) Corron

F Marchal

Silvana Condemi

Pascal Adalian

A critical response to "A critical review of sub-adult age estimation in biological anthropology" by Corron

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

A response to H.F.V. Cardoso's 2019 "A critical response to "A critical review of sub-adult age estimation in biological anthropology" by Corron, Marchal, Condemi and Adalian (2018)" L. Corron* Department of Anthropology, University of Nevada, Reno, USA F. Marchal S. Condemi P. Adalian ADES -Anthropologie bioculturelle, Droit, Ethique et Santé, UMR 7268, EFS, CNRS, Faculté de Médecine, Université Aix-Marseille, 13 344, Marseille cedex 15, France * Corresponding author at: Department of Anthropology, University of Nevada, Reno, 1664 N Virginia St MS 0096, Reno, NV 89557, USA. E-mail address: lcorron@unr.edu (L. Corron).

Letter to the Editor

Although, as scientists, we strive to be as objective and exhaustive as possible in our work, we gladly accept that our papers can be openly and constructively criticized. Dr H.F.V. Cardoso's relatively contentious response [START_REF] Cardoso | A critical response to "A critical review of sub-adult age estimation in biological anthropology[END_REF] to our article "A critical review of sub-adult age estimation in biological anthropology, Forensic Sci Int 2018 288:328.e.1-328.e.9" shows that at least one person thought we were suggesting that only 7 of the 269 subadult age estimation publications we included in our analyses were "fit for use" in biological anthropology. Our paper was a critical review, and evidently not "The 7 and only methods that comply with published methodological recommendations for sub-adult age estimation in biological anthropology". Dr Cardoso's letter mainly reinforces the point we, the authors, made in our article: "The purpose [ . . . ] was to draw attention to these difficulties pertaining to subadult age estimation and to illustrate that such publications are most often unfit, or at the very least questionable, for sub-adult age estimation in a forensic context [2, p.328.e.7]." However, his response indicates that we should have made this general take-home point more strongly and that some clarification is necessary. Dr Cardoso pointed out several issues with our study that seem to be more focused on details of the study rather than its general scope.

One critique was about the composition of the corpus and the context of the publications included in it. These publications were chosen because they were available in libraries or online and were all published after some form of peer-review, be it by an editorial board or a bioanthropological scientific committee for conference papers. Therefore, not all publications were strictly found in peerreviewed journals but also in peer-reviewed conference proceedings and in published biological and forensic anthropology books, available either online or in various university library databases. The publications included age estimation of the living or the deceased in both forensic and bioarcheological contexts. Dr Cardoso states that some publications did not concern sub-adult age estimation, but rather adult age estimation, and/or could not be considered as sub-adult age estimation methods sensu stricto. Indeed, they all relate to post-natal sub-adult age estimation sensu largo. Although some methods do include adults in their training sample, all samples cover at least a few years between birth to late teensearly 20-something individuals, which is when the last ossification centers of the clavicle, iliac crest and ribs are still fusing. These "older' individuals are therefore still considered as immature or sub-adults from a biological perspective. In fact, these individuals and age indicators are the main focus of many forensic anthropology papers published on determining whether an individual is minor or not.

In effect, not all of the publications in our corpus are sub-adult age estimation methods per se. For instance, some of them are atlases or reference data on skeletal and dental growth and development but they have been and are still being used as methods for sub-adult age estimation or indirectly applied as such in biological anthropology in both forensic and/or bioarcheological contexts. The reason for this is most likely multifactorial: it has historically been done and persists by habit, it depends on the elements available for analysis, which are covered more extensively by atlases and the like, and also on the accessibility of some newer methods and how easy they are to implement.

In our paper, we focused on method application in the forensic context, which is particularly sensitive to this methodological point, as we addressed it: "Methods must also comply to conditions of court admissibility [ . . . ] Methodological, ethical and legal discrepancies are therefore all potential sources of misestimation of age leading to possible errors of interpretation in forensic cases." [2, p 328.e7]. Proposing a well-argued reasoning for publication selection in accordance with the fact that methods comply with published recommendations is an important argument in court. Whether these publications should be used for such purposes is a corollary question Dr Cardoso ponders, the answer to which we also explicitly address in our paper: "The goal of this study was not to provide a clear definition of what constitutes a sub-adult age estimation method, but rather to give an overview of what material is available to anthropologists today for sub-adult age estimation in biological anthropology and how they compare to one another based on a standardized scale [ . . . ] [2, p. 328.e7]." Indeed, one of the conclusions of our study is that not all of them should be used as sub-adult age estimation methods, which reinforces our point: users should be critical of all aspects of a publication, including its initial purpose and potential misapplications. That is also why we used the general term of "publication" instead of "method" in our paper. Finally, known or less-known publications based on any modality (e.g. dry bone, medical imaging, histology, biochemistry) were included to the corpus to cover the variety of approaches to sub-adult age estimation as exhaustively as possible. Although their application may be limited, and context-or case-specific, we did not consider this as an exclusion criterion.

The second main critique was that the set of ten parameters used to qualify the publications and the database itself, consisting in 269 publications on sub-adults and sub-adult age estimation, were non-exhaustive, as only ten common parameters were used to evaluate the publications, and that some of these parameters, such as minimum sample size, were "fabricated". We have not "fabricated" any of these parameters. As stated in our article [START_REF] Corron | A critical review of sub-adult age estimation in biological anthropology: Do methods comply with published recommendations?[END_REF], all ten parameters describing sampling (age, sex, age distribution, sex distribution, sample size) and statistical aspects of the publications (reliability, accuracy, precision, observer errors, validation) were adapted and summarized from published peer-reviewed recommendations, such as the work by [START_REF] Cunha | The problem of aging human remains and living individuals: a review[END_REF] or [START_REF] Schmeling | Age estimation[END_REF]. These authors and the others explicitly present these parameters as guidelines for building standardized methods in forensic anthropology [START_REF] Franklin | Forensic age estimation in human skeletal remains: current concepts and future directions[END_REF][START_REF] Cunha | The problem of aging human remains and living individuals: a review[END_REF][START_REF] Rösing | Recommendations for the forensic diagnosis of sex and age from skeletons[END_REF][START_REF] Schmeling | Age estimation[END_REF]. These articles highlight the importance of representativity but make no mention of a clear-cut minimum sample size required for validity. A few publications present several formulae to calculate minimum sample size for methods aimed at estimating the elements of the individual biological profile (age, sex, ancestry, stature) [e.g., 7, p. 314-315] but all depend on the number of individual categories (e.g. age and/or ancestry groups) and the number of indicators used as predictors. This means that a single value for sample size cannot be generalized for all age estimation methods, as it depends on the age range covered by the sample, the number and type of predictor variables, the type of analysis used and its sensitivity to sample size, and other factors. It is therefore almost entirely method-specific. Moreover, as Dr Cardoso pointed out with the example of Moorrees et al.'s, 1963 publication [START_REF] Moorrees | Age variation of formation stages for ten permanent teeth[END_REF], sample size can vary within a given method 1 .

Large referenced sub-adult collections and sets of data were difficult to come by until the relatively recent dissemination and standardization of medical images in anthropological research. These new modalities result in the variety of sample sizes covered by the publications in our corpus, some of which go as far back as the 1920'-1930's. For these reasons, a somewhat subjective, but in no way "fabricated", decision /cut-off point of the "sample size" parameter's descriptor, not of the parameter itself, was made to enable analysis and method comparisons. By setting a valid sample size at 200 individuals or above, a lower number of publications would be "invalid" for that specific parameter, as we felt it was not as clear-cut as the other four. It is true that the number 200 was chosen as a compromise more than a definite standard. This is also clearly and discussed at length in our article. However, after rerunning the analyses with any sample size considered as valid (which in itself is extremely debatable), the results remained identical: the same seven out of the 269 publications respected all other valid parameters, meaning the cut-off point at 200 for sample size is not as influential on overall sampling and statistical validity as the other 9 parameters. However, to take into consideration sample representativity and still be able to compare publications based on that parameter, it was decided to keep that threshold for sample size.

Also part of Dr Cardoso's critique was that general rather than specific analyses pertaining to each publication were done, i.e. that different modes of method validation were clumped into one statistical parameter. We acknowledged this limitation in our paper but chose to do so for the purpose of clarity and to enable method comparison by using a limited number of homologous criteria. Overall, concerning these comments on the ten parameters used for method evaluation, our paper strongly and frequently emphasized that they should be considered by users to check each selected publication for all parameters before its application. In addition, although a method may be suitable in theory (i.e. all ten parameters are valid), it is not always the case in practice, as it depends on the context and the type of material available (e.g. it is based on histological slices, or it only applies to age estimation of the living). Finally, we showed that although the call for methodological rigor and standardization of sampling and statistical parameters was published within the forensic context [START_REF] Franklin | Forensic age estimation in human skeletal remains: current concepts and future directions[END_REF][START_REF] Cunha | The problem of aging human remains and living individuals: a review[END_REF][START_REF] Rösing | Recommendations for the forensic diagnosis of sex and age from skeletons[END_REF][START_REF] Schmeling | Age estimation[END_REF], it seems reasonable to assume these principles would be applicable to any and all contexts in biological anthropology, as it is safe to say all anthropologists aim for the most accurate and reliable estimates of the biological profile.

