characteristics and Limitations of CAT

CAT is largely based on Latent Dirichlet Allocation (LDA), a well-proven and well-established algorithm for knowledge mining from unstructured document sources. As it is based on statistical modelling, it requires very huge text corpora to function correctly, and is thus computationally expensive.

Studies linked to this research confirmed that CAT has indeed a lot of functionalities that can help researchers retrieve explicit or tacit knowledge from collections of research papers [START_REF] Riel | A Knowledge Mining Approach to Document Classification (Keynote paper)[END_REF]. However, in the application for this specific purpose, CAT has certain limitations. The limitations considered as most important are the following: 1. CAT is based on a probabilistic model, which leads to the fact that the results of several analyses of a given document collection may differ more or less significantly from one another. This can present a serious problem in terms of the repeatability as well as of the assessment of the quality and the reliability of a specific analysis.

CAT does not support incremental analysis and document

fold-in operations. Therefore, whenever one or several new documents are added to the corpus, a complete analysis of the updated corpus has to be done. Apart from the fact that computation times for analyses are in the order of several hours for huge corpora, this limitation makes it impossible to determine the relevance of a new document with respect to an existing corpus and topic structure. 3. CAT does not support a fully unsupervised process. A considerable amount of expert knowledge is required especially for the assessment of the result quality. 4. CAT has been conceived for analyses of very huge document corpora. However, there are no specific rules that allow determining the minimum number of documents which should lead to optimal and reliable results. 5. From a semantic point of view, CAT does not use "stemming" techniques which provide a way of treating different declinations, singular and plural, prefixes etc. of a specific word as one single word. Also, compound words are not recognized by CAT as such.

A more detailed analysis of CAT, its use and its underlying algorithm has been published in [START_REF] Uys | A Framework for Exploiting Electronic Documentation in Support of Innovation Processes[END_REF] and [START_REF] Du Preez | Customised high-value document generation[END_REF].

Encyclopaedic Keyword Extraction

LDA and related approaches perform the document corpus analysis in two main steps:

1. Build a knowledge model of words contained in the document corpus. 2. Identify topics based on the model built. All the knowledge available for the essential topic identification process is thus derived from the document corpus, which implies both a limitation to semantic performance and a computationally complex task. The question is if it was possible to replace this step totally by capitalizing on some kind of existing body of semantic knowledge which grows independently of the document corpora submitted to the analysis. Ideally, this knowledge body would be available for different languages. In this context the idea came up that the required external knowledge body essentially represents encyclopaedic knowledge. The authors" subsequent research revealed that there is in fact a research community which has succeeded in using the digital encyclopaedia Wikipedia exactly for this purpose. Particularly interesting and relevant contributions from this community can be found in [START_REF] Coursey | Using Encyclopedic Knowledge for Automatic Topic Identification[END_REF] and [START_REF] Mihalcea | Wikify! Linking Documents to Encyclopedic Knowledge[END_REF].

Overview of Wikify

Basically, the published Wikipedia-based approaches use a tool called Wikify, which is an unsupervised system to automatically identify the semantically important encyclopaedic terms (including compound words and acronyms) in an input text, and to link them to Wikipedia articles [START_REF] Tichkiewitch | Virtual Research Lab: A New Way To Do Research[END_REF]. Currently its main application is the semantic annotation of webpages, however the fact that it makes available practically the whole semantic intelligence of Wikipedia, opens up a wide and yet largely unexploited field of applications.

Using Wikify for knowledge mining applications conceptually has the potential of completely replacing the step of building a semantic model of words, as it uses the inherent semantic model of Wikipedia. For the purpose of identifying semantically important words in a text, the quality of the articles corresponding to the identified words is not at all an issue. This is important, as often in Wikipedia, words are added without an explaining article but instead with a call for an article. Other articles exist but have not yet been reviewed by experts. It would at the same time provide a solution to issues that are highly problematic in LDA and related probabilistic semantic modelling approaches, such as compound words, polysemy, synonymy, and multi-language. Also, to eliminate totally insignificant words for the analysis, there is no need for stop-lists, which are languagespecific and prone to be incomplete and outdated.

Characteristics and Limitations of Wikify

As Wikipedia is a universal encyclopaedia, its knowledge model poses two fundamental challenges to the automatic identification of significant keywords in research publications from a particular domain: 1. Terms can only be identified as being significant if they are known to Wikipedia, which is not necessarily the case for terms of cutting-edge research. However, due to the unequalled speed of growth of Wikipedia, missing terms are likely to be added very rapidly. 2. Far more than the potentially lacking depth in a particular domain, the immense breadth of knowledge contained in Wikipedia definitely creates a big challenge for the targeted knowledge mining application: Wikify identifies keywords and phrases in a text as significant irrespectively of their relevance to a chosen domain. Although this can help reveal unexpected information and knowledge in specific documents, it primarily leads to a high amount of keywords related to general knowledge and thus renders the analysis of domain-specific keywords more difficult and cumbersome.

Inspired from the characteristics of CAT and Wikify, which both represent cutting-edge text mining technology, the authors have found a way of combining the advantages and overcoming the limitations of both approaches to conceive a knowledge mining system according to the targets described in section 2.

Combining CAT and Wikify

CAT identifies topics in huge document corpora without external knowledge. All operations work on the entire corpus and a globally spanning statistical model, so the computation effort is very high. Wikify uses external knowledge from Wikipedia to do keyword extraction per document in a very efficient manner.

The key operation of the target application outlined in section 2 is relating a new document (e.g. a new research paper) to a given corpus of documents (e.g. published research papers from the manufacturing domain). Based on the findings above, the following procedure is proposed:

Step 1: Use CAT to automatically identify the keywords that characterise the document corpus, and group them into suggested topics, which can then be used to categorize the documents in the corpus. For each of these documents, the internal keywords are stored.

Step 2: Use Wikify to extract the keywords of a new document.

Step 3: Filter the keywords found by Wikify using the keywords identified by CAT.

Step 4: Match the list of filtered keywords found by Wikify with the list of internal keywords for each document of the document corpus and store the number of common keywords Step 5: Extract the most relevant documents relatively to the new document with the higher score of common keywords.

Step 6: Add the new document and the list of filtered keywords to the document corpus.

Step 7: Repeat Step 2 for any other new document, keeping unchanged the corpus-specific knowledge basis that was established in Step 1.

Step 8: Repeat Step 1 from time to time to improve the keywords of the new document corpus.

Step 6 assures that new keywords (that come up due to new research) become part of the document (knowledge) base whenever the latter is updated using CAT in Step 8. This makes sure that the knowledge base-including the keyword listevolves with the application of the system to new publications.

Case Study

This procedure was applied with a reference document corpus from the CIRP community composed of all the 240 papers of the CIRP-STCs (Scientific Technical Committee) Assembly (STC-A), Design (STC-Dn), and Optimization (STC-O) which have been published in the CIRP Annals from 2003 and 2008.

CAT was asked to identify 5 different significant topics in the CIRP document corpus. The computation time on an average PC was approximately 10 hours. The complete set of analysis results is available in an Excel file containing several different worksheets, which allow most notably to relate documents to topics, and documents to documents. From this analysis, Topic 1 was chosen as the reference topic. Its three most significant keywords were product, process, and knowledge, but it was characterised by a total of 73 keywords. Let the set of these keywords be KT1. For each of the 240 papers in the corpus, the global CAT analysis result file shows the degree of relevance of the respective paper to the topic. The 38 most relevant papers (with a degree of relevance >65%) were chosen from there, and for each of them the two most similar documents of the corpus were determined from the results file.

