Antoine Bourrier

Anna Szarpak-Jankowska

Farida Veliev

Renato Olarte-Hernandez

Polina Shkorbatova

Marco Bonizzato

Elodie Rey

Quentin Barraud

Anne Briançon- Marjollet

Rachel Auzely

Gregoire Courtine

Vincent Bouchiat

Cécile Delacour

Introducing a biomimetic coating for graphene neuroelectronics: toward in-vivo applications

Keywords: Biomaterial, graphene, surface functionalization, hyaluronic acid, bioelectronics, intracortical implant, neurons

ABSTRACT. Electronic micro and nano-devices are suitable tools to monitor the activity of many individual neurons over mesoscale networks. However the inorganic materials currently used in microelectronics are barely accepted by neural cells and tissues, thus limiting both the sensor lifetime and efficiency. In particular, penetrating intracortical probes face high failure rate because of a wide immune response of cells and tissues. This adverse reaction called gliosis leads to the rejection of the implanted probe after few weeks and prevent long-lasting recordings of cortical neurons. Such acceptance issue impedes the realization of many neuro-rehabilitation projects. To overcome this, graphene and related carbon-based materials have attracted a lot of interest regarding their positive impact on the adhesion and regeneration of neurons, and their ability to provide high-sensitive electronic devices, such as graphene field effect transistor (G-FET). Such devices can also be implemented on numerous suitable substrates including soft substrates to match the mechanical compliance of cells and tissues, improving further the biocompatibility of the implants. Thus, using graphene as a coating and sensing device material could significantly enhance the acceptance of intracortical probes. However, such a thin monolayer of carbon atoms could be teared off during manipulation and insertion within the brain, and could also display degradation over time. In this work, we have investigated the ability to protect graphene with a natural, biocompatible and degradable polymeric film derivated from hyaluronic acid (HA). We demonstrate that HA-based coatings can be deposited over a wide range of substrates, including intracortical probes and graphene FET arrays without altering the underlying device material, its biocompatibility and sensitivity. Moreover, we show that this coating can be monitored in-situ by quantifying the number of deposited charges with the G-FET arrays. The reported graphene functionalization offers promising alternatives for improving the acceptance of various neural interfaces.

A c c e p t e d M a n u s c r i p t INTRODUCTION. Since the early 80s, the emergence of the microelectronic industry and devices miniaturization has enabled the development of brain implants carrying microelectrode arrays capable of detecting single spikes from multiple individual neurons over days and months. [START_REF] Jun | Fully integrated silicon probes for high-density recording of neural activity[END_REF][START_REF] Kim | Recent Progress on Microelectrodes in Neural Interfaces[END_REF] These neurotechnologies led to pivotal discoveries in fundamental brain research and supported remarkable breakthroughs in neuroprosthetic medicine. [START_REF] Hochberg | Reach and grasp by people with tetraplegia using a neurally controlled robotic arm[END_REF][START_REF] Asboth | Cortico-reticulo-spinal circuit reorganization enables functional recovery after severe spinal cord contusion[END_REF] However, the poor biocompatibility of intracortical probes still prevents chronic sustainable recordings and thus restricts the spectrum of applications that could be addressed. As of today, the immune response of neural tissues and the low adhesion of neurons onto the electrode material limit the efficiency and time stability of current neural interfaces. [START_REF] Chen | Neural recording and modulation technologies[END_REF] While the electrical activity of neuron assemblies can be recorded remotely from the surface of neural tissues (with electroencephalography EEG or EcoG for instance), the detection of single spike requires a near field detection, i.e. approaching the sensing materials in close contact with the targeted neurons. This implies the insertion of electrodes within the brain. Consequently, the biocompatibility, the mechanical compliance, the surface charge and topography, and the chemical stability of implanted neural interfaces have critical impact on the performances of the sensors carried on the neural probe. [START_REF] Polikov | Response of brain tissue to chronically implanted neural electrodes[END_REF][START_REF] Lacour | Materials and technologies for soft implantable neuroprostheses[END_REF] Currently, the insertion of those devices through cortical brain areas leads to strong tissue response (trauma) that renders the coupling with the surrounding cells ineffective. In particular, a thick layer (about 100 -200 µm) of microglia and reactive astrocyte has been shown to surround the implanted devices after few weeks, and to prevent an intimate contact with the targeted neurons. [START_REF] Barrese | Failure mode analysis of silicon-based intracortical microelectrode arrays in non-human primates[END_REF] Consequently, this growing layer of glial cells partially shields the signal emitted by neurons and contributes to reduce the sensor signal-to-noise ratio over time, eventually leading to a high-rate of device failure. In addition, micro-movements of the rigid implant could also trigger an A c c e p t e d M a n u s c r i p t inflammatory response that further contributes to increase the distance between the cells and the sensors. Moreover, the presence of reactive oxygen species and free imbalanced charge can also damage the implanted electronics, both the sensors and the passivation layer, and further reduce the sensitivity, efficiency and time reliability of the devices. [START_REF] Barrese | Scanning electron microscopy of chronically implanted intracortical microelectrode arrays in non-human primates[END_REF] Over the past decade, graphene have attracted numerous interests to alleviate some of the issues faced by neuroelectronics. Indeed, it provides a unique combination of exceptional properties suitable for bio and neuroelectronics, such as its exceptional neural affinity, [START_REF] Park | Enhanced differentiation of human neural stem cells into neurons on graphene[END_REF][START_REF] Li | The promotion of neurite sprouting and outgrowth of mouse hippocampal cells in culture by graphene substrates[END_REF][START_REF] Veliev | Impact of crystalline quality on neuronal affinity of pristine graphene[END_REF] chemical inertness, bendability [START_REF] Lee | Measurement of the elastic properties and intrinsic strength of monolayer graphene[END_REF] (low bending rigidity while having a very strong tensile strength), anti-corrosive and anti-oxidative properties, [START_REF] Chen | Oxidation resistance of graphene-coated Cu and Cu/Ni alloy[END_REF][START_REF] Prasai | Graphene: corrosion-inhibiting coating[END_REF] as well as its high electrical conductivity and charge carriers mobility. Indeed its sensitivity and frequency range of operation exceed those of conventional semiconductors. Additionally, the low-cost and industrial scale production of polycrystalline monolayer obtained by chemical vapor deposition (CVD) growth method, further promotes graphene as an ideal material for future neural probes. [START_REF] Veliev | Recording spikes activity in cultured hippocampal neurons using flexible or transparent graphene transistors[END_REF][START_REF] Blaschke | Mapping brain activity with flexible graphene micro-transistors[END_REF] Using monolayer graphene has other advantages, regarding the low quantity of inserted electrodes material that reduces the toxicity of the implanted material. Also, monitoring the monolayer conductance provides an accurate control in-situ of its structural integrity.

However, owing to its ultimately small thickness, the possible degradation of graphene [START_REF] Girish | Confocal Raman imaging study showing macrophage mediated biodegradation of graphene in vivo[END_REF][START_REF] Kotchey | The enzymatic oxidation of graphene oxide[END_REF][START_REF] Kurapati | Dispersibility-Dependent Biodegradation of Graphene Oxide by Myeloperoxidase[END_REF] together with the mechanical frictions with surrounding cells and tissues could easily lead to device failures. To overcome this drawback, we have investigated the ability to functionalize intracortical probes and graphene monolayers with a biocompatible, soft and bioresorbable polymeric film. Such coating could protect the sensors during their insertion, and possibly favor the healing process around the implants by improving the chemical and mechanical compliance with the soft neural tissues. [START_REF] Minev | Electronic dura mater for long-term multimodal neural interfaces[END_REF]

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In recent years, hyaluronic acid HA has been widely used as a biomaterial for different clinical applications. [START_REF] Burdick | Hyaluronic acid hydrogels for biomedical applications[END_REF] This anionic polysaccharide is a major component of the extracellular matrix of connective tissues. The interactions of HA with cellular HA-binding proteins are important for cell adhesion, proliferation, wound healing and the HA binding sites might also provide the possibility for selective cell adhesion. [START_REF] Highley | Recent advances in hyaluronic acid hydrogels for biomedical applications[END_REF] In addition, HA monolayer could be used as basal layer for further hydrogel functionalization, to soften the interface and improve the mechanical compliance with neural cells, in order to promote neurite outgrowth [START_REF] Tarus | Design of hyaluronic acid hydrogels to promote neurite outgrowth in three dimensions[END_REF] or to provide new functionalities such as growth factors delivery for nerve regeneration. [START_REF] Knopf-Marques | Hyaluronic acid and its derivatives in coating and delivery systems: applications in tissue engineering, regenerative medicine and immunomodulation[END_REF] In addition with these many advantages, both the thickness and biodegradation rate of HA coatings can be controlled in order to maintain a close and tiny contact with cells for an efficient recording. Until now, some examples of HA-coated electrodes have been tested in-vivo [START_REF] Lee | Surface modification of neural electrodes with a pyrrole-hyaluronic acid conjugate to attenuate reactive astrogliosis in vivo[END_REF] or in-vitro with platinium, iridium microwires and silicon microelectrodes. [START_REF] Sridar | Peptide modification of polyimide-insulated microwires: Towards improved biocompatibility through reduced glial scarring[END_REF][START_REF] Grand | Short and long term biocompatibility of NeuroProbes silicon probes[END_REF] The challenge here lies in the maintenance of electrodes performances after the coating process.

Here, we report on the synthesis of HA-based films and show the ability to implement it onto intracortical probe and on monolayer graphene without altering both the material and device features, in term of biocompatibility, detection efficiency and sensitivity.