Dr Cardoso also implied that our analyses were positively biased towards our own and our coworkers' publications, writing that our study was done to "insure that certain methods were left out or were included in the list [START_REF] Cardoso | A critical response to "A critical review of sub-adult age estimation in biological anthropology[END_REF]." This brings us to his comment questioning the scientific integrity of our study: "Ultimately, it is surprising to see that 3 methods in the list of 7 are authored by Corron and co-workers and by some of Corron's co-authors. (Cardoso, 2019)". Our goal is to discuss, and possibly promote good methodological practices for building, selecting and applying sub-adult age estimation methods. Therefore, the methods we or our coworkers have published since the guidelines on sampling and statistical validity were first issued naturally strive to follow and respect them! As such, our efforts are put towards using samples composed of individuals of known age and sex; our publications explicitly present tests, tables and/or plots assessing even age and sex distributions; and the five statistical parameters cited above comply with validity standards as presented in these published recommendations [START_REF]Biométrie radiologique des os de la main : application à l'estimation de l'âge des individus immatures. 8emes Journées d'anthropologie de Valbonne[END_REF][START_REF] Daumas | Bidimensional data allow for better age estimation on immature specimens than unidimensional data: a preliminary study on the ilium[END_REF][START_REF] Corron | A new approach of juvenile age estimation using measurements of the ilium and Multivariate Adaptive Regression Splines (MARS) models for better age prediction[END_REF]. Whether these publications are suitable for use as sub-adult age estimation in any context is a different question that only the user can answer, as we clearly mentioned and advised in the paper.

Finally, Dr Cardoso suggested that we "provide the experts with the means to select the methods themselves, by critically reviewing the recommendations." We agree with this statement, which is why we published a follow-up article to do just that [START_REF] Corron | Sub-adult aging method selection (SAMS): a decisional tool for selecting and evaluating subadult age estimation methods based on standardized methodological parameters[END_REF]: Sub-adult Aging Method Selection, or SAMS, is a freely accessible online decisional tool to assist biological anthropologists, and forensic anthropologists in particular, in critically selecting and evaluating sub-adult age estimation publications. Users have complete freedom in the process of method evaluation and more flexibility to select methods adapted to their case or context, as additional descriptive parameters, too variable to be of any analytical use in the first study [START_REF] Corron | A critical review of sub-adult age estimation in biological anthropology: Do methods comply with published recommendations?[END_REF] were included. As Dr Cardoso pointed out, and because of the limited access to certain relevant publications, our database is still incomplete. However, we trust that the biological anthropology community will help us fill that gap with any existing missing publications. They will be bi-annually implemented into the SAMS database along with any new publications on the topic. Although users will be absolutely free to select any method of their choice, because we aim to remain as objectively critical as possible in method selection and evaluation, they will still be informed on how much a publication on sub-adult age estimation respects the 10 parameters for methodological validity via the two parameters we set up to characterize the publications in SAMS: Validity, Relevance and Score (see http://osteomics.com/SAMS/ for more details).

Although sample size for the central incisors is n=134 and n=236 for the rest of the dentition, the MFH method is still considered to respect the validity criteria of n

200, as this method is not recommended for use on a single tooth alone.

Funding

This work was funded by Ministère Français de la Recherche et de l'Enseignement Supérieur.

CRediT authorship contribution statement

L. Corron: Conceptualization, Writing -original draft, Writing -review & editing. F. Marchal: Conceptualization, Writing -review & editing. S. Condemi: Conceptualization, Writing -review & editing. P. Adalian: Conceptualization, Writing -review & editing.


Françoise Girardot

Séverine Allegra

Stéphane Pfendler

Cyrille Conord

Carine Rey

Benjamin Gillet

Sandrine Hughes

Anne Emilie Bouchardon

Anna Hua

Frédéric Paran

Françoise Girardot

Jean Luc Bouchardon

Olivier Faure

Francoise Girardot
email: francoise.girardot@univ-st-etienne.fr

Bacterial diversity on an abandoned, industrial wasteland contaminated by polychlorinated biphenyls, dioxins, furans and trace metals

Keywords: Brownfield, Polychlorobiphenyls, Polychlorinated dibenzo-p-dioxins and dibenzofurans, Metals, Community-level physiological profiling, 16S metagenomics

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

Introduction

Deindustrialization has left a legacy of many polluted wastelands. It is estimated that in French urban areas, brownfields represent an estimated real estate potential of 140,000 hectares (Plottu and Tendero, 2017). The French Database on Polluted Sites and Soils (BASOL) lists 7331 polluted sites requiring government action. Among them, 58% were polluted by at least 3 compounds and 5% by mixtures of 10 to 16 chemicals (BASOL, 2020).

Among pollutants, trace metals are a worldwide issue with more than 5 million polluted sites (He et al., 2015). Given that metals are persistent, they pose a threat to ecosystem functions and human health (Li et al., 2019;Liu et al., 2018). Persistent organic pollutants (POPs), such as polychlorinated biphenyls (PCBs), polycyclic aromatic hydrocarbons (PAHs), and polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs), are resistant to biodegradation and are thus of major environmental concern in most industrialized countries (Ma et al., 2005, IARC, 2016). Indeed, these ubiquitous toxic molecules may have numerous adverse effects on living organisms, particularly on human health, as they can affect the immune, nervous, endocrine and reproductive systems (Olanca et al., 2014). Furthermore, PAHs and PCDD/Fs are recognized as carcinogenic, while PCBs are probable human carcinogens (Breivik et al., 2004).

PAHs are a family of 136 fused benzene ring molecules naturally present in coal and petroleum products. They are also produced during incomplete combustion of organic compounds (Gupta et al., 2015). PCBs gather 209 organic chlorinated molecules differing by the number (up to 10) and the position of the chlorine substitutes on phenyl rings. These synthetic compounds were used from the 19th century to the 1980s, mainly as heat transfer fluids and insulators in electrical transformers and condensers. Numerous accidental releases or illegal disposal practices have resulted in PCBs being widespread environmental contaminants (Tehrani and Van Aken, 2014). PCDD/Fs, a family of 210 congeners, are by-products of several industrial processes (Dyke et al., 1997;Hutzinger and Blumich, 1985) or of combustion processes such as those of fossil fuel, PCBs, forest fires, and waste incineration (de Souza Pereira, 2004). In addition, the use of wood preservatives, herbicides and pesticides synthesized from chlorophenols has resulted in the release of large amounts of PCDD/Fs into the environment (Chen et al., 2016).

Precise and rapid analytical methods exist for identifying and quantifying PAHs, PCBs and PCDD/Fs from environmental samples. However, because of technical and financial constraints, only a reduced set of congeners are routinely monitored. For PCBs, a set of 7 congeners called indicator-PCBs 52,101,118,138,153 and 180) were selected because they were present at high levels in commercial mixtures. Similarly, 17 PCDD/Fs and 16 PAHs were identified as priorities by the US Environmental Protection Agency due to their toxicity and large presence in the environment (US EPA, 2007).

Nonetheless, the only quantification of POPs and trace metals does not provide any information regarding the possible interactions between the different molecules, their bioavailability, and ultimately their biological impact (Fontanetti et al., 2011), which are of prime interest when assessing contaminated sites. Consequently, for a more informative assessment of multi-contaminated soils, there is a genuine interest in combining chemical analysis with biological investigations.

The study site was a brownfield where several industrial activities were successively carried out starting in 1970 (BASIAS, 2020): scrap-yard and car body burning, copper recovery by open-air cable burning, incineration of pyralene transformers, storage of domestic fuel, surface treatment, and wood storage. In 2008, 25000 m 3 of reclaimed wood stored on the site caught fire and burned for 3 months. An investigation carried out in 2009 revealed total I-PCB levels ranging from 10 to 2.10 3 mg.kg -1 (unpublished data). In this context, we studied the soil biological functions and the structure of the bacterial populations occurring after 4 years on a small area of the brownfield that was climatically and pedologically homogeneous.

Microbial functions were investigated by community-level physiological profiling (CLPP), which allows the discrimination of communities according to the utilization pattern of 31 carbon sources (Aguirre de Carcer et al., 2007;Classen et al., 2003;Insam, 1997;Preston-Mafham et al., 2002). To investigate bacterial biodiversity, 16S metagenomics coupled with new generation sequencing using Illumina was used. We completed our investigation by characterizing plant communities and soil pedology. Furthermore, we determined which pollutant or abiotic parameter was the main driver of bacterial structure and function. Rather than solely reporting levels of contaminants, our study aims to provide a much more precise picture of the impact of abiotic factors on the bacterial fraction taken as an indicator of soil functioning. To our knowledge, this study is the first field investigation using these methods for assessing soils with multiple contaminants.

Materials and methods

Site description and sampling plots

The study site is located at Saint-Cyprien (Lambert-93 coordinates: X=795445, Y=6494391), approximately 30 km north of Saint-Etienne (Loire, France). It is listed in the Basol database (BASOL, 2020) under reference 42.0034. The site is an abandoned wasteland and approximately 8,000 m 2 . In 2009, the site was divided into 80 plots of 100 m 2 , and first I-PCB analyses (samples collected from the surface to 1 m in depth) were performed in the soil as part of the legal investigation (unpublished data). Based on these data, 4 plots were selected for this study (Fig. 1): the highest PCB-contaminated area in the north (F2) and the south (D10) and the lowest PCB-contaminated area in the north (C2) and the south (A10) of the parcel. Unlike the southern areas, the northern areas were flooded during the rainy season.

Soil sampling

Five sampling campaigns were performed in 2012 (April 19 th , June 1 st and 22 nd ) and 2013 (April 8 th and July 1 st ), and 5 soil samples per plot (0-10 cm in depth) were collected during each sampling after removal of the litter. In the soils, the leaching of PCPs is very low, and the molecules tend to accumulate at the surface. Therefore, the choice was made to harvest only the top fraction to avoid an underestimation of organic pollution. For microbial analyses, samples were collected aseptically in sterile containers and stored at 4°C before sieving through a 2-mm mesh sterile screen. Samples for 16S metabarcoding were stored at -80°C. The moisture content was determined in parallel with each analysis using the standardized ISO 11465 method (ISO11465, 1994).

Soil pedological characteristics

Pedological analyses (particle size distribution, organic carbon, total available phosphorus, total nitrogen, total carbonates, pH in water, and cation exchange capacity (CEC)) were performed by the Laboratory for Soil Analyses at the National Institute for Agronomic Research (INRA Arras, France accreditation n° 1-1380, https://www.cofrac.fr).