Algorithm used for the Study

In the next step each of these 38 papers was considered as Document Reference (DR) and analysed with Wikify using the following procedure: This algorithm can be fully automated and calculated with few computing resources. It determines the documents from the selected corpus which are considered most relevant to a given reference document from this corpus.

For all i [1,38] DR ← D i 1.

Results

Figure 1 shows an excerpt of the result table of the above algorithm for one particular reference paper. The column entitled "Keywords/Documents" contains the keywords identified by CAT from the corpus. Only an excerpt of the 73 keywords is shown. The grey-shaded column to the right indicates the binary pattern of the reference document, determined according to the algorithm shown in 6.1. The other columns which have a filename in their first line indicate the binary pattern of the respective document from the corpus. The line corresponding to a particular keyword contains "1" if this keyword appears at least once in the respective document, "0" otherwise. The red (dark grey) column to the right of each document column contains the result of applying the binary "AND" operation between the pattern of the corpus document on the left with the reference document pattern. The number on the bottom of each such column indicates the number of "1" in it, and corresponds to the number of keywords which appear both in the reference document AND the respective document from the corpus. The bottom part shows the filename and the title of the reference document, below in the "Wikify" section the filenames and titles of the corpus documents which have the highest number of keyword matches with the reference document. The "CAT" section shows the filename and the title of the corpus document which CAT considers most similar to the reference document. The complete result table reveals that for a very large part of the 38 papers there is at least one document from the corpus that is among the most relevant papers indicated by both CAT and Wikify. The other similar papers identified via Wikify are in fact also very relevant to the respective reference papers. These results clearly indicate that Wikify can lead quickly to accurate results when filtered by document-corpus specific word lists.

It has to be emphasized that this case study has been limited to three STCs for reasons of efforts and clarity. The presented approach can be applied without modification to a much larger CIRP document base, including publications from all STCs. This will enable users to find relevant papers from unexpected STCs, which can leverage inter-STC referencing and collaboration. A good example for a paper which is relevant to all STCs is [START_REF] Tichkiewitch | Virtual Research Lab: A New Way To Do Research[END_REF].

Conclusion

This paper suggests a system that supports researchers in finding publications that are relevant to their papers, and that consequently helps them build good bibliographies and increase citation indices. It introduces a novel approach to relating documents in a very efficient, reliable and accurate way. Its key characteristics can be summarized as follows: 1. The LDA-based CAT tool is used to identify topics which characterize the documents in the corpus. Each topic is defined by a list of keywords, sorted by their relevance to the topic. By providing a homogeneous corpus, where all documents are from one particular domain, one obtains topics and keywords that are characteristic and/or specific for a given domain (CAT itself is domain-independent). 2. The Wikipedia-based Wikify tool is used to identify significant words in a given document, sorted by the number of occurrences in this document. For this operation, Wikify uses sophisticated semantic concepts and the broad knowledge contained in Wikipedia. 3. Combining these two approaches and tools allows finding very quickly and automatically documents in the corpus that are similar or relevant to any given new document.

A method was shown that allows the programmatic implementation of this approach. However, this method does not yet exploit the latter"s full potential. Valuable and already available information, such as the keyword frequencies determined by Wikify, or the more complex semantic relationship between keywords and compound terms determined by Wikify and the individual keywords found by CAT, are not yet used. They may provide a very useful means to further improve the fidelity of the similarity measure. To investigate these improvements is the subject of the authors" future research.

Figure 1 .

 1 Figure 1. Excerpt from the analysis for one particular reference document

  Wikify the reference paper DR, and select only those (compound) words which match semantically with KT1. The result KDR is the subset of KT1 which can be found in DR.2. Build a binary representation of the relationship betweenKT1 and KDR such thatfor all k [1..73] BDR k ← 1 if KT1 k  KDR, else 0 3. For all j [1..38], i ≠ j, DC ← D j 3.1.Wikify the comparison paper DC, and select only those words and compound words which match semantically with KT1. The result KDC is thus the subset of KT1 which can be found in DC. 3.2. Build a binary representation of the relationship between KT1 and KDC such that for all k [1..73] BDC k ← 1 if KT1 k  KDC, else 0 3.3. Build a binary representation of the relationship between KDC and KDR such that for all k [1..73] BDD j,k ← 1 if BDR k = BDC k = 1, else 0 3.4. Calculate SDD j = ∑BDD j 4. The documents with the highest SDD are considered most relevant to the reference document DR.

Acknowledgements

The authors owe particular thanks to Kino Coursey and Rada Mihalcea for providing access to their Wikipedia-based tool suite WikiRank, and for their very helpful and immediate support.


Bing Wang

Caroline Renard

Isabelle Anselme

Amy François

De La Bretèque

Wang Bing belongs to the Tiananmen generation of Chinese filmmakers. Over the past 16 years, he has produced a body of work which blends time and reality in highly original ways, offering insight into the transformations taking place in Chinese society today. Born in 1967 in Shaanxi province, Wang Bing studied at the Beijing Film Academy. He first worked as a photographer on promotional film sets before embarking on what was to become a film career of major importance. Working virtually alone, without official authorization, using a digital camera, and relying on natural lighting and ambient sound, he strives to express the real by focusing on the minutiae of everyday life. He says that the spectacular holds no interest for him, and yet his films are monumental. He has directed a dozen films to date, most of them documentaries. A frequent choice at international film festivals, Wang Bing has received a number of awards for films which explore, with extraordinary aesthetic power, the shaping of collective memory. His meticulous and dedicated work and his intimacy with his subjects, create a space within contemporary cinema for an ethics of the imagination. The present volume contains several exclusive interviews with Wang Bing, as well as archival documents. Insight shared by Lihong Kong, who has produced a number of his films, occupies an importance place. The book also includes critical articles addressing the aesthetic, political and economic aspects of Wang Bing's considerable production.

Caroline

  Renard is a Lecturer in film studies at the University of Aix-Marseille where she is Chairman of the film department. Her research interests are in Cinema History and Aesthetics. Isabelle Anselme holds a PhD in law from the University of Aix-Marseille. She teaches Chinese culture and society at the University of Aix-Marseille and at the Institute of Political Studies of Aix-en Provence. François Amy de la Bretèque is Professor Emeritus of Cinema at the University Paul Valéry, Montpellier III. His research focuses primarily on relations between history and the cinema.

  [: WANG BING A FILM-MAKER IN CHINA TODAY


Fabien Colonnier
email: fabien.colonnier@nus.edu.sg

Soledad Ramirez-Martinez

Stéphane Viollet
email: stephane.viollet@univ-amu.fr

Franck Ruffier
email: franck.ruffier@univ-amu.fr

A Bio-inspired Sighted Robot Chases like a Hoverfly

Here we present a novel bio-inspired visual processing system, which enables a robot to locate and follow a target, using an artificial compound eye called CurvACE. This visual sensor actively scanned the environment at an imposed frequency (50Hz) with an angular scanning amplitude of 4.2 • and succeeded in locating a textured cylindrical target with hyperacuity, i.e. much finer resolution than the coarse inter-receptor angle of the compound eye. Equipped with this small, lightweight visual scanning sensor, a Mecanum-wheeled mobile robot named ACEbot was able to follow a target at a constant distance by localizing the right and left edges of the target. The localization of the target's contrasted edges is based on a bio-inspired summation of Gaussian receptive fields in the visual system. By means of its autoadaptive pixels, ACEbot consistently achieved similar pursuit performances under various lighting conditions with a high level of repeatability. The robotic pursuit pattern mimics finely the behavior of the male fly Syritta Pipens L. while pursuing the female. The high similarity in the trajectories as well as the biomimicry of the visual system provides strong support for the hypothesis that flies do maintain center the target and constant its subtended angle during smooth pursuit. Moreover, we discuss the fact that such simple strategy can also provide a trajectory compatible with motion camouflage.

