X Callies

C Fonteneau

C Véchambre

S Pensec

J-M Chenal

L Chazeau

L Bouteiller

G Ducouret

C Creton

Linear Rheology of Bis-Urea Functionalized Supramolecular Poly(butylacrylate)s : Part I -Weak Stickers

We investigated the linear viscoelastic properties in the melt of a series of nearly monodisperse poly(nbutyl acrylate)(PnBA) chains center-functionalized with a bis-urea sticker group, able to self-associate by quadruple hydrogen bonding. All materials are viscoelastic liquids at 40°C and their Newtonian viscosity varies from 100 to 5000Pa.s. However we show clearly that the viscosity changes non monotonously going through a minimum for a molecular weight (M n ) of 20 kg/mol and a sticker density of 1.1 wt%. We found two regimes: For M n < 20 kg/mol, the viscosity increases with decreasing M n , the linear viscoelastic properties change dramatically with temperature, forming a viscoelastic gel at 0°C and flowing at 40°C and the strength of the stickers association controls the size of molecular aggregates. However for M n > 20 kg/mol, the viscosity increases with M n , the rheology is controlled by the polymer dynamics and the stickers simply increase the terminal relaxation time relative to unfunctionalized PnBA of the same M n , as expected from sticky reptation theory. Despite clear evidence of sticker-sticker interactions by FTIR, none of the materials self-assemble at 20°C into structures with a long range order detectable by SAXS.

Introduction

During the last decade, supramolecular chemistry has shown its great potential for various applications in material science, with features such as self-healing 1,2,3 , stimuli-responsiveness 4 or mechanical strengthening 5,6 . The supramolecular materials are generally composed of polymer chains or oligomers functionalized by strongly interacting moieties. These moieties, sometimes called "stickers", can associate together by non covalent interactions (hydrogen bonds, ionic, metal coordination…). As recently pointed out by Seiffert and Sprakel 6 , two types of supramolecular polymers have been typically investigated: (1) entangled systems of supramolecular main-chain polymers formed by assembly of ditopic monomers and (2) covalent, permanent polymer backbones that can undergo reversible association by the interaction of "sticky" chain segments.

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2 Systems of type 1, sometimes named "living polymers", are subject to reversible, random chain scission and recombination. This strongly affects their rheological properties, which have however mostly been studied in solution 7,8,9,10,11 . The rheological properties of the latter systems (i.e. type 2) have been thoroughly studied, in particular in the melt but with a strong emphasis on polymer chains that bear at least two stickers per chain, in order to allow for an efficient elastic behavior 12,[START_REF] Colombani | Attempt toward 1D Cross-Linked Thermoplastic Elastomers: Structure and Mechanical Properties of a New System[END_REF][START_REF] Roosma | Supramolecular Materials from Benzene-1,3,5tricarboxamide-Based Nanorods[END_REF][START_REF] Sivakova | Utilization of a Combination of Weak Hydrogen-Bonding Interactions and Phase Segregation to Yield Highly Thermosensitive Supramolecular Polymers[END_REF][START_REF] Zhang | Heterogeneity, Segmental and Hydrogen Bond Dynamics, and Aging of Supramolecular Self-Healing Rubber[END_REF] . Many experimental and theoretical studies showed that in both cases the presence of these stickers strongly affects the rheological properties. In type 1 systems, the molecular dynamics is usually described by the Cates' model [START_REF] Cates | Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions[END_REF] while the mechanism of "sticky reptation" developed by Rubinstein and Semenov [START_REF] Rubinstein | Dynamics of Entangled Solutions of Associating Polymers[END_REF] is the most used theory for polymers with reversible cross-linkers. However, experimental studies in the melt revealed that the combination of polymer dynamics, sticker dynamics and dynamics of possible aggregated structures makes interpretation of the experimental data very difficult [START_REF] Herbst | Comparing solution and melt-state association of hydrogen bonds in supramolecular polymers[END_REF][START_REF] Herbst | Aggregation and Chain Dynamics in Supramolecular Polymers by Dynamic Rheology: Cluster Formation and Self-Aggregation[END_REF] . It is therefore essential to systematically characterize the rheology of well-defined model systems where the molecular weight of the polymer, the position of the sticker groups on the chain and the sticker concentration are systematically varied.

Among the possible systems, our group has focused in the past on self-assembly and adhesive properties of polyisobutylene chains bearing a single sticker per chain located in its middle. In solution these chains self-associate into cylindrical structures [START_REF] Pensec | Self-Assembly in Solution of a Reversible Comb-Shaped Supramolecular Polymer[END_REF] while in the melt they form highly dynamic structures which show some long range order below 50°C and have very interesting properties as soft adhesives [START_REF] Courtois | Supramolecular Soft Adhesive Materials[END_REF] .

Motivated by this first study, we now investigate systematically the viscoelasticity of supramolecular center-functionalized linear PnBA chains of different molecular weights (Scheme 1). PnBA is widely used as a base polymer for soft adhesives [START_REF] Creton | Pressure-sensitive adhesives: An introductory course[END_REF][START_REF] Lindner | Adhesive and rheological properties of lightly crosslinked model acrylic networks[END_REF] and its molecular weight can be conveniently controlled by Controlled Free Radical Polymerization. In this system an increase in molar mass of the polymer is equivalent to a dilution of the stickers relative to the polymer matrix. Thus, a transition between two kinds of dynamics is expected to occur at a critical molecular weight M c . Below M c , the density of stickers should be high enough to allow self-assembly into large aggregates and the rheological properties should be regulated by the scission and relaxation of these aggregates. Beyond M c , the stickers are dispersed in the PnBA melt and should behave as localized and transient attachment points between chains. In order to identify this transition, we investigated a wide range of molecular weights (5 to 115kg/mol) spanning from chains much shorter to much longer than the critical entanglement molecular weight M e (M e ~ 20-30 kg/mol for PnBA [START_REF] Jullian | Rheological Characterization and Molecular Modeling of Poly(n-Butyl Acrylate)[END_REF] ). Scheme 1: Structure of the studied PnBA. They were synthesized by ATRP according to Fonteneau et al [START_REF] Fonteneau | Versatile synthesis of reversible comb-shaped supramolecular polymers[END_REF] with molar masses ranging between 5 and 115kg/mol.

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3

The linear rheological properties for this series of bis-urea sticker center-functionalized PnBAs were characterized over a wide range of temperatures (-30°C to 50°C) and the data were analyzed by constructing master curves and by comparing them with those of unfunctionalized PnBA. All these results are then discussed in light of existing models.

Experimental

The polymers were synthesized by ATRP via a functional initiator approach, as reported by Fonteneau et al [START_REF] Fonteneau | Versatile synthesis of reversible comb-shaped supramolecular polymers[END_REF] . The number average molar mass M n and molar mass distribution Đ (Đ = M w /M n with the weight average molar mass M w ) were determined by size exclusion chromatography (SEC) in tetrahydrofuran, with a refractive index detector and a polystyrene calibration curve for samples PnBAX5 and PnBAX8 or with a triple detection set-up for the other samples (see Figure S1 for representative SEC curves). The average degree of polymerization DP and the sticker density Φ s in the polymer matrix are then estimated: DP = (M n -M s )/M bu and Φ s = M s /M n with the molar mass M s of the sticker and the molar mass M bu of the butylacrylate monomers. The glass transition temperature T g was determined by DSC with a Q2000 calorimeter (TA Instruments) at a rate of 20°C/min. In order to detect any residual solvent in PnBAX after synthesis, samples are analyzed by NMR H 1 (Bruker Avance 200) (see Figure S2). Dynamic rheological measurements were performed on a stress-controlled rheometer from Anton Paar equipped with a parallel plate geometry (diameter 8.0 or 25 mm, gap 1 to 2 mm). Frequency sweeps (0.02 to 20Hz) were carried out in the linear viscoelastic regime over a large temperature range (50 to -30°C) in order to construct master curves. At the end of the measurements, a frequency sweep is carried out at 25°C to check that the supramolecular structure of PnBAX did not vary during the rheological study, which could last up to 2 days. For all samples, the same frequency dependence of G' and G" at 25°C was observed, as shown in Figure S3 for PnBAX5. PnBAX were also characterized by

Samples

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thermogravimetric analysis (TGA) to check their thermal stability over the investigated temperature range (see Figure S4) and were found to lose weight only at T > 270°C.