MATERIALS AND METHODS

Biopolymer coating. For the HA/PLL multilayers deposition, the samples are exposed to a solution of hyaluronic acid (HA) (Mw = 200 kg/mol MEDIPOL Distribution, dissolved at 2 mg/ml in 0.15M NaCl solution adjusted at pH 6.5) for 10 min, then rinsed in three successive baths of 0.01M NaCl solution during 5 min. They are then exposed to poly-L-lysine (PLL) (2 mg/mL, Sigma-Aldrich), and further rinsed in 0.01M NaCl solution (pH 6.5). The procedure was repeated A c c e p t e d M a n u s c r i p t several times to obtain the desired number of HA/PLL bilayers (from n = 1 to 5). Alkylamino hydrazide derivatives of hyaluronic acid (-HA) were synthesized from HA as previously described, [START_REF] Kadi | Alkylamino hydrazide derivatives of hyaluronic acid: synthesis, characterization in semidilute aqueous solutions, and assembly into thin multilayer films[END_REF] and allowed to enhance the adhesion of the hyaluronic acid on the hydrophobic graphene samples. Alkyl chains having ten carbon atoms (C10) were grafted on HA backbone with a substitution degree (DS, number of substituents per repeating disaccharide unit of HA) of 0.1 or 0.2. The water used in all experiments was purified by a Millipore Milli-Q Plus purification systems, with a resistivity of 18.2 MΩ•cm. Samples are kept in stable pH solution (0.01M NaCl) until their used to preserve the polymers integrity. Shortly before cells seeding, the buffer solution is rinsed and replaced by the attachment culture medium. Finally, primary hippocampal neurons (extracted from mousse embryo E16, see methods) are introduced in the solution.

Pure neuron culture and immunofluorescent staining. Neurons were extracted from the hippocampus of mouse embryos (E16.5 pregnant mice from Envigo, killed by cervical elongation), dissociated and seeded with a density of 150 000 cells/cm 2 in attachment medium (MEM supplemented with 10% foetal bovin serum, 1% glutamine and 0.05% peniciline/streptomycine, Gibco). Neurons were then incubated at 37°C and 5% CO2, and the attachment medium was replaced few hours later by glial conditioned culture medium, supplemented with AraC (1 mM) to suppress the glial proliferation. The glial conditioned medium is previously obtained by culturing glial cells from the cortex in attachment medium until confluency. The cells were then cultivated with serum free Neurobasal medium (Invitrogen) and the glial conditioned medium was collected after 48 h for subsequent use on neuron cultures.

For the immunofluorescent staining, neurons were fixed in 4% formaldehyde (prepared from fresh paraformaldehyde) (10 min), permeabilized in PBS-0.25% Triton-X100, blocked in PBS-2% bovine serum albumin and finally immunostained with the anti-Synapsin (1:500, Millipore), anti-

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Tau (1:300, Millipore) and anti-YL1/2 (1:1000, BioRad) primary antibodies, and DAPI (1:1000, Sigma-Aldrich) for labeling the synaptic vesicles, the axon, the cytoskeleton and the nucleus respectively. Immunoreactions were visualized with appropriate secondary antibodies labeled with Alexa fluor® 488 or 594 or 647 (1:500, Life Technologies). Immunofluorescence images were collected using automatic Zeiss Axio-Imager M2 microscope, and the image processing was performed with ImageJ. [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF] Statistics. For cell density assessment, somas are counted using Image-J particles analysis plugin after picture conversion in 16 bits and threshold definition to reject the background noise. Soma size has first been measured manually on a dozen of neurons per picture in order to define the average soma area to detect. For groups of cells, each soma cannot be discriminated, thus the number is estimated by dividing the total area of clusters by the average soma size, and then verified with manual counting. The covering rate for neurite and axon have been extracted by adjusting the threshold and preserving a constant brightness level for each fluorescent antibodies.

Defocus -inducing less brightness and larger covering surfacesis taking into account by keeping the same threshold level of brightness between all pictures. For synapses counting, a high threshold was used to detect bright puncta around the soma, and a low threshold was used to detect puncta along neurites.

In-vivo assays. Six Adult female Lewis rats (200-225 grams, N.23, Charles River, UK) were housed individually on 12h light/dark cycle with access to food and water ad libitum. Before surgery, animals were first habituated to human presence and manipulation during 2 weeks.

Stereotaxic fixation was performed after administration of 0.1ml of Dorbene anaesthesia and surgeries were performed under inhalant anaesthesia of 2% diluted isofluorane in 2 L/min oxygen.

Briefly, we used 6 arrays with 32 recording channels: 3 arrays of coated microelectrodes, and 3

A c c e p t e d M a n u s c r i p t bare (uncoated) arrays for the control, leading to 96 independent microelectrodes tested for each conditions (182 electrodes in total) on 6 independent rodents. Each recording channel is a thin (100 µm) tungsten wire encapsulated by polyimide (from Tucker-Davis-Technologies, USA). The arrays were inserted into layer V of the leg region of the right motor cortex, which we previously identified anatomically and electrophysiologically. [START_REF] Digiovanna | Engagement of the Rat Hindlimb Motor Cortex across Natural Locomotor Behaviors[END_REF] Signal amplification and recording were made with the Tucker Davis Technologies PZ2 preamp and RZ2 amplifier at the sampling frequency of 25 kHz. Spike sorting is processed in real-time by using TdT© OpenEx© commercial software and spikes-of-interest were stored when spike occurrence was matching with the walking status. We labeled the corresponding sensors among the 32 recording sites of each implant. The experience was repeated once a week by in-cage free-movement recordings for all sensors and compared to previous results. All procedures and surgeries were approved by the Veterinary Office of the canton of Vaud and the Veterinary Office of the Canton of Geneva (Switzerland).

Histology. At the end of the experimental procedures, rats were perfused with Ringer's solution containing 100 000 IU/L heparin and 0.25% NaNO2 followed by 4% phosphate buffered paraformaldehyde, pH 7.4 containing 5% sucrose. The brains were dissected, post-fixed overnight, and transferred to 30% phosphate buffered sucrose for cryoprotection. After 4 days, the tissue was embedded and the brains sectioned in a cryostat (Leica, Germany) at a 40 μm thickness. Astrocyte and microglial reactivity were revealed by performing immunohistological stainings against glial fibrillary acidic protein (GFAP) and ionized calcium binding adapter molecule 1 (Iba1), respectively. Briefly, the brain sections were incubated overnight with the anti-Iba1 (1:1000, Abcam) or anti-GFAP (1:1000, Dako) primary antibodies. Immunoreactions were visualized with appropriate secondary antibodies labeled with Alexa fluor® 488 or 555 (Life Technologies). Fluorescence counterstaining of Nissl substance was done using neurotrace A c c e p t e d M a n u s c r i p t 640/660 solution (1:50, Invitrogen). Image acquisition was performed using a laser confocal scanning microscope (Leica SPE) and stacks were processed offline. Immunostaining density was measured using confocal image stacks per group acquired with standard imaging settings and analyzed using custom-written scripts according to previously described methods. [START_REF] Van Den Brand | Restoring voluntary control of locomotion after paralyzing spinal cord injury[END_REF] Briefly, confocal output images were divided into square regions of interest (ROI), and densities computed within each ROI as the ratio of positive signal (amount of pixels) per ROI area. ROI were defined as follow: DV: length of cortical column (from brain surface to corpus callosum); M/L: +/-1mm from the electrode tract. Files were color-filtered and binarized by means of an in-tensity threshold. Threshold values were set empirically and maintained across sections, ani-mals and groups. Computerized counts were performed blindly. [START_REF] Han | Homogeneous optical and electronic properties of graphene due to the suppression of multilayer patches during CVD on copper foils[END_REF] on copper foils (25 µm thick, 99.8% purity, Alfa-Aesar), using time-exposure of CH4 (2sccm 10s, then 60s off, repeated during an hour) flow in diluted H2 atmosphere (1000 sccm, 25 mbar pressure) to prevent the development of multilayer patches. Prior the growth, the Cu foil has been cleaned in acetone and further annealed in diluted H2 atmosphere (10% in Ar) at 1000°C for 2h.

Graphene substrates. Graphene monolayers have been grown by pulsed CVD technique

Then, 4x4 mm graphene pieces were transferred on 12 mm wide glass coverslip (Marienfeld) by polymer assisted wet transfer technique. The Cu foil, covered by PMMA resist on the graphene side, is wet-etched in ammonium persulfate solution (0.1 g/ml, 2h). Once the Cu-etching is complete, the floating graphene-PMMA bilayer is rinsed with several baths of DI water to remove all traces of the Cu-etchant solution, and then fished with a cleaned and hydrophilic substrate. The substrate coated with graphene-PMMA is dried at room temperature and PMMA is removed in an acetone bath (overnight, room temperature). The transferred graphene sheets are then characterized using atomic force microscope and Raman microspectroscopy.

A c c e p t e d M a n u s c r i p t

Field effect transistor array. As previously reported, [START_REF] Veliev | Recording spikes activity in cultured hippocampal neurons using flexible or transparent graphene transistors[END_REF] the graphene sheet is etched to define 20 × 10 µm² wide and long transistor channels, by using photoresist mask and oxygen plasma etching of the unprotected graphene parts. Then, this first photoresist mask is removed, and a second photoresist mask defines the negative pattern of the contact leads. A metallic thin film (Ti/Au) is then evaporated in vacuum, and the resist is removed in an acetone bath. Finally, a biocompatible SU-8 photo-sensitive polymer is used to insulate the contact leads from the top liquid and to expose the graphene transistors channel only (both DI water, PBS and cell medium culture were tested for the liquid gating experiment showing no significant difference on the result).

RESULTS AND DISCUSSION

Impact of hyaluronic acid on neurons adhesion and neuritogenesis in-vitro. Isolated hippocampal neurons have been selected to study the behaviour of nerve cells on HA films.

Because they are highly sensitive to their microenvironment (topography, chemistry, surface charges, rigidity of the substrate and surrounding medium), they are suitable candidates to evaluate the affinity of a micro-engineered interface. Their affinity to the environment is assessed by measuring their response in term of cell adhesion and neuritogenesis. For that purpose, neurons have been cultured on conventional glass coverslips coated with hyaluronic acid/poly-L-lysine (HA/PLL) multilayer films obtained by layer-by-layer LbL method, [START_REF] Szarpak | Designing hyaluronic acid-based layer-by-layer capsules as a carrier for intracellular drug delivery[END_REF] and on PLL single layers covered substrates, as control samples (figure 1).

When neurons were seeded on a single layer of negatively charged HA (glass-coated) substrate, we notice that they barely attached (figure 4c). This is in stark contrast to the behaviour of neurons seeded on single layer of PLL, or on multilayer films obtained by combination of HA and PLL, that promote adhesion and neurites regrowth (figure 1 and2).

