Karina Merloti

Romain Dubessy

Laurent Longchambon

Maxim Olshanii

Hélène Perrin
email: helene.perrin@univ-paris13.fr

K M O'hara

S L Hemmer

M E Gehm

Breakdown of scale invariance in a quasi-two-dimensional Bose gas due to the presence of the third dimension

Keywords: numbers: 67, 85, De

In this Rapid Communication, we describe how the presence of the third dimension may break the scale invariance in a two-dimensional Bose gas in a pancake-shaped trap. From the two-dimensional perspective, the possibility of a weak spilling of the atomic density beyond the ground-state of the confinement alters the two-dimensional chemical potential; in turn, this correction no longer supports scale invariance. We compare experimental data with numerical and analytic perturbative results and find a good agreement.

Introduction. Scale invariance-the absence of a length scale associated with interactions between particles in a many-body system-has attracted substantial attention in the past decade. The paradigmatic example of a scaleinvariant system is a three-dimensional unitary gas [1-5], which constitutes a quantum interacting system with no governing parameters at all. At the mean-field level, the two-dimensional finite-strength-interacting gases are governed by a single dimensionless coupling constant and thus also show scale-invariance, both in the bosonic [6] and in the spin-1/2-fermionic [7,8] cases. However, here, scale invariance becomes weakly broken under quantization [9], exhibiting a quantum anomaly.

The quantum anomaly [9]-a violation of scale invariance at the microscopic level, for a genuinely twodimensional gas-is not the only potential cause for lifting the scale invariance in the two-dimensional (2D) case. Since, empirically, the 2D gas is embedded in a 3D space, the third dimension may manifest itself as well. Already at the mean-field level, one can see that the interatomic pressure should push the atomic density beyond the ground-state of the confinement, thus modifying the dependence of the chemical potential on the 2D density [10]. Our Rapid Communication is devoted to the study of the consequences of this effect. Incidentally, the effects associated with the 2D-3D crossover are currently prominent in the physics of 2D Fermi gases [11][12][13].

The third dimension effectively introduces a new energy scale corresponding to the confinement energy quantum, ω z , and a new length scale, the confinement length ãz ≡ 2 /(mω z ). Recall that the length scale associated with the quantum anomaly [9] is represented by the two-dimensional scattering length

a 2D = C 2D ãz exp[-( √ π/2)(ã z /a 3D )].
Here, a 3D is the threedimensional scattering length and C 2D = 1.47 . . . [14]. In Ref. [15], Pitaevskii and Rosch have shown that one of the dynamical consequences of scale invariance for a two-dimensional harmonically trapped short-rangeinteracting gas is that the frequency of the lowest monopole excitation acquires a universal value Ω B = 2ω r , where ω r is the frequency of the two-dimensional trap. This property has been clearly confirmed experimentally for the pancake-shaped traps [6,7], and for the related case of a highly elongated trap [16]. In this Rapid Communication, we are investigating how the Ω B = 2ω r feature becomes violated, for a chemical potential becoming comparable to the vibrational quantum in the confined dimension.

Perturbative corrections to the collective frequencies due to corrections to the equation of state. To compute the shift of the two-dimensional breathing frequency, we follow the general procedure established by Pitaevskii and Stringari [17] for correcting the zero-temperature collective excitation frequencies when a small correction to the equation of state is added. Consider a zero-temperature gas governed by an equation of state µ(n), where µ is the chemical potential, and n is the density. Consider further small time-periodic excitation n(r, t) ≈ n(r) + δn(r) sin(Ωt) above a steady-state density distribution n(r). Then, the equation for finding frequencies Ω and mode functions δn(r) reads

- 1 µ ′ (n) ∇• µ ′ (n) 2 n∇δn (1) - 1 2 ∇• µ ′′ (n)∇n 2 δn = mΩ 2 δn , ∇ [µ(n(r)) + V (r)] = 0 , ( 2
)
where m is the particle mass, V (r) is an external trapping potential, µ ′ = dµ dn , and µ ′′ = d 2 µ dn 2 . Equation (1) is written in a manifestly Sturm-Liouville form. The induced inner product is

