Nicolas Lusinier

Isabelle Seyssiecq

Cecilia Sambusiti

Matthieu Jacob

Nicolas Lesage

Nicolas Roche
email: nicolas.roche@univ-amu.fr

A comparative study of conventional activated sludge and fixed bed hybrid biological reactor for oilfield produced water treatment: influence of hydraulic retention time

Keywords: Conventional activated sludge, fixed bed hybrid biological reactor, oilfield produced water treatment, hydraulic retention time

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

Abbreviations 1

Introduction

Oilfield-produced water (PW) is a wastewater stream generated during crude oil and gas extraction. It is basically composed of water originating from oil or gas reservoirs and crude processing. The PW flowrate increases with reservoir ageing. This increase is measured by the water to oil ratio (WOR) and represents the volume of PW to be managed per volume of crude oil. Currently, the average WOR ratio is 3:1 [START_REF] Aroswoshola | Global Water Intelligence, Produced water market: opportunities in the oil, shale and gas sectors in North America[END_REF]. Because of the aging of most oil reservoirs, this ratio is expected to increase [START_REF] Dores | Using Advanced Water Treatment Technologies To Treat Produced Water From The Petroleum Industry[END_REF].

PW composition is also site specific and depends on several factors, including the geological properties of the reservoir or even the composition of the crude oil and gas in contact with the water [START_REF] Veil | A white paper describing produced water from production of crude oil, natural gas, and coal bed methane[END_REF]. Basically, three families of compounds are found in PW:

(1) organic compounds including dissolved and dispersed hydrocarbons (aliphatic hydrocarbons, carboxylic acids, benzene, toluene, ethylbenzene, xylene (BTEX), polycyclic aromatic hydrocarbons (PAHs), phenols, heavy alkylphenols, heavy 1 BAF: Biological Aerated Filter, BTEX: Benzene, Toluene, Ethylbenzene and Xylene, CAS: Conventional Activated Sludge, COD: Chemical Oxygen Demand, DO: Dissolved Oxygen, EPA: Environmental Protection Agency, FBHBR: Fixed Bed Hybrid Biological Reactor, HRT: Hydraulic Retention Time, MBBR: Moving Bed Biofilm Reactor, MBR: Membrane Bioreactor, OLR: Organic Loading Rate, PAH: Poly Aromatic Hydrocarbon, PNEC: Predicted No Effect Concentration, PW: Produced Water, TN: Total Nitrogen, TSS: Total Suspended Solids, TOC: Total Organic Carbon, VOC: Volatile Organic Compounds, VSS: Volatile Suspended Solids, WOR: Water to Oil Ratio 3 hydrocarbons), (2) inorganic compounds i.e. dissolved anions and cations that contribute to the salinity of PW, trace metals (iron, chromium, lead, mercury, cadmium, copper, zinc and silver) and naturally occurring radioactive materials, and

(3) production chemicals (corrosion inhibitors, biocides, emulsion breakers, asphaltene inhibitor, H 2 S scavengers, etc.) that are used to insure the oil is extracted properly [START_REF] Al-Ghouti | Produced water characteristics, treatment and reuse: A review[END_REF]- [START_REF] Munirasu | Use of membrane technology for oil field and refinery produced water treatment-A review[END_REF]. Both the increasing amount of PW and its complex composition are raising new concerns and leading to new investigations of PW treatment and discharge.

Today, there is a change in the perception of PWs, which are now considered as a valuable resource, especially for reinjection in oil reservoirs, to reduce overall water consumption in water-stressed regions. Each water use requires that specific water quality standards be met, including the removal of dispersed phases before water reinjection and the removal of dissolved matter before discharge or reuse for irrigation. PW reinjection into oil producing reservoir enhances oil recovery, but requires treatment before reinjection to limit reservoir plugging and to insure longterm sustainable oil productivity in the long term [START_REF] Liang | Special Focus on Produced Water in Oil and Gas Fields[END_REF]. Today, PW reinjection is a common practice in onshore fields: 98% of onshore PW is reported to be reinjected in oil formations, whereas, in the USA, only 9% of offshore PWs are reinjected [START_REF] Clark | Produced water volumes and management practices in the United States[END_REF].

Increasing this ratio is an objective for Total, but this requires more efficient polishing processes at water treatment units (membranes, media filters, centrifuges, etc.) which is mainly challenging offshore. Additionally, regulations concerning PW discharge are becoming increasingly strict. The regulations are site specific and depend on the location of the production asset. For instance, the Convention for the Protection of the Marine Environment of the North-East Atlantic, (OSPAR) recommends PW discharge limits in the North Sea [START_REF]OSPAR Recommendation 2012/5 for a risk based approach to the management of roduced water discharges from offshore installations », Decisions, Recommendations & Agreements[END_REF]. OSPAR set the average 4 maximum discharge limit for dispersed oil at 30 mg.L -1 whereas the United States EPA set their value at 29 mg.L -1 and a daily maximum discharge limit of 42 mg.L -1 for oil and grease [START_REF] Zheng | Offshore produced water management: A review of current practice and challenges in harsh/Arctic environments[END_REF]. Recent regulations have also started to target dissolved organic compounds. To help oil producers deal with these new regulations, OSPAR recommendation 2014/5 produced a list of Predicted No Effect Concentrations (PNECs) for the most common dissolved organic compounds in PW [START_REF]Establishment of a list of Predicted No Effect Concentrations (PNECs) for naturally occuring substances in produced water (OSPAR agreement 2014/5) », Decisions, Recommendations & Agreements[END_REF]. Table 1 lists PNECs for the BTEX and PAHs found in PW. Treatment processes thus have to be strengthened and adapted to these new directives. PW treatments are usually physical-chemical processes [START_REF] Jiménez | State of the art of produced water treatment[END_REF]. Current treatments aim to remove dispersed hydrocarbons from PW to comply with existing recommendations, but these techniques do not remove dissolved hydrocarbons and 5 are not efficient enough to comply with the new recommendations. Furthermore, the physical-chemical processes, such as oxidation, used to treat dissolved hydrocarbons can produce potentially toxic by-products. Recent research has focused on biological treatments [START_REF] Lusinier | Biological Treatments of Oilfield Produced Water: A Comprehensive Review[END_REF]- [START_REF] Fakhru'l-Razi | Application of membrane-coupled sequencing batch reactor for oilfield produced water recycle and beneficial re-use[END_REF]. In these processes, the water is treated by the action of a bacterial community in an aeration tank. The wastewater provides the required nutrients and food for biomass growth. Biological treatment appears to be a viable alternative to physical-chemical processes as operating costs are lower, and the processes are eco-friendly [START_REF] Pendashteh | Evaluation of membrane bioreactor for hypersaline oily wastewater treatment[END_REF], [START_REF] Tong | Treatment of heavy oil wastewater by a conventional activated sludge process coupled with an immobilized biological filter[END_REF]. However, to date, research on the biological treatment of PW has been limited. Some studies used technologies such as conventional activated sludge (CAS) reactors, biological aerated filters (BAF), or membrane bioreactors (MBR) and reported good removal efficiency [START_REF] Pendashteh | Evaluation of membrane bioreactor for hypersaline oily wastewater treatment[END_REF]- [START_REF] Tellez | Performance evaluation of an activated sludge system for removing petroleum hydrocarbons from oilfield produced water[END_REF], but the influence of critical operating parameters such as hydraulic retention time (HRT) has not been studied in detail. This parameter is extremely important and must be as short as possible (without affecting COD removal efficiencies) to allow the treatment of high volumetric flowrates of PW in a minimum volume reactor to limit the process footprint particularly in offshore operations.