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While the number of attached soma are almost the same on the PLL and HA/PLL samples, the area covered by neurites is twice higher on the multilayer films than on single PLL layer after 5 in culture (figures 1b). Axonal differentiation and synaptogenesis are also significantly enhanced on the HA/PLL films, regarding the axon length and synapse density, respectively. Similar results were obtained for both studied HA/PLL films with PLL or HA as an outer layer, (HA/PLL)5/5 and (HA/PLL)5/4, respectively, with slightly higher values for films with PLL on the top. The positive impact of the HA/PLL film on neurons density and neurite spreading is also observed on mature network (figure 2 and figure S1,S2). The neurons density and the surface covered by neurites are still enhanced on the bilayers after 14 days (figure S1), indicating that HA/PLL films support longterm cell regeneration and survival. Moreover, neurons cultured on five (HA/PLL) bilayers deposited on graphene monolayer appears further developed (figure S1), combining both positive impacts of the monolayer graphene and the (HA/PLL) bilayers.

The lack of adhesion on negatively-charged HA monolayer and at the opposite the successful neural development on PLL-containing films confirm that the presence of positive charges impacts the adhesion and spreading rates of cultured neurons. Indeed, the negatively charged cell membrane tends to adhere on positively charged surfaces by electrostatic interaction, as already reported within numerous studies including on nanostructures, [START_REF] Xu | Amplified effect of surface charge on cell adhesion by nanostructures[END_REF] carbon nanotubes [START_REF] Mattson | Molecular functionalization of carbon nanotubes and use as substrates for neuronal growth[END_REF] and graphene. [START_REF] Veliev | Impact of crystalline quality on neuronal affinity of pristine graphene[END_REF] Similarly, Min Hu et al. showed earlier [START_REF] Hu | Improvement of Schwann cell attachment and proliferation on modified hyaluronic acid strands by polylysine[END_REF] that cross-linked HA strands does not permit attachment of Schwann cells. Adhesion and proliferation were possible only after coating the surface with PLL. Also, Z. Yue et al. [START_REF] Yue | Bio-functionalisation of polydimethylsiloxane with hyaluronic acid and hyaluronic acid-collagen conjugate for neural interfacing[END_REF] showed that HA alone was inefficient for cellular growth, consequently an additional modification of a surface with collagen was necessary to improve cell growth and neural differentiation of PC12.

A c c e p t e d M a n u s c r i p t

In addition to the presence of positive charges in the adhesion films, other material features seem to support neurons regrowth on the HA/PLL multilayers, as the adhesion and neurites outgrowth is higher on those samples than on PLL monolayer. Beside the type of biomaterial used to mimic the extracellular matrix ECM, the cells adhesion and outgrowth could be affected by many different cues such as growth factors, stiffness, topography and cell-to-cell contacts. [START_REF] Kreeger | Engineering Approaches to Study Cellular Decision Making[END_REF] We have shown previously that multilayer films of five bilayers are also thicker (> 80 nm) than a single monolayer of polymer (< 10 nm thick), [START_REF] Szarpak | Designing hyaluronic acid-based layer-by-layer capsules as a carrier for intracellular drug delivery[END_REF] and more soft than glass coverslip, with a Young's modulus of few kPa and hundreds of GPa respectively. [START_REF] Schneider | Polyelectrolyte multilayers with a tunable Young's modulus: influence of film stiffness on cell adhesion[END_REF][START_REF] Im | A review of electrodes for the electrical brain signal recording[END_REF] Consequently, the mechanical compliance with neurons might be enhanced on the thick multilayers, and this could improve the neuritogenesis as it was observed in our case on HA/PLL multilayers. Similar enhancement regarding the neurites spreading was also observed when using polydimethylsiloxane (PDMS)coated glass substrates instead bare glass coverslips (figure S3). The Young's modulus of such elastomers being one order of magnitude lower than for glass (1-10 MPa and 10 GPa respectively), [START_REF] Lacour | Flexible and stretchable micro-electrodes for in vitro and in vivo neural interfaces[END_REF][START_REF] Johnston | Mechanical characteriza-tion of bulk Sylgard 184 for microfluidics and microengineering[END_REF][START_REF] Rivnay | Nextgeneration probes, particles, and proteins for neural interfacing[END_REF] it should also soften the surface sensed by neurons. Although it remains higher than for the nervous system (in the kPa range). Recent works also showed that by regulating the HA hydrogels stiffness and cell-adhesive RGD ligand density, one can promote the neurite outgrowth within 3D matrix without using PLL. [START_REF] Tarus | Design of hyaluronic acid hydrogels to promote neurite outgrowth in three dimensions[END_REF] The topography of multilayer films could be another contributing factor, as it is an additional advantage for cell migration and neurite spreading. The presence of biomimetic niches within the HA/PLL film have indeed been shown to promote stem cells adhesion and maturation. [START_REF] Lee | Biomimetic niche for neural stem cell differentiation using poly-L-lysine/hyaluronic acid multilayer films[END_REF] These results show that combining HA and PLL polyelectrolytes, together with the lowered rigidity offered by multilayer film, positively impact the adhesion and spreading rates of primary hippocampal neurons in culture. The LbL method used for the film formation is an easy-to-use A c c e p t e d M a n u s c r i p t method which can be easily applied for coating different surfaces, including three-dimensional (3D) intracortical neural probes.

Impact of HA films on intracortical probe biocompatibility. We have investigated the biocompatibility of the HA/PLL coating in-vivo, by depositing the developed multilayer films on conventional intracortical electrodes (tungsten wires, Utah Array, from Tucker Davis technologies ©). These probes were inserted within deep cortical layers to monitor neural assemblies that command hindlimb motion. During 7 weeks of recordings, we have followed the efficiency of the coated electrodes to detect single spike associated to the walking status and their reliability in time.

We have also compared the glial cell proliferation around the functionalized (active) and bare (control) probes. These in-vivo investigations were performed as double-blind experiments.

In particular, we have functionalized 32 independent probes with five bilayers of HA/PLL (figure 3a), deposited by LbL method as for the previous in-vitro assays. The coated probes were compared with 32 independent uncoated probes (controls), in term of device and immune responses. The experiments were performed on two groups of independent rodents: one group of three control rats (uncoated probes), and a second group of three active rats (with the coated probes). The targeted axonal projections of motor neurons is located in the cortical layers V involved in the hindlimb locomotion command. [START_REF] Wenger | Closed-loop neuromodulation of spinal sensorimotor circuits controls refined locomotion after complete spinal cord injury[END_REF] Freely-moving recordings were performed once a week on each implanted rodents (supplementary video 1). After five weeks, recordings were performed during walking controlled motion on a treadmill, and compared with the muscle kinetics and locomotion behaviours. The detected neural spikes were then extracted from the voltage timetraces of the 32 probes acquired during rodent walks. Spikes were further analyzed in term of shape, amplitude and frequency to track motor neurons spiking activity. The electrodes which successfully detect single spiking events from motor neurons associated to walking status were followed along the 7 weeks.

Clear signals with high signal to noise ratio (S/N > 3) were extracted from the functionalized probes for all the three experiments (figure 3b-c). At the opposite, only a single experiment performed with uncoated control probes showed similar high-quality signals (figure S4). We checked that the single spikes detected with the functionalized probes were regular and synchronized with trunk and legs movements, demonstrating an efficient interfacing of motor neurons with the coated probes. Specially, we have compared the number of electrodes able to detect single spikes from individual motor neurons (spikes duration and amplitude being about 1ms and 100-200µV as shown figure 3c and3c, and associated to the walking status with and without the multilayers coating. Interestingly, the total number of operating electrodes appears to be slightly improved for the probes coated with the polymeric film, being almost twice higher than the number of uncoated (control) probes after the glial scaring process, i.e. 2 weeks typically (figure 3d).

We notice that the disruption of the blood vessels during the implantation surgery could be a source of variability, because of the large amount of blood macrophages and endothelial cells carried inside by the implant could further increase the gliosis and eventually the detection failure. Here, the probes coated with HA/PLL bilayers were still able to sense and discriminate single units (i.e. motor neuron spike) during the highest bleeding level (figures S4, S5 and S6), while no signal was recorded with the control (uncoated) probes at lower bleeding level which further demonstrates the positive impact of the multilayers.

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At the end of the recording procedure, the brains were dissected, post-fixed overnight, and transferred into 30% phosphate buffered sucrose for cryoprotection. Thin brains slices (40 μm thick) were stained with immuno-fluorescent proteins for labelling the neurons and the glial cells at the implantation sites. Figure 3e shows representative immuno-fluorescent micrographs of the whole coronal brain sections stained with GFAP or Iba1 and Dapi or Nissl, illustrating the proliferation of astrocytes or microglial cells (red), and the population of neurons (blue), respectively. As expected, those commercial probes caused a significant immuno-response (figure 3f). For some probes, the bleeding level was high and could have an impact on the glial cell populations (figures S5 and S6). Thus, the expression of GFAP and Iba1 (histogram figure 3f) are compared only when the bleeding level was the lowest (#482 and #479 for coated and bare electrodes). Although, data are also provided for the other groups (table figure 3f)The density of glial cell is significantly higher than the number neurons at the recording sites that explain the low number of operating sensors (figure 3d). Similar results were observed for the functionalized probes, the proliferation of glial cells being slightly reduced around the probes coated with the multilayers, especially for microglias (figure 3f). Interestingly, this slight improvement is accompanied by a slight increased of the number of operating sensors. These results further demonstrate the biocompatibility of the HA/PLL multilayer films in term of chemical and mechanical inertness. The electrical and histological analyses provide evidences that hyaluronic acid based films do not depress the responses of the sensors and the brain cells. The observations with the functionalized probes are at least similar to those obtained with the control (uncoated) probes, and even slightly improved in term of number of : (1) successful experiments (3/3 versus 1/3), (2) amount of operational sensors (twice higher) and (3) proliferation of glial cells (slightly reduced).