Results

M n dependence of the viscoelastic properties

Figure 1 shows frequency sweeps performed on bis-urea sticker center-functionalized PnBAs in the linear regime at 20°C. Figure 1a shows the rheological properties of the lower molecular weight polymers and it is clear that, while all three are viscoelastic fluids, the viscosity η* and terminal relaxation time τ d , defined as 1/ω at the crossing point between the storage modulus G' and the loss modulus G" increase with decreasing molecular weight. On the contrary Figure 1b shows that for higher molar masses, η* and τ d increase with molecular weight (data for PnBAX60 are not shown for clarity but follow a similar trend). Maybe more directly revealing is the value of the complex viscosity η* at ω = 1 rad/s and T = 20°C as a function of molecular weight or sticker concentration (Figure 2). The results show two regimes with a clear minimum in complex viscosity. Yet the graph is markedly asymmetric. For Mw < 20 kg/mol, the viscosity increases steeply with increasing sticker concentration, while for Mw > 20 kg/mol corresponding to ~1 wt% of stickers the weaker increase in viscosity with increasing molecular weight is due to the increase in molecular size and to the progressive entanglement of the PnBA chains. The asymmetry in behavior is also seen by a quick glance at the temperature dependence of the two materials with the highest and lowest sticker concentration. Figure 3 shows the linear viscoelastic properties of PnBA X5 and PnBAX115 at three different temperatures. While for PnBAX115 a horizontal shift clearly leads to a master curve, for PnBAX5 (Figure 3a) the much more pronounced temperature dependence suggests a change in structure.

Master Curves at low Temperature

In linear rheology, the construction of master curves using the time-temperature superposition principle is in principle only possible when the material structure does not depend on temperature. As discussed by Seiffert et al 6 , this condition is not easily fulfilled for supramolecular systems which are composed of aggregates or networks assembled by mobile non covalent bonds. However, the successful or unsuccessful construction of such curves is a good probe of molecular dynamics and structure for a given material. In particular, this method was recently used by different authors [START_REF] Feldman | Model Transient Networks from Strongly Hydrogen-Bonded Polymers[END_REF][START_REF] Lewis | The Influence of Hydrogen Bonding Side-Groups on Viscoelastic Behavior of Linear and Network Polymers[END_REF][START_REF] Yan | Nanostructure and Rheology of Hydrogen-Bonding Telechelic Polymers in the Melt: From Micellar Liquids and Solids to Supramolecular Gels[END_REF][START_REF] Stadler | Linear Viscoelastic Rheology of Moderately Entangled Telechelic Polybutadiene Temporary Networks[END_REF] to identify the sticker contribution to the chain dynamics.

As explained in the Supporting Information (see Figures S5 andS6), horizontal shift factors a (T) are determined by superposing the tan δ curves and then, if this first step works, vertical shift factors b (T) are determined by superposing the G" (a (T) ω,T) curves. Since the tan δ curves are more sensitive to changes of dynamics or structures in the materials, they will be presented first. The reference temperature T ref =7°C is the minimal temperature for which the superposition of the experimental data works for PnBAX20.

For the two lowest M n , the superposition of the tan δ (ω, T) curves fails clearly at low temperature in Figure 4. The plot highlights the decrease of the minimum of tan δ in the zone of the elastic plateau (tan δ < 1) and thus, the supramolecular polymers becomes more and more elastic as the temperature decreases. As shown in Figure S7, the superposition of the viscoelastic moduli G' and G" doesn't work either as one would expect.

For M n ≥ 20kg/mol, the superposition of the tan δ (ω, T) curves works well for the low temperatures where the elastic plateau is observed over the experimental range of frequencies (see Figure 5). However, the superposition of tan δ (ω, T) curves fails at higher temperatures where these materials are more viscous. Figure 5 highlights that the terminal time τ d (T ref ) of these supramolecular viscoelastic fluids, determined at the end of the elastic plateau by tan δ =1, increases with increasing molecular weight and thus with the length of the side chains. From

τ d (T ref ) = 1/ω ≈ 3.10 -2 s at 20kg/mol, τ d (T ref ) reaches τ d (T ref ) = 1/ω ≈ 5s at 115kg/mol.
The dominant role of the dynamics of the side chains in the rheological response of the material at high M n is confirmed by the horizontal shifts a (T) displayed in Figure 6. These factors measured for M n ≥20kg/mol are surprisingly similar to those obtained for our reference non functionalized PnBA107. For M n ≥ 20kg/mol, G' and G'' master curves provide a snapshot of the viscoelastic properties over a large frequency range at T ref =7°C. As illustrated by PnBAX20 and PnBAX40 in Figure 7, a typical response of lightly entangled polymer is observed for this M w range: a viscous regime at low a (T) ω (G'<G"), a viscoelastic part at intermediate a (T) ω (G" ≈ G') and then again a dissipative behavior at high a (T) ω. The Figure 7 and S8 show clearly the appearance of an elastic plateau at intermediate a (T) ω due to the increase of the length of the side chains. The vertical shifts required for the construction of G' and G" master curves are close to 1 for the investigated temperature range as observed PnBA homopolymers (see Figure S9).

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PnBAX20 -30°C G' G'' -20°C G' G'' -10°C G' G'' 0°C G' G'' 7°C G' G''
-10°C G' G'' 0°C G' G'' 10°C G' G'' 20°C G' G'' 25°C G' G'' PnBAX40 -30°C G' G'' -20°C G' G'' M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 9
Zero-shear Viscosity While viscoelastic behaviors are observed below room temperature, a liquid-like behavior is observed at higher temperatures for all molecular weights investigated; the viscous modulus G" is always higher than the elastic modulus G' over the experimental range of frequencies at T≥40°C (see Figure S10). The power law exponents at low frequency displayed in Figure S11 are close to what is predicted for a newtonian liquid (G'~ ω 2 & G" ~ ω). As G">10G' in the terminal part of all relaxation spectra, the complex viscosity η* measured at low frequency (0,1-1rad/s) can be considered as the zero-shear viscosity η 0 by using the empirical Cox-Merz rule: η 0 ≈ lim ω→0 (G"/ω) Figure 8 shows the value of the zero-shear rate viscosity obtained in oscillatory shear by using the Cox-Merz rule for all the materials and temperatures where a limiting viscosity was observed. The dependence of η 0 follows the Arrhenius law,

η 0 = Aexp(E a /RT) (1)
with E a , the activation energy, R the gas constant and A, a prefactor. E a , which characterizes the temperature dependence of the viscosity η 0 , decreases with increasing M n and approaches the value of E a measured for non-functionalized PnBA. This decrease of E a is consistent with the decrease of the density of stickers when M n increases. However, the remaining difference between the activation energy of PnBAX115 and that of PnBA107 seems to show that the effect of the presence of stickers is not negligible. As shown in Figure 9, the terminal time of PnBAX is much higher than that of unfunctionalized PnBA in the first regime but tends towards it in the second regime. This comparison shows clearly that the contribution of the side chains becomes increasingly important in the molecular dynamics of the supramolecular material when the molecular weight increases and sticker concentration decreases.

Regime 1: Viscoelasticity regulated by Supramolecular Aggregates

For M n ≤ 8kg/mol, the large discrepancy between the terminal times of PnBAX and PnBA as well as the failure to construct proper master curves suggests the existence of supramolecular objects formed by the self-assembly of polar stickers by urea-urea interactions. As the process of self-assembly is fa-

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11 vored by the drop in temperature, an increase in average size of the supramolecular aggregates could explain the increase in elastic character observed at low temperatures in Figure 4. In fact larger objects are more likely to jam and to form a gel than smaller and more mobile objects. On the opposite, when the temperature increases, the scission of aggregates is favored; the average size of such supramolecular aggregates decreases and speeds up diffusion. In addition to the normal decrease in friction coefficient between butylacrylate monomers with increasing temperature, the decrease of the average size of the aggregates could explain the more pronounced temperature dependence of the viscosity η 0 observed for PnBAX than for PnBA (Figure 8). Consequently the terminal time τ d of these systems can be considered as the longest relaxation time of these supramolecular objects via diffusion or scission process.

To validate this hypothesis, the structure of all samples was investigated in the scale domain of [10 nm-4µm] by small and wide angle X-ray scattering and by AFM at room temperature. Surprisingly and regardless of the molar mass of the PnBAXs, no distinctive peak, characteristic of a self-assembly of the molecules over a long range, was detected (see Figure S16 for WAXS). In addition, the AFM observations did not show any evidence of the presence of supramolecular objects. Nevertheless, FTIR spectroscopy unambiguously showed the presence of inter-urea hydrogen bonding in non polar solution [START_REF] Fonteneau | Versatile synthesis of reversible comb-shaped supramolecular polymers[END_REF] . This suggests that in PnBAX, conversely to previous findings in PIBUT systems, the stickers do not form a supramolecular structure with a long range order. Moreover, if they exist, the supramolecular objects formed by stickers association should be very small, i.e. made of very few associations.

In earlier investigations of our group, the self-assembly and rheology of Ethyl Hexyl bis-Urea Toluene (EHUT), a strongly interacting polar molecule, in a non-polar solvent was extensively studied [START_REF] Knoben | Dynamics of reversible supramolecular polymers: Independent determination of the dependence of linear viscoelasticity on concentration and chain length by using chain stoppers[END_REF][START_REF] Ducouret | Rheological characterisation of bis-urea based viscoelastic solutions in an apolar solvent[END_REF] . This small molecule (M n ~ 400 g/mol), chemically close to our bis-urea sticker, self-assembles into long rods in non polar solvents and the viscoelastic behavior of such solutions was well described by the theory of living polymers [START_REF] Cates | Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions[END_REF] proposed by Cates in the fast scission regime. This regime, in which the scission/recombination mechanism is faster than the diffusion of aggregates, is characterized by the Maxwell-like behavior in the terminal part of the relaxation spectrum. Closer to our system, centerfunctionalized poly(isobutylene) chains self-assemble into comb-shaped aggregates [START_REF] Catrouillet | Competition Between Steric Hindrance and Hydrogen Bonding in the Formation of Supramolecular Bottle Brush Polymers[END_REF][START_REF] Pensec | Self-Assembly in Solution of a Reversible Comb-Shaped Supramolecular Polymer[END_REF] in solutions of a non-polar solvent and form a less well-defined structure in the melt [START_REF] Courtois | Supramolecular Soft Adhesive Materials[END_REF] with the polymer side chains playing the role of a viscous solvent. These results encouraged us to look for the characteristic rheological signature of worm-like micelles in our PnBAX supramolecular system in the first regime.