To meet this challenge, hybrid processes could have certain advantages over standard ones. Hybrid technologies, generally described as the combination of two or more treatment processes in one reactor, have produced promising results. For instance, combining different biological processes to remove recalcitrant compounds may be more efficient due to synergistic effects [START_REF] Grandclément | From the conventional biological wastewater treatment to hybrid processes, the evaluation of organic micropollutant removal: A review[END_REF]. In this category of new processes, attention should be paid to fixed bed hybrid biological reactors (FBHBR).

The FBHBR process, in which free biomass (activated sludge) and fixed biomass (biofilm) are combined in the same bioreactor, has attractive features among which higher concentrations of biomass can be achieved than with conventional 6 technologies. For the same concentration of biomass (i.e. biofilm and suspended sludge), the FBHBR leaves a smaller footprint than a CAS reactor, thus reducing the size of treatment plant [START_REF] Ødegaard | A new moving bed biofilm reactorapplications and results[END_REF], [START_REF] Tseng | Molecular Characteristics and Differences of Effluent Organic Matter from Parallel Activated Sludge and Integrated Fixed-Film Activated Sludge (IFAS) 37 Processes[END_REF]. For this reason, this process should be of particular interest for offshore implementations. Furthermore, the simultaneous presence of activated sludge and biofilm significantly increases bacterial biodiversity in the hybrid biological reactor, which in turn, should improve the removal of poorly biodegradable compounds. Biofilms are also more resistant to toxic compounds than free biomass thanks to their gel-like structure. The extracellular matrix secreted by the biofilm reinforces the diffusion barrier and limits contact between toxic compounds and bacteria [START_REF] Cohen | Biofiltrationthe treatment of fluids by microorganisms immobilized into the filter bedding material: a review[END_REF]. FBHBRs have also been proved to be mass transfer efficient [START_REF] Machat | Effects of C/N Ratio and DO concentration on Carbon and Nitrogen removals in a Hybrid Biological Reactor[END_REF], [START_REF] Zerari | Enhancement of oxygen mass transfer coefficients in a hybrid membrane bioreactor: Enhancement of oxygen mass transfer coefficients in a HMBR[END_REF].

While studying oxygen transfer in a hybrid membrane bioreactor in several model fluids, Zerari et al. [START_REF] Zerari | Enhancement of oxygen mass transfer coefficients in a hybrid membrane bioreactor: Enhancement of oxygen mass transfer coefficients in a HMBR[END_REF] observed an up to 46% increase in the oxygen transfer coefficient with the presence of packing (for biofilm growth) compared to an empty reactor. This underlines the mechanical role played by the packing material in limiting the bubble coalescence that can occur in free sludge processes. This type of bioreactor has already proven its efficiency in domestic wastewater treatment [START_REF] Ruys | Study of Carbonaceous and Nitrogenous Pollutant Removal Efficiencies in a Hybrid Membrane Bioreactor[END_REF].

Dong et al. [START_REF] Dong | Treatment of oilfield wastewater in moving bed biofilm reactors using a novel suspended ceramic biocarrier[END_REF] reported that adding modified ceramic biocarriers in a moving bed biofilm reactor (MBBR) for PW treatment enhanced removal performances and allowed better resistance to loading shocks by the bioreactor. Up to now, few studies have reported the use of FBHBRs for PW treatment. In a FBHBR, and with identical packing material, biofilm growth should be greater as there would be no shear stress on the carriers, which do not detach the biofilm, thus avoiding detachment of the film from their external surface, and the extensive development of biofilm would improve the performance of the bioreactor. Further, assessing the bacterial population is a good way to understand the behavior of such bioreactors and to what extent they 7 differ from conventional technologies. Huang et al. [START_REF] Huang | Characterization of microbial communities during start-up of integrated fixed-film activated sludge (IFAS) systems for the treatment of oil sands process-affected water (OSPW)[END_REF] used a FBHBR to treat oil sands process-affected water and characterized the microbial population in their bioreactor. Their results showed that biofilm growth was associated with high microbial diversity.

The aim of this work was to use a FBHBR to treat PW to demonstrate the advantages of a hybrid technology for the treatment of industrial wastewater in a compact bioreactor compared to a conventional biological process. The process comprised a biological reactor containing a combination of activated sludge and a fixed biofilm. Particular attention was paid to reducing the HRT to identify the limits of CAS under reduced operating conditions.

Materials and Methods

Experimental Setup

The laboratory scale experimental device consisted in two Identical bioreactors made of cylindrical clear PVC columns (Figure 1a). The inner diameter of both bioreactors was 19 cm, the total height was 107 cm, and the working volume 30 L. Figure 1b is a schematic diagram of the experimental system. One bioreactor was configured as a CAS reactor and the other as a FBHBR. Cylindrical solid packing rings (AnoxKaldnes ® ) were inserted in the column of the FBHBR to enable colonization by the biofilm. In the working volume (30 L), 10 L was filled with the packing material, corresponding to a filling ratio of 33% v/v, chosen based on the results of previous studies [START_REF] Zerari | Enhancement of oxygen mass transfer coefficients in a hybrid membrane bioreactor: Enhancement of oxygen mass transfer coefficients in a HMBR[END_REF], [START_REF] Ruys | Study of Carbonaceous and Nitrogenous Pollutant Removal Efficiencies in a Hybrid Membrane Bioreactor[END_REF]. The geometrical parameters of the packing material are listed in Table 2. To prevent the bed from moving, the packing rings were placed in a closed 7-mm stainless steel grid basket. The solid-liquid separation step was carried out in a 5 L gravity settler. The settled sludge was recirculated to the bioreactors by a 8 peristaltic pump (Masterflex). The recirculation rate was set at 200% of the feed rate to prevent sludge from accumulating in the settlers. The synthetic PW was also fed into the bioreactor by a peristaltic pump (Masterflex). The feed rate was set as a function of the targeted HRT. Compressed air was supplied to the system through a porous membrane at the bottom of the column (Jäger). Air flowrates were measured using a rotameter (Analyt). Air input ranged between 120 L.h -1 and 960 L.h -1 . Two control valves were placed at the bottom of the column to prevent water entering the air supply system.

Synthetic produced water

The experiments were performed using a synthetic PW representative of a real PW.

As the concentrations of targeted pollutants may be low to insure the viability of the biomass, dissolved organic compounds and nutrients were added to target values of Chemical Oxygen Demand (COD), Total Nitrogen (TN) and Total Phosphorous (TP) of 1600, 20.6, and 4 mg.L -1 respectively. The detailed composition of the feed water is given in Table 3.