Introduction

Highly efficient target tracking behaviors have been observed throughout the animal kingdom [START_REF] Land | Visual tracking and pursuit: Humans and arthropods compared[END_REF]. Particularly, small insects, despite their limited sensory system, display impressive capabilities like catching preys or mates, in order to survive in their ecological environment. For example, the housefly (Fannia canicularis) tracks the female by consistently flying towards it, making most likely no assumptions about its quarry's future position [START_REF] Land | Chasing behaviour of houseflies (fannia canicularis)[END_REF]. Likewise, Syritta pipiens L. hoverflies follow their potential mates, keeping the same distance away before trying to catch them. Depending on the position of the female in its field of view, the male will perform either body saccades and sway movements when the target is located on the side, or adopt a smooth pursuit strategy [START_REF] Collett | Visual control of flight behaviour in the hoverfly syritta pipiens l[END_REF] when the female is upfront. The male Lucilia can also follow its target for a while before deciding whether it will be a suitable mate [START_REF] Boeddeker | Chasing a dummy target: smooth pursuit and velocity control in male blowflies[END_REF]. Based on field observations, these Lucilia flies seem to use the size of their target in their Field-Of-View (FOV) and hold its position on the frontal midline of the head. Others, like the robber fly (Holcocephala fusca), chase their target with a constant bearing angle [START_REF] Wardill | A novel interception strategy in a miniature robber fly with extreme visual acuity[END_REF]. More complex chasing strategies have also been observed in hoverflies Eristallis and Volucella [START_REF] Collett | How hoverflies compute interception courses[END_REF] or in the dragonflies [START_REF] Olberg | Prey pursuit and interception in dragonflies[END_REF], where it seems that a prediction of the target trajectory is involved [START_REF] Dunbier | Predictive response facilitation to moving targets in an insect neuron[END_REF].

The studies of the dragonfly visual system taught us that specific neurons called Elementary Small Target Motion Detectors (ESTMDs) are implicated in the target detection and tracking [START_REF] Nordström | Feature detection and the hypercomplex property in insects[END_REF][START_REF] Nordström | Neural specializations for small target detection in insects[END_REF]. A bio-inspired algorithm derived from these observations was shown to be efficient and accurate [START_REF] Bagheri | Performance of an insect-inspired target tracker in natural conditions[END_REF] compared to the state of the art in computer vision [START_REF] Wu | Online object tracking: A benchmark[END_REF] and applicable in a robotic context [START_REF] Bagheri | An autonomous robot inspired by insect neurophysiology pursues moving features in natural environments[END_REF]. Another bio-inspired example of target tracking on a mobile robot has been made using an Event-based camera [START_REF] Liu | Combined frame-and eventbased detection and tracking[END_REF].

In this study, we focused on a pursuit scenario in which a holonomic mobile robot (the pursuer) tracks a mobile target, maintaining its visual contact with the target at all times and keeping a constant distance. It was assumed that the pursuer knows the size of the target and that the speed of the target is bounded, as hypothesized by Collett and Land [START_REF] Collett | How hoverflies compute interception courses[END_REF]. Previous authors have tackled target following challenges using an omnidirectional camera without any communication between the pursuer and the target, and by planning a suitable trajectory for the pursuer [START_REF] Mariottini | Vision-based localization for leader-follower formation control[END_REF][START_REF] Das | A vision-based formation control framework[END_REF][START_REF] Cowan | Vision-based follow-the-leader[END_REF]. Follow-the-leader scenarios can be said to be a particular case of target tracking, as the leader is identified and can provide the follower(s) with relevant information. Some authors of robotic studies have used infrared (IR) beacons [START_REF] Roberts | 3-d relative positioning sensor for indoor flying robots[END_REF][START_REF] Wenzel | Visual tracking and following of a quadrocopter by another quadrocopter[END_REF][START_REF] Faessler | A monocular pose estimation system based on infrared leds[END_REF][START_REF] Shishika | Bio-inspired pursuit with autonomous hovercraft using lyapunov-based control[END_REF], visual pattern recognition processes [START_REF] Saska | Mav-swarms: Unmanned aerial vehicles stabilized along a given path using onboard relative localization[END_REF] based on the open-source code Whycon [START_REF] Nitsche | Whycon: an efficient, markerbased localization system[END_REF], and acoustic signals either alone [START_REF] Basiri | On-board relative bearing estimation for teams of drones using sound[END_REF] or combined with radio signals to estimate the distance from a moving target [START_REF] Maxim | Trilateration localization for multi-robot teams[END_REF]. Stereo vision was also used on a UAV to intercept a moving colored target [START_REF] Strydom | Uav guidance: A stereobased technique for interception of stationary or moving targets[END_REF]. On the control point of view, pursuit has been largely studied for missile guidance with Line-Of-Sight techniques [START_REF] Shneydor | Missile guidance and pursuit: kinematics, dynamics and control[END_REF]. Some elaborated controllers have been designed to be robust to unknown target acceleration and more energy efficient [START_REF] Shishika | Bio-inspired pursuit with autonomous hovercraft using lyapunov-based control[END_REF], or optimize the time to capture [START_REF] Lim | A time-optimal control strategy for pursuit-evasion games problems[END_REF], whereas others took the visual sensor FOV into account [START_REF] An | Move like humans: End-to-end gaussian process regression based target tracking control for mobile robots[END_REF]. Motion camouflage is also a complex pursuit strategy, which aims to make the pursuer either static or producing an optic flow compatible with a fixed object onto the target retina. It has been suggested to be biologically relevant [START_REF] Srinivasan | Strategies for active camouflage of motion[END_REF] and observed on the dragonfly [START_REF] Srinivasan | Motion camouflage in dragonflies[END_REF]. Several theoretical studies have proposed algorithms to perform such behavior [START_REF] Anderson | Model of a predatory stealth behaviour camouflaging motion[END_REF][START_REF] Justh | Steering laws for motion camouflage[END_REF][START_REF] Reddy | Motion camouflage with sensorimotor delay[END_REF][START_REF] Strydom | Uas stealth: target pursuit at constant distance using a bioinspired motion camouflage guidance law[END_REF].