The signature of a Maxwellian behavior is the fit of the viscoelastic data by a semi-circle in the Cole-Cole representation (see Figure 10.B). The slight discrepancy observed at high frequency is usually attributed to Rouse-like or breathing mechanisms. As For PnBAX5 and PnBAX8, the superposition of the viscoelastic data with a semi-circle fails clearly at low and high frequency, as shown in Figure 10.A. Therefore, unlike EHUT or worm-like micellar solutions, the molecular dynamics of PnBAX at low M w cannot be modeled by the fast scission regime of Cates' model. If comb-shaped aggregates exist in PnBAX like in PIBUT, this result suggests that the scission/recombination of stickers is much slower in PnBAX5 than in EHUT solutions, probably due to the presence of the PnBA chains which [START_REF] Ducouret | Rheological characterisation of bis-urea based viscoelastic solutions in an apolar solvent[END_REF] ). The experimental data for PnBAX5 were measured at different temperatures while the experimental measures for EHUT solutions were obtained at different concentrations from c=2.9 to c=10g/L in dodecane, increasing in the direction of the arrow.

Regime 2: Viscoelasticity regulated by PnBA Relaxations

At M n ≥ 20kg/mol, the good superposition of the viscoelastic data at high frequency and the similarities of shift factors a (T) with those of pure PnBA suggest that the molecular dynamics of PnBAX is mainly governed by the relaxation of the side chains at short time scales. The terminal time τ d of these systems, determined by the crossing point between G' and G'' is the longest relaxation time of the side chains. In this M n range, this relaxation is so dissipative than the scission/recombination dynamics of stickers is only observed at long time scale t >> τ d . The signature of such scission dynamics is the poor superposition of G' and G'' at low ω in Figure 5 as well as the stronger temperature dependence of the zero shear viscosity η 0 in Figure 8. Although the characteristic time τ d is regulated by the relaxation of the side chains beyond 20kg/mol, the comparison between our experimental curves for the PnBAX and the numerical simulations for unfunctionalized PnBA chains in this M w range shows that the relaxation process at short time scales is still influenced by the presence of stickers. The G' and G" curves of unfunctionalized poly(butylacrylate) were calculated by using a combination of our experimental data (PnBA107) and a linear viscoelastic model [START_REF] Jullian | Rheological Characterization and Molecular Modeling of Poly(n-Butyl Acrylate)[END_REF] (see Figures S12 to S15). For PnBAXs, a short elastic regime is observed at an intermediate value of ω (tan δ < 1) for all M n while the behavior remains dissipative for all ω for the unfunctionalized PnBA20 and PnBA40 (see Fig 11 .A). The minimum of tan δ is also observed to be lower for PnBAX than pure PnBA (see Figure 11.A or S17) at a fixed molecular weight. The more pronounced elastic character and the higher viscoelastic moduli observed for PnBAX (see Fig 11.B) suggests the presence of small supramolecular aggregates which modify the relaxation of PnBA side chains around them. These small aggregates formed by the self-assembly of stickers would play the role of fillers in the PnBA matrix and would make the materials more elastic. As stickers are expected to self-assemble into comb-shaped aggregates according to our previous studies in solution [START_REF] Pensec | Self-Assembly in Solution of a Reversible Comb-Shaped Supramolecular Polymer[END_REF][START_REF] Fonteneau | Versatile synthesis of reversible comb-shaped supramolecular polymers[END_REF] , the comparison of our rheological results with numerical models designed for star or comb-shaped polymers would be extremely interesting in order to check this hypothesis. Unlike other supramolecular systems described in the literature [START_REF] Lewis | The Influence of Hydrogen Bonding Side-Groups on Viscoelastic Behavior of Linear and Network Polymers[END_REF] , the change of the molecular dynamics by the stickers is not due to an increase of the glass transition temperature T g since the same T g is observed for both regimes (see table 1). Like in the work of Yan et al [START_REF] Yan | Nanostructure and Rheology of Hydrogen-Bonding Telechelic Polymers in the Melt: From Micellar Liquids and Solids to Supramolecular Gels[END_REF] , the analysis of our rheological data by using the time-temperature superposition principle suggests the presence of supramolecular aggregates formed by the self-assembly of bis-urea xylene stickers in the PnBA matrix. However the lack of structure observable by SAXS and AFM would suggest small sizes and no local correlation in orientation for the aggregates.

The qualification of bis-urea as weak stickers may be surprising in view of previous studies on similar studies in apolar solvents or with PIB as the polymer. Yet it is clear that the ester groups on the PnBA compete with the urea groups for hydrogen bonding and weaken the driving force for association of the bis-urea, demonstrating that indeed the definition of strong or weak sticker is completely dependent on the nature of the polymer to which the stickers are attached. Supramolecular systems with similar chain architecture but stronger stickers will be published in a second article. This paper will highlight the role of the strength between stickers on the structure and the rheological properties.

Conclusion

In our study, the linear viscoelastic behavior of an original supramolecular system composed of bisurea center-functionalized linear and nearly monodisperse PnBA chains was extensively characterized.

The synthesis of various samples with well-defined molecular weights with the same sticker reveals a transition between two viscoelastic regimes at a critical molecular weight M c ~ 20 kg/mol. For M n < M c the molecular dynamics is regulated by the relaxation of supramolecular aggregates with a random and temperature dependent distribution of sizes. At higher molecular weights, the hydrogen bonding units are diluted in the polymer matrix and the rheological properties become very close to those of unfunctionalized linear PnBA chains but with a longer terminal relaxation time due to sticker/sticker interactions.

Thermogravimetric Analysis (TGA)

PnBAX were characterized by thermogravimetric analysis (TGA) in order to check if these materials were stable over the investigated temperature range in the rheological study. As illustrated with PnBAX60 in Figure S4, degradation of PnBAX occurs at temperature T ≈ 270°C.

Figure S4: Thermogravimetric analysis of PnBAX60, evolution of the weight (%) with temperature (temperature ramp 20°C/min)

Construction of Master Curves -Data Treatment

Master Curves -PnBAX at T ref =7°C

Figure S7: Attempts of construction of Master Curves for PnBAX5 and PnBAX8 at T ref =7°C

Figure 1 :

 1 Figure1: Frequency sweeps at 20°C in the linear regimes for M w ≤ 20kg/mol (A) and for M w ≥40kg/mol (B). G': full symbols; G": hollow symbols.

5 Figure 2 :

 52 Figure 2: Evolution of η*(ω=1rad/s) at 20°C versus M w or sticker concentration

Figure 3 :

 3 Figure 3: Storage modulus G' and damping factor tan δ = G"/G' as a function of frequency at 0°C, 20°C and 40°C for PnBAX5 (A) and PnBAX115 (B). G': solid line symbols; G"/G': dashed lines.

7

 7

Figure 4 :

 4 Figure 4: Attempts to superpose the tan δ (ω, T) curves for the two lowest M w . The dashed line (tan δ =1) allows to identify the elastic plateau (tan δ <1).

Figure 5 :

 5 Figure 5: Attempts to superpose the tan δ (ω, T) curves for M w ≥ 20kg/mol. The dashed line (tan δ =1) allows to identify the elastic plateau (tan δ <1).

8 Figure 6 :

 86 Figure 6: Horizontal shifts for the tan δ master curves showed in Figures 4 & 5.

Figure 7 :

 7 Figure 7: Master Curves for PnBAX20 and PnBAX40 T ref =7°C. G': filled markers; G": void markers.

Figure 8 : 10 Discussion

 810 Figure 8: Evolution of η 0 (left) with temperature for Low-M w PnBAX (Dashed lines are best fits) and variation E a with the molecular weight and the sticker density (right).

Figure 9 :

 9 Figure 9: τ d (T=20°C) vs M w for PnBAX (circle) and unfunctionalized PnBA (cross). The dashed line materializes the sticker regime at low M w and the side chains regime at high M w .

Figure 10 :

 10 Figure 10: Cole-cole plot for PnBAX5 (A) and solutions of EHUT (B) in dodecane (reprinted from reference[START_REF] Ducouret | Rheological characterisation of bis-urea based viscoelastic solutions in an apolar solvent[END_REF] ). The experimental data for PnBAX5 were measured at different temperatures while the experimental measures for EHUT solutions were obtained at different concentrations from c=2.9 to c=10g/L in dodecane, increasing in the direction of the arrow.