Analyses of organic pollutants

PCBs, PCDD/Fs and PHAs were analysed by the INRA Laboratory for Soil Analyses.

The toxicity equivalent concentrations (Teq) for the PCDD/Fs and PAHs were calculated as follows (WSDE, 2007): where C n is the concentration of the individual PCDFs, PCDDs or PAHs, and TEF n is their toxic equivalency factor. For PCBs, Teq was calculated with only 2 dioxin-like PCBs recorded, i.e., PCB-105 and PCB-118 congeners.

Trace metal determination

The total trace elements (TM) were determined by X-ray fluorescence. Available trace elements were extracted with 0.01 M calcium chloride as previously described (Houba et al., 2000) and measured by inductively coupled plasma mass spectrometry (ICP-AES).

Plant survey

A survey of the main plant species present in each plot was carried out 5 times in 2012 and 2013 by 2 experienced field botanists. Plant names were standardized according to the Plant List Database (http.theplantlist.org). For each species, Raunkiaer's life-form type and Ellenberg's autoecological ratings (preferences for light, temperature, pH, N-P-K nutrients, salinity, and soil humidity) were calculated from the Baseflor database (Julve, 1998).

Ellenberg's indicator values (EIVs) for each plot were calculated as the median value of all species identified in the plot.

Community-level physiological profiling

EcoPlates (Biolog, France) contain 96 wells with 3 replicates of 31 carbon substrates and a control well without any carbon source (Insam, 1997). Samples were prepared by mixing 10 g fresh soil with 90 mL of sterile 0.2% w/v sodium hexametaphosphate at room temperature for 30 min. The suspension was then diluted 100-fold in phosphate-buffered saline to minimize background colour. Each well was then inoculated with 150 µL of the suspension. Three plates were used for each plot, and data were collected after 45 h of incubation, corresponding to approximately the mid-exponential growth phase. Formazan production was quantified by measuring the optical density at 590 nm (OD 590 ) with a microtiter plate reader spectrophotometer (Tecan, Switzerland). Initial OD 590 values were measured immediately after inoculation and were subtracted from subsequent readings. Plates were then kept at 25°C in the dark, and the raw OD 590 was read regularly until it reached a plateau. The mean raw OD 590 of each similar well was calculated, and the raw OD 590 values were corrected for the background colour in the control well. Wells with OD 590 values>0.25 were considered positive (Garland, 1996), while others were set to zero. Data were normalized by dividing the OD 590 of each well by the dry mass of the soil samples (Classen et al., 2003). For each plot, the overall microbial activity was estimated by calculating the average well colour development (AWCD). Functional diversity was estimated by assessing both the substrate richness (S) and Shannon's diversity index (H) as previously described (Garland, 1996;Weber et al., 2007).

Soil DNA extraction, 16S amplification and sequencing

Total DNA was extracted from 0.25 g of soil for each of the 12 samples (4 plots and 3 sampling dates in 2012 and 2013) using the Power Soil TM DNA extraction kit (Mo BIO Laboratories, Carlsbad, CA, USA) and according to the manufacturer's instructions.

The V3 region of the bacterial 16S rRNA gene was amplified following the protocols detailed in Téfit et al. (2018), except that 25 PCR cycles were performed. After construction of new generation sequencing (NGS) libraries and equimolar mixing, the amplicons were sequenced in a PGM sequencer (Ion torrent) using Ion 318 chips (Téfit et al 2018). Several procedures to avoid and monitor exogenous bacterial DNA contamination with multi-step controls were strictly followed: mainly, experiments were conducted in pre-and post-PCR dedicated rooms, with UV decontamination and mock extraction, and the negative and aerosol PCR controls were performed as detailed elsewhere (Téfit et al., 2018).

Metagenomics analysis

First, the quality of the reads was checked, and sequences shorter than 300 bp, with quality scores less than 20 or containing one or more unknown bases were deleted using Trimmomatic (Bolger et al., 2014). Then, the reads were re-assigned to each sample according to their unique barcode with no mismatch using FASTX-Toolkit software. The barcodes were removed before subsequent analysis. Finally, taxonomic assignment and operational taxonomic unit (OTU) definition were performed using the Mothur pipeline (Schloss et al., 2009) following the steps detailed below.

First, the sequences were aligned to the SILVA database (Quast et al., 2013) (restricted to the 16S V3 domain) using the Needleman-Wunsch distance. Reads with weak alignment scores were discarded (SearchScore < 60 and SimBtwnQuery&Template < 80).

Then, sequences were pre-clustered at 99% to reduce sequencing noise and computational effort during the taxonomic assignment of each cluster representative in the SILVA database.

Next, OTUs were defined using abundance-based greedy clustering (AGC) at 97% sequence similarity. All scripts used for the analyses are available upon request. Finally, 122401 OTUs were obtained for the 12 samples. The data have been submitted to the NCBI bioproject database under the number PRJNA647634 and sequence data for all samples are available with the accession numbers going from SAMN15595561 to SAMN15595572.

Statistical analysis

Statistical analyses were performed using R software v. 1.0.136 (R core team, 2016).

Differences were considered significant for p values <0.05. The distribution-free Kruskal-Wallis test, followed by the Steel-Dwass-Critchlow-Flignerwas (SDCF) multiple comparisons tests, was used to compare pedologic descriptors among the samples. Principal component analysis (PCA) was performed to compare the CLPP patterns of substrate utilization and 16S metagenomics data for each plot. Additionally, microbial community composition was calculated using the SHiny Application for Metagenomics Analysis (Shaman) based on the DESeq2 R package (Quereda et al., 2016).

For TM analysis, the results were pre-treated to obtain compositional data (relative proportion of the compound in the sample) and were log-ratio centred and scaled to improve the outputs from the multivariate analyses (Hervé et al., 2018). A redundancy analysis (RDA) was used to test the simple and interactive effects of one or more explanatory variables on the differences in the elementary profiles using a permutation test.

Results

Pedological characteristics of the four sampling plots

Table 1 shows the pedological characteristics of the 4 studied plots. Soils were characterized by a high sand content (>70%) and low clay (6-11%) and silt (9-17%) contents.

There was a significant difference (p<0.05) in the sand content between plots C2 and D10 and in the clay content between plot A10 and plots C2 and F2. According to the United States Department of Agriculture texture classification, plot C2 was sandy loam, whereas the other plots were loamy sand. The contents of organic carbon, total nitrogen, available phosphorus, total carbonates and CEC were not significantly different between the plots. The C/N ratio was significantly lower in the F2 plot than in the other plots (14 for F2 and > 20 for the other plots). The soil pH in the water was significantly higher in the A10 plot (8.1) than in the F2 (6.9) and D10 (7.1) plots.

Levels of POPs in the 4 sampled plots

The levels of POPs in the 4 sampled plots are given in Table 2 (see supplementary material Table S1 and Fig. S1 for more details). In addition to the 7 I-PCBs generally monitored for soil pollution characterization, we analysed 13 supplemental congeners to better cover the range of potential chlorination levels and to obtain insight about highly chlorinated congeners. On average, the 7 I-PCBs represented 70-75% of the total concentration of the 20 selected PCBs. High heterogeneity in the concentrations was observed, ranging from approximately 8 mg.kg -1 DW in the C2 plot to close to 1.5 10 3 mg.kg - 1 DW in the D10 plot (Table 2). The distribution pattern of the studied congeners was almost the same for the C2, A10 and D10 plots and was characterized by a high proportion (more than 75%) of highly chlorinated molecules with 6 or more chlorine atoms. In contrast, in the F2 plot, the most prominent congeners were tetra-, penta-and hexa-chlorinated PCBs, together representing close to 95% of the total PCBs. Soil contamination with PCDD/Fs was also highly heterogeneous (supplementary material, Fig. S1c), ranging from approximately 0.5 g Teq.kg -1 DW in the A10 plot to 7.9 g Teq.kg -1 DW in the D10 plot (Table 2). In the C2 plot, more than 80% of the PCDD/Fs were hepta-and octo-chlorinated congeners (supplementary material, Fig. S1d). In contrast, in the D10 plot, more than 80% of the PCDD/Fs were congeners with 4 to 6 chlorine substitutes. In the A10 and F2 plots, approximately one half of the congeners were molecules with 4 to 6 chlorines, and the other half were heavier molecules with 7 or 8 chlorine substitutes.

PAH contamination followed the same trend as PCB contamination, with a clear concentration gradient (supplementary material, Fig. S1e), ranging from 1 µg Teq.kg -1 DW in the C2 plot to 260 µg Teq.kg -1 in the D10 plot (Table 2). The distribution pattern of the PAH congeners was almost the same in plots A10, F2 and D10, with approximately 75% of the molecules consisting of 4 to 6 rings. By contrast, in plot C2, almost 90% of the congeners were lighter molecules with 2 or 3 rings, the most prominent of them being naphthalene (approximately 60% of the total PAHs).

Levels of trace metals in the 4 sampled plots

The levels of trace metals in the 4 sampled plots are shown in Table 2. In all plots, the levels of Cu, Zn and Pb were higher than 187, 217 and 372 mg.kg -1 , respectively. Regardless of the TM considered, the highest levels were measured in plot C2, while the lowest levels were found in plot F2. Concerning CaCl 2 -extractible trace metals, the highest levels were found in the C2 plot for Cu but in the plot D10 for Pb and Zn. TM patterns were analysed by compositional PCA. The two first components explained 71% of the variance (Fig. 2). The C2 plot was separated from the other plots on the component 1 axis; by contrast, the second principal component clearly separated the F2 plot from the A10 and D10 plots, which were grouped. The C2 plot differed from the other plots by its levels of Cu, Pb and Zn (Fig. 2;

Table 2), and the F2 plot was characterized by a globally lower content of TM.