A c c e p t e d M a n u s c r i p t

Compatibility of HA coating and graphene bioelectronics. Among all materials used in neuroprostheses, the improvements gained by graphene are clearly significant on the neurons adhesion and outgrowth. [START_REF] Park | Enhanced differentiation of human neural stem cells into neurons on graphene[END_REF][START_REF] Li | The promotion of neurite sprouting and outgrowth of mouse hippocampal cells in culture by graphene substrates[END_REF][START_REF] Veliev | Impact of crystalline quality on neuronal affinity of pristine graphene[END_REF] For instance, graphene allows neurons to attach and grow without any adhesive coating such as poly-L-lysine (figure S7). Additionally multilayer films can introduce significant improvements for in-vitro cell cultures for instance (figure 2 andS1), and for protecting the monolayer from degradation or delamination during in-vivo assays. Thus combining these two materials could open new perspectives for improving the biocompatibility and the lifetime of neural interfaces. Moreover, the naturally secreted enzyme hyaluronidase [START_REF] Kurisawa | Injectable biodegradable hydrogels composed of hyaluronic acid-tyramine conjugates for drug delivery and tissue engineering[END_REF] can dissolve the HA coating and reveal the graphene at a predetermined speed rate, in function of the amount of protecting layers. Thus, it enables a direct contact restoration between electronics and cells, together with conferring a progressive drug delivery property thanks to a drug encapsulation in the film. This could further favor the healing process at the implantation site which is a current limitation for numerous brain interfaces, such as the intracortical probes.

However, the functionalization could change the device or material features. To assess such possible drawbacks, we have followed the impact of the HA polymer bounding to graphene. One of the crucial issues is to keep the structural integrity of the monolayer graphene, as well as its high neuronal affinity and its global electrical performance such as high conductivity (mobility and square resistance of CVD graphene being typically around µ=5000 cm2⋅V-1⋅s-1 and R□ = 500 Ω/□) and device sensitivity (4mS/V for GFETs). [START_REF] Veliev | Recording spikes activity in cultured hippocampal neurons using flexible or transparent graphene transistors[END_REF][START_REF] Blaschke | Mapping brain activity with flexible graphene micro-transistors[END_REF] Raman spectroscopy and AFM micrographs have been performed on high quality CVD-grown monolayer graphene before and after HA adhesion (figure 4a-e) to assess the possible impact of the functionalization on the structural properties of the monolayer. In addition to the characteristic peaks of graphene (G and 2D band peaks), the Raman spectra show additional resonant modes at A c c e p t e d M a n u s c r i p t low frequency (899-950 cm -1 , 1090 cm -1 , 1180 cm -1 , 1410-1460 cm -1 ) which are characteristic of HA polymer (figure 4b). [START_REF] Bansil | Raman spectroscopy: a structural probe of glycosaminoglycans[END_REF][START_REF] Barrett | Laser Raman inelastic light scattering investigations of hyaluronic acid primary and secondary structure[END_REF] The contributions of carboxyl and methyl groups CH, CH3 and COO - (1330 cm -1 and 1370 cm -1 ) are certainly superimposed with the defects-related D-band peak (1350 cm -1 ) of graphene. Most of all, the amplitude of the D-band peak remains low (ID /IG <0.06) after the functionalization, revealing the low density of lattice defects [START_REF] Das | Raman spectroscopy of graphene on different substrates and influence of defects[END_REF] induced by the binding with HA polymers. These results confirm the adhesion of HA onto graphene, and demonstrate that the HA polymer and the coating procedure do not affect the crystalline quality of the graphene monolayer.

The atomic force micrographs performed before (figure 4c) and after the polymer deposition (figure 4d-e) further confirm the integrity and the overall high quality of the graphene monolayer previously transferred on glass substrates. The HA monolayer deposited onto graphene appears first granular at the graphene substrate (figure 4d), certainly because of the high graphene hydrophobicity. Consequently, the homogeneity of the coating is significantly enhanced when adding hydrophobic alkyl (C10) chains on the HA polymer backbone to obtain -HA (depicted figure 4a), as shown within figure 4e. Contact angle measurements show the higher hydrophilicity of the graphene substrates coated with the derivative -HA polymers (figure S8). As expected, the hydrophilicity gets higher when the density of the alkyl chains grafted on the HA backbone is increased, from 10 to 20 % (i.e. on average 10 and 20 chains every 100 repeating disaccharide units of HA). The presence of hydrophobic alkyl chains on the HA backbone promotes adsorption of this polymer on hydrophobic graphene monolayer, simultaneously rendering the surface exposed to the liquid or cells more hydrophilic.

As mentioned previously, HA promotes neurons adhesion and outgrowth in culture when combining it with a positively charged layer such as PLL (figure 1). Interestingly, combining HA with positively charged graphene monolayer enables also the adhesion of neurons and an efficient neurites spreading (figure 5a), which are crucial maturation stages for culturing primary neurons and for in-vitro assays. Main cell features, such the number of attached neurons, neurites number and length, are comparable on the active (graphene/HA coated glass) and control (PLL coated glass) samples (figure 5a and b respectively). We notice a slightly higher expression of Tau proteins labeling the axon (red) on the graphene substrates, suggesting an earlier polarization of the axon and thus an improvement in the maturation process which is as expected for graphene substrates. [START_REF] Veliev | Impact of crystalline quality on neuronal affinity of pristine graphene[END_REF][START_REF] Bendali | Purified neurons can survive on peptide-free graphene layers[END_REF] Here, our observations show that the high neural affinity of the underneath graphene remains despite the functionalization. As mentioned above, combining graphene with (HA/PLL) multilayers enable also neurons adhesion and outgrowth (figure 2). The neurons density and the surface covered by neurites are further enhanced on the bilayers deposited on graphene after 14 days (figure S2), indicating that combining Graphene and (HA/PLL) films support long-term cell regeneration and survival.

Finally, we have investigated the impact of HA polymers on the electronic transport properties of graphene devices, and in particular by measuring the characteristics of graphene field effect transistor (G-FET), as they offer promising alternatives for future neuronal interfaces. [START_REF] Veliev | Recording spikes activity in cultured hippocampal neurons using flexible or transparent graphene transistors[END_REF][START_REF] Blaschke | Mapping brain activity with flexible graphene micro-transistors[END_REF] Several G-FETs have been fabricated on sapphire substrates (figure 6a-b) and their maximum transconductance 𝑔 𝑚 = 𝜕𝐼 𝐷𝑆 𝜕𝑉 𝐺 ⁄ was measured before and after the functionalization. This transconductance is a physical parameter that can illustrate the impact of the HA polymers on the device sensitivity S which can be expressed as:

𝑆 = ∆𝐺 𝐺 = 𝑔 𝑚 × ∆𝑉 𝐺 × 1 𝑉 𝐷𝑆 • 𝐺
with G the conductance of the graphene transistor channel, IDS and VDS the drain-source current and voltage, and VG the top-gate voltage applied with a quasi-reference Pt-electrode (figure 6a).

The dependence of the channel current with the liquid gate voltage VG shows a typical symmetric ambipolar field effect behavior with a charge neutrality point at VD ~ 0.4 V (figure 6c). The sensitivity S reaches its maximal value at the inflections of the field effect curve where the transconductance is the highest.

While PLL does not affect the G-FETs properties, [START_REF] Veliev | Recording spikes activity in cultured hippocampal neurons using flexible or transparent graphene transistors[END_REF][START_REF] Wang | Synthesis of a hydrophilic poly-L-lysine/graphene hybrid through multiple non-covalent interactions for biosensors[END_REF] HA polymer slightly reduces the transconductance and shifts the charge neutrality point VD toward more positive values (red curves, figure 6c), in agreement with the overall negative charge of HA polymer. However, the minimum of conductance remains unchanged, assessing the fact that the HA polymer and the coating procedure did not damage the integrity of the graphene transistor channel.

The reduced transconductance could stem from a lower value of the charge carrier mobility, and also because the hyaluronic acid changes the interfacial capacitance. The capacitance of the graphene/liquid interface CG is not directly measurable. It results from the serial contribution of the geometric (Helmholtz and diffusive) CGeo and the quantum CQ capacitances of graphene, expressed as the following 1/CG~1/CGeo+1/CQ. For liquid-gated graphene field effect transistor, the quantum capacitance cannot be neglected, and its variation with the gate voltage should be taken into account to extract the charge carrier mobility values from the transfer curve IDS -VLG. [START_REF] Xia | Measurement of the quantum capacitance of graphene[END_REF] Dedicated methods have been previously developed to model liquid gated G-FETs and extract the mobility and capacitance values in this top gating configuration. [START_REF] Ferreira | Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers[END_REF][START_REF] Vieira | Graphene field-effect transistor array with integrated electrolytic gates scaled to 200 mm[END_REF] The conductivity  of liquid gated graphene transistors is function of the Fermi level and the scattering induced by disorder (adsorbed impurities and defects). It can be expressed as:

𝜎 = 𝐺. 𝐿 𝑊 = 𝑔 0 6√3 4𝜋 𝑎 0 2 𝛼 𝑛 𝑖 |𝑉 𝐿𝐺 -𝑉 𝐷 |𝑙𝑛 2 (√𝛼𝜋|𝑉 𝐿𝐺 -𝑉 𝐷 |𝑟)
with g0 (0.039 mS) the quantum of conductance, a0 (1.42 Å) the C-C lattice bond length in graphene, and r ~ a0 the short range potential induced by defects scattering, the fitting parameter being  (= n/VLG) a model interfacial capacitance, and ni the density of impurity or defect.

Figures 5d and 5e compare the fitting curves before and after HA deposition respectively. Adding HA results in a slight increase of defect density ni, from 0.5 to 0.66 × 10 12 cm -2 , while the total interfacial capacitance CLG =  × e is decreasing, from 0.56 to 0.53 µF.cm -2 with and without HA respectively. The total interfacial capacitance includes the serial contribution of the electrical double layer at the interface with the Pt reference electrode, the HA capacitance and the second electrical double layer capacitance at the interface with graphene (figure 6a).