Parameter

Microbial inoculum

The activated sludge used to inoculate the bioreactors was taken from the activated sludge recycle line of a municipal wastewater treatment plant (Aix en Provence, France). The original concentration of total suspended sludge (TSS) was 4 g.L -1 in the two bioreactors. The biomass was slowly acclimated by gradually increasing the pollutant concentrations over a period of two months. To this end, the synthetic PW was diluted to reach 400 mg.L -1 of COD for 8 days, 700 mg.L -1 for 26 days and 1,000 mg.L -1 for 30 days. The sludge retention time (SRT) was set to a constant value of 20 days throughout the experiment (i.e. withdrawal of 1.5 L of free biomass from both bioreactors each day). It is important to note that acclimation ended when removal 12 performances rose to satisfactory levels and when the biomass concentration stabilized, which corresponded to 6 times the SRT.

Experimental Schedule

When acclimation was complete, the 133-day experiment began. It was divided into four stages. Each stage consisted in a decrease in the HRT. Four HRTs were successively studied: 24, 22, 18 and 12 hours. The concentrations of pollutants at the inlet were kept constant in each stage, leading to an increase in the organic loading rate (OLR) with an increase in the feed flowrate. It is worth noting that the working volume (30 L in both CAS reactor and FBHBR) was included in the calculation of OLR. The values of these key parameters are summarized in Table 4. Each step lasted at least 20 days to overcome the SRT and was stopped once the bioreactors (or at least one of the two bioreactors) appeared to have reached steady state. and volatile suspended solids (VSS) were measured in both the CAS reactor and the 13 FBHBR using standard methods [START_REF] Eaton | American Public Health Association, American Water Works Association, et Water Pollution Control Federation[END_REF]. In the FBHBR, the quantity of biofilm was assessed at end of the experimental period. The biofilm was weighed using an experimental procedure described elsewhere [START_REF] Abtahi | Micropollutants removal in tertiary moving bed biofilm reactors (MBBRs): Contribution of the biofilm and suspended biomass[END_REF].

Physical-chemical parameters

The inlet and outlet water in the two bioreactors were monitored daily to calculate the efficiency of the treatment at each stage. Dissolved oxygen (DO) concentrations, pH and temperature in the two bioreactors were measured by oxygen electrodes (LDO10101, Hach, USA) and pH electrodes (PHC101, Hach, USA) connected to a

Hach HQ40D digital multimeter ( Hach-Lange®, USA). All water samples were filtered using 0.45 µm polyether sulfone filters before analysis. COD and phenol were analyzed by spectrophotometry using Hach DR6000 analytical kits. BTEX (toluene, m-xylene and o-xylene) were analyzed using a standardized chromatographic method (Headspace GC/MS) [START_REF] Afnor | Water quality -Determination of benzene and some derivatives -Part 1: head-space gas chromatographic method[END_REF]. PAHs (naphthalene, phenanthrene, benzo[a]pyrene) were analyzed by gas chromatography coupled with mass spectrometry [START_REF]DIN ISO 28540 of 2014-05-01. Water Quality -Determination of 16 Polycyclic Aromatic Hydrocarbons (PAH) in Water -Method Using Gas Chromatography with Mass Spectrometric Detection (GC-MS)[END_REF].

Ecotoxicity measurements

Ecotoxicity tests were performed to assess the potential toxicity of treated waters.

Five samples were taken for each assessment, i.e. at the feed inlet, at the outlet of the CAS reactor at the end of stages III and IV, and at the outlet of the FBHBR at the end of stages III and IV. Standardized tests used were the Microtox (Vibrio fischeri) acute toxicity test [START_REF] Afnor | inhibitory effect of water samples on the light emission of Vibrio fischeri (Luminescent bacteria test) -Part 3: method using freeze-dried bacteria[END_REF], the freshwater algae (Pseudokirchneriella subcapitata) acute toxicity test [START_REF] Afnor | Water quality -Fresh water algal growth inhibition test with unicellular green algae[END_REF], the Daphnia Magna acute toxicity test [START_REF] Afnor | Crustacea) -Acute toxicity test[END_REF], and the Brachionus chronic toxicity test [START_REF] Afnor | Water quality -Determination of the chronic toxicity to Brachionus calyciflorus in 48 h[END_REF]. The analysis also enabled calculation of the Shannon-Weaver index representing biomass diversity: the higher the ecological index, the higher the biomass diversity.

Results and discussion

Total suspended solids

Figure 2a shows changes in free total suspended solids (TSS) concentrations in both bioreactors over time in all four experimental stages. The concentration of free sludge ranged from 1.4 g.L -1 at the beginning of the experiment in the two bioreactors to a maximum of 4.2 g.L -1 in the FBHBR and of 3.8 g.L -1 in the CAS bioreactor. A bulking phenomenon occurred in both bioreactors that explained the decrease in free TSS concentrations between day 29 and day 48. Consequently, fresh sludge was added in both bioreactors to increase TSS concentrations and led to higher values at day 49. TSS concentrations showed the same behavior from the end of stage II to stage 15 IV, with a value ranging from 1.4 g.L -1 to 4.2 g.L -1 in the FBHBR and from 1.2 g.L -1 to 3.8 g.L -1 in the CAS bioreactor. At the end of stage IV, TSS concentrations in the CAS reactor decreased significantly from 2.9 g.L -1 to 1.1 g.L -1 .

Changes in free volatile suspended solids (VSS) followed the same trend as that of free TSS. In particular, calculation of the VSS/TSS ratio provided further information on the behavior of the biomass in both bioreactors. The results of biofilm quantification indicated significant growth of biofilm on all the surfaces (internal and external) of the Kaldnes® rings in the FBHBR (Figure 4). After drying, biofilm weight was approximately 3.26 mg per carrier. In the FBHBR, 10 L of raw packing was inserted corresponding to a total of 10,800 rings. The total weight of 16 the biofilm was 35.2 g, corresponding to an average biofilm concentration of 1.17 g.L -

1

. With an average free biomass concentration of 2.75 g.L -1 , the total biomass concentration was approximately 3.92 g.L -1 . The biofilm thus contributed up to 30% of the total biomass in the FBHBR. As the overall performance of a bioreactor is proportional to the concentration of biomass, the biofilm increased the treatment capacity of the FBHBR. It has been reported that biofilm adhesion depends on operational conditions such as biofilm age, concentrations of nutrients, concentrations of suspended cells, pH, surface roughness of the packing material, and fluid velocity [START_REF] Chen | Effects of operating conditions on the adhesive strength of Pseudomonas fluorescens biofilms in tubes[END_REF]. Thus, the presence of a significant biofilm seems to indicate that the operational conditions were satisfactory for biofilm growth in the FBHBR.