Plant community structure

The species composition of the plant communities found in each plot is shown in the supplemental material (Table S2). Within the 4 investigated plots, 71 different species from 25 different families were identified. The number of species per plot varied from 33 (F2 plot) to 41 (A10 plot). Thirteen species were found in each plot, while 33 were identified in only one plot. The visual estimate of plant cover was approximately 50% in all plots except at F2, where it was close to 70%. The Asteraceae family was predominant in all plots except in the F2 plot, where Fabaceae were the most represented. Most species were Hemicryptophytes (i.e., perennial grasses and herbs), accounting for 45% (F2 plot) to 62% (D10 plot).

Therophytes (i.e., annual grasses and herbs) accounted for 27% (F2 plot) to 37% (A10 plot) of the plant communities. Geophytes (i.e., perennial plants with bulbs or rhizomes) accounted for between 5% (D10 plot) and 15% (F2 plot) of the plants, and Phanerophytes (i.e., shrubs and bushes) accounted for between 0% (A10 and D10 plots) and 12% (F2 plot).

The EIVs (Fig. 3) showed that plant communities in each plot had the same ecological requirements except for edaphic humidity, which was slightly higher in plots C2 and F2 than in the other plots.

Community-level physiological profiling

The assessment of the bacterial communities by CLPP showed that in all plots, 7 substrates out of 31 were never used (D-xylose, phenylethylamine, L-threonine, Dglucosaminic acid, glycyl-L-glutamic acid, -ketobutyric acid and -D-lactose), while 9 of them were catabolized in all the plates (D-galacturonic acid, L-asparagine, tween 40, tween 80, D-mannitol, 4-hydroxybenzoic acid, L-serine, N-acetyl-D-glucosamine, and putrescine).

The other substrates were differentially metabolized according to the samples. Substrate richness (S), Shannon's diversity index (H) and AWCD values (Table 3) were the highest in the F2 plot, followed by the C2 plot. The lowest values were found in the A10 and D10 plots and were not significantly different. Substrate utilization patterns were further compared using PCA (Fig. 4a). The two first components explained 83% of the variance. The first axis (62%) was mostly driven by 4hydroxybenzoic acid, D-galactonic acid--lactone, pyruvic acid methyl ester, D-galacturonic acid, D-mannitol, itaconic acid and putrescine, while the second axis (21%) was mostly driven by 2-hydroxybenzoic acid, D-malic acid, D,L--glycerol phosphate, cyclodextrine and L-serine (supplementary material,Fig. S2a). The scatter plot of principal component scores showed a clear separation of the studied plots. The C2 plot was mainly separated from the other plots on the first axis; by contrast, the second principal component clearly separated plot F2 from the other studied plots.

Taxonomic composition of the soil samples and comparison of bacterial communities

A total of 122,401 OTUs were obtained from the data analysed. The OTUs were grouped into 32 phyla, 923 families and 983 genera. The bacterial community (Fig. 5) was mainly represented by Proteobacteria (30 to 50%), Acidobacteria (10 to 40%) and Actinobacteria (12 to 35%). The profiles obtained for the different sampling campaigns showed similar patterns. In each plot, the 3 main orders were Sphingomonadales, Rhizobiales and Acidobacteriales. However, their respective contributions to the bacterial community varied between plots: Acidobacteriales was dominant in the A10 and D10 plots with 27% and 48% OTUs, respectively; Sphingomonadales was dominant in the C2 plot (16%), and

Rhizobiales was dominant in the F2 plot (26%). The fourth bacterial group was Actinobacteria (6 to 7%), which was present in all plots except C2, where it was Chloroflexi (8.5%) was dominant. The family richness was similar between the F2 and C2 plots (477±20 and 470±34, respectively) but significantly lower for the A10 and D10 plots (395±32 and 403±3, respectively).

The PCA carried out at the family level is shown in Fig. 4b and supplementary material, fig. S2b. The first axis (31.5%) clearly separated plots A10 and D10 from plots C2 and F2. In addition, the second axis (19.4%) separated the F2 plot from the 3 other plots.

Discussion

Study site has unusual high levels of PCBs and PCDD/Fs

In European countries, the background concentration for PCBs in soils is approximately 2.5 g.kg -1 (INERIS, 2012;Li et al., 2010). In comparison with these reference values, the values in the 4 studied plots had marked PCB contamination (Table 2), reaching between 2.4 x 10 3 -fold (int the C2 plot) and 6 x 10 5 -fold (in the D10 plot) the background level. It is noteworthy that no site listed to date at a global scale had such levels of PCBs (IARC, 2016). The studied site also showed very high PCDD/F contamination, with concentration values ranging from 250-fold (the A10 plot) to 3,900-fold (the D10 plot) the background level of 0.002 µg Teq.kg -1 , as determined for European soils (Bodenan and Michel, 2013). In contrast, PAH contents were in the range of the background levels for European soils, that is, <2 10 3 µg TE.kg -1 (Nam et al., 2008). Moreover, the levels of PAHs did not exceed the predicted non-effect concentration (PNEC) of 320 µg.kg -1 established for benzo(a)pyrene (INERIS, 2006) or the ecological soil screening level (Eco-SSL) of 18 mg.kg - 1 established by the US EPA (US EPA, 2007) for high molecular weight PAHs. Therefore, although no PNEC or Eco-SSL has been published to date for PCBs and PCDD/Fs, we c conclude that the POPs of concern at the study site are PCBs and PCDD/Fs but not PAHs.

Moreover, the 4 sampled plots differed in their POP profiles. This was particularly noticeable for the PCBs in the F2 plot, which showed a higher proportion in minimally chlorinated congeners compared with that in the other plots. This was also the case for PCDD/Fs, which were enriched in highly chlorinated congeners in the C2 plot, while they were mostly minimally chlorinated in the D10 plot. It has been demonstrated (Correa et al., 2010) that PCB toxicity towards bacteria varies among congeners and is higher for highly chlorinated congeners. At the other end of the spectrum, the bioavailability of PCBs and PCDD/F in soils, i.e., their capacity to interact with biological targets, generally decreases with the level of chlorination (Shiu and Mackay, 1986). In addition, the toxicity of POPs depends on the content and form of organic matter in soil (Kim and Lee, 2002) and could increase due to synergistic interactions with trace metals.

Trace metal contamination was identified for Pb, Cu and Zn compared to their background levels in agricultural French soils (Baize, 2000). Due to the local geology, some

Zn and Pb could be linked to the presence of zincblende (ZnS) and galena (PbS) in detrital materials. However, the high quantities of Zn and Pb in the study area are more likely due to former car-burning activities, as paint residues, tire debris and motor oil are sources of Zn and Pb (Garba and Abubakar, 2018). The high copper concentrations are probably related to the burning of electrical cables.

In our study, 0.1 to 0.3% Cu, less than 0.02% Pb and 0.05 to 1.6% Zn were extracted by CaCl 2 . These low percentages are similar to those obtained in a study with loamy sandand sandy loam-contaminated and uncontaminated Japanese soils (Kashem et al., 2007).

Metal availability depends on metal concentrations and soil properties such as pH, organic matter, CEC or clay content (Almas andSingh, 2017, Giller et al., 2009). Although plot C2 had the highest total TE levels, the CaCl 2 -extractable fraction of Pb and Zn was higher in plot D10. This is likely because of heterogeneities in the pedological characteristics since metal availability depends on metal concentrations as well as on soil properties (Almas andSingh, 2017, Giller et al., 2009). In addition to PCB and PCDD/F toxicity, Cu, Zn and Pb toxicity towards soil biota could be expected.

In summary, the 4 studied plots showed a clear concentration gradient for PCBs increasing in the order of C2<A10<F2<D10, PCDD/Fs increased in the order of C2/A10<F2<D10, and total trace metals followed the order of F2<A10/D10<C2. However, the PCAs had 2 different major patterns: (i) the A10 and D10 plots, located in the south part of the parcel, showed similar metal pollution levels and could be compared based on their difference in POP levels, and (ii) the F2 and C2 plots, located on the north of the site, in a periodically flooded area, showed either high metal pollution (C2) or very high POP levels (F2). Comparing the F2 and C2 plots could help determine the main driver among the metal and organic pollutants shaping bacterial communities.

Plants

The vegetation at the site was dominated by perennial and annual grasses and herbs.

Except in the F2 plot, where the plant cover was significantly higher than in the other plots, the vegetation was sparse and exhibited areas with bare soil, as is commonly observed in metal-polluted soil (Heckenroth et al., 2016;Nagendran et al., 2006). Vegetation also included plants able to accumulate Zn (Silene vulgaris and Hypericum perforatum) or Pb (Festuca ovina), 50% of the plants were typical of abandoned lands (e.g., Bromus tectorum L.

and Senecio inaequidens DC) and 5 pioneer plants (e.g., Silene vulgaris and Alisma plantagoaquatica L.) were found. We also found 1/4 of annual commensal plants associated with crops (e.g., Senecio vulgaris and Sonchus asper)

According to Ellenberg index values (EIVs), the difference in the moisture content between the plots was the main driver of vegetation. Similarly, studies comparing EIVs with field measurements have shown discrepancies (Chytry et al., 2009), and EIVs do not take pollution into account.

Functional diversity of microbial communities depends on plot localization

CLPP is regarded as a culture-based assay even if both culturable and non-culturable bacteria can contribute to tetrazolium salt reduction. Some authors have claimed that CLPP highlights a very small fraction (i.e., <1%) of a bacterial community (Torsvik and Ovreas, 2002) and that fast-growing species skew the test (Preston-Mafham et al., 2002). Moreover, some bacteria are not able to reduce the tetrazolium dye, and therefore, the functional ability of the entire community is not measured (Ros et al., 2008). On the other hand, some researchers have reported that culture methods are more appropriate for studying the effect of contaminants because cultivable bacteria "may constitute the ecologically relevant genetic pool in soils" (Puglisi et al., 2012). In this study, CLPP showed that the bacterial activities in the A10 and D10 plots were very similar and clearly separated from those in the C2 and F2 plots. Therefore, CLPP reflected differences related to the presence of TM.