14 BFigure 11 :

 1411 Figure 11: Comparison of our experimental master curves with numerical simulation of monodisperse linear PnBA

Figure S5 :

 S5 Figure S5: Step 1 of the construction of G' and G'' master curves: calculation of horizontal shifts a (T) by superposition of tan δ = G''/G' curves.

Figure S6 :

 S6 Figure S6: Step 2 of the construction of G' and G'' master curves: calculation of vertical shifts b (T) by superposition of G'' curves after applying a (T ) .

Figure S8 :FigFigure S11 :

 S8S11 Figure S8: Master Curves for PnBAX60 and PnBAX115 at T ref =7°C

Table 1 :

 1 Characteristics of the samples: number average molar mass M n , molar mass distribution Đ, sticker density Φ s in the polymer matrix, average degree of polymerization DP and glass transition temperature T g .

		M n (g/mol) Đ	DP	Φ s (wt%)	T g (°C)
	PnBAX5	5400	1.18 38	4.1	-49
	PnBAX8	7500	1.23 54	2.9	-47.5
	PnBAX20	19800	1.23 150	1.1	-48.7
	PnBAX40	43000	1.2	330	0.51	-46.6
	PnBAX60	60400	1.22 470	0.36	-48.7
	PnBAX115 115000	1.34 890	0.19	-49.4
	PnBA107	107000	1.4	840	0	-54.8

Acknowledgement

Support from the French Agence Nationale de la Recherche is acknowledged (project ANR-10-BLAN-0801 Supradhesion).

Supporting Information

Representative SEC curves

Nuclear Magnetic Resonance (NMR) Analysis

After synthesis, PnBAX are purified in ethyl acetate. In order to detect any residual solvent in PnBAX, samples were dissolved CDCl 3 and then, characterized by NMRH 1 (Bruker Avance 200). As shown in the Figure S2, the characteristic singlet of ethylacetate at 2.05ppm is not observed and thus, no residual solvent seems to remain in our sample when they are characterized in linear rheology.

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RMN 1H (200 MHz, CDCl 3 ) d (ppm) : 0.89 (t, (CH3-CH2-)n), 1.3 (m, (CH3-CH2-)n), 1.51 (m, (CH3-CH2-CH2)n), 1.77 (br, (CH2-CH-COO)n), 2.2 (br, (CH2-CH-COO)n), 3.99 (br, (CH2-O)n), 7.2 (s, 1H, Ph-H).

Stability of PnBAX during the rheological process

At the end of the measurements, a frequency sweep is carried out at 25°C to check the good stability of PnBAX during the rheological analysis, which could last up to 2 days. For all samples, the same frequency dependence of G' and G" at 25°C was observed, as shown in Figure S3 for PnBAX5.

Numerical model for Linear Unfunctionalized Poly(butylacrylate)

8.1 Molecular Processes for Linear Entangled Polymer Chains An extensive experimental and numerical study on linear polydisperse PnBA chains was recently published by Jullian et al 1 . In their model 2 , the relaxation modulus can be considered as the sum of four molecular processes, A, B, C and D for M w ≥ 2M e .

G(t) is measured in a stress relaxation experiment. In our study, the relaxation spectrum G*(ω) was determined by strain controlled shear experiments. Thanks to the Fourier transform linearity, G*(ω) can be written as follows:

As G*(ω) = G'(ω) + iG''(ω), with the storage modulus G' and the viscous modulus G'' :

In our study, the polydispersity of our polymers is considered low enough to use a rheological model for monodisperse linear chains. This assumption makes the calculation much simpler compared with those in the polydisperse case. The Process A considers the Rouse-like relaxation of monomers between the transient cross-linking points, called "entanglements ". The maximal characteristic time of this process is the characteristic time τ a with τ a= τ 0 N e 2 /6. τ 0 is the monomer characteristic time and N e the average number of monomers between two entanglements, N e =M e /m 0 with M e the entanglement molecular weight and m 0 the monomer molecular weight. For the butyl acrylate, m 0 =128g/mol.

Relaxation modulus : G

The process B considers a Rouse-like diffusion of the entanglement segment through the reptation tube 3 .

With N, the number of entanglements segments, N=M/M e and the characteristic time τ b = τ a /2.

The process C is the reptation diffusion of the polymer chain through its tube. The following equation uses the development brought by Doi 4 by considering the tube length fluctuation.

τ C is the characteristic time of the reptation diffusion 5,6,,7 :

According the study done by Majesté 7 between the transition between unentangled and entangled regimes, the adjustable parameter 8,9,10 can be estimated as the sum of the Rouse-like relaxation G R t) and a T g relaxation, i.e. the process D previously described.

The modulus in the Rouse model is proportional to the density ρ of the polymer but inversely proportional to its molecular weight M w .

G 0 R = ρRT/M w (S22)

Transition Rouse regime / Entanglement Regime

Between M e and 2M e , the polymers chains are lightly entangled and their molecular dynamics is highly influenced by the Rouse-like relaxations at short time scales. In order to fit the experimental curves in this M w range, Majesté and coworkers 7 proposed to suppress the process B and to replace the process A by a Rouse-like relaxation R on the entire chain.

Consequently for this M w range, the authors proposed :

These equations were successfully used to fit the viscoelastic moduli measured on linear polystyrene chains 7 .

Adjustment of Parameters with experiments

The master curve of the reference synthesized PnBA (M w =107kg/mol, Ip=1.4) was used to determine the parameters of the viscoelastic model displayed in part 6.1. As the characteristic times τ 0 and τ hf depend only on the nature of monomer, we decided to keep the same values found by Jullian et al 1 . Consequently the molecular weight between entanglements M e and the modulus G 0 N were adjusted to fit the experimental measurements, as shown in Figure S12 and S13. These parameters were compared with those calculated by Jullian et al in figure S14.

We found a molecular weight between entanglements M e = 29kg/mol slightly higher for our material than in the reference publication (M e = 23kg/mol). The difference with the value could be due to the chains polydispersity, i.e. the presence of shorter chains in our reference

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

sample. Oligomers or small molecules are known to play the role of plasticizers that facilitates the chains diffusion. The main consequences on the rheological properties are the decrease of the viscosity and the characteristic time of the overall material and thus, are similar to those resulted from an Me increase for a fixed molecular weight. The inclusion of polydispersity in the Jullian et al's study explains their low value for Me.

The value obtained for the modulus G 0 N = 50kPa is also slightly lower in our work than in the reference study (G 0 N = 78kPa). The sensitivity of the rheometer may be at the origin of the slight difference. In the previous section, the fit of the experimental measurements of PnBA107 was used to determine M e and G 0 N and thus, to predict the viscoelastic moduli G' and G'' for linear unfunc-tionalized PnBA for M w ≥ 2M e =2*29=58kg/mol. For Mw ≤ 2M e G 0 R (M w ) was adjusted by assuming that the equations (S2) and (S23) must be equivalent for M w = 2M e , i.e. at the transition between the Rouse regime and the reptation regime. As shown in Figure S15, the equation (S23) with G 0 R = 29kPa gives similar viscoelastic moduli over a large experimental frequency range than the equation (S1). This modulus is a little bit lower than the one obtained by equation (S22):

If T=293K and ρ PNBA =1030kg/m 3 (1) , G 0 R (M w = 2M e )=43kPa. At small angles, no peak was observed and thus, no structuration at long distance range [10nm-4µm] was detected. At wide angles, the two characteristic peaks of the Van der Waals interactions between butylacrylate monomers 11,12 are only observed. (see Figure S16).

Wide Angle X-ray Scattering (WAXS)

Comparison of Viscoelastic Properties between PnBAX and PnBA


Benjamin Vadant

Mamoun Gharbi

Rachid Alami

Thierry Siméon

Being safe around the robot

This paper is about cost based approaches for motion planning in HRI setups. A general approach (TRRT) developed at LAAS is presented as well as some previous cost based work on human aware motion generation.

We also introduce a way to handle dangerous object using this approach: sharp edges and other dangerous object parts should never be directly exposed to the human. A cost function is computed to tackle this issue. Finally we are presenting first results about a new extension of TRRT which is used in HRI motion generation.

I. INTRODUCTION

Robots are coming into our houses. They appeared in factories where safety was satisfied by physically separating them from humans (fig. 1). In the near future, in our day to day environment, robots are going to interact with us, thus being in close proximity of humans. This raises concerns about the safety and the comfort of humans around robots. Indeed, the difficulty is not just being able to move safely around humans but also to generate legible behaviors complying with social rules.

In order to facilitate the introduction of robots into our homes, robots have to be safe to be around and they should induce a safety feeling to humans around them. This feeling, often assimilated with the expression of comfort, is the key for a good human-robot interaction. Plus, the novelty is always bad for humans. So, the randomness of the trajectories generated by probabilistic methods while allowing to generate safe trajectories quickly, makes them unacceptable in numerous cases. This unpredictable motion may surprise the humans and making him feel uncomfortable. In addition to that, a surprise may induce the human to have an unpredictable reaction that can be dangerous for himself (e.g. stepping back and colliding with a furniture).