δn I |δn II ≡ η d d r µ ′ (n(r))δn I (r)δn II (r) , (3)
where the measure µ ′ (n) is assumed to be everywhere positive and finite, and η is an arbitrary positive real constant. Here, d is the dimensionality of space. For Bose condensates, where µ(n) = gn, the most natural choice for η is η = 1/g: in this case, the product (3) becomes the conventional inner product between two functions. For a proper choice of boundary conditions at the edge of the atomic cloud, the Liouvillean L ≡ - 2 on the left-hand side of Eq. 1 becomes self-adjoint with respect to the inner product (3). However, the boundary conditions are dictated by the physics of a particular problem at hand, and they may or may not support this property.

1 µ ′ (n)m ∇µ ′ (n) 2 n∇ -1 2m ∇• µ ′′ (n)∇n
Consider now the particular case of a two-dimensional gas in a radially symmetric potential well. Assume that its chemical potential µ(n) is an analytic function of the density n, and its Taylor expansion at small density starts from a nonzero linear term: µ(n) = gn + O(n 2 ). In this case, one can show that any solution of the eigenmode equation (1) behaves, at the edge of the cloud r ≈ R, as δn(r, Θ) = A(Θ) ln(R -r) + B(Θ) + O(R -r), where R is the radius of the cloud, (r, Θ) are the polar coordinates, and A(Θ) and B(Θ) are arbitrary functions of the polar angle Θ. The logarithmic divergence per se does not a priori mean that a particular mode is not physical: in particular, no divergence in the number of atoms follow. However, one can further look at the small excitations of the gas using the Lagrange representation of the hydrodynamic equations [START_REF] Landau | Fluid Mechanics: v. 6 (Course of Theoretical Physics[END_REF]. There, one considers the Lagrange trajectories of the particles of the constituent gas, r(t, r), as functions of time t and the initial coordinate r. It is easy to show that for small amplitude excitations, the following relationship between the Euler (conventional) and Lagrange variables applies:

δn(r) ≈ ∇ • [n(r)δ r(r)] , (4)
where the density is again n(r, t) ≈ n(r) + δn(r) sin(Ωt), and the inverse of a Lagrange trajectory, r(t, r), is r(t, r) ≈ r + δ r(r) sin(Ωt). According to the relationship (4), a logarithmic divergence of the density at the edge of the cloud, together with the linear decay of the steady-state density, n(r) ∝ R-r, leads, at best, to a logarithmic divergence in r(r). In turn, such a divergence would mean that the particles at the edge of the cloud were initially positioned infinitely far from it. To ensure the physical significance of the solutions of Eq. ( 1), one would need to impose the following boundary condition on the mode functions:

δn(r, Θ) = A(Θ) ln(R -r) + B(Θ) + O(R -r) A(Θ) = 0 . (5)
Furthermore, it is easy to show that the Liouvillean L is self-adjoint on the space of small excitations obeying the boundary condition (5), for the bilinear form (3) regarded as the inner product. The self-adjoint property of the operator L leads to dramatic simplifications of the expressions for the corrections to excitation frequencies under small modifications of the equation of state. Superficially, such calculation would require the knowledge of all unperturbed mode functions and all unperturbed frequencies. But the existence of an inner product (3) with respect to which the unperturbed Liouvillean is self-adjoint implies-similar to what happens in quantum mechanics-that the dominant correction to Ω 2 depends only on the mode function of the mode whose frequency is corrected:

∆(Ω 2 ) = δn 0 | ∆ L | δn 0 . (6)
Here, δn 0 is an eigenmode of the unperturbed Liouvillean L0 : i.e. L0 δn 0 = Ω 2 0 δn 0 ; the full Liouvillean is supposed to consist of L0 and a small perturbation ε∆ L: i.e. L = L0 + ε∆ L, where ε = 1 is a dummy "small" parameter; the square frequency is assumed to be Taylor-expanded onto a power series in the powers of ε:

Ω 2 = Ω 2 0 + ε ∆(Ω 2 ) + O(ε 2 )
; the mode function δn 0 is normalized as δn 0 | δn 0 = 1. The inner product in ( 6) is understood as being based on the unperturbed measure. Notice that for the validity of the relationship (6) (unlike for the validity of the perturbation theory corrections of the higher order) it is sufficient that the unperturbed Liouvillean L0 alone be self-adjoint.