Substrate richness (S) and Shannon's diversity index (H) AWCD were highest in the F2 plot, where POP levels were very high, and the lowest in the A10 and D10 plots, which had both high metal and organic pollution. The C2 plot, which was the most contaminated with TM, showed intermediate S, H and AWCD. Taken together, these results suggest that neither TM alone nor POPs alone were major limiting factors for bacterial activities. In contrast, the combination of TM plus POPs had a significant impact on bacterial communities at this site. Studies on the effects of metal or organic pollutants on bacterial communities are contradictory (Puglisi et al., 2012, Valentin et al.2013), but it is assumed that many bacterial functions are redundant and can quickly replace those lost due to a given environmental stressor (Allison andMartiny, 2008, (Maron et al., 2018). However, in the case of multiple stressors, such as metals plus organic pollutants, the response is more complex, depending on soil properties and the type of stressors (Azarbad et al., 2015). In our study, the combination of metal stress and PCBs-PCDD/Fs was detrimental to bacterial activities.

Pattern of bacterial taxa may be affected by pollution

Proteobacteria are usually the dominant phylum in soils, followed by Acidobacteria, Actinobacteria and Verrucomicrobia (Bruns, 2017). Firmicutes, Planctomycetes, Chloroflexi, Gemmatimonadetes, and Cyanobacteria are generally found at levels of 1 to 5% (Bruns, 2017). In an Italian wasteland, Ventorino et al. (2018) showed that uncontaminated areas consisted of 39% Actinobacteria. However, in areas contaminated by Zn, Cu and PHAs, the abundance of Actinobacteria, Firmicutes, Gemmatimonadetes and Chloroflexi significantly dropped, while the relative abundance of Proteobacteria, Acidobacteria, Verrucomicrobia and Bacteroidetes increased. In another study comparing river sediments (Yin et al., 2015), in comparison to other phyla, Firmicutes, Chloroflexi and Acidobacteria were more represented in highly TM contaminated samples. In our study, Proteobacteria, Acidobacteria and Actinobacteria were the most abundant phyla in each plot. However, Verrucomicrobia was hardly detected (0.7% of OTUs), and Chloroflexi was the fourth most dominant phylum. At the study site, Actinomycetes did not exceed 7% of the 10 major taxa. TM pollution could be responsible, as it has been shown that Actinobacteria are sensitive to metals (Lugauskas et al., 2005;Yin et al., 2015).

Additionally, Rhizobiales (a subgroup of -Proteobacteria) were approximately 2-fold higher in the F2 plot (which also had the greatest richness of OTUs) than in the other plots.

Several studies (Chaudri et al., 2008;Giller et al., 1989;Hirsch et al., 1993) have shown that most Rhizobiales are Zn sensitive (killed or lose their ability to fix nitrogen). Because F2 had a relatively low Zn content, we may assume that Zn pollution could be responsible for the relatively low abundance of Rhizobiales in metal-contaminated plots.

Bacterial communities are shaped by metal and POP pollutants

Acidobacteria (e.g., RB41 family, subgroup 6, Candidatus Solibacter and Candidatus Koribacter) were dominant in the D10 plot and second most dominant in the A10 plot, although the soil pH was neutral to alkaline. It has been demonstrated that exposure to highly chlorinated PCBs (such as those found in the D10 and A10 plots at a high level) results in a higher abundance of members of Acidobacteria to which the most PCB degraders belong (Aguirre de Carcer et al., 2007). Moreover, Acidobacteria subgroup 6 is known for its high metal resistance (Yin et al., 2015), and a positive correlation between Cu, Pb and Zn and the abundance of Acidobacteria, such as Candidatus Koribacter, has been recorded (Wang et al., 2018). Therefore, the abundance of Acidobacteria in the A10 and D10 plots could be linked to their capability to cope with metals and PCBs simultaneously.

Geodermatophilaceae and KD4-96, which belong to Chloroflexi, were well represented in the C2 plot. Both groups are linked in the literature with highly heavy metal-or TE-polluted soils (Normand et al., 2014;Yin et al., 2015). Sphingomonadales were very abundant in all plots. Members of this taxa are able to degrade minimally chlorinated PCBs and dioxins using aerobic pathways (Abraham et al., 2002;Field and Sierra-Alvarez, 2008), as is also the case for Hyphomicrobium present in the F2 plot.

Conclusions

The study site was one of the most PCB-and PCDD/F-polluted sites ever described worldwide (IARC, 2016), and it has accumulated significant metallic pollution. Our study showed clear biological and chemical differences between plots. The assessed characteristics of the plots, including total elements, microbial activities, bacterial composition and, to a lesser extent, vegetation, provided evidence that the C2 and F2 plots were clearly different and distinct from each other from the A10 and D10 plots, which appeared similar. The combined presence of both metals, PCBs and PCCD/Fs (e.g., in the D10 and A10 plots), was probably the cause of the poorer functional diversity in these plots than in the other plots. TM impaired the bacterial community structure through the inhibition of Rhizobia and Actinobacteria. However, we determined that the bacterial groups present were able to cope with multi-contamination of the soil (Acidobacteria, Sphingomonadales, and Chloroflexi).

These observations show that this brownfield site should be popular choice for further studies.

6-Acknowledgements

This project was financially supported by Saint Etienne Metropole. We thank the University of Saint Étienne, IGFL and Mines Saint Etienne for their support. We thank Thibault Munoz for his technical assistance and the students of the Biology Master (ENS Lyon/UCBL) from the UE "Practicals in NGS" 2018 and its organizer Marie Sémon for the metagenomic analysis.

Tables Table 1: Median (median absolute deviation between brackets) of selected pedological characteristics of the 4 studied plots (n=5). In a same column, different letters indicate significant differences between plots at p<0.05. C org: organic carbon; N tot: total nitrogen; CaCO 3 : total carbonates; CEC: cationic exchange capacity; P 2 O 5 : available phosphorus.

Plots

  Bacterial activities as determined by CLPP. Substrate richness (S), Shanon's diversity index (H), and Average well color development (AWCD). Mean values, n=3, standard deviation between brackets. Different letters in a same column indicate significant differences at p<0.05.

Figures

  Figures

Fig. 1 :

 1 Fig. 1: (a) Aerial view of the study site. (b) General view of the site. (c) Ranges of I-PCBs contamination (mg.kg -1 DW), as measured in 2009 in a first pollution assessment (hatched areas were not sampled). Plots selected in the present study are A10, C2, D10 and F2.

Fig. 2 :

 2 Fig. 2: Compositional principal component analysis of total TM values from the four studied plots.

Figure

  Figure Click here to download Figure: Figures_revision.docx

Fig. 4 :Fig. 5 :

 45 Fig. 4: Principal component analysis of Biolog ecoplates values (a) and bacterial diversity observed with 16S sequencing at the family level for the 12 taxa that contribute the most to the axis diversity (b) from the four studied plots.

Table Click here to download Table: Tables_ Anapop_revised.docxTable 2 :

 Click2 Levels of organic (POPs) and total concentration of selected TM (n=4, standard deviation between brackets). Teq : toxic equivalents. According to usual TM levels in agricultural soils(Baize, 2000), * indicates moderate anomalies, ** major anomalies and *** above major anomalies. Lowest and highest values are shown in the table in light grey and dark grey, respectively.


J Begey

M Etiévant

J Quispe

A Bolopion

M Vedrines

J Abadie

S Régnier

N Andreff

P Renaud

A Manipulability Criterion for Magnetic Actuation of Miniature Swimmers with Flexible Flagellum

The use of untethered miniature swimmers is a promising trend, especially in biomedical applications. These swimmers are often operated remotely using a magnetic field commonly generated using fixed coils that can suffer from a lack of compactness and heating issues. The analysis of the swimming capabilities is still an ongoing topic of research. In this paper, we focus on the ability of a magnetic actuation system to operate the propulsion of miniature swimmers with flexible flagellum. As a first contribution, we present a new manipulability criterion to assess the ability of a magnetic actuation system to operate a swimming robot, i.e. to ensure a displacement in any desired direction with a fixed minimum speed. This criterion is developed thanks to an analogy with cable-driven parallel robots. As a second contribution, this manipulability criterion is exploited to identify the dexterous swimming workspace which can be used to design of new coil configurations as well as to highlight the possibilities of moving coil systems. A case study for a planar workspace surrounded by three coils is in particular carried out. The accompanying video illustrates the application of the proposed criterion in 3D, for a large number of coils.

I. INTRODUCTION

Positioning and steering magnetically actuated devices have attracted wide attention due to the large range of applications, in particular for the biomedical domain. Such a remote actuation approach was considered for minimally invasive operations, targeted drug delivery, displacement toward hard-to-reach areas, or micromanipulation [START_REF] Sitti | Miniature devices: Voyage of the microrobots[END_REF][START_REF] Nelson | Microrobots for Minimally Invasive Medicine[END_REF]. Magnetically actuated swimmers emerged as viable candidates for such tasks at a small scale in fluidic environments, but their control is still a challenge. By definition, in a low Reynolds number environment, viscous forces are indeed dominant. Thus, volumic forces tend to be negligible and the Navier-Stokes equation becomes time-independent [START_REF] Purcell | Life at low reynolds number[END_REF][START_REF] Chaillet | Microrobotics for Micromanipulation[END_REF]. This is why it becomes fundamental to base swimming sequence on non-reciprocal animations [START_REF] Taylor | Analysis of the swimming of microscopic organisms[END_REF], i.e. a succession of movements that do not counterbalance each other. Magnetic actuation of micro-robots can be split into two categories, force-based, and torque-based approaches. The first one requires a magnetic gradient in order to induce pulling force [START_REF] Mahoney | Five-degree-of-freedom manipulation of an untethered magnetic device in fluid using a single permanent magnet with application in stomach capsule endoscopy[END_REF][START_REF] Kummer | Octomag: An electromagnetic system for 5-dof wireless micromanipulation[END_REF]. The second one is bio-inspired [START_REF] Peyer | Bio-inspired magnetic swimming microrobots for biomedical applications[END_REF], using an analogy with the Escherichia Coli bacteria, rodhobacter spheroids, spermatozoon among others. The corkscrew-like motion and the undulating flexible flagella motion have been extensively reviewed in the literature [START_REF] Zhang | Robotic micromanipulation: Fundamentals and applications[END_REF][START_REF] Mahdy | Characterization of helical propulsion inside in vitro and ex vivo models of a rabbit aorta[END_REF]. Alternatively, new locomotion methods have also been proposed using magnetic torques and forces. For instance, in [START_REF] Lu | A bioinspired multilegged soft millirobot that functions in both dry and wet conditions[END_REF], magnetic fields are used to obtain the displacement of a bio-inspired robot by deforming a soft multi-legged body. In [START_REF] Kim | Printing ferromagnetic domains for untethered fast-transforming soft materials[END_REF], ferromagnetic ink is interestingly used during a 3D printing manufacturing process and allows to print soft materials with programmed ferromagnetic domains presenting new behaviors for locomotion. In any case in liquid environment, as the size of the object decreases, the viscous forces become predominant compared to the volume forces. This phenomenon is discussed in [START_REF] Abbott | How should microrobots swim?[END_REF] and it is then outlined that swimming with a magnetically driven helical or elastic-tail propulsion is more efficient compared to direct pulling on the body as the robot size decreases. Actuation through magnetic torques is then considered in this paper.