Biofilms provide greater resistance to toxic compounds than free biomass. In biofilms, microorganisms secrete an extracellular matrix to enable them to attach to the bedding material. This extracellular matrix tends to increase the diffusion barrier and slow down the transfer of toxic compounds in the biofilm [START_REF] Cohen | Biofiltrationthe treatment of fluids by microorganisms immobilized into the filter bedding material: a review[END_REF]. This process is advantageous in the treatment of an industrial wastewater such as PW. 17 for an HRT of 24, 22 and 18 h. The same behavior was observed in the CAS and FBHBR. After biomass acclimation, COD removal efficiency reached more than 95%

(day 0-28) due to sufficient contact time between the acclimated biomass and the wastewater. After each decrease in the HRT, removal efficiency decreased (down to 30% in the CAS reactor and to 25% in the FBHBR) as the experimental conditions changed. Yet, after a few days, COD removal efficiencies again reached steady high values (80-99%). It is worth noting that stabilization took longer at each decrease in the HRT. Nonetheless, the biomass microorganisms proved their ability to adapt to more difficult conditions under shorter HRTs. At 12 h HRT, the CAS reactor was not able to maintain high removal efficiency and decreased continuously to finally reach only 34% of COD removal when the experiments were stopped. In the FBHBR, removal remained high (77-99%) after the stabilization phase, certainly due to the greater quantity and higher diversity of biomass. The decrease in VSS linked to the loss of bacteria and to the absence of a biofilm in the CAS reactor may have caused this significant drop in removal efficiency. Dong et al. [START_REF] Dong | Treatment of oilfield wastewater in moving bed biofilm reactors using a novel suspended ceramic biocarrier[END_REF] studied the influence of an HRT reduction in a MBBR to treat oilfield wastewater. At an HRT of 36 h to 10 h, corresponding to an increase in the organic loading rate (OLR) of 1.17 kg COD .m -3 .d -1 to 4.21 kg COD .m -3 .d -1 , these authors observed high removal efficiencies with long HRTs. When the HRT was reduced, they noted that moving bed biofilm reactors performed better than CAS reactors under the same operating conditions, confirming 21 that biofilm bioreactors resist loading shocks better. Further, the good performances were linked to the presence of biofilms on the surface of the carriers.

Removal of pollutants

Phenol removal efficiency at each equilibrium stage is shown in Figure 5a for each bioreactor. High removal efficiencies were observed whatever the period. Several measurements were made at the end of each stage to calculate the overall phenol removal efficiency. In the CAS bioreactor, this value reached 99%, 88% and 92% at an HRT of 24 h, 18 h, and 12 h, respectively. These high values suggest biomass acclimation in the CAS bioreactor was satisfactory. The slight decrease observed at an HRT of 18 h was probably due to the bulking phenomenon and the addition of fresh sludge: as the new bacteria added in the bioreactor were not acclimated to phenol, there was a drop in phenol removal efficiency. In the FBHBR, overall phenol removal efficiencies were 94%, 91% and 96% at an HRT of 24 h, 18 h and 12 h, respectively. Here again, the high values confirmed the satisfactory acclimation of the biomass in the FBHBR. Degradation of phenolic compounds from heavy oil wastewater was studied by Tong et al. [START_REF] Tong | Treatment of heavy oil wastewater by a conventional activated sludge process coupled with an immobilized biological filter[END_REF]. Their bioreactor, which consisted in a conventional activated sludge process coupled with an immobilized biological filter, was able to completely remove phenolic compounds from the wastewater, confirming the ability of biological technologies to completely remove phenol from PW.

Equivalent efficiency can also be obtained with more compact processes, as shown in the present study. Figure 5c shows PAH removal efficiencies in the two bioreactors. Here again, high removal efficiencies were obtained in both bioreactors. Naphthalene removal efficiency was more than 97% and phenanthrene removal efficiency more than 88%.

In their study, Dong et al. [START_REF] Dong | Treatment of oilfield wastewater in moving bed biofilm reactors using a novel suspended ceramic biocarrier[END_REF] obtained 79% of removal efficiency for both naphthalene and phenanthrene. Removal mechanisms may include bacterial degradation but also adsorption on biomass (biofilm and free sludge) and volatilization.

Ecotoxicity measurements

Water toxicity was assessed at HRTs of 18 h and 12 h in both the CAS bioreactor and the FBHBR. Results expressed as EC50 are listed in Ten samples were analyzed to obtain an overview of the bacterial population in the two bioreactors under each HRT. Sequencing of the samples generated a total number of 295 k sequences. The number of operational taxonomic units (OTU), determined by a minimum of 97% similarity with referenced units, was 1,058 in the inoculum. When the bioreactors were operated at an HRT of 24 h, the number of OTUs was 728 for CAS suspended flocs, 804 for FBHBR suspended flocs, and 807 for FBHBR biofilm. When the HRT was reduced to 18 h, the number of OTUs increased to 834 for CAS suspended flocs, to 1,099 for FBHBR suspended flocs and to 1,047 for FBHBR biofilm. Finally, at the end of the test program at an HRT of 12 h, the number of OTUs was 498 for CAS suspended flocs, 770 for FBHBR suspended flocs, and 944 for FBHBR biofilm. It is worth noting that the number of OTUs was higher in the FBHBR (in both suspended flocs and biofilm) than in the CAS bioreactor, suggesting higher richness in both suspended flocs and biofilm in the FBHBR. In addition, the number of OTUs was always higher in the biofilm than in the suspended flocs in the FBHBR. This highlights one of the main advantages of biofilm over suspended flocs. This high diversity could play a major role during treatment of synthetic oilfield PW and explain the significant performance of the FBHBR under low HRTs. These results are consistent with those obtained by Huang et al. [START_REF] Huang | Characterization of microbial communities during start-up of integrated fixed-film activated sludge (IFAS) systems for the treatment of oil sands process-affected water (OSPW)[END_REF] in an integrated fixed-film activated sludge system treating oil sands process-affected water.

Figure 6a shows the changes in the Shannon-Weaver index in the bioreactors. The Shannon-Weaver index of the inoculum from the WWTP was 4.94. This high value indicates a diverse bacterial population, typical of municipal treatment plants.

Changes in diversity in the CAS bioreactor points to microbial specialization. Indeed, 25 at an HRT of 24 h, the index decreased to 4.27. This suggests that biomass acclimation depends on the dominance of certain bacterial species. Interestingly, at an HRT of 18 h, the index increased to 5.11 due to the addition of fresh sludge in the CAS bioreactor during the bulking phenomenon. At an HRT of 12 h, the index again decreased to 3.93, indicating specialization. The specialization in the CAS bioreactor suggests the PW was toxic to some bacterial species and confirms the low resistance of suspended flocs in conventional technologies.