The pursuit scenario is here achieved by using a bio-inspired artificial compound eye called CurvACE featuring an optical resolution of only a few degrees imposed by the angle between two adjacent artificial ommatidia (photoreceptor + lenslet) [START_REF] Floreano | Miniature curved artificial compound eyes[END_REF]. The relatively coarse optical resolution and its low sensitivity (see fig. 15 in [START_REF] Viollet | Hardware architecture and cutting-edge assembly process of a tiny curved compound eye[END_REF]) was greatly improved by applying small periodic mechanical vibrations to the whole eye, which resulted in a visual micro-scanning of the environment. Many visual sensors based on active retinal micro-movements (see [START_REF] Viollet | Vibrating makes for better seeing: from the fly's micro eye movements to hyperacute visual sensors[END_REF] for a review) have been used for various robotic purposes, such as enhancing edge detection [START_REF] Prokopowicz | The dynamic retina: Contrast and motion detection for active vision[END_REF][START_REF] Hongler | The resonant retina: exploiting vibration noise to optimally detect edges in an image[END_REF] and improving obstacle avoidance [START_REF] Mura | Visual guidance of a small mobile robot using active, biologicallyinspired, eye movements[END_REF]. Recent studies featuring hyperacuity, i.e. "locating features with a greater accuracy than that corresponding to the resolution imposed by the photoreceptor's limited pitch" as defined by [START_REF] Westheimer | Visual hyperacuity. Sensory Physiology[END_REF], have focused on the processing of the amplitude of the photosensor's output signals to locate an edge/bar using only 2 pixels [START_REF] Kerhuel | The vodka sensor: A bio-inspired hyperacute optical position sensing device[END_REF], to locate and track a white cross using complex calibration process [START_REF] Manecy | Novel hyperacute gimbal eye for implementing precise hovering and target tracking on board a quadrotor[END_REF] or to measure robot 1D egomotion [START_REF] Colonnier | A smallscale hyperacute compound eye featuring active eye tremor: application to visual stabilization, target tracking, and short-range odometry[END_REF]. The visual sensor is a vibrating artificial compound eye called Active CurvACE (i.e. the scanning version of the CurvACE sensor) : Active CurvACE was developed to locate features with hyperacuity [START_REF] Colonnier | A smallscale hyperacute compound eye featuring active eye tremor: application to visual stabilization, target tracking, and short-range odometry[END_REF]. The CurvACE sensor is endowed with bio-inspired micro-scanning movements imposed by a tiny motor and an eccentric mechanism [START_REF] Juston | A miniature bio-inspired position sensing device for the control of micro-aerial robots[END_REF][START_REF] Colonnier | A smallscale hyperacute compound eye featuring active eye tremor: application to visual stabilization, target tracking, and short-range odometry[END_REF]. The Active CurvACE sensor is characterized by 4 specific bio-inspired principles:

• local light adaptation at the pixel level,

• a similar inter-ommatidial angle ∆ϕ to that observed from the fruitfly's eye,

• a Gaussian shaped angular sensitivity function at the level of each artificial ommatidium,

• a micro-scanning movement with its visual signal processing providing hyperacuity.

In addition, a new algorithm is introduced, inspired by the fusion of angular Gaussian receptive fields observed by Heiligenberg on the electric fish [START_REF] Heiligenberg | Central processing of sensory information in electric fish[END_REF], to aggregate the visual signals of the artificial ommatidia. The algorithm takes advantage of the angular Gaussian response of the sensors to improve the linearity of the angular position of the target placed in the FOV of the Active CurvACE sensor. This new linear characteristic was used to make a pursuer robot follow a target. Then, we established that the pursuer equipped with a bio-inspired non-emissive visual sensor was capable of achieving smooth pursuit when following a mobile cylindrical target at a constant distance. Section 2 presents the experimental setup and the objectives. Section 3 describes the bio-inspired visual processing, including a receptive fields summation method used to locate the cylindrical target over a large angular position range within the horizontal FOV of Active CurvACE. Section 4 describes the control system and the kinematics of the pursuer robot. Section 5 shows the performance of the pursuit obtained under 3 different lighting conditions, the repeatability and the comparison with hoverfly trajectories with a discussion on the motion camouflage. Section 6 draws some conclusions and suggests some perspectives.

Experimental setup and objectives

The pursuer equipped with a bio-inspired visual sensor using only 23 artificial ommatidia was able to perform smooth pursuits when following another mobile robot (the cylindrical target) at a constant distance. The FOV covered by the 23 photosensors was about 97 • . As shown in figure 1a, the two robots were used to test the pursuit scenario: • The pursuer, named ACEbot, which stands for "Active Compound Eye on a robot", was a yellow rover equipped with a vibrating artificial compound eye, called Active CurvACE visual sensor (see figure 2), and Mecanum wheels (see figures 1 and E1).

• The target was a non-holonomic rover carrying a textured cylinder (see figure 1a).

The two contrasting edges of the cylinder with respect to the background were the two visual cues used by the sighted pursuer to track the target's movement.

As depicted in figure 1b, the following notation is used throughout this paper:

• θ Lef t , θ Right are the angular position of each edge in the eye's FOV,

• r is the retinal error, i.e. the position of the target in the eye's FOV,

• α is the subtended angle, i.e. the size of the target in the FOV,

• R cyl is the radius of the cylinder.

3. Bio-inspired receptive fields summation to localize a target with hyperacuity

From modulated visual signals to Gaussian-like responses

The first step of the visual processing is to perform a demodulation of the artificial ommatidia signals which are submitted to a 50Hz scanning. It should be noticed that though bio-inspired, the sensor scanning is made at a higher frequency than the one observed on the fly (between 5 -7Hz, see [START_REF] Viollet | Vibrating makes for better seeing: from the fly's micro eye movements to hyperacute visual sensors[END_REF] for a review). Figure 3a details the demodulation strategy. First, a peak filter centered on the scanning frequency extracts the modulated signal, removing the constant value and some of the noise. The absolute value allow to double the frequency, to facilitate the envelope detection. Then, an envelope detector allow a first low-pass filtering without delay and finally a low-pass filter smooth out the demodulated signal.

Compared to [START_REF] Colonnier | A smallscale hyperacute compound eye featuring active eye tremor: application to visual stabilization, target tracking, and short-range odometry[END_REF], the modification of the processing were the addition of the envelope detector and modified filters. All these improvements enabled to increase the dynamic response of the demodulation. Indeed, the cutoff frequency of the last low-pass filter have been increased (from 5 to 20Hz), thus increasing the bandwidth of the visual processing.

To test the responses of the visual processing algorithm, the artificial eye was rotated back and forth in front of the target by activating the visual micro-scanning movements. As shown in figure 3c, the "Edge receptive field" of each pixel's output signal, denoted P h D , can be approximated with a Gaussian-like function centered at the angular position of the contrasting edge with respect to the eye (the gaze).

3.2.

From Gaussian-like responses to angular position measurement within the triplet's FOV 3.2.1. Localization using Gaussian receptive fields Heiligenberg [START_REF] Heiligenberg | Central processing of sensory information in electric fish[END_REF] has established that the Weighted Sum (W S) of an array of overlapped Gaussian receptive fields in an electric fish can provide a linear response to a stimulus position. W S computations on an array of sensors with a Gaussian shaped response give an approximation of a straight line (W S(x, σ) ≈ √ πσx, with x being the stimulus position). Appendix C.1 provides the mathematical definition of the W S and further details about the computation in the case of perfect Gaussian receptive fields. The validity of this linear approximation was proved in [START_REF] Baldi | How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers[END_REF]. ). Three Gaussian shaped optical angular sensitivities of the Active CurvACE (defined by its acceptance angle ∆ρ) are shown. The CurvACE readout circuit is in charge of digitizing each pixel's output signal here at a sampling frequency of 500Hz. The subsequent digital demodulation steps are performed using a peak filter center at the scanning frequency cascaded with an absolute value function connected to a digital envelope detector and a low-pass filter (see Appendix B). b) Scheme of the Active CurvACE sensor in front of the target. c) Normalized Gaussian-like "Edge receptive fields" (defined by their standard deviation σ) of 3 vibrating photosensors after the demodulation process during two back and forth rotations of Active CurvACE (vibration turned ON) in front of left and right edges of cylindrical target.