To operate the aforementioned robots, two main types of magnetic actuation systems have been developed. The first one is an arrangement of multiple stationary coils located around the workspace. Helmholtz (resp. Maxwell) coils are used to generate uniform field (resp. gradients) [START_REF] Kummer | Octomag: An electromagnetic system for 5-dof wireless micromanipulation[END_REF]. Magnetic-resonance-imaging devices are also used when strong gradients are required [START_REF] Martel | Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system[END_REF][START_REF] Kratochvil | Minimag: a hemispherical electromagnetic system for 5-dof wireless micromanipulation[END_REF][START_REF] Diller | Six-degree-offreedom magnetic actuation for wireless microrobotics[END_REF]. The magnetic field is then modulated thanks to current variations in the coil. These systems often suffer from low compactness, poor accessibility [START_REF] Pourkand | A critical analysis of eightelectromagnet manipulation systems: The role of electromagnet configuration on strength, isotropy, and access[END_REF], and the need for active cooling when large currents are required [START_REF] Ongaro | Design of an electromagnetic setup for independent three-dimensional control of pairs of identical and nonidentical microrobots[END_REF]. In an alternative way, mobile permanent magnets have been also considered. Their relative displacements allow shaping the magnetic field obtained in the workspace [START_REF] Wright | The spherical-actuator-magnet manipulator: A permanent-magnet robotic end-effector[END_REF][START_REF] Kratchman | Guiding elastic rods with a robot-manipulated magnet for medical applications[END_REF]. These kind of systems can produce fields of high intensity, well suited to control swimmers in a large workspace. Nevertheless, unlike electromagnet systems, the magnetic field produced by a permanent magnet device cannot be switched off, which can raise safety issues.

Considering the advantages and limitations of these two types of manipulation systems, a moving coil handling system was proposed in [START_REF] Véron | Geometric analysis of the singularities of a magnetic manipulation system with several mobile coils[END_REF]. The concept was further developed with the DeltaMag system which comprises three electromagnets able to rotate about an axis [START_REF] Yang | Deltamag: An electromagnetic manipulation system with parallel mobile coils[END_REF], while the ARMM system employs a 6 Degrees-of-freedom mobile coil system [START_REF] Sikorski | The armm system: An optimized mobile electromagnetic coil for non-linear actuation of flexible surgical instruments[END_REF]. Aiming to increase the size of the workspace while reducing coil heating issues, interest around moving coil architectures is growing. In this paper, we thus consider how to help to understand and design such systems.

Building magnetic navigation devices requires tools to characterize micro-robot behavior. When miniature swimmers are considered, kinematic analysis of the swimming abilities is then crucial. The evaluation of kinematic capabilities has been thoroughly studied in robotics by developing manipulability criteria. These criteria aim at determining the global capacity of a mechanism to generate velocities at a given pose of the workspace. The first manipulability criterion was proposed in [START_REF] Yoshikawa | Manipulability of Robotic Mechanisms[END_REF] and variations have then been proposed, e.g. in [START_REF] Merlet | Jacobian, Manipulability, Condition Number and Accuracy of Parallel Robots[END_REF]. To describe the capability to generate a velocity in any direction, i.e. to get an isotropic behaviour, other indices such as the conditioning index [START_REF] Gosselin | A Global Performance Index for the Kinematic Optimization of Robotic Manipulators[END_REF] have then been proposed. In [START_REF] Chen | Performance metrics for a robotic actuation system using static and mobile electromagnets[END_REF], the authors develop such a criterion for a magnetic manipulation task based on the isotropy of the magnetic field or gradient. The evaluation was achieved through the study of an actuation system similar to the Octomag [START_REF] Kummer | Octomag: An electromagnetic system for 5-dof wireless micromanipulation[END_REF] . This criterion is then used to evaluate if isotropic kinematic performances can be obtained in an heterogeneous magnetic field.

In this paper and as the main contribution, we go beyond these results by proposing a complementary manipulability criterion to assess the ability of a magnetic actuation platform to propel a flexible swimmer in any direction at a minimum velocity. Such an index is of high interest to analyse the capabilities of a given system, to develop methods for the design of the magnetic actuation system and to propose new control laws. Through the closeness between the problem formulation of the wrench feasible workspace and the magnetic actuation formulation, the definition of this criterion and the way to derive it are proposed in analogy with kinematic assessment of cable-driven parallel robots. This criterion allows to analyze the swimming workspace of a flexible swimmer in a new way. The possibilities of new coil configurations and moving coil systems are then highlighted as a second contribution. In particular, a focus on the influence of moving coils on heating issues is proposed as it is a major limiting factor for implementation and safety of such devices.

A video showing the propulsion of the swimmer, the construction of the criterion and its computation on a case study is attached to the paper. The paper is composed of five sections. We first raise the theoretical background for magnetic manipulation in Section II with a particular emphasis on the flexible swimmer manipulation. Section III focuses on the evaluation of the swimming performances and introduces the proposed manipulability criterion. Then Section IV depicts a case study. The propulsion requirements of a flexible swimmer are first experimentally determined in a controlled environment. The manipulability maps are then built using the proposed methodology. Simulation based on a reliable computation of the magnetic fields are presented to assess the results. Thanks to these maps, the advantages of the use of mobile coils are highlighted. Conclusions and perspectives are drawn in Section V.

II. MAGNETIC PROPULSION FOUNDATIONS

A. Magnetic actuation

In a general case, magnetic forces and torques are applied to move a micro-robot. To do so, we consider a magnetic actuation system composed of a set of coils located around the workspace in which a miniature magnetic swimmer is placed. When a magnetic element, described by its dipole moment m, is immersed in a quasi-static magnetic field b, it experiences a magnetic force f and a torque t given by:

f = ∇(m • b) = (m • ∇) b (1) t = m ∧ b (2)
In the following, we consider that the magnetic superposition theorem holds. This is well verified when using coreless coils, for which magnetic coupling can be neglected. When soft-magnetic core electromagnets are used, this assumption is valid as well, under the hypothesis detailed in [START_REF] Kummer | Octomag: An electromagnetic system for 5-dof wireless micromanipulation[END_REF]. The magnetic field amplitude is then varies linearly with respect to the current in the coil. Thus, the magnetic field at a given point p can be computed as the sum of the magnetic fields generated by each coil:

b(p) = n j=1 b j (p) = n j=1 i j bj (p) (3)
with n the number of coils, b j the field contribution of the coil j, bj the unit-current contribution, and i j the electric current of the coil j with j = {1, . . . , n}. Because of hardware limitations, the coil current is i j ∈ [-i max , i max ]. Equation (3) can be reformulated as:

b(p) = b1 (p) . . . bn (p)    i 1 . . . i n    = B(p)i (4)
with B(p) the m × n matrix mapping the currents to the magnetic field [START_REF] Kummer | Octomag: An electromagnetic system for 5-dof wireless micromanipulation[END_REF][START_REF] Chen | Performance metrics for a robotic actuation system using static and mobile electromagnets[END_REF] with m the dimension of the swimming space, i.e. m = 2 in the plane and m = 3 in the space. The j-th column of B(p) is the magnetic field produced along the cartesian coordinates by the j-th coil at the considered point p.

B. Swimming propulsion

When moving in a fluid media, the Reynolds number reflects how the robot should act. In a low Reynolds number environment, the volumic forces exerted on it tend to be negligible compared to the viscous ones. Thus, it becomes energetically unattractive to exert a magnetic force to move the robot. This is why swimmers are used. Only the magnetic field b drives them [START_REF] Abbott | How should microrobots swim?[END_REF].

To compute the velocity of the swimmer based on the efforts applied on it, a propulsion matrix has been introduced for helical swimmers in [START_REF] Purcell | Life at low reynolds number[END_REF], then developed in [START_REF] Abbott | How should microrobots swim?[END_REF]. This is no such simple relationship for a flexible swimmer. That is why experimental evaluations are performed in this paper to determine the velocity of the swimmer actuated by a magnetic field. Miniature swimmers have to perform non-reciprocal patterns to self-propel [START_REF] Purcell | Life at low reynolds number[END_REF]. An additional requirement is related to the ratio between viscous forces and elastic forces, described by a scalar value designated as the sperm number [START_REF] Dreyfus | Microscopic artificial swimmers[END_REF]. This number describes how flexible or rigid the robot structure should be for an efficient swimming. To achieve a good robot performance, the sperm number should be in the order of 1 [START_REF] Abbott | How should microrobots swim?[END_REF][START_REF] Lowe | Dynamics of filaments: modelling the dynamics of driven microfilaments[END_REF]. This constraint can be tuned for a given environment by adapting the robot geometry or material as well as using a suitable oscillation frequency.