From those values, we can estimate the carriers mobility in the hole and electron regimes, µ ℎ,𝑒 = 𝐿 × 𝑔 𝑚 /(𝑊 × 𝑉 𝐷𝑆 × 𝐶 𝐿𝐺 ), with gm the maximum transconductance for holes and electrons extracted from the transfer curve 𝜕𝐼 𝐷𝑆 𝜕𝑉 𝐺 ⁄ (𝑉 𝐺 ) at the maximum inflection points. On bare G-FETs (before HA coating), hole and electron mobilities show slightly asymmetric values, being higher in the hole conduction regime µh = 1881 cm².V -1 .s -1 , while only reaching µe = 1631 cm².V - 1 .s -1 in the electron conduction regime. These values are consistent with previous studies. [START_REF] Ferreira | Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers[END_REF] After HA deposition the mobility is slightly reduced for the both (hole and electron) conduction regimes, being almost the same µh,e = 1283 -1296 cm².V -1 .s -1 for holes and electrons respectively. Considering Mk = 0.65 e -for HA, [START_REF] Ben Abdallah | Quantum molecular modeling of free radical saccharides from hyaluronan[END_REF] and a = 4% for grafted dipole on carbon latice, [START_REF] Zhao | Gas molecule adsorption in carbon nanotubes and nanotube bundles[END_REF] we found an amount of charge carried by the HA coating of about nHA = 4.10 6 e -. This value matches well the excess number of holes (∆nHA ∼ -∆nh) within the graphene channel. This result shows that monitoring the shift of the charge neutrality voltage VD could indeed be used to monitor in-situ the adhesion and degradation in time of HA coatings to restore a direct contact with cells.

At the end, we show the overall homogeneous coating of HA/PLL multilayer films onto graphene samples, similar to the films previously investigated in-vitro and in-vivo on intracortical probe A c c e p t e d M a n u s c r i p t

(figure 1, 2 and 3 respectively). Graphene substrates (monolayer graphene previously transferred on glass coverslips) were coated with one and five HA/PLL bilayers. Fluorescein isothiocyanate FITC grafted PLL (FITC-PLL) was used as the top layer in both cases to assess for the bilayers deposition. Figure 7 shows the frontier between the graphene and the graphene-free glass substrate.

As expected, the fluorescence intensity is higher above the graphene-free area. [START_REF] Chang | Graphene fluorescence resonance energy transfer aptasensor for the thrombin detection[END_REF] The ratio of fluorescence intensity over these two areas without and with graphene is about Iwo/Iw = 2.40 when coating the substrate with one HA/PLL bilayer (figure 7a), and is reduced twice (Iwo/Iw = 1.24)

when increasing the number of bilayer up to five (figure 7b). The reduced quenching effect observed for five bilayers is related to the higher distance of FITC-PLL from the graphene substrate, confirming the higher thickness of HA/PLL deposited film. Interestingly, this multilayer coating exhibit ripples at the graphene/glass border (close-up view figure 7b), suggesting possible edge effects, or mechanical strains either within the multilayer film or within the graphene monolayer. These results demonstrate the overall homogeneity of the HA/PLL multilayer film and the ability to implement it on large graphene monolayer.

In perspective to this study, the controlled enzymatic degradation of HA coatings should be investigated to restore progressively a direct contact with the cells at the recording sites, and still protect the graphene monolayer during its insertion through the brain tissues and deep cortical layers. Moreover, the type and dynamics of synapses that are overexpressed on the bilayers film could be further assessed, as well as the possible impact of the coatings on the electrical activity of the network either by using conventional patch-clamp technique or the GFET array.

Conclusion.

All together these results show that HA polymeric films could be implemented on intracortical probes and graphene substrates, without altering the material and device features, as well as the neurons and tissues response, either in culture or within intracortical brain layers. These

  The shift of the charge neutrality voltage (noted VD in the following) toward more positive values indicates an increase of the hole carrier density. This is consistent with the negative charges doping brought by HA polymers. This variation of charge -expressed as ∆n h = ∆V D × c i e ⁄ with ci the A c c e p t e d M a n u s c r i p t interfacial capacitance -is about ∆nh = 3.10 6 (with ci = 1.06 pF, and ∆VD = 0.46 mV). At the charge neutrality point VD, this value should be almost opposite and equal to the positive charges carried by the HA polymers over the transistor channel ∆nh = -∆nHA. Because this value can be estimated and monitored in-situ, it provides an interesting way to follow the integrity of the HA coating when interfacing neurons. Indeed, the total amount of charge carried by HA is given by (1) the number of HA molecules over the G-FET channel, and (2) the number of charges that a molecule can exchange with the graphene layer. The number of HA molecules depends on the polar surface coverage PSC, i.e. the projected surface of HA molecule on the surface, as the following: N HA = L × W PSC HA ⁄ , with L and W the length and width of the G-FET channel. Hyaluronic acid being constituted by D-Glucuronic acid and N-acetyl-D-Glucosamine chains for which PSC = 1.25 nm², 56 a full covering should provide almost 1.7×10 8 molecules over the G-FET channel. Finally, the number of charges carried by the NHA molecules can be estimated as the following ∆𝑛 𝐻𝐴 = 𝑎 × 𝑀 𝑘 × 𝑁 𝐻𝐴 , with Mk the Mulliken charge for an absorbed molecule, i.e. the amount of charge that a molecule can exchange with a surface, and a a variable parameter taking into account the availability of charge in a dipole.

A c c e pFIGURESFigure 1 .

 1 FIGURES

Figure 2 .

 2 Figure 2. In-vitro assays DIV14. Immuno-fluorescent micrographs of neurons at DIV14, cultured on PLL-coated glass, and on five HA/PLL bilayers deposited on glass and on monolayer graphene. For each condi-tion, neurons are stained with DAPI, YL1/2 and synapsin to label the soma, the neurite and the synapses. Scale bars are 50 µm. For the bilayers deposited on graphene and glass, A c c e p t e d M a n u s c r i p t

Figure 3 .

 3 Figure 3. Impact of HA films on intracortical probes. Five HA/PLL bilayers were deposited on commercial tungsten electrodes arrays, implanted in the motor cortex of rats, and compared to control samples (same probes without coating). (a) Fluorescent micrographs of the coated electrodes. FITC-PLL (exc = 488 nm) was deposited as the top layer for assessing the multilayer deposition. (b) Typical (surimposed) spikes recorded during locomotion. Scale bar 100 µV and 1ms. Single spikes are extracted from the voltage time trace shown in (c). Scale bar 100 µV. (d) Percent of control (black) and coated (orange) electrodes enable to detect single spikes. (e) Postmortem immuno-fluorescent micrographs of neural tissues (7 weeks after implantation surgery) showing the astrocytes (GFAP) and microglia (IbA1) around the coated (active) and bare (control) electrodes, on the left and right column respectively. Scale bar 2 mm. (f) Corresponding histograms, comparing the total surface covered by astrocytes and microglia in each conditions, i.e. with (active) and without (control) HA/PLL bilayers, when the bleeding level was the lowest (#482 and #479 for coated and bare electrodes).Table shows the results obtained for the other groups.

Figure 4 .

 4 Figure 4. HA adhesion onto monolayer graphene. (a) Schematics of the biopolymer customization for a homogeneous adhesion on hydrophobic graphene monolayers. The HA backbone is functionalized with alkylated hydrophobic (CH3)-chains promoting polymer attachment onto the hydrophobic substrate. (b) Typical Raman spectrum acquired on HA-coated graphene samples. (c-e) Atomic force micrographs of typical bare graphene monolayer (c), then coated with a single layer of (d) HA and (e) HA modified with hydrophobic chains -HA. Bottom : z-profiles of the two coatings, left: HA and right: -HA, measured along the green line in (d) and (e).

Figure 5 .

 5 Figure 5. Neurons adhesion on HA-coated graphene. Immuno-fluorescent micrographs of primary hippocampal neurons cultured on glass coverslips covered with graphene and HA monolayers (a), and coated with a PLL (b) and HA (c) single layer (control samples). The soma, neurites, and axon are labeled in blue (DAPI), green (YL1/2), and red (Tau). 1 Day-in-vitro.

A c c e p t e d M a n u s c r i p tFigure 6 .

 6 Figure 6. Impact of HA on the electronic properties of G-FETs. (a) Schematics of the functionalized graphene field effect transistors G-FETs. The electrical equivalent circuit illustrates the coupling between the liquid gate and the graphene FET channel. Optical micrographs of the G-FET array before (zoomed view) and after the passivation of the Ti/Au metallic leads. The graphene FET channels are 10 × 20 µm long and wide. (c) The G-FET conductance -before (gray) and after (red) HA depositionis recorded as a function of the liquid gate voltage VG applied with a quasi-reference Pt electrode. Each curve corresponds to a different device. Thicker curves are the mean average value over all tested devices. The average curves are fitted to extract the charge carriers density and mobility, before (d) and after (e) functionalization (see text for fitting parameters).

Figure 7 .

 7 Figure 7. Adhesion of HA/PLL multilayer film on graphene monolayer. Fluorescent optical micrographs of one (a) and five (b) HA/PLL bilayers deposited on monolayer graphene previously transferred on glass coverslips. FITC-PLL (exc = 488 nm) was used for deposition of the last layer. Exposure time is 1500 ms (a), and 500 ms (b). Inset: zoomed view of the frontier with graphene.A c c e p t e d M a n u s c r i p t

Figure 7 .

 7 Figure 7.

ACKNOWLEDGMENTS

The authors thank the help provided by nanofabrication (Nanofab) and biotechnology (Biofab) facilities at Neel Institute. This work is partially supported by la Région Rhône-Alpes, and by the french Agence Nationale de la Recherche, under the projects ANR-10-LABX-51-01 (Labex LANEF du Programme d'Investissements d'Avenir) the Lab Alliances on Nanosciences -Energies for the Future, and ANR-18-CE42-0003-01 NANOMESH. ABBREVIATIONS

AUTHOR INFORMATION

Corresponding Author *E-mail: cecile.delacour@neel.cnrs.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest. AUTHOR SUBMITTED MANUSCRIPT -BPEX-101491.R2


Marceau Métillon
email: marceau.metillon@ls2n.fr

Philippe Cardou
email: philippe.cardou@gmc.ulaval.ca

Kévin Subrin
email: kevin.subrin@ls2n.fr

Camilo Charron
email: camilo.charron@ls2n.fr

Stéphane Caro
email: stephane.caro@ls2n.fr

Marceau M Étillon

K Évin Subrin

St Éphane Caro

A Cable-Driven Parallel Robot with Full-Circle End-Effector Rotations

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Introduction

A Cable-Driven Parallel Robot (CDPR) belongs to a particular class of parallel robots where a moving platform is linked to a base frame using cables. Motors are mounted on a rigid base frame and drive winches. Cable coiled on these winches are routed through exit points located on the rigid frame to anchor points on the moving platform. The pose (position and orientation) of the moving platform is determined by controlling the cable lengths.