Multiple approaches to the social motion generation exist but here, we focus on a generic approach based on cost methods. Although creating robots that co-exist with us requires working on navigation and manipulation, this paper will focus on the issue of handling objects around and with the human. Section II clearly states the limit of the problem we chose to address here. Section III discusses related work. Section IV is a reminder on how the TRRT algorithm is working. Finally, we present our ongoing work on the matter in Section V.

II. PROBLEM STATEMENT

The problem we address in this paper is how to make a human feel comfortable around a manipulation robot. Even though this field is linked to subjects such as navigation in human vicinity( see the survey of Kruse & al. [START_REF] Kruse | Human-aware robot navigation: A survey[END_REF] for recent results), or human safety near a robot, we are not addressing those two fields here, our interest is mainly the manipulation part and the comfort that it should bring.

As said in the previous section, one of the keys to a good Human-Robot Interaction (HRI) is the psychological safety and the comfort of the humans. In this view, a robot needs to follow a set of unwritten rules called "the social rules". Those rules differ from one place to another, but there are still some common bases that we try to approach in our work. Here are some examples:

• Motion speed: The trajectory execution speed should be neither too fast nor too slow, both would induce unwanted side effects.

• Motion Smoothness: Blows and discontinuities on trajectories should be avoided.

• Human motion awareness: The robot should not put the human in an uncomfortable physical position as much as possible (e.g. weird handovers).

• Distances: The robot should respect the proxemics theory [START_REF] Twitchell | The hidden dimension[END_REF], by not getting too close to the human with any part of the robot.

• Human gaze: The human gaze and field of view should be taken into account, hidden motions can be disturbing.

• Possible objects hazard: sharp objects can be dangerous, and should be handled with extra care around the human.

Our approach consists in using cost functions to evaluate a set of observable constraints linked to these rules, and to choose the solution with the smallest cost. In the next section, different approaches are presented including our previous work concerning the costs.

III. RELATED WORK

The problem being stated, different approaches have been used in the literature. First we detail control approaches. In order to have smooth motions around the human the actuator must be controlled with precision and flexibility. In their work, Broquere & al. [START_REF] Broquere | Soft motion trajectory planner for service manipulator robot[END_REF] show a jerk limited controller that communicates with the motion planner to create human aware trajectories. In [START_REF] Gerelli | A discrete-time filter for the on-line generation of trajectories with bounded velocity, acceleration, and jerk[END_REF], they bounded both velocity and jerk by a filter at the controller level. Others [START_REF] De Luca | Integrated control for phri: Collision avoidance, detection, reaction and collaboration[END_REF], use a depth sensor and force detectors to slow and/or stop the robot motion if the human gets too close or touches it.

A second approach is the generation of legible trajectories and motions for the robot in a human environment. In [START_REF] Bennewitz | Learning motion patterns of people for compliant robot motion[END_REF], the robot learns how the humans are navigating in order to limit its interference in their path. [START_REF] Sasaki | Human observation based mobile robot navigation in intelligent space[END_REF] chooses to use the human path: the behavior of the robot seems then more logic to the humans. When the robot is interacting with humans while navigating, it has to maintain a certain distance with the humans defined in the concept of proxemics [START_REF] Edward | Proxemics [and comments and replies[END_REF]. For instance, [START_REF] Yoshimi | Development of a person following robot with vision based target detection[END_REF] uses this approach with a robot following a person. For the manipulation tasks, [START_REF] Ikuta | Safety evaluation method of design and control for human-care robots[END_REF] presents a danger index evaluating the trajectory used by the robot. In [START_REF] Nokata | Safety-optimizing method of human-care robot design and control[END_REF] this index is minimised in order to obtain a safe path. [START_REF] Vj Traver | Making service robots human-safe[END_REF] uses a danger index based on the position of the human's head thus integrating the perception of the human to generate safe and "seemingly" safe paths.

Here at LAAS: The main approach developed at LAAS is the use of cost functions that enable the robot to have behaviors that are socially acceptable by the human. In [START_REF] Akin Sisbot | A human aware mobile robot motion planner[END_REF], we use the costs to find places where the robot should avoid to navigate: behind obstacles for example. In addition to that, as seen in the proxemics theory [START_REF] Twitchell | The hidden dimension[END_REF], the robot should avoid entering the personal space of a human (which size varies depending on posture). In the particular case of an interaction meant with a human, the robot should be visible as much as possible while approaching the human given his field of view and obstacles. This approach has been tested in [START_REF] Kheng | Exploratory study of a robot approaching a person in the context of handing over an object[END_REF] where Koay et al. show, in addition to confirm the cost based approach, that humans prefer the robot to approach them from the sides when sitting.

Concerning manipulation planning, we also use costmaps integrating human field of view and robot-human distances in order to compute comfortable motions. This approach is presented in [START_REF] Akin Sisbot | Spatial reasoning for human robot interaction[END_REF]. A part of this paper addresses another problem which is choosing target position by considering the human comfort. As in [START_REF] Mainprice | Planning safe and legible hand-over motions for human-robot interaction[END_REF], this choice results on a cost computation of the human comfort, based on human displacement from initial position and members potential energy. The same costs, and others, concerning the human's will to move, have been used in [START_REF] Mainprice | Sharing effort in planning human-robot handover tasks[END_REF] to predict human navigation motions and a good handover position.

On a more algorithmic level, Jaillet & al. [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF] presents a probabilistic method using RRT applied to costmaps named TRRT. In [START_REF] Mainprice | Planning human-aware motions using a sampling-based costmap planner[END_REF], they propose an application of this TRRT method to HRI problems like handing over objects in human vicinity, using field of view and distances to compute the needed costmap. The next section will detail the TRRT algorithm which can be considered as a general approach to HRI problems.

IV. THE TRRT ALGORITHM

The TRRT method [START_REF] Jaillet | Sampling-based path planning on configuration-space costmaps[END_REF] uses the exploratory strength of RRT algorithms to allow a fast search of the environment and a cost function in order to implement stochastic optimisation methods : thanks to transition tests, potential configurations are selected according to their quality.

In Algorithm 1, we present the pseudocode of this planner. It is quite similar to a RRT-Extend method [START_REF] Steven M Lavalle | Rapidly-exploring random trees a new tool for path planning[END_REF]. The main difference is the presence of the T ransitionT est and M inExpandControl functions.

Algorithm 2 shows the pseudocode of the T ransitionT est function. This part of the TRRT method has 2 roles : on one hand, accepting and rejecting configurations depending on their cost (lines 2 to 5), and, on the other hand, making sure the algorithm doesn't fall in a local minima by accepting certain increasing values. Plus, it integrates some adaptive tuning of a temperature parameter to control the strength of the filtering. The T ransitionT est is the key feature that makes the TRRT method a generic approach to a large number of problems, including the HRI domain.

The M inExpandControl function makes sure that the planner explores correctly the search space. In order to achieve this goal, it tests the distance between q near and q rand against an increment step δ. If the distance is bigger then we accept q rand as it explores the search space far from the current tree. Else, it tests the refinement of the tree. If it has reached the maximum value, q rand is rejected. Else it is accepted.

As a result, by defining adapted cost functions, we can use the same algorithm to navigation, manipulation and mobilemanipulation in the presence of humans.

V. ONGOING WORK

Our recent work concerns an update of the TRRT algorithm in order to handle a more specific problem: how to handle dangerous objects, with cutting edges for example. We developed a new extension to the TRRT that exposed in this section.

A. Dangerous object handling

This subsection is in-between industrial and HRI settings. Indeed, robots equipped with grippers can handle dangerous objects such as knives, screwdrivers, hatchets... And when the robot is moving such objects, it becomes a real hazard for its surroundings (living people or furnitures). As a result, it is important to minimize the risk of collision and if the collision is unavoidable, to make it as painless and harmless as possible.

In order to know how to avoid this dangerous situation, it is important to consider what is making those objects dangerous. We used the work of Haddaddin in [START_REF] Haddadin | On making robots understand safety: Embedding injury knowledge into control[END_REF]. This paper shows the consequences of impact on flesh depending on (C) shows a trajectory generated using TERRT, the object is oriented along the path in such a manner that the dangerous direction is presented toward the human at the end of the motion. the root q init and the goal q goal Output: the tree T begin 1 T ← InitT ree(q init ); 2 while not StopCondition(T, q goal ) do 3 q rand ← SampleConf (CS); 4 q near ← BestN eighbor(q rand , T ); if not Extend(T, q rand , q near , q new ) then T ransitionT est(c(q near ), c(q new ), d near-new ) and M inExpandControl(T, q near , q rand ) then AddN ewN ode(T, q new );

9
AddN ewEdge(T, q near , q new ); 10 end 11 the shape, the mass, the velocity and the orientation of the effector. Following the result of this study, we divided the cost function design into the next two parts.

1) The position of the object: In order to avoid collision, one could simply pass by as far as possible from the obstacles. Unfortunately, this distance is not sufficient enough in certain cases. Thus, it is important to focus on the dangerous object the robot is handling. The shape of this object defines dangerous direction(s): if the object has a sharp edge, the dangerous direction will be the normal to this edge. If it has a tip, the dangerous direction will be in the same direction as this tip etc.