An adaptation of this principle was used here for the first time in the context of bio-inspired artificial vision. It was applied to a group of three in-line adjacent pixels (called a triplet) showing overlapped Gaussian-like responses of their "Edge receptive field" (see figure 3)c, and showed that once the WS has been normalized, this system produces a reliable output signal which can be used to locate an edge with great accuracy. Although biologically plausible, no founding proves that it is how the flies and more generally insects are processing the visual information. It is only a suggestion which in the context of the study is working reliably.

Normalized Weighted Sum (NWS) Computation

In the case of the present visual system, the amplitude of the P h D signals depends on three main parameters: the ambient illuminance, the contrast and the scanning frequency. The novel feature of our approach is that it makes the visual sensor's output signal independent of these parameters by normalizing the W S by the sum of the P h D signals. As shown in the Appendix C.2, the output of the normalized W S (W S norm = W S/S) is still linear and bounded. The hyperacuity of the W S norm was also established because the maximum linearity error amounts theoretically to less than 7% of the spacing between the receptive fields δ. This makes it possible to measure the position of a contrasting edge. However, only one edge at a time must be present in the FOV of the photosensors used for the computations at a time. It is therefore best to use as few photosensors as possible. It was decided to use only three neighboring photosensors, i.e. one triplet, in the W S norm , because when an edge is in the neighborhood of the center of one triplet's FOV (± δ 2 ), its 3 photosensors are contributing more than 99% to the total Sum.

To provide the pursuer with the angular position of one given edge, it is necessary to scale the W S norm value, depending on the spacing between each pixel. The mathematical expression of the normalized and scaled W S (later noticed N W S) applied to an array of pixels featuring Gaussian angular sensitivities separated by an angle ∆ϕ can therefore be written as follows:

N W S(i) = ∆ϕ • i+1 k=i-1 k • P h D (k) i+1 k=i-1 P h D (k) + bias (1)
where P h D denotes the photosensors' demodulated signals and bias is a calibrated offset used to set the zero position. Here, we intended to aligned the center of the cylinder with the center of the eye. Figure 4a displays a schematic view of the computation from the pixel to the N W S computation.

NWS(i)

(see eq. 1)

NWS(i-1) NWS(i+1)

Ph D (i-1) Ph D (i) Ph D (i+1) NWS Values [°]

Characterization of the vibrating visual sensor

To test the responses of the hyperacute visual sensor (i.e., the Active CurvACE) depending on its orientation (denoted ψ gaze ) with respect to a textured cylindrical target, the visual sensor was turned towards a fixed target (a textured cylinder 30cm in diameter, placed 91cm ahead) and rotated stepwise about its vertical axis via an accessory position servo (not shown here) driven by a 0.1 • staircase signal, as in figure 3. The responses of each of the 21 N W S were monitored at each azimuthal orientation of the gaze ψ gaze with respect to the target. The various N W S were calculated by applying equation [START_REF] Land | Visual tracking and pursuit: Humans and arthropods compared[END_REF]. Figure 4b gives the results of all the N W S calculations. With a theoretical uniform background, one can expect a constant response when no contrasts is present in the FOV. However, in a real scenario, contrast variations always appear as shadows or small changes in color. As the normalization makes the N W S independent to contrast amplitude, it is difficult to identify the right contrast to track. Thus, a selection process is needed to obtain the N W S of greatest interest, which will be used to locate the target.

Weighted Sum Selection : edge localization over a large angular position range

As shown in figure 4, a selection process was required to obtain the N W S values corresponding to an edge. This process was performed using the following criteria:

S Criteria (i) = P h D (i -1) + 2 • P h D (i) + P h D (i + 1) (2)
The index c j , giving the N W S having the contrast j in its FOV at time t, is then updated as follows:

c j (t) = arg max i∈[c j (t-1)-1,c j (t-1)+1] S Criteria (i) (3)
This selection process was based on the assumption that the target is not moving faster than ∆ϕ between two successive sampling times. This means that an edge can only be located either via the same selected N W S or via its nearest neighbor (c j (t) -1 or c j (t) + 1). In this study, the sampling frequency of the measurements was 500Hz.

The selection process can be applied to any number of edges to be followed. In the present case, as the target is a cylinder, two edges were tracked. Therefore, the edges positions are given as follows:

θ Lef t = N W S(c Lef t ) θ Right = N W S(c Right ) (4)
Figure 5 summarizes the complete algorithm to get the edges localization and displays the comparisons of the measurements of the two edges compared to ground truth.

Application to Target localization

The two measured angular positions resulting from the selection process are denoted θ Lef t and θ Right .

This algorithm makes it possible to locate two contrasting edges at the same time if they are separated by a sufficiently large angle, i.e. 2∆ϕ, in line with the hypothesis that only one contrast can be located at a time in the FOV of 3 photosensors. Assuming that these two edges belong to the same target, it is therefore possible to calculate its orientation r and its subtended angle α defined as follows:

r = (θ Lef t + θ Right )/2 α = θ Lef t -θ Right (5) b)
Demod.

Demo d.

Demod.

Demod.

Demo d.

S criteria (i)

(see eq. 2)
NWS(i)

(see eq. 1)
S criteria (i-1)

NWS(i-1) S criteria (i+1) NWS(i+1)
NWS(i)

(see eq. 1) 23 21
S criteria (i)

(see eq. 2)
23 [START_REF] Shishika | Bio-inspired pursuit with autonomous hovercraft using lyapunov-based control[END_REF] Index Selection Comparisons between the measured angular positions (red) and the ground truth values (green) based on a motion capture system showed that the linearity error of the sensor amounted to only 5 percent. The resolution (equivalent to 6 times of the signal standard deviation σ) was as small as 0.78 • with a signal-to-noise ratio of 20.7dB. The two frames highlights that the same results as in figure 4b are presented here differently.

(see eq.
Table 1 sums up the Active CurvACE performances.

Nonlinear control and kinematics of the pursuer robot

The artificial eye was placed on a robot equipped with Mecanum wheels (see Appendix E for details), which allows omnidirectional movements. The maximum speed that the robot was able to reach was equal to 0.5m.s -1 . The control laws implemented onboard the pursuer were drawn up using the kinematic model described previously by [START_REF] Tsai | Motion controller design and embedded realization for mecanum wheeled omnidirectional robots[END_REF][START_REF] Viboonchaicheep | Position rectification control for mecanum wheeled omni-directional vehicles[END_REF]. The control strategy implemented was based on a non-linear approach to control each degree of freedom and a bounded control strategy adapted from [START_REF] Guerrero-Castellanos | Trajectory tracking of a mobile robot (3,0) by means of bounded control[END_REF] to control the 4-wheeled robot and also used in [START_REF] Raharijaona | Local positioning system using flickering infrared leds[END_REF]. This controller takes in account the wheel speed limits, as it is impossible to go at full forward speed and rotate in the same time. Figure 6 shows the ACEbot's control strategy. The setpoints X * are the desired position of the robot in the target frame. As the target is cylindrical, it has the same shape when viewed from all directions in the azimuthal plane. The robot's x direction in the local target reference frame was therefore taken to be always co-linear with the pursuer-to-Target's direction, as shown in figure 1b. Therefore, the x reference is the distance requirement, which has to be negative. The y reference in the target frame is null to ensure that ACEbot is aligned with the Target. It also means that no sideway movement will occur. The heading angle ψ was controlled in the closed-loop mode so as to keep the retinal error r equal to zero.