In the FBHBR, diversity remained high in both the biofilm and in the suspended sludge whatever the HRT. At an HRT of 24 h, the Shannon-Weaver index for suspended flocs was 4.8, and 4.94 for the biofilm in the FBHBR. It is also worth noting that the addition of fresh sludge at an HRT of 18 h increased the Shannon Weaver index of suspended flocs to 4.95 and of the biofilm to 5.53. Finally, at an HRT of 12 h, the Shannon-Weaver index remained high with values of 4.86 for suspended flocs and 4.97 for the biofilm. Diversity in the FBHBR was similar to that of the inoculum. At each stage of the process, the Shannon Weaver index of the biofilm was higher than that of the free sludge. This resulted in higher bacterial diversity in the biofilm than in the free sludge. Because of this particular growth mechanism, biofilms present significant heterogeneity. The oxygen and nutrient gradients in the biofilm enable slow growing microorganisms to develop, thereby further increasing biofilm diversity [START_REF] Cohen | Biofiltrationthe treatment of fluids by microorganisms immobilized into the filter bedding material: a review[END_REF]. Taken together, the number of OTUs, the Shannon Weaver index and the Simpson reciprocal index suggest that microbial species diversity is higher in the FBHBR than in the CAS bioreactor. In particular, diversity of the biofilm was significantly higher than that of the suspended flocs in the FBHBR. This underlines one of the main advantages of biofilm-based hybrid processes over conventional processes. Different behaviors were observed in the two bioreactors. While in the FBHBR, biomass diversity remained high due to the presence of the biofilm, specialization occurred in the CAS bioreactor, i.e. some bacterial species became much more dominant in the CAS bioreactor. It is worth noting that the sludge retention time (SRT) governed biomass diversity in the CAS bioreactor. In this case, an SRT of 20 days limited the biomass diversity in the CAS bioreactor to bacteria that require less than 20 days to develop. Conversely, in the FBHBR, the retention time of the biofilm is much longer 27 (infinite if no detachment occurs). In contrast to the CAS bioreactor, this particularity enables the development of bacteria in the biofilm that require more than 20 days to develop. Slow-growing bacteria can consequently develop and increase microbial species diversity in the FBHBR to a greater extent than in the CAS bioreactor. High Shannon indices in FBHBR treating oil sands process-affected water were also reported by Huang et al. [START_REF] Huang | Characterization of microbial communities during start-up of integrated fixed-film activated sludge (IFAS) systems for the treatment of oil sands process-affected water (OSPW)[END_REF]. In their study, the Shannon weaver indices of biofilm were higher than those of suspended sludge, testifying to higher diversity. High microbial species diversity in the FBHBR should have advantages including better biomass acclimation, as specific pollutant-degrading bacteria could grow thanks to the biofilm. In turn, this could increase the resistance of the biomass to loading shocks in the presence of toxic inhibitor compounds. This indicates that the number of non-dominant species was higher in the FBHBR than in the CAS bioreactor and consequently, that diversity was higher in the FBHBR than in the CAS bioreactor. In the CAS bioreactor, Brevundimonas sp. appeared to be dominant. In the FBHBR, suspended flocs and biofilm were colonized by 30 Roseivivax sp. These bacteria have been reported to be hydrocarbon degrading bacteria [START_REF] Harwati | Characterization of Diverse Hydrocarbon-Degrading Bacteria Isolated from Indonesian Seawater[END_REF], [START_REF] Wang | Bioremediation of marine oil pollution by Brevundimonas diminuta : effect of salinity and nutrients[END_REF]. This suggests that the biomass was properly acclimated to the synthetic effluent containing hydrocarbons.

To summarize, bigger changes in bacterial populations were observed in the FBHBR than in the CAS bioreactor. At low HRT (i.e. 12 h), COD removal performances were much better in the FBHBR than in the CAS bioreactor. This suggests that satisfactory performances could be obtained in a more compact process, which is a key to offshore implementation. Microbial analyses also revealed higher diversity in the FBHBR, which could lead to better robustness and to better ability to degrade specific pollutants in the FBHBR.

Conclusion

This study focused on the development of hybrid biological reactors for the treatment of oilfield produced water (PW). To face more stringent regulations and the complex composition of PW, the performances of a fixed bed biofilm bioreactor (FBHBR) were assessed and compared to the performances of a conventional activated sludge reactor (CAS reactor). The main conclusions are:

-Under the same operating conditions as those used in a CAS reactor, the addition of a packing material allowed the development of a fixed biofilm. The biofilm concentration at the end of the experiment was 3.26 mg per carrier.

This development should enhance the efficiency of FBHBR.

-The reduction in hydraulic retention time (HRT) from 24 h to 18 h, corresponding to a subsequent increase in organic loading rate from 1.6 to 2.1 kg COD .m -3 .d -1 , did not affect the performance of either the CAS reactor or the FBHBR regarding COD removal efficiencies (> 95%).

-At HRTs of 24 h, 22 h and 18 h, both the CAS bioreactor and the FBHBR were able to handle loading shocks and return to stable COD removal, evidence for good robustness, considering the marked temporal variability of the composition of produced water. A disturbance to the process (addition of fresh sludge due to a bulking phenomenon) caused no significant reduction in the performances of the processes (there was a slight drop in phenol removal performance but a subsequent return to stability). But under reduced conditions (HRT of 12 h), only the FBHBR was able to cope with the loading shock, showing better robustness than the CAS bioreactor.

34

-At the lowest HRT (12 h, OLR of 3.2 kg COlD .m -3 .d -1 ), only the FBHBR was able to maintain high COD removal efficiency. The ability of FBHBR to work under such a low HRT is a key factor for the compactness of treatment processes, especially for offshore applications. The removal of dissolved organic components (phenol, BTEX, and PAH) by both the CAS and the FBHBR was high, indicating good acclimation of the biomass.

-Absence of toxicity in the outlet waters after treatment was achieved by both bioreactors, which was directly linked to the removal of pollutants in the treated effluents.

-Bacterial characterization revealed major differences between the CAS bioreactor and FBHBR. Biomass diversity was higher in the FBHBR than in the CAS bioreactor, particularly in the biofilm. The assessment of the bacterial populations revealed marked similarity between the free biomass and the biofilm in the FBHBR suggesting that the renewal of the free biomass was mainly due to biofilm detachment.

In future work, analyzing the influence of salinity will be of major importance since it can reach high levels in produced water. This paper demonstrated the efficiency of FBHBR. However, the drop in pressure needs to be further investigated to fully confirm the efficiency of the FBHBR since the presence of the packing material caused liquid to flow differently in the FBHBR than in the CAS bioreactor.

Figure 1 .

 1 Figure 1. Laboratory pilot plants (CAS and FBHBR). (1a) photograph; (1b) schematic diagram of the experimental setup

2. 5 . 4

 54 Characterization of the microbial population 14 Changes in the microbial population in both the CAS bioreactor and FBHBR were investigated between the different key stages of the experiment: at the beginning of acclimation, at the 24-hour HRT equilibrium, the 18-hour HRT equilibrium and the 12hour HRT equilibrium. Sample preparation and analysis were performed at the INRAE Transfer Laboratory (Narbonne, France). The samples were stored at -60 °C until DNA extraction. Extractions were performed using the DNEasy PowerSoil Kit (Qiagen). All ribosomal RNA genes were amplified by polymerase chain reaction through oligonucleotides targeting preserved regions common to all microorganisms. Sequencing was performed with a MiSeq sequencer (Illumina). Primers targeted the variable region V4-V5 of the 16S rRNA ribosomal sequence. Data from the sequences were pretreated by the INRAE Transfer pipeline. Bioinformatic analysis of the sequence data enabled taxonomic identification of microorganisms (phylum and genus). Identification was based on the Greengenes taxonomy for bacteria/archaea.

  From stage I (HRT= 24 h) to stage III (HRT= 18 h), the mean ratio was 0.81 in the CAS reactor and 0.86 in the FBHBR. These high values, which are typical of synthetic wastewater, suggested good bacterial development in the two bioreactors and no accumulation of inert materials, as explained by Sambusiti et al.[START_REF] Sambusiti | Influence of HRT reduction on pilot scale flat sheet submerged membrane bioreactor (sMBR) performances for Oil&Gas wastewater treatment[END_REF]. Interestingly, during the last stage of the process, different behaviors were observed in the CAS bioreactor and in the FBHBR. As shown in Figure3(HRT of 12 h), the mean ratio remained constant in the FBHBR with a mean value of 0.83, whereas in the CAS bioreactor, the concentration of free VSS decreased from 1.71 g.L -1 to 0.63 g.L -1 , and the VSS/TSS ratio decreased from 0.82 to 0.60. The simultaneous decrease in the free VSS concentration and in the VSS/TSS concentration suggests loss of bacteria in the CAS bioreactor. The decrease in HRT from 18 h to 12 h was associated with an increase in the OLR from 2.1 kg COD .m -3 .d -1 to 3.2 kg COD .m -3 .d -1 . The decrease in free TSS and in free VSS showed that the biomass in the CAS could not handle the operating conditions. These results suggest hybrid technologies are more efficient for PW treatment at reduced HRT.