CDPRs have several advantages compared to classical parallel robots. They are inexpensive and can cover large workspaces [START_REF] Hussein | Geometric optimization of a large scale cdpr operating on a building facade[END_REF]. The lightweight cables contribute to the lower inertia of the moving platform and consequently to a better dynamic performance over classical parallel robots [2]. Another characteristic of the CDPRs is their reconfigurability. Changing the overall geometry of the robot can be done by changing the exit points and anchor points.

Reconfigurability of the CDPRs is suitable for versatile applications especially in an industrial context [START_REF] Gagliardini | Discrete reconfiguration planning for cabledriven parallel robots[END_REF][START_REF] Rasheed | Wrench-Feasible Workspace of Mobile Cable-Driven Parallel Robots[END_REF]. CD-PRs have drawn researchers' interests towards robotic applications such as pick-and-place operations, robotic machining, manipulation, intralogistics measurements and calibration systems [5,6].

CDPRs can offer an extremely large three-degrees of freedom translational workspace, but their orientation workspace is usually limited due to cable/cable and cable/moving platform collisions [7]. Cable interferences can be divided into cable-cable and cable-environment interferences [8]. For a given pose of the moving platform, cablecable collision may occur by changing the moving platform orientation. Cable-environment collisions refer to the interferences between the moving platform and its surrounding environment.

This paper presents the concept of a hybrid manipulator with decoupled translation and orientation motions of the moving platform. It is called hybrid since two parallel mechanisms are connected in series [9], namely, a CDPR and a Parallel Spherical Wrist (PSW). In [START_REF] Miermeister | Design of cabledriven parallel robots with multiple platforms and endless rotating axes[END_REF], a hybrid CDPR equipped with multiple platforms and up to nine cables is able to orientate a end-effector around an axis with an unlimited range of rotation. In [START_REF] Nagai | Proposal of a redundant drive wire mechanism for producing motions with high acceleration and high precision[END_REF]12], redundant drive wire mechanisms are used for producing motions with high acceleration and good precision. In [START_REF] Khakpour | Workspace augmentation of spatial 3-dof cable parallel robots using differential actuation[END_REF][START_REF] Khakpour | Synthesis of differentially driven planar cable parallel manipulators[END_REF]15], differential cables are used to increase the size of the manipulator workspace. Differential cables consists into a set of two independent cables connecting the platform to two different winches, the latter being actuated by a differential mechanism driven by a single actuator. In [16], two spring-loaded cable-loops allows for the control of a two-DOF planar CDPR with only two actuators. Loaded springs ensure the compliance given by the variation of cable lengths and grants a higher stiffness to the mechanism. In [17], a bi-actuated cable is used in order to improve the orientation capacity of the end-effector of planar cable-driven robots. In [18] a hybrid CDPR uses a cable-

A 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 F 0 x 0 y 0 z 0 O 0 rigid
F 1 x 1 y 1 z 1 O1 B 1 B 2 B 3 B 4 B 5 B 6 B 7 B 8 x 2 y 2 z 2 O 2 F 2
Fig. 1: CDPR with full-circle end-effector rotations loop for remote actuation of an embedded hoist mechanism on the moving platform. In [19], a moving-platform embedding a two-DOF differential gear set mechanism is presented allowing the two-DOF unlimited rotational motions of the end-effector. Thanks to cable-loops (bi-actuated cables), the embedded mechanisms are actuated by transmitting power through cables from motors, which are fixed on the ground, to the moving platform [START_REF] Le | Configuration of redundant drive wire mechanism using double actuator modules[END_REF]. Therefore, by remote actuation through cable-loops, the tethering of the power cable to the moving platform is eliminated [START_REF] Lessanibahri | A cable-driven parallel robot with an embedded tilt-roll wrist[END_REF]. Moreover, a lower mass and a lower inertia of the moving platform are obtained due to the remote actuators.

In this paper the mechanical design of the manipulator under study is presented in Section 2. Its kineto-static model is described in Section 3. The static workspace of the manipulator is studied in Section 4. The methodology followed to determine the optimal cable arrangement of the system is explained in Section 5. The developed prototype of the mechanism at hand and some experimental results are shown in Section 6. Conclusions and future work are drawn in Section 7.

Description and Parametrization of the Manipulator

The kinematic architecture of the manipulator consists of two parallel manipulators mounted in series. A CDPR grants a large translation workspace and a PSW grants an unlimited orientation workspace. This hybrid manipulator is able to combine advantages of both mechanisms in terms of large translation and orientation workspaces.

Overall Architecture

Figure 1 shows the overall architecture of the manipulator with its main components, namely, winches, exit-points and the moving platform. The winches control the cable lengths, which move and actuate the moving platform. Cables are routed through exit-points located on the rigid frame and connected to anchor-points located on the moving platform.

Figure 1 shows the moving platform, which hosts a top plate assembly and embeds the PSW. The end-effector of the wrist is a sphere actuated by three cable-loops, which transmit the required power from motors fixed on the ground to the end-effector of the moving platform, namely the sphere.

The PSW is described in detail in Sec. 2.2 while the cable-loop system is presented in Sec. 2.3. The top plate has the six-DOF and the PSW grants a large orientation workspace to the sphere providing an overall nine-DOF workspace to the spherical end-effector regarding the base frame F 0 .

Three-DOF Parallel Spherical Wrist

The concept of the PSW relies on the Atlas platform principle [START_REF] Hayes | Atlas: A novel kinematic architecture for six dof motion platforms[END_REF]. An end-effector is linked to the base of the wrist using a spherical joint. Three omni-wheels are linked to the wrist base with revolute joints. The end-effector is a sphere actuated by the rotation of the omni-wheels. The position of the wheel relative to the sphere surface was defined to allow a singular-free and unlimited orientation of the sphere around the global x 0 , y 0 and z 0 axes as discussed in [START_REF] Platis | Isotropic design of the spherical wrist of a cabledriven parallel robot[END_REF].

Here, the top plate of the CDPR amounts to the wrist base. Three carriage sub-assemblies are rigidly attached to the top plate. Every carriage hosts an omni-wheel. A three rigid arm platform hosts the sphere using three caster balls. Three anti-backlash compression springs are mounted on threaded rods using nuts, thus ensuring the connection of the arm platform to the top plate. The springs ensure an adjustable contact force of the omni-wheels on the sphere. The omni-wheels transmit torque to the sphere thanks to friction.

Each omni-wheel is independently driven by a cable-loop system.

Cable-Loop Principle

Figure 2 represents a simplified form of the cable-loop system. The latter consists of a single cable of which both ends are actuated by two motors while passing through exitpoints, namely, A 1 , A 2 , and anchor-points, namely, B 1 , B 2 . The cable-loop is coiled up around a drum on the moving platform. The cable-loop drum then acquires one rotational DOF with respect to the moving platform. These can be used to actuate an embedded mechanism or to control additional degrees of freedom such as rotations over wide ranges. The purpose of the cable-loop is double. Firstly, its aim is to translate the top plate as two single cables would do when the coiling directions of both motors are the same. Secondly, it actuates the embedded drum by circulating the cable when coiling directions of the two actuators are different.

motor 1 motor 2 base top plate t 1 ω τ t 2 drum r B 1 B 2 A 1 A 2

Fig. 2: Representation of a cable-loop

By controlling the difference of tension in both ends of the cable loop, namely δt 12 = t 1 -t 2 , it is possible to transmit torque τ to the pulley. This capacity can be used to increase the orientation workspace of the end-effector when the pulley is used to rotate the end-effector or the pulley can actuate an embedded mechanism without having the drawbacks of embedding the actuators on the platform. Here, three cable loops are used to actuate independently the three omniwheels in contact with the sphere as illustrated in Fig. 2.

Overall Parameterization

As shown in Fig. 1, F 0 denotes the frame fixed to the base of origin point O 0 and axes x 0 , y 0 and z 0 . F 1 is the frame attached to the top-plate of origin point O 1 and axes x 1 , y 1 and z 1 . F 2 is the frame attached to the end-effector, i.e., the sphere, of origin point O 2 , the geometric center of the sphere and axes x 2 , y 2 and z 2 .

It is noteworthy that F 0 and F 1 have a translational and orientational relative movement while F 1 and F 2 only have a relative rotational movement.

The exit points A i are the points belonging to the frame through which the cables are routed between the winch and the top plate. The anchor points B i are the points belonging to the TP where the cables are connected. It is noteworthy that the cables are connecting exit points and anchor points accordingly and a unit vector expresses the cable direction. Therefore, the loop-closure equations associated with each cable are expressed as follows:

0 l i = 0 a i -0 p -0 R 1 1 b i (1) with i ∈ [[1, . . . , 8
]] where 0 l i is the i-th cable vector, 0 a i is the corresponding anchor point expressed in the base frame, 1 b i is the coordinate vector of exit point in the platform frame, 0 p is the position vector of the platform frame and 0 R 1 is the rotation matrix from F 0 to F 1 .

We can then write the i-th unit cable vector as:

0 u i = 0 l i l i (2)
with l i being the i-th cable length.

Kinetostatic Model of the Manipulator

In this section, we proceed to the kinetostatic modelling of the overall manipulator. We write the static equation of the manipulator as follows:

Wt + w e = 0 9 (3)
with W being the wrench matrix, t being the cable tension vector and w e being the external wrenches applied on the platform. In our case, we only consider the action of the weight of the moving platform as external wrench.

The wrench matrix of the manipulator W is the concatenation of the wrench matrices of both mechanisms:

W = W T P W SW 9×8 (4)
where W T P is the wrench matrix associated to the top plate and W SW is the wrench matrix related to the PSW. Similarly, the wrench vector of the manipulator consists of the wrench vector of both mechanisms:

w g = w T P g w SW g 9×1 (5)
where w T P g is the wrench vector associated to the top plate and w SW g is the wrench vector exerted on the PSW. W T P and w T P g are defined in Section 3.1 while W SW and w SW g are defined in Section 3.2.