ACEbot

The estimated state vector can be expressed as follows:

X1,2,3 =    x rob y rob ψ rob    =    -cos(ψ * ) • Rtarget sin(α/2) -D eye 0 -ψ *    (6)
where D eye is the distance from the eye to the ACEbot center. It can be noticed that -x rob corresponds to the distance measurement (noted D meas in Table 1). The kinematic model is the transfer matrix from the velocity of the robot's centre to the wheel speed:

     ω * 1 ω * 2 ω * 3 ω * 4      = 1 R w      1 -1 -(l + L) 1 1 (l + L) 1 1 -(l + L) 1 -1 (l + L)         v * x v * y ω * z    (7)
where v * x , v * y and ω * z are the robot speed control inputs. R w , L, l are the wheel radius, the wheelbase and the track width, respectively. The linearization is the transfer matrix from the global frame, or in this case, the Target, to the ACEbot frame, which is expressed as follows:

v * x = cos(ψ rob ) • r 1 + sin(ψ rob ) • r 2 v * y = -sin(ψ rob ) • r 1 + cos(ψ rob ) • r 2 ω * z = r 3 (8)
where r i denotes the bounded control output signals. This transformation was also useful for decoupling the control of each degree of freedom in the global frame.

Considering the notation e i = X * i -Xi , the r i are the results of the following calculation:

r i = σ M i3 Ẋ * i + σ M i2 a i1 e i + σ M i1 (a i2 e i + a i1 a i2 e i ) ( 9
)
where the saturation function is defined as:

σ M (s) = s, if | s |< M sign(s) • M, otherwise (10)
The values a ij and M ij are given in the Appendix D. It should be highlighted that this control strategy does not use any measured or estimated target speed as input. Therefore, there is no prediction on the future location of the target.

Experimental pursuit performances

Experimental setup

The experiments shows different pursuit trajectories. In all of them, the objective is to keep the retinal error r to zero and a constant distance to the target, 0.7m in sections 5.2 and 5.3 and 0.9m in section 5.4, respectively. The Target robot was controlled either by a manual remote control system or via a feedback loop, using a VICON Motion Capture System. This system can provide the position of the robots at a refresh rate of 500Hz with a precision of less than 1.5mm (see the Appendix B in [START_REF] Manecy | X4-mag: A low-cost open-source microquadrotor and its linux-based controller[END_REF]) and was used as the ground truth. ACEbot and the robotic Target were equipped with infrared (IR) LEDs used as active markers for the VICON system. The IR strobes of each VICON camera were disabled to prevent any visual perturbations from occurring due to the strong flickering infrared lighting.

Ambient Light Variations

Figure 7a shows the trajectory of the Target in green and that of the ACEbot in yellow. The positions of both robots are shown every 8s, and it can be seen that the ACEbot always kept close to the Target, while keeping it in its line of sight. The dark blue triangle shows the measured subtended angle.

In this experiment, the Target followed an imposed smooth trajectory with some small curves and ACEbot, after detecting the Target, was able to follow it unfailingly. As the photosensors in the artificial eye adapted fast to changes in the light level [START_REF] Floreano | Miniature curved artificial compound eyes[END_REF], this pursuit behavior was consistently repeated under the various ambient lighting conditions tested. The tests of figure 7 (and also in the video in the supplementary data), were performed in a single experimental run, starting in the dark, where the target was detected and followed up to the end of the arena before returning close to the starting-point. The light was turned on when the target came to a stop. The pursuit was repeated and the blinds of the robotic arena were finally opened for the last pursuit. During this experiment, the target was remotely controlled by hand, giving similar trajectories.

It can be seen from figure 7 that the distance was accurately estimated and remained constant, although slightly above the reference value. This error was due to the fact that the ACEbot's speed is not large enough and no target speed is used in the control loop. The ACEbot's pursuit performances of the whole run are summarized in the table 1.

Repeatability

To test the robustness of both the visual algorithm and the robot's control strategy, the target's and pursuer's trajectories were repeated 20 times under the same lighting conditions (fig. 8). It is worth noting that the pursuer took the same trajectory and never lost visual contact with the target. The standard deviations of both the target's and pursuer's trajectories were under 3cm. order to determine the subtended angle and the orientation of the target in the pursuer FOV. The measured subtended angle can be converted into a distance measurement on the assumption of a known target size. These measured orientation and distance are assessed so as to keep r and d equal to 0 • and 0.9m, respectively.

Collett and Land [START_REF] Collett | Visual control of flight behaviour in the hoverfly syritta pipiens l[END_REF] observed some trajectories of the hoverfly Syritta Pipens L. that achieved a chasing behavior with a precision of 1cm at a distance of 10cm. Similar trajectories between robotic and insect observations were achieved (see figure 9). Therefore, the strategy that consists of keeping the target in the middle of the FOV seems to be compatible with the biological observations. It should be highlighted that the insects are also using visual cues to maintain the distance from the mate. However, establishing a difference between a controller based on either the distance or the subtended angle measurement is difficult. The Syritta pipiens L. seems to follow and maintain distance to its potential mate before trying to catch it using two different pursuit behaviors, possibly depending on the position of the mate in its field of view. It uses mostly continuous tracking when it is upfront but does body saccades and sway movements when the target is on the side. Sometimes, it was also observed that hoverfly does sideways movement even if the mate is in front of it, but these movements were unpredictable [START_REF] Collett | Visual control of flight behaviour in the hoverfly syritta pipiens l[END_REF].

Discussion on motion camouflage

In [START_REF] Srinivasan | Strategies for active camouflage of motion[END_REF], the authors hypothesize that the male hoverfly follows the female while performing motion camouflage, i.e. assess its movement in order to appear as static onto the female retina, based on observations presented in [START_REF] Collett | Visual control of flight behaviour in the hoverfly syritta pipiens l[END_REF]. One can notice that Collett and Land in their analysis did not suggested a motion camouflage behavior but only a pursuit at constant distance by keeping the target in the center of the FOV of the pursuer. In addition, only three motion camouflage trajectories were reported for the hoverfly Syritta Pipens L. (two in [START_REF] Srinivasan | Strategies for active camouflage of motion[END_REF] and one here).

Figure 10 takes the same trajectories as in figure 9 with the addition of the directions linking the target to the pursuer for several positions. Three dense areas of successive connecting line crossings can be identified, similar for the insects and robots trajectories. One can say that a first stationary point is selected and changed during the pursuit to another one. For the hoverflies, it would have happened between time 2 and 3 and again between 5 and 6 (see figure 10a), where the areas are nearly aligned.

In this paper, we showed that a motion camouflage pattern can be observed when two simple rules are applied, keeping the target (i) in the center of the FOV of the pursuer by yaw rotation and (ii) at a constant distance (or constant subtended angle) by translation along the pursuer longitudinal axis (i.e. the pursuer-target direction).

Finally, with this simple control law, the resulting trajectory can create stationary points from the target perspective during the pursuit. Hence, is the pursuit of the male hoverfly the result of a specific strategy for motion camouflage or a consequence of a simpler vision-based strategy (as the one proposed in this paper)? More neuroethological researches should be done to be able to answer this question.