Figure 2 . 18 Figure 3 .Figure 4 . 19 Figure 5 . 1

 218341951 Figure 2. Changes in free TSS concentrations (a) and COD removal efficiencies (b) in the CAS bioreactor (square symbols) and in the FBHBR (black triangles

Figure 5b shows the

  Figure5bshows the removal efficiency of volatile organic compounds (VOCs)

Figure 6b shows changes

  Figure6bshows changes in the Simpson's reciprocal index in the two bioreactors.

Figure 6 .Figure 7

 67 Figure 6. Changes in the Shannon Weaver index (a) and in the Simpson reciprocal index (b) in the two bioreactors

32 Figure 7 .

 327 Figure 7. Microbial population in the two reactors at the genus level: (a) graphical representation and (b) list of species

Table 1 .

 1 Summary of PNECs for BTEX and common PAHs in PW[START_REF]Establishment of a list of Predicted No Effect Concentrations (PNECs) for naturally occuring substances in produced water (OSPAR agreement 2014/5) », Decisions, Recommendations & Agreements[END_REF]

	Compound	PNEC (µg.L -1 )
	Benzene	8
	Toluene	7.4
	Ethylbenzene	10
	Xylene	8
	Naphthalene	2
	Anthracene	0.1
	Phenanthrene	1.3
	Benzo[a]pyrene	0.00017
	Fluorene	0.25
	Phenols (and C 1-3 alkylphenols)	7.7

Table 2 .

 2 Geometrical properties of AnoxKaldnes rings

Table 3 .

 3 Composition of the synthetic produced water

	Compound	Concentration (mg.L -1 )
	COD (adjusted with ethanol, sodium acetate, urea, and peptone)	1600
	TOC	379
	TN (from NH 4 Cl, urea and peptone)	20.6
	TP (from KH 2 PO 4 )	4
	Phenol	12
	Toluene	8
	o-Xylene	1
	m-Xylene	3
	Naphthalene	0.2
	Phenanthrene	0.05
	Benzo[a]pyrene	0.0002

Table 4 .

 4 Steps in the experimental bioreactors

	Phase	I	II	III	IV
	Time (days)	1-28	28-58	58-98	98-133
	HRT (h)	24	22	18	12
	OLR (kg COD .m -3 .d -1 )	1.6	1.8	2.1	3.2
	2.5 Analytical methods
	2.5.1 Measurement of the concentration of solids
	Concentrations of solids were determined in both bioreactors to quantify the amount

of biomass over the whole experimental period. Free total suspended solids (TSS)

Table 5

 5 Results showed that the inlet water was highly toxic to freshwater algae and Brachionus calyciflorus and slightly toxic to Daphnia magna and Vibrio fischeri.These results highlight different degrees of sensitivity among organisms, Brachionus calyciflorus and Pseudokirchneriella subcapitata being more sensitive than Vibrio fischeri and Daphnia magna. After treatment, no toxicity remained for Daphnia magna and Vibrio fischeri, and a major reduction in toxicity for Brachionus calyciflorus and Pseudokirchneriella subcapitata, was observed in both bioreactors.The absence of toxicity was due to the elimination of pollutants in both bioreactors and provides evidence that biological treatments such as CAS or FBHBR can efficiently eliminate the toxicity of a synthetic PW. These results confirm those of by Sambusiti et al.[START_REF] Sambusiti | Influence of HRT reduction on pilot scale flat sheet submerged membrane bioreactor (sMBR) performances for Oil&Gas wastewater treatment[END_REF].

	. A minimum EC50

sensitivity of Daphnia magna, Pseudokirchneriella subcapitata (freshwater algae), Brachionus calyciflorus (rotifer) and Vibrio fischeri (i.e. Microtox test) to the inlet water 23 were tested.

Table 5 .

 5 Ecotoxicity measurements of inlet water and outlet water in the CAS reactor and FBHBR expressed as EC50 (%) (NT Non-toxic)

			HRT = 18 h	HRT = 12 h
	Microorganism	Inlet	Outlet	Outlet	Outlet	Outlet
			CAS	FBHBR	CAS	FBHBR
	Daphnia magna (48 h)	61.3	89	NT	NT	NT
	Rotifers (i.e.
	Brachionus	12.5	> 90	> 90	43.6	> 90
	calyciflorus)
	Freshwater algae
	(i.e. Pseudokirchneriella	15.1	> 90	70	> 90	> 90
	subcapitata)
	Microtox test (i.e. Vibrio fischeri)	> 80	59.8	NT	> 80	NT
	3.4 Assessment of bacterial populations
	3.4.1 Changes in microbial diversity


Wanda Zhao
email: wanda.zhao@ls2n.fr

Anatol Pashkevich
email: anatol.pashkevich@imt-atlantique.fr

Alexandr Klimchik
email: a.klimchik@innopolis.ru

Damien Chablat
email: damien.chablat@cnrs.fr

Kinematic Control of compliant serial manipulators composed of dual-triangles

Keywords: compliant manipulator, tensegrity mechanisms, kinematic control, geometric redundancy, elastostatic behavior. I

come

INTRODUCTION

Compliant serial manipulators attracted much attention in robotics in recent years [START_REF] Frecker | Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization[END_REF][2] [START_REF] Wang | Compliant Mechanism Optimization: Analysis and Design with Intrinsic Characteristic Stiffness[END_REF]. Numbers of novel mechanisms appeared recently, which include not only rigid components but also elastic ones, allowing to achieve excellent flexibility and ability of shape-changing in accordance with the environment. One of the promising trends in this area is using tensegrity mechanisms, whose important advantages are simple design and low weight. However, because of the geometric redundancy and complicated elastostatic properties, the kinematics control of such manipulators is not simple and requires the solution of some theoretical problems considered in this paper.

Robotic manipulators are normally classified into three types conventional discrete, serpentine, and continuum robots [START_REF] Robinson | Continuum robots -a state of the art[END_REF] [START_REF] Chirikjian | Kinematically optimal hyperredundant manipulator configurations[END_REF][6] [START_REF] Chirikjian | A modal approach to hyperredundant manipulator kinematics[END_REF], the typical earlier hyper-redundant robot designs can be date back to 1970s [8] [START_REF] Gravagne | Kinematic transformations for remotely-actuated planar continuum robots[END_REF]. While designing such a manipulator, researchers are inclined to use a series of similar segments. Relevant studies based on the tensegrity mechanisms focus on the compressive elements and tensile elements (cables or springs). To achieve the desired configurations while working, the manipulators must avoid reaching the unstable equilibriums, but as the number of the mechanism segments increase, the kinematic analysis and control are more and more difficult [START_REF] Skelton | Tensegrity systems[END_REF] [START_REF] Moored | Analytical predictions, optimization, and design of a tensegritybased artificial pectoral fin[END_REF][12] [START_REF] Furet | Kinematic Analysis of Planar Tensegrity 2-X Manipulators[END_REF].