Kinetostatic Model of the Top Plate

In this section we write the kinetostatic model of the top plate. The static equilibrium of the platform can be written as:

W T P t + w T P g = 0 6 (6)
W T P takes the following form:

W T P = 0 u 1 0 u 2 0 u 3 0 u 4 0 u 5 0 u 6 0 u 7 0 u 8 0 d 1 0 d 2 0 d 3 0 d 4 0 d 5 0 d 6 0 d 7 0 d 8 6×8 (7)
with 0 d i being the cross-product of vectors b i and u i expressed in the base frame F 0 as:

0 d i = 0 R 1 1 b i × 0 u i (8)
We define the wrench vector of the top plate w T P as follows:

w T P g = f T P m T P 6×1 (9)
where f T P is the 3-dimensional force and m T P is the 3dimensional moment exerted on the top plate.

Kinetostatic Model of the Parallel Spherical Wrist

The parametrization of the PSW is illustrated in Fig. 3 anddescribed below: C i : Contact point between the ith omni-wheel and the sphere Π i : Plane passing through the contact point C i and tangent to the sphere α: Elevation angle of point C i , α ∈ [0, π] β: Angle between the tangent line L i and the actuation force of the omni-wheel, β ∈ [-π 2 , π 2 ] γ i : Angle between x 1 and the vector pointing from point H to point C i , i = 1, 2, 3 r s : Sphere radius r o : Omni-wheel radius φi : Angular velocity of the i-th omni-wheel v i : Unit vector along the actuation force produced by the i-th omni-wheel on the sphere n i : Unit vector normal to plane Π i

The optimal set of the parameters of the wrist was defined in [START_REF] Platis | Isotropic design of the spherical wrist of a cabledriven parallel robot[END_REF] in order to maximize the amplitudes of its orientation as well as its dexterity. The following hypotheses are taken into account for the wrist modelling and analysis: (i) The omni-wheels are normal to the sphere; (ii) The contact points between the omni-wheels and the sphere belong to the circumference of a circle. The latter is the base of an inverted cone, its tip being the centre of the sphere. The angle between the vertical axis and the cone is named α; (iii) In the plane containing the cone base, the three contact points form an equilateral triangle.

r s r o O 2 H C i n i ϕ i α β γ i x 1 y 1 z 1 Π i L i v i
omni-wheel sphere The angular velocity vector of the sphere ω = [ω x , ω y , ω z ] T is expressed as a function of the angular velocity vector of the omni-wheels φ = [ φ1 , φ2 , φ3 ] T , as follows:

Aω = B φ (10)
A and B are the forward and inverse Jacobian matrices of the PSW, which take the form:

A = r s   (n 1 × v 1 ) T (n 2 × v 2 ) T (n 3 × v 3 ) T   (11)
and,

B = r o 1 3×3 (12)
From Eq. ( 11), matrix A is expressed as a function of angles α, β and γ i as:

A = r s   S β Cγ 1 -CαCβCγ 1 -S β Cγ 1 -CαCβCγ 1 S α C β S β Cγ 2 -CαCβCγ 2 -S β Cγ 2 -CαCβCγ 2 S α C β S β Cγ 3 -CαCβCγ 3 -S β Cγ 3 -CαCβCγ 3 S α C β   ( 13
)
where

C k = cos(k) and S k = sin(k), k = α, β, γ 1 , γ 2 , γ 3 .
From [START_REF] Platis | Isotropic design of the spherical wrist of a cabledriven parallel robot[END_REF], the PSW is fully isotropic from a kinematic viewpoint if and only if α = 35.2 • and β = 0 • . Therefore, those values are selected in what remains. Equation ( 10) is rewritten as follows:

ω = J ω φ ( 14
)
where J ω = A -1 B, is the Jacobian matrix of the wrist, i.e., J ω is the mapping from angular velocities of the omni-wheels into the required angular velocity of the end-effector. Based on the theory of reciprocal screws [START_REF] Ball | A treatise on the theory of screws[END_REF], it turns out that:

m T SW ω = τ T φ ( 15
)
where m SW = [m x , m y , m z ] T is the output moment vector of the sphere and τ = [τ 1 , τ 2 , τ 3 ] T is the input torque vector, namely the omni-wheel torque vector. By substituting Eq. ( 14) into Eq. ( 15), we obtain:

τ = J T ω m SW = W ω m SW (16)
The wrench matrix W ω = J T ω maps the output torque of the sphere to the omni-wheels torques. As shown in Fig. 4, τ can be expressed as a function of the cable tensions such that:

τ 1 = r d (t 1 -t 2 ) ( 17
)
τ 2 = r d (t 3 -t 4 ) (18)
τ 3 = r d (t 5 -t 6 ) (19)
where r d is the radius of the embedded drum of the cableloops.

From Eqs. ( 17) to (19), the omni-wheel torque vector τ is expressed as a function of the cable tensions as follows:

τ = W c t ( 20
)
where t = [t 1 , . . . , t 8 ] T is the cable tension vector and W c is the matrix assigning the cables to the cable-loops. If cable pairs (1, 2), [START_REF] Gagliardini | Discrete reconfiguration planning for cabledriven parallel robots[END_REF][START_REF] Rasheed | Wrench-Feasible Workspace of Mobile Cable-Driven Parallel Robots[END_REF] and (5, 6) respectively correspond to cableloops 1, 2 and 3, W c will take the form:

W c =   r d -r d 0 0 0 0 0 0 0 0 r d -r d 0 0 0 0 0 0 0 0 r d -r d 0 0   (21)
The equilibrium of the wrench applied on the PSW is expressed as:

m SW = W SW t (22)
with m SW being the external moments applied by the environment onto the PSW. The wrench matrix W SW expresses the relationship between the cable tensions and the moment applied on the wrist.

W SW = W ω W c (23)
The orientation of the sphere with respect to the base frame is defined by the pitch angle θ, the yaw angle ψ and the roll angle χ while following the ZYX-Euler-angles convention. Those three angles are the components of the orientation vector q SW of the wrist, namely,

q SW =   θ ψ χ   ( 24
)
t i+ t i- r d ω i τ i
Fig. 4: Representation of a cable-loop drum

Workspace Analysis

The static workspace of the manipulator consists of the set of positions and orientations of the moving platform and the orientations of the end-effector, namely, 0 p and 0 R 1 and 0 q SW , which satisfies the static equilibrium of the manipulator.

The cable tension set T amounts to a hyper-cube in an eight-dimensional space:

T = {t ∈ R 8 : t min ≤ t ≤ t max } (25)
where t min and t max are respectively the lower and upper bounds of the cable tension.

The static workspace of the manipulator is defined as follows:

S = {( 0 p, 0 R 1 , 0 q SW ∈ R 3 × SO(3) × R 3 : ∃t ∈ T , Wt + w e = 0 9 } (26)
where SO(3) is the group of proper rotation matrices. The static workspace in a nine-dimensional space is expressed using the Equation (26). As the visualization of such highdimensional space is impossible with common human perception in 3D, we define the static workspace of the manipulator for a simplified case. We define S for a constant orientation of the top-plate. The former subset, namely, S AO is a set for a given orientation of the top-plate while the wrist is free to rotate:

S AO = { 0 p ∈ R 3 | 0 R 1 = I 3 | -π ≤ θ, ψ, χ ≤ π : ∃t ∈ T , Wt + w e = 0 9 } (27)
The discretization of the Cartesian space is made so that n x , n y and n z are the numbers of discretized points along x 0 , y 0 and z 0 axes, respectively. R S is defined as the proportion of the static workspace to the overall space occupied by the manipulator:

R S = N S (n x + 1)(n y + 1)(n z + 1) (28)
with N S being the number of points inside the discretized static workspace S.

Optimal Cable Arrangement

This section deals with the cable arrangement of the manipulator for obtaining the maximum size of the static workspace. The i-th cable arrangement is the association of anchor points B i to exit points A i . The top plate has fifteen points for anchor points and the manipulator has a maximum of eight actuators. Therefore, the optimal cable arrangement is defined as the association of eight anchor points to eight exit points such that the workspace is maximized.

The number of exit point combinations, N e is:

N e = n e n c (29)
with n e and n c being the numbers of available exit-points and cables, respectively. The number of anchor-points combinations, N a , consists in the number of permutations of the set of points, which is given by: R 1

R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 R 10 R 11 R 12 R 13 R 14 R 15 F 1 O 1 x 1 y 1
Fig. 5: The fifteen points for the anchor points on the moving-platform

N a = n a n c n c ! (30)
n a being the number of selected anchor points. S C is the set of possible cable configuration, the number of cable configuration N C = dim(S C ) is thus given by:

N c = N a N e = n e n c n a n c n c ! (31)
Figure 5 shows all the available anchor points, namely, r i , i = 1, 2, . . . , 15, which are divided into two groups: S CL = {R 3 , R 4 , R 8 , R 9 , R 13 , R 14 } which is the set of points associated to cable-loops and S SC =

{R 1 , R 2 , R 5 , R 6 , R 7 , R 10 , R 11 , R 12 , R 15 }
which is the set of points associated to the simple cables. Six points amongst the fifteen points are selected to make the three cable loops. Therefore, nine remaining anchor points host the remaining two single-actuated cables.

n c = n SC + n CL (32)
The number of available anchor points for the single and bi-actuated cables are denoted as n aSC and n aCL :

n a = n aSC + n aCL (33)
The number, N CL , of combinations considering cableloop is given by:

N CL = n e n c n aSC n SC n c ! (34)
Six points are associated to the wrist actuation and consequently to the three cable-loops: n aCL = 6. The remaining nine anchor points are to be assigned to simple cables n aSC = 9. Finally, N CL , expressed in Eq. ( 34) is given by:

N CL = 8 8 9 2 8! = 1 451 520 (35)
As N CL is very large, for computing-time sake, the number of available points for anchor points is supposed to be equal to three. Thus S SC = {R 1 , R 6 , R 11 }. By substituting n aSC = 3 into Eq. ( 34) we obtain:

N CL = 8 8 3 2 8! = 120 960 (36)
The static workspace is computed for the 120 960 cable arrangements. Figure 6 illustrates the cable arrangement corresponding to the largest workspace. Figure 6a shows a schematic of the anchor-plate as well as the optimal cable arrangement. Figure 6b shows the corresponding static workspace with R S = 65%.