We are currently working on a cost function which allows us to minimize the dangerousness of the generated path. It is composed by two parts depending on :

• the distance to collision : humans directly feels it as a "time to collision" thus it is important that if collision is possible, it should be as far as possible.

• the orientation toward the human : in such case where avoiding the collision is not possible at all, the orientation of the dangerous object is important to increase the comfort of the humans around the robot. Our current implementation of this cost function is the following :

C q = e wα.α.(1+ w d d )
With w α the weight applied to the orientation of the object, w d the weight applied to the distance to collision. d is the closest distance between the human and the dangerous object and α is the angle between the dangerous direction and the vector between the pair of closest points between the dangerous tip and the human.

In the future, the idea would be to put the same function for obstacles as well and find the right tuning in order to achieve safe motion for the human AND his environment.

This first function can be directly implemented in a TRRT algorithm as it tests configuration.

2) The motion of the object: Sometimes, it is required to move dangerous objects closer to humans or obstacles. It is even possible to have to present to the human the dangerous direction. In that case, a simple TRRT would prefer shorter trajectories in order to diminish the whole cost of the motion. This would result in frightening motions with, for example, direct approach. To avoid this situation, we consider an extension of the TRRT algorithm : TransitionEdgeRRT. This method tests also the evolution of the cost of the edges before and after the old configuration. By adding this T ransitionT estEdge , we hope to achieve safer transition. The test is a simple transition test but, instead of comparing the cost of the "old" and the "new" configurations we wish to connect, we compare the cost of the possible new edge to the maximum cost of the directly preceding edges.

This new extension allows to join the simplicity of TRRT and motion consideration without having to use kinodynamic planner. To demonstrate the idea, we thought of calculating the angle between the translation vector and the dangerous direction along the path. By maximizing this criterion, we prevent harmful collisions (like stabbing). We concentrated our effort on translation as it is the type of hazard the most present in object handling. We plan to investigate further to integrate rotating motions in the future.

Finally, we want to modulate speed at the controller level in order to take into consideration the importance of velocity in an impact. In figure 2, we present 3 examples in order to compare the trajectories obtained with or without TRRT and TERRT. The first figure shows a trajectory where the human was not taken into consideration. The second one shows that the robot performs a detour in order to reach the close proximity of the human as late as possible. Finally, the TERRT method generates a trajectory where the hachet is directed toward the human only by rotation : during the motion, the dangerous direction and the motion direction are not colinear so the safety of the human is improved.

B. TRRT byproduct : the cost functions

Using the TRRT algorithm forces us to create cost functions to generate eligible motions. These functions can have other applications such as the evaluation of trajectories in a database (like the one used in [START_REF] Phillips | E-graphs: Bootstrapping planning with experience graphs[END_REF]) in order to sort them. For now, an implemented version of the TRRT is running on the PR2 robot (from Willow Garage), using a cost function based on distances computation and human field of view (FoV). The cost is low when the handled object is far from the human and in his FoV. If the object gets closer or get out from the FoV, the cost raises. Another application of a cost based algorithm is the handover where the choice of position can be handled by costs: the robot needs to be seen from the human, the handled object too, and a respectable distance should separate the human from the robot. The cost are here hand tuned. For each different example, they may need adjustment, one of the next steps is to introduce machine learning processes in order to enhance the cost usage.

VI. CONCLUSION

In this paper, we presented the main approach we use, here at LAAS, concerning HRI motion generation: our work is focused on cost-based methods. We talked about previous work at the origin of our current approach. In a second part, we showed some of our ongoing work on the matter : the creation of cost functions which can be used to handle safely dangerous objects around humans. Finally, we introduced first results about a new extension of the TRRT method, TransitionEdge RRT. This variant is intended to provide a simple way for considering the direction of the motion in the cost function.

In a future work, as all our methods contain weights, we will need to test the generated behaviour in real life, first with roboticists then with common people. This can only be achieved by putting in place a strict protocol taking into account physical criteria such as those we identify earlier and psychological aspects we will define with specialists. To improve furthermore our methods, we will in the future take into considerations the incertitude of the perception of the human: current methods can give false positives. We recently began to work on a way to slow down the reaction of the robot which shows promising results for now. Finally, in order to make the generated motions of our algorithms more logical for the human, we plan to investigate further the definition of the search space. By limiting the area around the human the robot can reach, we hope to obtain simpler trajectories.

Fig. 1 .

 1 Fig. 1. Factory robots working in a secluded areas

Fig. 2 .

 2 Fig. 2. (A) represents a trajectory generated with only a RRT, the trajectory is straight without any consideration for human safety. (B) is a trajectory generated using TRRT with the cost function in VI.a.1, the trajectory takes into account the proximity of the human and try to approach it at the very end.(C) shows a trajectory generated using TERRT, the object is oriented along the path in such a manner that the dangerous direction is presented toward the human at the end of the motion.

Algorithm 1 :

 1 Transition-based RRT Input: the configuration space CS the cost function c : CS → R + *

5

 5

Algorithm 2 : 11 if nF ail > nF ail max then 12 T = T * α; 13 nF

 2111213 TransitionTest(c i , c j , d ij ) begin 1 if c j > c max then 2

ACKNOWLEDGMENT

This work has been supported by EU FP7 "SAPHARI" under grant agreement no. ICT-287513.


Rachid Alami

Mamoun Gharbi

Benjamin Vadant

Raphaël Lallement

Adolfo Suarez

On human-aware task and motion planning abilities for a teammate robot

Human-robot collaboration requires to equip the robot with explicit reasoning on the human and on its own capabilities to achieve its tasks in a collaborative way with a human partner. This paper presents and discusses three humanaware planners which can provide to a teammate robot the ability to asynthesize pertinent and acceptable behaviour in an industrial context. The illustrative context is inspired by a realistic project to involve collaborative mobile manipulators in the assembly of some components of the Ariane launcher.

I. INTRODUCTION

Endowing the teammate robot with explicit reasoning on the human and on its own capabilities to achieve its tasks in a collaborative way with a human partner is a key issue. We present and discuss here a number of decisional abilities which globally belong to the human-aware task planning problem in order to facilitate human and robot interleaved task achievement. These planning functions have been incrementally investigated in the framework of a larger initiative which consists in building and deploying a robot control system especially designed for a cognitive robot which shares space and task with a human.

We illustrate such capacities through the use of a realistic example. The question was to identify a set of tasks and situations where it is possible to introduce robot advanced robot planning functions which could facilitate a close collaboration between a robot and a worker in a factory. The planners we propose integrate in their model human abilities as well as the constraints imposed by the presence of humans, their needs and preferences. Cost-based search plan techniques can then be devised to elaborate plans and behaviours which not only satisfy a given goal but also promote "good" plans.

II. A CONTEXT FOR HUMAN-ROBOT COLLABORATION IN AN INDUSTRIAL SETTING

Aircrafts assembly includes the installation of electrical systems. These are mainly individual or bundled wires of several meters in length used to power and to control all the electrical elements (sensors, actuators and controllers). A large number of brackets are manually positioned and fixed to the structure. They hold the electrical systems to the structure at short intervals in order to restrict their movement during flight. The introduction of a collaborative robot to assist the operator on the bracket mounting process is considered. In particular two tasks could be performed in collaboration:

• First, the fetching of both the brackets and the products (solvent, glue) used to fix them. These items are stored in boxes or specific containers and the operator typically walks back and forth from their storage position to the bracket insertion position. The introduction of a collaborative mobile manipulator allows the operator to reduce his travel distances and to focus on higher added value tasks. There is consequently a need for the robot to navigate in order to achieve fetch)and-carry tasks and to hand over objects to the workers.

• Second, the correct bracket position can be pointed out by the robot. For this operation, thanks to is ability to localise itself very precisely in the environment, the robot could be used to indicate to the human the exact spot where the task should take place (e.g. by projecting an image using an augmented reality technique). Besides, the robot should adopt a posture which does not disturb the worker or prevent him to achieve his own task in a convenient way.

We propose here below, three human-aware planners which could provide to the mobile manipulator robot capacities to synthesize a pertinent behaviour. These planners are based on previous published work. Our goal here is to adapt them and discuss their relevance to the specific context of this study: 1) a planner called "hand-over placement planner" (section III) which is able to compute, depending on the context, where a human-robot hand-over operation can be performed. Indeed, depending on the situation, the "standard" solution, which consists in computing a path for the robot to reach the human and deploy its arm, can be insufficient. The worker can be in a place where he is not reachable by the robot or he can be under time pressure. In such cases, we would like the robot to compute a "rendez-vous" place and configuration of both agents (the worker and the robot) and to pro-actively head towards it; 2) a human-aware motion planner (section IV) which is able to produce safe and human-friendly motion (navigation and/or manipulation) in the workshop between human workers and also to compute placements and postures of the robot which limit discomfort of the workers when they are in a working place; 3) a high-level task planner (section V) which provides to the robot the ability to schedule on-line its next actions as a teammate resulting in what can be seen as a "shared plan" involving interleaved human(s) and robot(s) actions. Here again there is a benefit to produce a plan that not only achieves the goal but also reduces burden and unnecessary actions of the human workers.