A new type of compliant tensegrity mechanism was proposed in our previous papers [START_REF] Zhao | Stiffness Analysis of a New Tensegrity Mechanism based on Planar Dualtriangles[END_REF] [START_REF] Zhao | The Stability and Stiffness Analysis of a Dual-Triangle Planar Rotation Mechanism[END_REF]. It is composed of two rigid triangle parts, which are connected by a passive joint in the center and two elastic edges on each side with controllable preload. In this paper, we study a compliant serial manipulator composed of the dual-triangle segments mentioned above, concentrate on the redundancy problem based on the kinematic analysis. Relevant results will be a good base for further investigation.

II. MECHANICS OF DUAL-TRIANGLE MECHANISM

Let us consider first a single segment of the total serial manipulator to be studied, which consists of two rigid triangles connected by a passive joint whose rotation is constrained by two linear springs as shown in Fig. 1. It is assumed that the mechanism geometry is described by the triangle parameters (a 1 , b 1 ) and (a 2 , b 2 ) , and the mechanism shape is defined by the angle that can be adjusted by means of two control inputs influencing on the spring lengths L 1 and L 2 . Let us denote the spring lengths in the non-stress state as 0 1 L and 0 2 L ,and the spring stiffness coefficients k 1 and k 2 . To find the mechanism configuration angle q corresponding to the given control inputs 0 1 L and 0 2 L , let us derive first the static equilibrium equation. From Hook's law, the forces generated by the springs are 0 () [START_REF] Albu-Schaffer | Soft robotics[END_REF], where L 1 , L 2 are the spring lengths |AD|, |BC| corresponding to the angle q. These values can be computed using the formulas

i i i i F k L L  (i =1,
22 1 2 1 2 ( ) 2 cos( ) i i i L c c c c     (i =1, 2).
Here

22 i i i c a b  (i =1, 2
), and the angles 1  , 2  are expressed via the mechanism parameters as 1 12 q   ,   . The torques M 1 =F 1 ·h 1 , M 1 =F 2 ·h 2 in the passive joint O can be computed from the geometry, so we can get

 0 1 1 1 1 1 1 2 1 0 2 2 2 2 2 1 2 2 ( ) (1 ( )) sin( ) ( ) (1 ( )) sin( ) M q k L L c c M q k L L c c         
where the difference in signs is caused by the different direction of the torques generated by the forces F 1 , F 2 with respect to the passive joint. Further, taking into account the external torque M ext applied to the moving platform, the static equilibrium equation for the considered mechanism can be written as M 1 (q)+ M 2 (q)+M ext =0.

Let us now evaluate the stability of the mechanism under consideration. In general, this property highly depends on the equilibrium configuration defined by the angle q, which satisfies the equilibrium equation M(q)+ M ext =0. As follows from the relevant analysis, the function M(q) can be either monotonic or non-monotonic one, so the single-segment mechanism may have multiple stable and unstable equilibriums, which are studied in detail [14][15]. As Fig. 2 shows, the torque-angle curves M(q) that can be either monotonic or two-model one, the considered stability condition can be simplified and reduced to the derivative sign verification at the zero point only, i.e. M'(q) q=0 <0, which is easy to verify in practice. It represents the mechanism equivalent rotational stiffness for unloaded configuration with q=0.

For the symmetrical case, when

a 1 =a 2 =a, b 1 =b 2 =b, k 1 =k 2 , 0 i L = 0 L , expressions (1)
can be essentially simplified and investigated in detail. It can be proved that relevant torqueangle relations can be either monotonic or non-monotonic, as presented in Fig. 2. It can be also shown that the monotonicity condition can be expressed as follows [START_REF] Zhao | Stiffness Analysis of a New Tensegrity Mechanism based on Planar Dualtriangles[END_REF][15]

   02 2 1 ( ) L b a b    
which is easy to verify, and will be used in the following sections to ensure the stability of the kinematic control.

III. KINEMATICS CONTROL OF MANIPULATOR

As follows from the mechanism structure (see Fig. 1), the desired configuration is defined by a single variable q which is adjusted by two control variables 0 2 ( )sin( ) sin( 2) cos( 2)

q M k b a q L b q a q         
and present the corresponding control law () q  for the unloaded case (

0 ext M  ) in the following way    0 2 2 ( ) sin( 2) ( )sin( ) cos( 2) q L b q b a q a q       
It should be noted that the desired configuration defined by the angle q should always satisfy the geometric constraints derived in our previous paper [14][15]. The obtained results are presented in Fig. 3. Also, for the proposed control strategy it is necessary to carefully select initial values of control inputs 00

12

LL 

, in order to avoid the negative equivalent rotational stiffness causing instability of the desired configuration of the mechanism.

In a more general case when 0 ext M  , to achieve the desired configuration with the angle q and the external loading ext M , the control input  should be computed using a revised expression

 0 2 2 2 sin( 2) ( )sin( ) ( , ) cos( 2) ext ext M k L b q b a q qM aq      
which shows that in the loaded case, the symmetrical configuration with q 0 =0 is achieved by applying a non-zero control input Δ that compensate the external loading. However, it is necessary to be also careful here about the selection of the parameter L 0 , which in some cases can cause negative stiffness leading to the buckling phenomenon.

Let us consider now a compliant manipulator composed of three similar segments connected in series as shown in Fig. 4, where the left-hand-side is fixed and the initial configuration is a "straight" one (q 1 =q 2 =q 3 =0). This configuration is achieved by applying equal control inputs to all mechanism segments. For this manipulator, to derive the desired control algorism, it is necessary to evaluate the influence of the external force F e =(F x , F y ), which causes the end-effector displacements to a new equilibrium location ( , ) (6 , )

TT xy

x y b   corresponding to the nonzero configuration variables (q 1 , q 2 , q 3 ). It is also assumed here the external torque M ext applied to the end-effector is equal to zero. It can be easily proved from the geometry analysis that the configuration angles satisfy the following direct kinematic equations

2 2 ; 2 2 x b bC bC bC y bS bS bS         where   123 1 2 3 cos C q q q    ,   123 1 2 3 sin S q q q    ,   12 1 2 cos C q q  ,   12 1 2 sin S q q  , 11 cos
Cq  , 11 sin Sq  . These two equations include three unknown variables 1 2 3 ( , , ) q q q and allow us to compute two of them assuming that the remaining one is known. For instance, if the angle 1 q is assumed to be known, the rest of the angles 2 q , 3 q can be computed from the classical inverse kinematics of the two-link manipulator as follows