Regarding the actuation magnetic field, this latter can be decomposed into driving and steering magnetic fields (respectively b d and b s ) as follows:

b = b d + b s (5)
Without loss of generality, we can consider that the robot moves in a direction denoted x. To induce this displacement, an oscillating field has then to be created around this swimming direction. Let y be an orthogonal direction to x. In [START_REF] Dreyfus | Microscopic artificial swimmers[END_REF], the expression of the driving magnetic field b d is given by:

b d = b x x + b y cos(ωt)y (6)
with b y the oscillation amplitude, and b x the magnitude of magnetic guidance as displayed in Fig. 1. Swimming motion requires a minimal magnetic torque. This torque is linked to the values of b x and b y for a given oscillation frequency (Eq. ( 2)). Thus, a minimal magnetic field is needed to achieve the desired swimming motion.

III. ANALYSIS OF THE SWIMMING PERFORMANCES A. Analysis of the magnetic field

So that a swimmer located at a position p moves at a desired minimal velocity v min , a minimal magnetic field magnitude must be ensured. It is denoted b min in the following. The magnetic field amplitude b e along a direction e is given for the configuration vector q which reflects the poses of the coils at a given position p by:

b e (q, p) = | n j=1 b j (q, p) • e| (7)
To obtain swimming capabilities, the condition (8) below must be ensured for given q and p.

b e (q, p) ≥ b min (8)
The respect of such a condition is indeed analog to a wellknown problem for Cable-Driven Parallel Robots (CDPR) with the determination of the Wrench-Feasible Workspace (WFW). Cable-driven parallel robots are composed of a platform attached to the base frame with actuated cables which are in tension. To ensure that the cables are always pulling and prevent their deterioration, their tensions are usually bounded [START_REF] Gouttefarde | Wrench-Feasible Workspace of Parallel Cable-Driven Mechanisms[END_REF]. The WFW is the reachable workspace for a set of wrenches that can be applied to the platform while the tensions of the cables stay in their limits. To determine this WFW, a zonotope of reachable wrenches can be built for a simple end-effector pose using the tension limits in the cables [START_REF] Bouchard | On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches[END_REF]. As defined in [START_REF] Mcmullen | On Zonotopes[END_REF], a zonotope is a vector sum of a finite number of closed line segments in some Euclidean space. The zonotope zone(Y) is expressed as in [START_REF] Bouchard | On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches[END_REF], with Y = {y 1 , y 2 , . . .

y n } ∈ R d a set of vectors: zone(Y) =    x ∈ R d |x = n j=1 α j y j , 0 ≤ α j ≤ 1    (9)
For a CDPR a wrench is part of the WFW if it is included in a zonotope-shaped set called available wrench set defined for a given pose of the platform.

In our context, the available magnetic fields that can be generated by n coils in the space are included in the set A B defined using Eq. ( 3):

A B =    b(p) ∈ R m |b(p) = n j=1 i j bj (p), |i| ≤ i max    (10)
with m the dimension of the swimming space. It is interesting to note that the set A B can then be expressed as a zonotope, with B = { b1 , b2 , . . . bn } ∈ R m :

A B = zone({i max B, -i max B}) (11)
An analogy with the determination of the WFW can then be carried out to characterize the swimmer propulsion.

B. Magnetic swimming manipulability

Here, we propose a new manipulability criterion for miniature swimmers noted µ(q, p) which represents the ability to propel in any direction at a minimum velocity for given q and p. µ(q, p) is defined as the maximal magnetic field that can be generated along all directions (see attached video). This criterion is then analogous to the search of the maximal wrench that can be applied along all directions to a CDPR such as it stays in the WFW. Therefore, it is the radius of the largest sphere of center p for a given q that is inscribed in A B . This sphere is also called a Chebyshev ball, which is the general term for the largest Euclidean ball inscribed in a polytope [START_REF] Christophersen | Optimal Control of Constrained Piecewise Affine Systems[END_REF]. In our case, the radius of this ball can be expressed as:

µ(q, p) = min e | n j=1 b j (q, p) • e| (12)
A Chebychev ball, and so the manipulability µ(q, p), can be determined in several ways [START_REF] Christophersen | Optimal Control of Constrained Piecewise Affine Systems[END_REF]. We here exploit the fact that µ(q, p) is the minimal distance between the position p and the limits of A B . The faces of a zonotope are supported by hyperplanes [START_REF] Bouchard | On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches[END_REF]. The distance d between the point P defined by the position p and one hyperplane is expressed as:

d = n • hp n ( 13
)
with H a point of the hyperplane and n a normal vector to the hyperplane. To compute the manipulability, the distance between P and each hyperplane supporting A B is determined using Eq. ( 13). Finally, the smallest distance is identified and it is the manipulability µ(q, p).

C. Dexterous swimming space

The manipulability criterion µ(q, p) is then used to define the dexterous swimming space W s . This swimming space is the set of swimmer positions in which no limitation on the swimming directions exists, to ensure the desired performance v min for a configuration q. The latter is defined as the set of coil poses included in all eligible configurations Q. For sake of clarity of the notations, the dependency in q and p is omitted. The dexterous swimming space is then expressed as:

W s = {p | ∃ q ∈ Q where µ ≥ b min } (14)
To illustrate these notions, a simplified example with two coils in the plane is provided in Fig. 2. For such a case, A B is a parallelogram. The Chebyshev ball inscribed in this parallelogram is a circle, represented in green dashed line, and which defines the manipulability µ. From Fig. 2, we can directly observe if the position p is in the dexterous swimming space W s by comparing radius µ with b min . We can see that in configuration #1 (Fig. 2a) b min is included in the set of magnetic fields that can be generated, i.e. b min < µ. Then, p ∈ W s . However, in configuration #2 (Fig. 2b) b min can not be reached in most of the directions as b min > µ. Therefore, if the coils are fixed and Q = q, p ∈ W s .

Based on an analogy with analysis methods used for cable-driven parallel robots, the manipulability index for miniature swimmers as well as the dexterous swimming space were proposed. The mathematical foundations of the proposed tools are generic in coil number and space dimension. This criterion can then be used to analyze actuation systems composed of any finite number of coils, in 2D or 3D space and considering any available coil configurations. As an illustration, the zonotope and the manipulability are computed for an Octomag-like system, i.e. in 3D space and with 8 coils, and the results are displayed in the attached video.

IV. CASE STUDY

In the following, a case study is presented to illustrate the methodology proposed in the previous section. This study is composed of two parts. First, the requirements in terms of minimal magnetic field b min necessary to propel the swimmer at a minimum velocity v min is determined experimentally in a controlled environment. Second, the magnetic field in the whole swimming space is computed using a numerical method proposed in [START_REF] Etiévant | An improved control-oriented modeling of the magnetic field[END_REF] and the manipulability maps are computed.

A. Assessment conditions

For sake of clarity, the case study is carried out with planar motions in the xy plane. The target swimming space is disc-shaped with a 150 mm diameter.

An actuation system composed of three coreless coils is considered. The coils must not penetrate the swimming space. The minimal distance r 0 between the center of the swimming space and the coil edge is then set. The coils can be displaced by rotation around the swimming space center with a radius r 0 , keeping the coil axes intersecting at this center. In this way, the distance between coils and the swimming center is always minimum, which maximizes the intensity of the magnetic field. The coil configurations are defined by the angles θ k , k = {1, 2, 3} as illustrated in Fig. 3. The swimmer position is denoted p and the coil

q = [θ 1 , θ 2 , θ 3 ] T (15)

B. Swimmer description and minimal magnetic field determination

To determine experimentally the magnetic field that must be produced to generate a minimum velocity v min , a centimetric swimmer presented in Fig. 4a) is considered. The swimmer's tail is fabricated using a silicone elastomer. The tail is glued to a 1-mm disc-shaped Neodymium magnet. To emulate the behaviour of the robot at a small scale, pure glycerol is used to produce a low Reynolds number environment, as in [START_REF] Xu | Planar path following of 3-d steering scaled-up helical microswimmers[END_REF]. In our case, the Reynolds number has an order of magnitude about 10 -5 . Experiments are carried out by measuring the forward speed of the swimmer for different magnetic field amplitudes using a 3D Helmholtz coil system. This setup allows to generate a uniform magnetic field avoiding magnetic force disturbances. The system was calibrated by measuring the magnetic field at the center of the workspace by a Hirst GM08 magnetometer. The measurements are performed for b x and b y (see Eq. ( 6)) in [0, 2] mT with a step of 0.5 mT. For this field magnitude, the cut-out frequency being about 1.5Hz, experiments were conducted with an oscillation frequency of 1Hz. For all experiments, the robot is 3D tracked through a visual servoing technique based on ViSP libraries. Each experiment is carried out for more than 80 seconds to estimate the average robot speed. With b y = 0 mT, the robot should stay stationary since there is no oscillatory part. However, when velocities are computed, a drift generated by different factors, e.g. tracking error, or parasitic magnetic field gradients, is observed. It has a value of 0.003 mm/s. This can be considered as noise on the velocity measurements. In Fig. 4b) the robot speed is depicted for the aforementioned range of magnetic field components b x and b y . According to the results, an increase of the oscillation component b y tends to increase the forward speed. Similarly, the decrease in the steering component b x results in some improvement in speed up to some extent. This behaviour can be explained through the robot oscillation angle α. This angle is defined as α = 2 arctan(b y /b x ) and is represented in Fig. 1. When the oscillation angle increases, the robot bends much more properly up to a certain point. Thus, it generates a larger thrust and forward speed is increased. Nevertheless, when the component b x is nearly null, the oscillation angle tends toward π/2 and does not generate a proper tail bending.