Conclusion

The Active CurvACE was used here as a biomimetic device to test successfully bioinspired strategy constrained by a bio-plausible visual sensor on a mobile robot. The high similarity in the robots and hoverflies trajectories as well as the biomimicry of the robotic visual system and of the summation processing provides support for the hypothesis that flies do maintain center the target and make its subtended angle constant during smooth pursuit. Indeed, the assessment of these two variables is sufficient to reproduce the hoverfly behavior. It is worth noting that the same sensorimotor control strategy was used in both cases: target following and fly-like smooth pursuit. The trajectories obtained were also compatible with motion camouflage.

On the robotic side, it was established here that only 23 pixels part of a vibrating artificial compound eye was able to locate a robotic target with hyperacuity and to pursue it with great accuracy. Compared to a previous study [START_REF] Manecy | Novel hyperacute gimbal eye for implementing precise hovering and target tracking on board a quadrotor[END_REF], we obtained a similar linearity in the target localization within a much larger visual range and without the need of a complex calibration process. The robot's orientation and its distance from the mobile target were precisely estimated under various lighting conditions. Table 1 gives the detailed results for the entire duration of the tests provided in the supplemental video. The novel computationally lean, small, lightweight bio-inspired visual sensor presented here is suitable for use in target following tasks.

The limitations of the present strategy concerned the existence of a sufficiently subtended angle of the Target in the FOV (theoretically 2∆ϕ) and the presence of a nearly uniform background or one without any sharp contrasts. An improvement of the pursuer dynamic responses could also be explored by providing the robot with In the future, this active device could be embedded for example onboard a Micro-Aerial Vehicle (MAV). However, in the case of free flight, a second active Curvace or a 2D scanning would be required to detect the elevation of the target. In the automotive framework, a non-emissive optical sensor, like Active CurvACE, sensitive over a large angular position range and over a high range of light level could also provide a suitable alternative for the classical ultrasonic sensors and LIDARs which are being widely used these days in adaptive cruise control applications. it can be deduced that, If is bounded, we establish here that W S norm is similar to a linear function with a slope of 1. on and off. The wheel speed setpoints computed on the Gumstix were transmitted through a serial bus (UART) to the Arduino-compatible motor control board, which then controlled each wheel's speed with a PI controller. A WiFi connection between the robot and the ground station was used to monitor the variables of interest during the experiments and provided the rover with setpoints. The ACEbot robot was powered by a 3-cell lithium polymer battery.

W S norm = x -2πσ 2 ∞ k=1 k • e -σ 2
Bibliography

Figure 1 .

 1 Figure1. a) An experimental situation where the pursuer (i.e., the yellow robot ACEbot) is following the target (a textured cylinder mounted on a moving wheeled rover) at a constant distance. Thanks to its hyperacute visual sensor, the robot ACEbot is able to lock its heading onto the target and keep a constant distance from the target. b) Scheme of the various parameters and angles used in the control strategy implemented here (see equation (5)).Stepper motor (vibration actuator)

Figure 2 .

 2 Figure 2. a) Picture of the ACEbot's visual sensor called Active CurvACE and the photodiode used for the illuminance measurements. b) Diagram of the mechanical system, the eccentric shaft is used with a roller bearing to limit the wear in the slotted hole. This Active CurvACE assembling is very compact (40 × 27 × 15mm) and light (12.5 grams).

Figure 3 .

 3 Figure 3. a) The demodulation signal processing algorithm applied to the visual signals delivered by the vibrating artificial compound eye (Ψ mod = A sin(2π50t) where A ≈ ∆ϕ 2). Three Gaussian shaped optical angular sensitivities of the Active CurvACE (defined by its acceptance angle ∆ρ) are shown. The CurvACE readout circuit is in charge of digitizing each pixel's output signal here at a sampling frequency of 500Hz. The subsequent digital demodulation steps are performed using a peak filter center at the scanning frequency cascaded with an absolute value function connected to a digital envelope detector and a low-pass filter (see Appendix B). b) Scheme of the Active CurvACE sensor in front of the target. c) Normalized Gaussian-like "Edge receptive fields" (defined by their standard deviation σ) of 3 vibrating photosensors after the demodulation process during two back and forth rotations of Active CurvACE (vibration turned ON) in front of left and right edges of cylindrical target.

Figure 4 .

 4 Figure 4. a) Layout of the computation of the Normalized and scaled W S. The P h D signals obtained after the demodulation process are the inputs of the different N W S computations. b) N W S values of the 21 triplets as a function of the visual sensor's gaze (ψ gaze ) with respect to the fixed cylindrical target. The parts resulting from the selection process (see section 3.3) are highlighted.

3 )Figure 5 .

 35 Figure 5. a) Layout of the N W S computation and the S criteria b) Scheme of the computation from the pixel to the cylinder edges position measurement, through demodulation, N W S processing and selection. c) Measured angular position of each target's edge (left and right) versus the visual sensor's gaze.Comparisons between the measured angular positions (red) and the ground truth values (green) based on a motion capture system showed that the linearity error of the sensor amounted to only 5 percent. The resolution (equivalent to 6 times of the signal standard deviation σ) was as small as 0.78 • with a signal-to-noise ratio of 20.7dB. The two frames highlights that the same results as in figure4bare presented here differently.

Figure 6 .

 6 Figure 6. ACEbot non-linear controller scheme. The robot is using visual cues ( r , α) to assess its orientation and distance to the target by controlling the 4 wheel speeds.

Figure 7 .

 7 Figure 7. Three different following trajectories under different ambient light conditions. a) The trajectories of the center of inertia of the target and the pursuer ACEbot are presented in green and orange, respectively. The robots are drawn every 8s, with the full FOV of ACEbot in light blue, and the measured subtended angle of the target in dark blue. b-i) The retinal error r , i.e. position of the target in the FOV of ACEbot, with the setpoint, the measured angle and the ground truth in dashed black, black and grey, respectively. b-ii) depicts the distance from the target, and b-iii) the equivalent subtended angle in the FOV. The reference, the measurement and the ground truth are in dashed black, black and grey, respectively. b-iv) Dynamic responses of the light sensor shown in fig.2a, reflecting the changes in the ambient lighting, which measured 100 Lux in 1 , 780 Lux in 2 and 1500 Lux in 3 . These responses show the robustness of the visual processing system with respect to several light levels.

5. 4 .Figure 8 .

 48 Figure 8. 20 recordings of target following tasks. The target's and pursuer's trajectories are plotted in green and yellow, respectively. This pursuing episode shows the excellent repeatability of the robot's ability to follow a target moving along several similar paths. The ACEbot consistently produced the same behavior, thus showing the high robustness of the visual processing algorithm.

Figure 9 .

 9 Figure 9. Comparison between the smooth pursuit observed during Syritta pipens L. mating process (a) and the target following trajectories of ACEbot (b, c and d). In a), the female and the male are represented in black and grey respectively. Dots are representing the head position and the lines are the orientation of the body. Each are spaced by 40ms in time and the numbers indicate a 400ms interval. Redrawn from[START_REF] Collett | Visual control of flight behaviour in the hoverfly syritta pipiens l[END_REF]. Hoverfly picture source wikimedia commons. In b-d), the target is represented by a green dot and a continuous line for the whole trajectory. ACEbot, the pursuer, is represented in yellow; the dot is the eye position and the line represents the robot orientation. The markers are separated by 400ms and the numbers indicate a 4s interval.