    3 3 3 2 1 1 3 3 1 atan atan( 2 2 ) atan 2 q S C q y bS x b bC bS b bC q            where     22 22 3 1 1 2 2 5 4 C x b bC y bS b b         , 2 33 1 SC   
. It is clear that the latter expressions provide two groups of possible solutions corresponding to the positive /negative configuration angles 3 0 q  and 3 0 q  . To achieve the desired end-point position (x, y), it is clear that there is an obvious redundancy here related to the selection of three configuration angles 1 2 3 ( , , ) q q q allowing to reach the target point described by two Cartesian Coordinates (x, y), but this problem is outside of the stiffness analysis and should be solved using other techniques (obstacle avoidance, minimization of joint motions, etc.) The simplest way to overcome the redundancy problem is to minimize the joint motions by moving from the initial configuration ( , , ) q q q to a final one ( , , ) q q q corresponding to the desired end-point (x, y). This objective can be expressed formally in several ways, for example as a) Minimization of the total sum of the joint angle increments: It is clear that such an optimization problem should be solved with respect to the two scalar constraints arising from [START_REF] Yang | Synthesis and analysis of a flexible elephant trunk robot[END_REF]. The latter gives us a simple numerical technique where the joint angle q 1 is an independent variable and angles q 2 , q 3 are computed via the inverse kinematics [START_REF] Chirikjian | A modal approach to hyperredundant manipulator kinematics[END_REF] taking into account the duality expressed by the '  ' sign. An example of this approach is presented in Fig. 5 where the objectives (a) and (b) give slightly different solutions both of which are acceptable in practice. There is also an alternative approach, c) Minimize the total sum of joint angle increment squares

:   3
               J  T 00 ( , ) x x y y    p  and o o o 1 1 2 2 3 3 ( , ,
) T q q q q q q     Δq , Such approach leads the following constraint optimization problem: minimize the function of the joint angle increments 1 2 3

,,

q q q       222 1 2 3 1 2 3
( , , ) 2 min f q q q q q q          @  subject to the equality constraints

     1 1 2 3 11 1 12 2 13 3 2 1 2 3 21 1 22 2 23 3 ( , , ) 0
( , , ) 0 g q q q x J q J q J q g q q q y J q J q J q

                      @ @ . 
These problems can be solved using the Lagrange technique by minimizing the function of five variables

1 2 3 1 2 1 1 2 2 ( , , , , ) (.) (.)
(.) min L q q q f g g           @ , 
where 1

 and 2  are Lagrange multipliers. Further, after setting to zero the gradient 0 L , which is composed of the partial derivatives, one can obtain the following scalar equations with respect to the variables i q and j  ,(

).

 2 3 3 12 1 1 1 0 ; ; i j ji i i i i j i i q J J q x J q y              
 that can be presented in the matrix form as follows

3 3 3 2 3 1 2 3 2 2 T                          I J q 0 J0 λ p ,  where   T 12 ,   λ
. Using the block matrix inverse, the desired solution can be expressed as , LL ).To simplify the mechanism control, let us apply the symmetrical approach in previous, which allows using only three control variables ( 1 2 3

,,    ) producing six physical control inputs

00 1 ii LL    , 00 2 ii LL    with 1, 2, 3 i 
, where the values of i  are computed using formulas from the one-segment mechanism control law (4).The above-described approach gives us the following algorithm for the control of the three-segment mechanism:

1) Using the direct equations [START_REF] Yang | Synthesis and analysis of a flexible elephant trunk robot[END_REF] and additional objectives allowing to resolve the kinematic redundancy, compute the configuration angles 1 ( , ) q x y , 2 ( , ) q x y and 3 ( , ) q x y corresponding to the desired end-point position ( , )

xy and ensuring the manipulator "minimum motions" of the joints.

2) Using expression (4), compute the control inputs 11 () q  , 22 () q  and 33 () q  for the three segments corresponding to the configuration angles (q 1 , q 2 , q 3 ).

An example of computing based on the above algorithm is presented in Fig. 6, where the mechanism parameters a/b=1.1, L 0 /b =0.7 were chosen to ensure the mechanism stability in the unloaded mode 0 ext M  , and the initial configuration is 0 ( 0.1, 0.1, 0.1) q  . In more general case when the external forces ( , xy FF) are not equal to zero, it is also suggested to solve the redundant inverse kinematic problem using the above-presented objectives (a), (b), (c) (i.e. to use the configuration angles q 1 , q 2 , q 3 from the unloaded case), but to compute the modified control inputs allowing to compensate the external load. The corresponding algorithm implementing this technique is presented below. 1) Using the direct kinematics equations ( 6) and additional objectives allowing to resolve the kinematic redundancy, compute the configuration angles 1 ( , ) q x y , 2 ( , ) q x y and 3 ( , ) q x y corresponding to the desired end-point position ( , )

xy and ensuring the manipulator "minimum motions" of the joints. 2) Compute the joint torques 1 2 3 ( , , )

q q q M M M corresponded to the external force ( , xy FF) applied at the manipulator end-point.

3) Using expression [START_REF] Chirikjian | Kinematically optimal hyperredundant manipulator configurations[END_REF], compute the control inputs 11 () q  , 22 () q  and 33 () q  for the three segments corresponding to the configuration angles (q 1 , q 2 , q 3 ) and the joint torques q q q M M M .

It can be demonstrated that such algorism can ensure the stable configurations of the manipulator.

IV. CONCLUSION

The paper focuses on kinematic control of the compliant serial manipulator composed of a new type of dual-triangle tensegrity mechanisms, which are composed of rigid triangles connected by passive joints. The manipulator shape is controlled by adjusting the initial lengths of the elastic components located on two edges of each compliant segment. The main difficulties in control of such mechanisms are related to geometric redundancy and complicated behavior under the loading, which may be unstable if the control inputs are not selected properly.

The developed control algorism allows users to compute the control variables, which ensure the end-effector displacement to the desired location using very efficient motion that corresponds to minimum increments of all joint coordinates simultaneously. Besides, during such motion, these control inputs ensuring elastostatic stability of the manipulator shape with respect to the external forces/torques applied on the end-effector. The proposed algorism were carefully investigated via simulation, which confirmed via the results presented in this paper. Further research based on this study will focus on the more complicated manipulator motions in a constrained environment.

Figure 1 .

 1 Figure 1. Geometry of a single dual-triangle mechanism.

Figure 2 .

 2 Figure 2. The torque-angle curves and static equilibriums for 00 12 LL ( 0 0 q  ).

1 L and 0 2 L 1 L and 0 2 L 1 LL    and 00 2 LL

 121212 . The latter creates redundancy and ambiguity in control inputs selection. To eliminate this difficulty, it is reasonable to define 0 in a symmetrical way, i.e. as 00    . This allows us to write the static equilibrium equation for every single segment as follows 2 2 0

Figure 3 .Figure 4 .

 34 Figure 3. Relations between the control input  , sensitivity coefficient K, and the desired configuration angle q

Figure 6 .

 6 Figure 6. Relations between the control inputs ( 1  , 2  , 3  ) and the desired end-point position (x, y) with an initial configuration 0 ( 0.1, 0.1, 0.1) q  and parameters a/b=1.0, L o /b=1.0 (unloaded case

Figure 5 .

 5 Figure 5. Kinematic control of a redundant manipulator via minimization of objectives (a) and (b).

  noticed that the latter expression is similar to the matrix pseudo-inverse of Moore-Penrose. Besides, to achieve the equilibriums corresponding to the desired configurations, the three-segment mechanism must be controlled by three pairs of the control inputs (

ACKNOWLEDGMENT

This work was supported by the China Scholarship Council ( No. 201801810036 ).