III. A HANDOVER PLACEMENT PLANNER

In this section we address the problem of handing over small objects to the human while taking into account feasibility and interaction constraints.

Problem: Let us consider the configuration space C formed by the cartesian product between the robot configuration space C r and the human configuration space C h . Formally the inputs of the problem are the initial configurations of the robot q init r and of the human q init h . The problem also takes as input their kinematic model and the representation of the workspace.

Thus, solving the handover problem consists in computing a handover configuration q handover = (q r , q h ) ∈ C and a motion plan composed of two paths: the robot path (τ r ) and the human path (τ h ).

The configuration q handover belongs to a restriction of C regarding the constraints listed below: a) Collision free: at q handover , the robot and the human have to be collision free.(subspace C f ree ) b) Reachability: at q handover , the object to be exchanged has to be reachable by both partners. (subspace C reach ). c) Stability: at q handover , the robot and the human have to be stable regarding newton law of mechanics. (subspace C stab ) d) Accessibility: this constraint corresponds to the existence of a collision free path between q handover and q init .

The planner implements a cost-based search in order to find q handover and a path for both agents (the human and the robot) to reach it.

Our approach: In order to account for the safety of the interaction and the legibility of the robot's intentions, Kulic and Croft [START_REF] Kulic | Pre-collision safety strategies for human-robot interaction[END_REF], Sisbot and Alami [START_REF] Akin | A Human-Aware Manipulation Planner[END_REF] introduced a set of HRI constraints that, basically, rely on and extend notions from the proxemics theory Hall [START_REF] Edward | A system for the notation of proxemic behavior[END_REF].

In the handover context, we formulate these constraints in three sets (Mainprice et al. [START_REF] Mainprice | Sharing effort in planning human-robot handover tasks[END_REF]). First, we consider comfort constraints (computed as a cost c comf ) that prevent -or, more precisely, try to avoid -generating awkward human postures. Second, we consider motion constraints to generate reasonable effort on the human side. These constraints depend on two parameters (displacement, and standing) and are computed as a cost c mot . Finally, we also account for fluency constraints, limiting the total duration (computed as a cost c length ) of the handover, and favouring efficient plans.

Some of these desired properties such as the human displacement and the action duration may contradict one another. To balance the impact of the different properties on the output plan, we introduce a "mobility" parameter reflecting the human physical capabilities and his eagerness to obtain (or to give to the robot) the object.

Indeed, the handover duration may generate discomfort if it does not match with the human possible eagerness or urgency to get the object. High "mobility" values will balance motion and comfort constraints to favour quicker plans, resulting in the final cost defined as :

c = (c mot + c conf ) * (1 -m) + c length * m
where m ∈ [0 1] is the "mobility" factor. Our approach relies on a combination of grid-based and sampling-based algorithms that consider the workspace obstacles and the kinematic models of both the human and the robot. In the initialization phase, navigation and accessibility grids are computed for the human and for the robot. Then an iteration is started, where the first step is to find a suitable human position. Next, a handover configuration (including both human and robot kinematics) is found based on this human position. Finally, a path is computed for the robot. If one of those steps fails, the algorithm loops back, otherwise a cost c is computed and if the solution is better then previous ones, it is stored. The process is stopped when the maximum allowed time reached or when it detects than no improvement is obtained.

Example: Figure 2 illustrates two possible solutions produced by the planner. We consider that the robot has already a bracket in its hand and need to give it to the human. In the case where the human is busy in his current place, the shared effort should be reduced to minimum by setting the "mobility" parameter to 0 resulting in a solution (see fig. 2a) where the human needs only to rotate to get the object (this small rotation is also computed). In the case where the robot is informed that its human partner is eager to get the object as soon as possible, the "mobility" parameter is set to 1 and the resulting solution (see fig. 2b) will involve a "shared effort" from both the human and the robot.

IV. PLANNING HUMAN AWARE MOTION

Human-aware motion planning integrates in the environment description the position and posture (and possibly the motions) of the humans present in the robot vicinity. Since the emergence of Rapidly exploring Random Tree (RRT) algorithms, computing a path between two configurations has become a fairly simple task. It can be time-consuming but, except in highly constrained situations, it is almost always successful. However, the consideration of human-centered constraints calls for more specific planning schemes.

For instance, given a task including navigation and manipulation, the problem consists in finding a set of motion steps that are safe, readable and comfortable.

Safe Motion: To obtain a safe motion, using a simple RRT could be enough. By avoiding collision with the environment and the humans, the robot makes sure that nothing is damaged. Readable Motion: A one step motion planning instance, based only on a start position and a goal robot position, can result in a path that is difficult to interpret. We basically decompose such a motion into several, distinguishing steps where the robot and a human are really close and perform manipulation motion, and steps where the robot navigates in an environment populated by humans. In the example illustrated by figure 3, we define threes three steps: a "disengagement" Comfortable Motion: In a order to take into account such constraints, we propose to use a TRRT (Transition-based RRT [START_REF] Jaillet | Transition-based rrt for path planning in continuous cost spaces[END_REF][START_REF] Mainprice | Planning human-aware motions using a sampling-based costmap planner[END_REF]) algorithm with a human-aware cost-grid centered on humans Example: In our example, the robot has to go from one side of the human to the other. The RRT generates a trajectory that is pretty close of the human whereas our method creates a trajectory that goes around the chair to avoid to navigate too close to the human (if possible). We illustrate this example with the Figure 3. In comparaison, in Figure 5, the path is computed based on a standard a RRT.

V. ELABORATING SHARED PLANS

This section involves the ability for the robot to elaborate a plan, i.e. a set of actions to be achieved by the robot and its human partners. This is the role of a so-called Human-Aware task Planner (HATP) [START_REF] Alili | HATP task planner for social behavior control in autonomous robotic systems for hri[END_REF][START_REF] Lallement | Hatp: An htn planner for robotics[END_REF].

Such plan elaboration can be implemented based on Hierarchical Task Network (HTN) refinement which performs an iterative task decomposition into sub-tasks until reaching atomic actions [START_REF] Nau | SHOP2: An HTN Planning System[END_REF]. The planning domain defines a set of methods describing how to decompose a task and can be seen as the How-to knowledge of the robot.

In HTN planning framework most part of the knowledge about the domain is provided in a procedural way to the planner which, in the industrial case, is really suitable because there are experts that have a higher view on the work to accomplish.

There are two types of tasks: methods and actions. A method is composed of subtasks (methods or actions again) that are partially-ordered. Those ordering constraints allow to force precedence of a task over other tasks. However a method can have several of such partially-ordered tasks which allows to give several ways to accomplish the task the method solves. On the other hand an action is a elementary task, that can not be decomposed, and that can be executed by the system. One important issue is to produce plans for the robot actions as well as for the other participants (humans or robots). It can be tuned by setting up different costs depending on the actions to apply and by taking into account a set of constraints called social rules.

Agents and action streams: The robot plans not only for itself but also for the other agents. The resulting plan, called "shared plan" is a set of actions that form a stream for each agent involved in the goal achievement. Depending on the context, some "shared plans" contain causal relations between agents. For example, the second agent needs to wait for the success of the first agent's action to be able to start its own action. When the plan is performed, causal links induce synchronization between agents.

Action costs and social rules: A cost and a duration function is associated to each action. The duration function provides a duration interval for the action achievement and is used, in one hand, to schedule the different streams and, in the other hand, as an additional cost function. In addition to these costs, HATP also takes into account a set of social rules. Social rules are constraints aiming at leading the plan construction towards the best plan according to some human preferences. The social rules we have defined so far deal with:

• undesirable states: to avoid a state in which the human could feel uncomfortable;

• undesirable sequences: to eliminate sequences of actions that can be misinterpreted by the human;

• effort balancing: to adjust the work effort of the agents;

• wasted time: used to avoid long delays between the actions of the human partner;

• intricate links: to limit dependencies between the actions of two or more agents.

In our planner, an action can be executed by one or several agents, in this last case it is called a joint action. The "social rules" are used as a filtering rules to penalize plans that would not ease the interaction between humans and robots. For instance, one of those rules controls the plan intricacy. It applies a cost for every causal link that goes from a stream to another since it would require synchronization during the actual execution. There is also a penalty which comes from the joint actions. In the current version, we decided to apply an exponential cost depending on the number of agents involved in a joint action. This highlights the difficulty of such actions as it requires all agents to be available at the same time and to contribute to a synchronized process. However, those rules only apply penalties. So even the best plan can be intricate when it is of absolute necessity.