Figure 10 .

 10 Figure 10. Connecting lines has been drawn between target-pursuer position on the trajectories presented in figure9. Convergence zones of these connecting lines have been been highlighted. These zones of convergence indicates apparent static positions of the pursuer to the target. The convergence zones appear between large pursuer translation. The large radius of the convergence zone ellipses can be assessed to be below 10cm in the robotic case.

Figure C1 .

 C1 Figure C1. Presentation of the Weighted Sum and its normalization for perfectly Gaussian receptive fields. a) An array of Gaussian receptive field response spaced by an unitary space and with a half height width equal to one (i.e. σ = 1/(2 √ ln 2) ≈ 0.6). b-d) The theoretical Weighted Sum, the Sum and the normalized Weighted Sum (W S norm = W S/S) expressed for various standard deviation σ.

k 2 π 2 sine

 2 -σ 2 k 2 π 2 cos(2πky) (C.7)The error (using W S norm = x + ) can therefore be deduced as follows:= -2πσ 2 ∞ k=1 k • e -σ 2 k 2 π 2 sin(2πky) 1 + 2 ∞ k=1 e -σ 2 k 2 π 2 cos(2πky) (C.8)

Figure E1 .

 E1 Figure E1. Picture from above of the robot, showing the electronic hardware. The Gumstix communicates with the ground station through Wifi as well as with the Motor control board and with the Teensy through an UART bus. Neither boards are visible on the picture as they are under the robot.

Table 1 .

 1 Active CurvACE and ACEbot performance summary Active CurvACE characteristics Static Optical parameters ∆ϕ = ∆ρ = 4.2 • FOV 96.6 • Scanning frequency 50Hz Scanning angular amplitude A 2.1 • (≈ ∆ϕ 2 ) Sampling frequency 500Hz Visual processing bandwidth 20Hz Hyperacuity resolution 0.78 • = 19% of ∆ϕ Linearity 95% (R 2 = 0.99) Signal to Noise Ratio 20.7dB Estimated Target localization using Active CurvACE with respect to the Ground Truth (GT) (mean ± std) Target ang. position rmeasr GT -0.62 ± 1.28 • Subtended angle α meas -α GT -1.78 ± 1.49 • Target distance D meas -D GT 3.1 ± 2.7cm Closed-loop ACEbot pursuit accuracy with respect to Ground Truth (GT) (mean ± std) Target ang. position * rr GT -0.67 ± 2.63 • Subtended angle α Ref -α GT -2.40 ± 5.09 • Target distance D Ref -D GT 2.8 ± 7.9cm information about the target speed.

Acknowledgments

We thank M. Boyron and J. Diperi for assembling ACEbot, A. Manecy for designing the target robot's control, J.F. Guerrero-Castellanos for his advice on the robot's control and E. Loret for her help with the wheel speed control. This research was supported by CNRS (Life Science; Information Science; Engineering Science and Technology), Aix-Marseille University and the French National Research Agency (ANR) (IRIS project under ANR grants' number ANR-12-INSE-0009).

Appendix

Appendix A. Supplementary materials Videos of the experiences described in sections 5.2 and 5.4, can be found at the following links https://youtu.be/kdjJ6t7d2pM and https://youtu.be/ fciQr0o0G7g, respectively.

Appendix B. Demodulation processing details

The demodulation processing presented in figure 3 is the combination of different filters that need to be tuned, a peak filter, an envelope detector and a low pass filter. All of them are processed at a sampling frequency f s of 500Hz.

The peak filter is actually the combination of a second-order peak filter H pf and an equalizer filter H eq . The peak filter has a peak frequency f 0 at 50Hz. Its z-transform is expressed as follows:

where

The z-transform of the equalizer filter is expressed as follows:

where G = 1.5 and G B = 1.155. The envelope detector reproduces digitally the behavior of an analogic envelop detector. It means that its output (out) is following the input signal (in) when this one is increasing. But it has an exponential decay when the input signal is decreasing. Mathematically, it is defined as follows:

where T s and τ are the sampling time and the time constant of the exponential decay, respectively. τ is chosen to be smaller than the modulation period, in our setup it is twice the period (i.e. 40ms).

Finally, the low-pass filter is simply a third-order low-pass filter with a cutoff frequency of 20Hz.

Appendix C. Details about the Heiligenberg Weighted Sum and the proposed normalization

Appendix C.1. Theoretical presentation of the Normalized Weighted Sum Given that the response of a Gaussian receptive field according to a stimulus position x can be expressed as e -( x-k σ ) 2 , the equation proposed by Heiligenberg [START_REF] Heiligenberg | Central processing of sensory information in electric fish[END_REF] reads as follows:

as e -( x-k σ ) 2 describes a Gaussian function, where σ is the standard deviation. Let S(x, σ), the sum of the Gaussian receptive fields, be defined as:

Figure C1 displays the responses of the W S, S and W S norm , which is equal to W S/S. It highlights that the Heiligenberg weighted sum linearity and its slope depend on the Gaussian overlapping. However, it can be seen that the normalization by the sum is helping, as it reduces the variation and ensures a constant slope whatever the width of the Gaussian.

Appendix C.2. Linear approximation and error estimation for the Normalized Weighted Sum computation

In order to bound the normalized weighted sum, we will apply a similar demonstration to the one used in [START_REF] Baldi | How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers[END_REF]. Let x = n + y with n ∈ Z and y ∈ [0, 1], which means that:

where W S and S have been defined in equations (C.1) and (C.2), respectively. It was established in [START_REF] Baldi | How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers[END_REF], that:

From the definition, y = x -n, which means that S(x, σ) = S(y, σ) because S is periodic with a period of 1. The ratio of the weighted sum over the sum of the Gaussian functions is equal to W S norm = W S(x,σ) S(x,σ) . From that:

From [START_REF] Baldi | How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers[END_REF], crude bounds can be computed for the series, if the inequality

Thus, the absolute value of can be bounded as follows:

In the present case, if we adopt the assumption that ∆ρ = ∆ϕ, σ = ≤ σ, the error will be equal to 7% of the spacing between each pair of photosensors. This value results from a crude mathematical error calculation, because one can obtain an error of 6.5% numerically with only 3 Gaussian functions.

Appendix D. ACEbot control parameters

The values for each control parameter are equal to: a 11 = 22.5, a 12 = 0.0225, a 21 = 22.5, a 22 = 0.0225, a 32 = 45.0, a 33 = 0. These values make the trajectories very close to the linear region and guarantee the stability of the system. The limits M ij for i, j = 1, 2, 3 are described in table D1.

Appendix E. Information about the Robotic platform ACEbot

The product reference of the platform is "Nexus 4WD Mecanum wheel mobile robot kit 10015" but the ultrasonic sensors are not used in the present application.

As regards the electronics, the main program was running on a Gumstix Overo board, which, thanks to the RT-MaG toolbox, can be programmed directly from Matlab/Simulink [START_REF] Manecy | RT-MaG project[END_REF]. This Linux based Computer-On-Module (COM) was running the signal processing algorithm for the 23 photosensors received from CurvACE through a synchronous serial bus (SPI). It was also connected through UART to a Teensy board. The latter was in charge of the acquisition of the photo-current sensor to record the ambient light level and to switch the stepper motor in charge of the eye's periodic tremor