The selection of v min should be based on the application requirements. Here, the minimal swimming velocity is then arbitrarily set to v min = 0.1 mm/s. This value does not impact the nature of the discussion conducted in the rest of the paper. Using the results displayed in Fig. 4b) multiple choices of b x and b y are available. We choose the one with the lowest norm among the measured points. Therefore, it leads to b x = 0.5 mT and b y = 2 mT. Finally, it yields to b min = 2.06 mT.

C. Dexterous swimming space with fixed coils

To evaluate the dexterous swimming space that can be expected with such a system, numerical analyses are carried out to compute manipulability maps. First, we consider fixed coils. Two typical coil configurations are chosen. First, an intuitive configuration with the coils uniformly distributed around the swimming space is selected, i.e. θ 1 = 0 rad, θ 2 = -2π/3 rad and θ 3 = 2π/3 rad (Fig. 5a). Second, the configuration which maximizes the minimal value of the manipulability in the whole swimming space is chosen. This configuration cannot be trivially determined. Its determination was achieved by first computing manipulability maps with the proposed criterion for all possible coil configurations, i.e. all the possible coil poses without collisions. It was then observed that the best configuration corresponds to the case where the coils are gathered at the top of the swimming space with θ 1 = 0, θ 2 = -2ϕ 0 and θ 3 = 2ϕ 0 (Fig. 5b). The angle ϕ 0 is defined in Fig. 3 and is expressed as:

ϕ 0 = arctan r coil r 0 (16)
To compute and display the dexterous workspace maps, the swimming space is discretized with a grid of 60 × 60 points and the manipulability µ is computed for each one of them for a given current limit. The coils are composed of 40 × 110 loops and have a radius r coils = 50 mm. To compute the field generated by a single coil b j , we used the elliptical integral formulation proposed in [START_REF] Etiévant | An improved control-oriented modeling of the magnetic field[END_REF]. We then use i max = 1 A to generate unitary maps which correspond to the unit current contribution proposed in Eq. ( 3). These results can easily be extrapolated to other values of i max by scaling the maps with a factor of i max . The maps obtained for the first and second coil configurations are displayed in Fig. 5a) and in Fig. 5b).

When uniformly distributed coils are considered, only a small dexterous workspace is obtained in the center of the swimming space for i max = 1 A. Moreover, four distinct areas separated by a low manipulability region can be observed. In the low manipulability area, there exist configurations where µ can be close to 0 with a minimal value of 0.37 mT. It means that there is at least one direction along which the required magnetic field cannot be generated, i.e. B is rank deficient. In analogy with the kinematic analysis of conventional robots discussed in Section III, we can consider these configurations as close to singularities. The magnetic field being proportional to the current and as b min = 2.06 mT, it means that a current of 5.56 A is required to ensure that the whole swimming space is dexterous, i.e. µ ≥ b min . Actions of avoiding or going through such singular configurations have been thoroughly studied in serial and parallel robotics. It might then be possible to find ways to reach the whole swimming space with the miniature swimmers. However, it would certainly require specific control schemes and trajectory planning that can be avoided by proper selection of coil configuration as outlined below.

In the second configuration, when the coils are gathered on top of the swimming space, no singularity is observed. However, as the magnetic field decreases with the distance, the bottom side of the swimming space presents low manipulability values. For i max = 1 A, the lowest manipulability value is of 0.55 mT. In this case, a current of 3.74 A is needed to obtain a fully dexterous swimming space.

D. Dexterous swimming space with moving coils

We now consider that the pose of the coils can be dynamically modified. The angular ranges of the coils are chosen to avoid collisions and are expressed as:

     - π 2 ≤ θ 1 ≤ π 2 ϕ 0 -π ≤ θ 2 ≤ -2ϕ 0 2ϕ 0 ≤ θ 3 ≤ π -ϕ 0 (17)
A manipulability map could be displayed for each eligible configuration of the coils. However, to better visualize the dexterous swimming spaces we can obtain, the maximum manipulability for all available q ∈ Q, with Q defined by the system of equations [START_REF] Pourkand | A critical analysis of eightelectromagnet manipulation systems: The role of electromagnet configuration on strength, isotropy, and access[END_REF], is displayed in Fig. 6. With the use of coil reconfigurations, the minimum manipulability in the whole swimming space is equal to 2.0 mT. It means that to obtain a minimal manipulability of 2.06 mT, the current limit needs to be set to 1.03 A. In Fig. 7, q is chosen to obtain a compromise between the two fixed coil configurations proposed previously. The manipulability map of such configuration is interesting as it shows that the positions of the singularities observed in Fig. 5a) are modified. Thanks to moving coils, it is also possible to change the singular configurations.

These results are presented to illustrate the methodology proposed in III. For sake of clarity, a magnetic actuation system composed of 3 coils, and planar displacements are presented in this case study. However, the methodology is generic and can be applied in 3D to complex actuation system, as demonstrated in the accompanying video.

E. Discussion

Adding motions to the coils is interesting in several ways, whether the whole set of coils is moved or only relative motions between the coils are carried out. First, it allows modifying the shape of the manipulability maps to be able to reach the whole swimming space. In particular, when the relative poses of the coils are modified, the manipulability maps change allowing to move the singularities whereas simultaneous motions of the whole set of coils tend to improve the overall manipulability. Second, with this example, the needed current to ensure dexterity in the whole swimming space has been reduced from 5.56 A and 3.74 A to 1.03 A, i.e. by a factor of 5.4 and 3.6, thanks to simple coil motion identified by the use of the proposed manipulability criterion. The joule effect being a function of the square of the current, it means that the power leading to the coil heating is diminished by a factor of 29 and 13. The system is then less affected by coil heating issues, thus lowering the overall price as well as the design complexity of cooling systems. Moreover, it allows reducing the temperature of the environment which can be of interest, e.g. when considering bio-medical applications or when manipulating cells.

Moving coils may also be interesting as it allows to adjust local behavior and even singularity locations. The latter may be exploited to restrict the swimming space when obstacles must be avoided or if a restricted swimming space is desired for safety reasons. In particular, it can be seen from Fig. 7 that it is possible to have multiple high manipulability areas separated by low manipulability ones or singularities. This means exploiting mobile coils could help for independent control of multiple swimmers.

V. CONCLUSIONS AND PERSPECTIVES

In this paper, we proposed a manipulability criterion to assess the capacity of a magnetic actuation platform to propel in any direction a miniature swimmer with flexible flagellum at a given minimal velocity. The proposed formulation is generic and can therefore be used for actuation devices with any number of coils in 2D or 3D situations. It was then applied to a case study and allowed to carry out new observations on the magnetic actuation of miniature swimmers. It showed that moving coils are of interest for the control of the swimmers, especially in biomedical applications.

Due to the use of coreless coils, magnetic couplings have been neglected. Nevertheless, the proposed criterion can be used as long as the couplings are taken into account while computing the magnetic field. The proposed criterion is a first step towards new methods for the design and the control of miniature swimmers and gives several perspectives. First, this criterion is based on a minimal magnetic field constraint which can be formulated as the search of the Chebyshev ball in a zonotope. If such a problem can be formulated for other untethered swimmers or other robots, the proposed methodology could also be exploited. Moreover, these constraints are not strictly related to the use of magnetic fields. Indeed, any bounded constraint can be considered. Therefore, a first perspective is to extend this criterion to other devices. The second perspective is to study the design of magnetic navigation devices based on this criterion. Further discussions on the design of devices for the manipulation of the coils will be carried out and focus will be also given to the overall energy efficiency of such systems. Finally, swimmer control based on moving coil systems will be studied and experimental evaluations will be conducted. In particular, careful attention will be given to the different time constants obtained with both actuation principles: the a priori slow reconfiguration of the coils and the fast current modulation.

Fig. 1 :

 1 Fig. 1: Notations used for the propulsion foundations of a miniature swimmer with flexible flagellum.

Fig. 2 :

 2 Fig. 2: Schematic representation of the magnetic field that can be generated thanks to two identical coils. Coils L1 and L2 are represented with dashed axes, the arrows describe the magnetic field of each coil at point p for ±imax and the gray area represents AB. The dotted circle represents the magnetic field required bmin to obtain the desired propulsion. The dashed green circle is the limits of the Chebyshev ball inscribed in AB which is used to compute the manipulability. The hatched areas depict the needed magnetic fields that cannot be generated. a) Configuration #1 coil axes are orthogonal. b) Configuration #2 coil axes are almost colinear.

Fig. 3 :

 3 Fig. 3: Considered system to illustrate the methodology proposed to evaluate the dexterous swimming space. It is composed of three coils in the xy plane with their axis in dashed lines and the swimming space in light gray.

Fig. 4 :

 4 Fig. 4: Flexible robot description and experimental evaluation of its swimming velocity. a) Flexible robot dimensions. b) Experimental forward speed of the swimmer for different magnetic amplitudes at 1 Hz.

a)

  Fixed coils uniformly distributed. b) Fixed coils gathered.

Fig. 5 :

 5 Fig. 5: Manipulability maps displayed in the xy plane for i = 1 A. Colors represent the manipulability. In green, the level lines for be = bmin = 2.06 mT and be = 1 mT, in plain and dotted lines respectively. a) Fixed coils uniformly distributed around the swimming space. b) Fixed coils gathered at the top side of the swimming space.

Fig. 6 :

 6 Fig. 6: Maximum manipulability obtained at each point for all possible poses of the coils and for i = 1 A.

Fig. 7 :

 7 Fig. 7: Manipulability map obtained for θ1 = 0 rad, θ2 = -2ϕ0 rad and θ3 = 2π/3 rad for i = 1 A.

ACKNOWLEDGMENT This work is part of Multiflag project (ANR-16-CE33-0019) funded by the French National Research Agency (ANR) and supported by EIPHI Graduate School (Contract No. ANR-17-EURE-0002), by the COErCIVe région Bourgogne Franche-Comté project, by Labex CAMI (Contract No. ANR-11-LABX-0004) and the Grand Prix Scientifique 2018, Fondation Charles Defforey, Institut de France.