Example: The aim of this example section is to highlight the features of our planner. It consists of a task where two humans have to fix brackets with the help of a robotic assistant. The robot's aim is to ease the process, the humans will only focus on the task while the robot brings the parts and tools for all operations. The problem is such that some parts are easier for the human to do, such as pick a bracket from a box of tangled Fig. 6. This decomposition contains methods (grey rectangular shapes), and actions which are represented by colored ovals (with a specific color per agent or for joint actions involving two agents). The top-level method is BracketsProc which is decomposed in two methods one for each human. AssembleBrackets is hence called once per human, and contains the two main operations to assemble a bracket: clean the spot and glue the bracket. Both PrepareSurface and GlueBracket need a product to be carried out (respectively the cleaner/solvent and the glue). The robot has then two ways to fetch a product: go to the stock and grab it, or get it from the other human. The crossed circle (bottom right in the figure) represents the case where the human already has the needed product. brackets, which is too challenging for the robot. On the other hand the robot plays a role in the assembly since it places itself near the human and project the exact position where to put the bracket as it is capable to locate itself more precisely that what a human could do.

The goal, is to assemble a bracket but in order to glue it in the right position some operations are needed: first the spot should be cleaned by the human, the robot should then give the bracket to the human, the robot then places itself near the human (see previous section) and projects on the scene the exact spot where the bracket should be placed. The human can then place and glue the bracket. However the glue and the solvent (the cleaning product) are only in limited quantity so the robot has to bring them at the right moment to one worker or the other. At the beginning of the experiment there are two tubes of solvent and one tube of glue. Their initial location might change from a run to the other, but they can be on one of the humans' desk or in one of the two stocks (the stock that is close to the desks or the one that is far).

The domain description to this problem is depicted in figure 6. Considering all the possible decompositions and variable bindings we get a total of 160 possible plans. The solution found reduces as much as possible the use of GetFromH and make the robot go to the stock to fetch the products, even if the geometric path seems longer. Indeed the penalty of joint actions is a lot higher than the cost to go to the stock. We set a high penalty to prevent the robot from disturbing the humans. The "best" task plan solution is presented in figure 7.

VI. RELATED WORK

We briefly discuss here related work. Concerning the human-robot handover, Strabala et al. [START_REF] Strabala | Learning the communication of intent prior to physical collaboration[END_REF] uses experimental set up to find the cues that lead to a handover. Cakmak et al. [START_REF] Cakmak | Using spatial and temporal contrast for fluent robot-human hand-overs[END_REF] show that the intent of the handover can be made explicit through a spatial and temporal contrast: by moving from a passive posture to a handover posture at the right moment, the robot is able to show his intent. Complementing this approach, Cakmak et al. [START_REF] Cakmak | Human preferences for robot-human hand-over configurations[END_REF] have tried different postures for the robot to handover objects, where the naturalness of the posture and its consistency with previous occurrences play a major role beside the object position while handing it over.

Another ability is to share tasks and objectives with the humans, Nikolaidis and Shah [START_REF] Nikolaidis | Human-robot teaming using shared mental models[END_REF] and Nikolaidis and Shah [START_REF] Nikolaidis | Human-robot interactive planning using cross-training: A human team training approach[END_REF] show the importance and pertinence of having the the human and the robot share mental model to achieve a collaborative task.

In the context of planning Human-Robot interactive motion, an evaluation of the relative configurations and motion has been proposed in Kulic and Croft [START_REF] Kulic | Safe planning for human-robot interaction[END_REF]. Sisbot et al. [START_REF] Akin Sisbot | A human aware mobile robot motion planner[END_REF] use a cost function inspired from proxemics theory Hall [START_REF] Twitchell | The hidden dimension[END_REF] in order to generate paths which limits the discomfort of the human and promotes legibility of robot behaviour. Koay et al. [START_REF] Kheng | Exploratory Study of a Robot Approaching a Person in the Context of Handing Over an Object[END_REF] show how the posture of the humans influences his appreciation of the motion of the robot towards him. Another approach is the generation of legible trajectories and motions for the robot in a human environment. In Bennewitz et al. [START_REF] Bennewitz | Learning motion patterns of people for compliant robot motion[END_REF], Chung and Huang [START_REF] Yun | Incremental learning of human social behaviors with feature-based spatial effects[END_REF], the robot learns how the humans are navigating in order to limit its interference in their path. Sasaki and Hashimoto [START_REF] Sasaki | Human observation based mobile robot navigation in intelligent space[END_REF] chooses to use the human path: the behavior of the robot seems then more logical to the humans. When the robot is interacting with humans while navigating, it has to maintain a certain distance with the humans defined in the concept of proxemics Hall et al. [START_REF] Edward | Proxemics [and Comments and Replies[END_REF]. A recent survey has by produced by Kruse et al. [START_REF] Kruse | Human-aware robot navigation: A survey[END_REF].

On the matter of task planning, there are a numerous approaches. From state space planning such as STRIPS Fikes and

GoTo

(ROBOT AssemblyPost2 AssemblyPost1 )

GiveProduct

(ROBOT HUMAN_2 Glue_01 )

Bring

(ROBOT AssemblyPost1 AssemblyPost2 Glue_01 )

TakePosition (ROBOT AssemblyPost2 ) Glue (HUMAN_2 AssemblyPost2 Bracket_02 ) ProjectPlacement (ROBOT AssemblyPost2 ) LeavePosition (ROBOT AssemblyPost2 ) 1 2
Fig. 7. The best solution task plan; yellow actions belong to the robot (ROBOT), the blue ones belong to the first human (HUMAN 1) and the green ones to the other worker (HUMAN 2). One can see that the robot does most of the job since it is responsible for carrying the different products and parts. The action depicted in the blue dashed rectangle 1 is a handover. It is a joint action which involves the robot and the first human. The second rectangle presents actions that the robot and the agent do in parallel. In this case actions are needed before and after to synchronize the actions and to ensure that the robot stays during all the glueing process.

Nilsson [START_REF] Richard | STRIPS: A new approach to the application of theorem proving to problem solving[END_REF], to plan-space planning such as UCPOP Penberthy et al. [START_REF] Scott Penberthy | UCPOP: A Sound, Complete, Partial Order Planner for ADL[END_REF], to hierarchical task planning such as SHOP Nau et al. [START_REF] Nau | SHOP: Simple hierarchical ordered planner[END_REF] and many others. However there are very few planners that actually explicitly consider the human while planning. To consider the human means to have it as an agent of the system but also to take in account special constraints to ease its interaction with the system. Some works Hoffman and Breazeal [START_REF] Hoffman | Cost-Based Anticipatory Action Selection for HumanRobot Fluency[END_REF] try to predict the next action the human might do to prepare the system to those events. On the other hand Cirillo et al. [START_REF] Cirillo | Human-Aware Task Planning for Mobile Robots[END_REF] tries to predict the actions on a wider timescale. Instead of predicting its actions we decided to plan for the human, following the idea from Alami et al. [START_REF] Alami | When the robot considers the human[END_REF], in order to have plan where both robots and humans act together depending on their capabilities. Finally some system do consider the human at all the levels Breazeal [START_REF] Breazeal | Toward sociable robots[END_REF] and Fong et al. [START_REF] Fong | The human-robot interaction operating system[END_REF].

VII. DISCUSSION

We have presented a set of human-aware task and motion planners and illustrated how they can be pertinent to endow a collaborative robot with capacities to reason about humans and produce efficient and acceptable behaviours. We have also shown that it is interesting in some situations to have the robot plan for itself but also for the human. This can be used when the robot is asked to perform a given action of set of actions that belong to a collaborative activity. They can also be used in order to endow the robot with pro-active behaviour based on an estimation of what the human can do. Finally, we have presented how cost-based plan search can be used in such a context, in motion planning but also in task planning.

Fig. 1 .

 1 Fig. 1. Ariane 5 launcher (left) and the upper skirt (right). The upper skirt is the section located on the top of the main cryogenic stage and below the payload area (satellites). An enlarged view of a bracket is shown above.

Figure 1

 1 Figure 1 shows an Ariane 5 launcher (left) and the upper skirt (right). The complete bracket assembly operations are performed manually and individually at the time.The introduction of a collaborative robot to assist the operator on the bracket mounting process is considered. In particular two tasks could be performed in collaboration:

Fig. 2 .

 2 Fig. 2. Figures (a) and (b) represent 2 different situations where the needs of the human are different. In (a) the human needs the bracket to be delivered as fast as possible, the robot chooses the path with shortest estimated time and consequently involves also a contribution of the human to the effort. In (b) the human cannot move (due to his current occupation), the robot "does all the job".

Fig. 3 .Fig. 4 .

 34 Fig.3. The 3 steps: disengagement; navigation, reengagement/placement in shared space with the human. In figure3a, the robot puts its arm in a safe position for navigation. Then in figure3c, the robot navigates to the goal position but, instead of taking the shortest trajectory (i.e. between the human and the chair), the generated path passes away the chair in order to optimize the HRI cost of the motion. Finally, figure3brepresents the last step which is positioning the arm correctly for the task. Please notice that the configuration of the arm is prepared far from the human and then rotated toward him : this is an effect of the optimization of the HRI cost.

Fig. 5 .

 5 Fig. 5. Figure representing the same task as Figure 3 but planned with a simple RRT (Rapidly-exploring Random Tree [21]). The robot passes really close to the human.

VIII. ACKNOWLEDGMENTS This work has been conducted within the EU SAPHARI project (http://www.saphari.eu/) funded by the E.C. Division FP7-IST under Contract ICT-287513.