Prototyping and Experimentation

The prototyping of a CDPR with full-circle end-effector rotations is presented in this section. The base frame of the prototype shown in Fig. 7 is 4 m long, 3.5 m wide and 4 m high. The full-circle end-effector rotations are obtained thanks to the PSW shown in Fig. 8. The PSW is mainly made up of a top plate, three double omni-wheels and a transparent sphere. The three-DOF rotational motions of the sphere are obtained from the rotations of the omni-wheels. Each omni-wheel is driven by a cable loop, the strands of the cable being respectively wound around two actuated reels fixed to the ground. A flight controller c Pixhawk, embedded in the sphere, is used to measure its orientation, angular velocity and linear acceleration. This controller, equipped with a gyroscope, an accelerometer and a magnetometer, acts as a data-logger device to record measurements. The overall mass of the PSW is equal to 1.87 kg. It should be noted Figure 9 shows the main hardware of the prototype, which consists of a PC (equipped with c MATLAB and c ControlDesk software), eight c PARKER SME60 motors and TPD-M drivers, a c dSPACE DS1007-based real-time controller and eight custom-made winches.

B 1 ≡ R 14 B 2 ≡ R 9 B 3 ≡ R 11 B 4 ≡ R 4 B 5 ≡ R 6 B 6 ≡ R 13 B 7 ≡ R 3 B 8 ≡ R 8 B 3 B 4 B 5 B 6 B 7 B 8 B 1 B 2 F 1 O 1 x 1 y 1 (a)
Slippage between the omni-wheels and the sphere inevitably leads to drift in the orientation when tracking a prescribed trajectory. Therefore, this robot is intended for teleoperation applications where an operator can compensate for the errors that accumulate over time. In this context, the robot performance is best assessed by comparing its angular velocity response to an angular velocity input rather than by looking at its ability to track position and orientation over a trajectory.

The performances of the protoype were experimentally evaluated along the following three trajectories:

Trajectory 1: Pure rotational motions of the sphere about axes parallel to x 0 , y 0 and z 0 , respectively, while the top plate is fixed to its support. A fifth-order polynomial is used to obtain continuous velocity and acceleration trajectory profiles. Trajectory 2: Pure translational motions of the top plate along four successive straight line segments whereas the sphere does not rotate. A fifth-order polynomial is used to determine the velocity and acceleration profiles along each line segment. Trajectory 3: The top plate performs a vertical translational motion while the sphere rotates. Figures 10(a)-(c) depict the difference between the desired and measured angular velocities ω x (ω y , ω z , resp.) about axis x 0 (y 0 , z 0 , resp.) of the sphere expressed in frame F 0 . As shown in Fig. 11, the maximum error on the sphere angular velocity along Trajectory 1 is about 30 deg/s. It should be noted that the root-mean square error of the angular velocity of the sphere is smaller about x 0 than about z 0 . Although errors are present between the desired and obtained angular velocities of the end-effector, those experiments confirm the fidelity of the PSW kinematic model obtained in Eq. ( 23), the kinematic Jacobian matrix of the cable-actuated PSW being the opposite of the transpose of the wrench matrix W SW . The errors between measured and desired endeffector angular velocities are mainly due to the slippage between the omni-wheels and the sphere.

The experimental motions of the wrist along Trajectory 2 are shown in the video 1 from 1min 7s to 3min 41s. Let θ e denote the rotation angle of the top plate. θ e is defined from 0 R 1 as follows:

θ e = arccos tr( 0 R 1 ) -1 2 , 0 ≤ θ e ≤ π (37)
Figure 12 shows the evolution of θ e , i.e., the parasitic inclination of the top plate, along the four straight line segments of Trajectory 2. Figure 12 illustrates the large translation workspace of the manipulator as presented in Figure 6b. It is apparent that the maximum parasitic inclination angle of the top plate along this trajectory is about 10 deg. Furthermore, Fig. 12 shows the validity of the kinematic model of the top plate defined in Eq. ( 7). The kinematic model of the robot is well validated quantitatively considering the small value of the parasitic inclinations. Nevertheless, its static model could not be validated other than by observing that inclinations of the top plate are mainly due to friction in the PSW to be identified and errors in the identified Cartesian coordinates of the cable exit points.

The experimental motions of the wrist along Trajectory 3 are shown in the video 1 from 3min 41s to 5min 38s. It is noteworthy that parasitic inclinations of the top plate appear once the sphere starts rotating. These parasitic motions are caused by several factors. Some improvements in the PSW design and robot control are needed to address these weaknesses. First, the cable anchor points located on the top plate and shown in Fig. 5 are very close to each other leading to a high sensitivity of the orientation of the top plate to variations in cable lengths. Thus, this kinematic sensitivity should be reduced by moving the cable anchor points away from each other on the top plate. Besides, it is difficult to manage (i) the friction between the sphere and the three bearings that support it, (ii) the friction and contact between the omni-wheels and the sphere, and (iii) the friction and slippage between the cable loops and the three pulleys around which the cables are wrapped. Indeed, it can be noted in the previous videos that the omni-wheels sometimes start to slide on the sphere and that they do not turn at other times when the cable loop is supposed to circulate. To resolve these issues, im t is necessary to better manage the cable tensions and improve the manufacturing and assembly of some parts such as the connection between the double omni-wheels and the top plate. Finally, the flexibility of the three arms holding the sphere may be responsible for bad contacts between the sphere and the omni-wheels.

Conclusions

This paper dealt with the design, modelling and prototyping of a hybrid robot. This robot, which is composed of a CDPR mounted in series with a PSW, has both a large translational workspace and an unlimited orientation workspace. It should be noted that the six degrees of freedom motions of the moving platform of the CDPR, namely, the base of the PSW, and the three-DOF motion of the PSW are actuated by means of eight actuators fixed to the base. As a consequence, the overall system is underactuated and its total mass and inertia in motion is reduced.

The kinetostatic model of the hybrid robot was expressed in order to determine its static equilibrium condition and find the cable arrangement maximizing its static workspace. A prototype of the CDPR with full-circle end-effector rotations was realized. The performances of the prototype were experimentally evaluated by measuring its angular-velocity response over and parasitic inclinations along three test trajectories. It appears that the maximum angular velocity error of the sphere is about 30 deg/s along the first trajectory for which the top plate remains on its support. Future work will focus on reducing parasitic inclinations of the end-effector thanks to an improved design of the wrist and better management of the cable tensions.

Fig. 3 :

 3 Fig. 3: Parametrization of the Parallel Spherical Wrist

Fig. 6 :Fig. 8 :

 68 Fig. 6: Optimum cable arrangement and static workspace

Fig. 9 :

 9 Fig. 9: Equivalent architecture of the prototype

Fig. 10 :

 10 Fig. 10: Desired and measured angular velocities of the sphere along Trajectory 1

Fig. 11 :

 11 Fig. 11: Maximum and root mean square errors on the sphere angular velocity along Trajectory 1

Fig. 12 :

 12 Fig. 12: Parasitic inclination of the top plate along Trajectory 2

F 0 (F 1 (O 1 , x 1 , y 1 , z 1 ) 1 W

 0111111 O 0 , x 0 , y 0 , z 0 ) Base frame attached to the rigid frame of the robot Frame attached to the top plate F 2 (O 2 , x 2 , y 2 , z 2 ) Frame attached to the end-effector of the Parallel Spherical Wrist l i i-th cable vector pointing from B i to A i , i ∈ [[1, . . . , 8]] a i Cartesian coordinates vector of point A i , i ∈ [[1, . . . , 8]] b i Cartesian coordinates vector of point B i , i ∈ [[1, . . . , 8]] p Cartesian coordinates vector of point P u i i-th cable unit vector, i ∈ [[1, . . . , 8]] t Cable tension vector w e External wrench vector w T P g External wrench vector associated to the top plate w SW g External wrench vector associated to the Parallel Spherical Wrist d i Cross-product of b i and u i , i ∈ [[1, . . . , 8]] f T P Force applied on the top plate m T P Moment applied on the top plate m SW External moments applied by the environment onto the end-effector v i Axis of actuation force produced by the i-th omni-wheel on the sphere n i Unit normal vector of i-th omni-wheel on plane π i at point C i q SW Orientation vector of the end-effector l i i-th cable length, i ∈ [[1, . . . , 8]] r s Radius of the sphere r o Radius of the omni-wheels r d Radius of the embedded drum of the cable loop A i i-th cable exit point, i ∈ [[1, . . . , 8]] B i i-th cable anchor point, i ∈ [[1, . . . , 8]]C i Contact point between the i-th omni-wheel and the sphere, i ∈ [[1, 2, 3]] R i Available anchor point on the top plate i ∈ [[1, . . . , 15]] φi Angular velocity of the i-th omni-wheel, i ∈ [[1, 2, 3]] ω 3-dimensional angular velocity of the end-effector α Angle associated to the position of the contact points C i on the sphere, α ∈ [0, π] β Angle between tangent to the sphere and the actuation force of the omni-wheel, β ∈ [-π 2 , π 2 ] γ i Angle between the contact points C i and x 1 , i ∈ [[1, 2, 3]] θ Pitch angle of the end-effector ψ Roll angle of the end-effector χ Yaw angle of the end-effector τ i i-th omni-wheel torque 0 R 1 Rotation matrix from frame F 0 to frame F Wrench matrix W T P Wrench matrix related to the top plate W SW Wrench matrix related to the Parallel Spherical Wrist A Forward Jacobian matrix of the Parallel Spherical Wrist B Inverse Jacobian matrix of the Parallel Spherical Wrist W c Wrench matrix of the cable-loop Π i Plane passing through the contact point C i and tangent to the sphere, i ∈ [[1, 2, 3]] L i Line tangent to the sphere on C i in the plane ( x 1 , y 1 ) S Static workspace of the manipulator S AO Static workspace of the manipulator with a given orientation of the top plate R S Proportion of the static workspace to the overall space occupied by the manipulator N S Number of points inside the discretized static workspace N e Number of exit point combinations N a Number of anchor points N C Number of cable configurations N CL Number of cable configurations considering cableloop n e Number of available exit-points n c Number of cables n a Number of selected anchor points n aSC Number of available anchor points for the single cable n aCL Number of available anchor points for cable-loop S C Set of possible cable configurations

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Acknowledgements

This work was supported by both the ANR CRAFT project, grant ANR-18-CE10-0004 and the RFI At-lanSTIC2020 CREATOR project. Assistance provided by Dr. Saman Lessanibahri and M. Julian Erskine through the experimentation process is highly appreciated.

Nomenclature