Next, we consider how a small perturbation ε ∆µ(n) to the unperturbed equation of state µ 0 (n) affects the Liouvillean L. The procedure to obtain the first-order correction ε ∆ L is as follows. There are two distinct contributions. One, obviously, comes from the correction to the dependence of the chemical potential on the density. However, the steady-state density distribution n = n0 + ε∆n + O(ε 2 ) also acquires an

ε 1 correction ∆n = -∆µ(n 0 ) + (∆µ) N )/µ ′ 0 (n 0 ) , (7)
where the correction to the chemical potential (∆µ) N ≡ d d r ∆µ(n 0 )/µ ′ 0 (n 0 ) / d d r/µ ′ 0 (n 0 ) is introduced to ensure that the number of atoms in the perturbed system is the same as in the unperturbed one. The density correction (7), in turn, independently contributes to L. The final expression for the correction ∆ L reads, in a compact form,

∆ L = ∂ ∂ε L µ(n) → µ0(n) + ε ∆µ(n) + . . . n → n0 + ε ∆n + . . . ε → 0 .
Alternatively, corrections associated with the potential changes in the number of particles can be accounted for as follows. (i) The corresponding correction to the chemical potential is set to zero:

∆n = -∆µ(n 0 )/µ ′ 0 (n 0 ) . (8)
In this case the density correction (7) will correspond to the same position of the edge of the cloud for both unperturbed and perturbed equations of state, but different numbers of particles. (ii) The correction to the frequency is represented by two terms:

∆(Ω 2 ) = δn 0 | ∆ L | δn 0 - ∂ ∂N (Ω 2 0 ) ∆N , (9)
with ∆N = -d d r ∆µ(n 0 )/µ ′ 0 (n 0 ) being the correction to the number of atoms. The purpose of the second term in the expression (9) is to "undo" the correction to the unperturbed frequency associated with a modification of the number of particles induced by the expression (8). Note that this term is identically zero for Bose condensates.

The confined-dimension-induced shift for a quasi-twodimensional Bose gas. Let us now turn to the concrete example of breathing frequencies of a quasi-twodimensional Bose gas in a radially symmetric harmonic trap.

The unperturbed equation of state reads µ 0 (n) = gn, where g = 4 √ π( 2 /m)(a 3D /ã z ) is the two-dimensional coupling constant. This expression assumes that, in the confined dimension, atoms occupy the ground vibrational state only. A better approximation for the chemical potential can be obtained by using the exact ground-state chemical potential of an infinite two-dimensional transversally harmonic slab:

µ(n) = µ 1D g1D =g3D n -1 2 ω z , where µ 1D is the ground-state chemical potential of the one-dimensional nonlinear Schrödinger equa- tion -( 2 /2m)∂ 2 /∂z 2 + mω 2 z z 2 /2 + g 1D |φ(z)| 2 φ(z) = µ 1D φ(z)
c 2 = - 3 π ∞ m=1 1 2 m • m • m! +∞ -∞ dξe -2ξ 2 H m (ξ) 2 (10) = -0.033 . . . ,
and H m (ξ) are the Hermite polynomials. This number is also confirmed by a straightforward numerical simulation of the ground-state of the one-dimensional nonlinear Schrödinger equation. Now, we invoke the actual unperturbed steady-state density, n0 (r) = n0 (r = 0)(1 -(r/R TF ) 2 ) and the unperturbed mode function, δn 0

(r) = 3/π (1 - 2(r/R TF ) 2 )/R 2 TF .
Here, R TF = ((4gN )/(πω 2 r m)) 1/4 is the Thomas-Fermi radius that defines the position of the edge of the cloud, and N is the number of atoms. Finally, applying formula (6), we get the following expression for the third-dimension-induced relative shift of the breathing frequency of a two-dimensional Bose gas:

∆Ω B /(Ω B ) 0 = -π|c 2 |α + O(α 2 ) , (11)
where c 2 is given by ( 10), (Ω B ) 0 = 2ω r is the unperturbed frequency, and the governing small parameter 11) that describes the effect of a weak "spilling" of the condensate wave function along the confined dimension. The upper black horizontal dot-dashed line is the frequency 2 ωr predicted by scale invariance. The lower one, 10/3 ωr, is the limit of a large chemical potential, µ ≫ ωz, where the Thomas-Fermi profile in the confined direction is reached. The short thin solid horizontal line (blue online) reflects the effect of the quantum anomaly [9]-a genuinely two-dimensional effect originating from the microscopic contributions to the macroscopic equation of state. Note that the two-dimensional chemical potential µ(n) will differ from the full chemical potential µ3D = µ(n) + 1 2 ωz by the confinement ground-state energy.

α ≡ µ(n(r = 0))/(2 ω z ) is given by the ratio between the chemical potential in the center of the trap and the minimal relative-motion energy of a two-body collision needed to excite any non-trivial transverse vibrations; the factor of 2 is due to parity conservation in the twobody collisions.

Experiment. We now present the experimental measurement of ∆Ω B . 87 Rb atoms are confined to the quasi-two-dimensional regime in a very anisotropic adiabatic potential resulting from the combination of a quadrupole magnetic field and a radiofrequency (rf) field [START_REF] Merloti | [END_REF]. The strong vertical oscillation frequency ranges from ω z /(2π) = 1.2 to 2.5 kHz, which corresponds to a dimensionless interaction constant g = mg/ 2 between 0.087 and 0.12. The two-dimensional harmonic isotropic potential in the horizontal plane is very smooth: it possesses the frequency ω r /(2π) ranging from 18.3 Hz to 25.0 Hz. The in-plane trap anisotropy is kept below 3%, which corresponds to a monopole frequency shift below 0.1%, well below the resolution of our measurement. This is achieved by adjusting the polarization of the rf field in order to balance the horizontal frequencies, measured at the 0.3% level by recording the center-of-mass oscillations in the horizontal plane [START_REF] Merloti | [END_REF]. The value of α is controlled by changing the initial atom number N and the trap parameters ω r and ω z . For each experimental point of Fig. 1, α is estimated from the measured atom number and trap frequencies, the chemical potential being calculated from its expression for a two-dimensional gas in the Thomas Fermi regime: α ≃ N g/(4π) ω r /ω z .

To measure ∆Ω B , we proceed as follows. (i) A quantum-degenerate sample of about 2 × 10 4 atoms, with a temperature of the order or below the transverse energy ω z , is prepared following the procedure described in [START_REF] Merloti | [END_REF]. The monopole mode is excited either by a resonant parametric modulation of the radial trapping frequency-via modulating the magnetic quadrupole field gradient-or by a sudden change in this frequency, achieved in turn through a change in the rf frequency. In both cases, the excitation process is slow as compared to the vertical trapping frequency. While in the former case the monopole mode is selected resonantly, in the latter case the symmetry of the excitation allows one to favor this mode over other modes of similar frequency, owing to the fact that their angular momentum is different from zero. (ii) The subsequent cloud dynamics is recorded after a given holding time in the trap. We measure the cloud size by absorption imaging along the horizontal direction after a 25 ms time-of-flight expansion. The cloud becomes very elongated, reversing the anisotropy [START_REF] Merloti | [END_REF]; the horizontal Thomas-Fermi radius is deduced from a bimodal fit. The monopole frequency is obtained from the time evolution of the horizontal radius.

The fitted radial cloud size exhibits time-dependent oscillations whose frequency is estimated using a sinusoidal fit, allowing one to measure the oscillation frequency of the mode. An example of such fitted oscillatory data can be found in our previous publication, see Fig. 6 of Ref. [START_REF] Merloti | [END_REF]. The independent measurement of ω r gives access to the ratio Ω B /ω r plotted on Fig. 1. We repeat this procedure for different values of α.

We observe a good agreement between the experimental data and the prediction (11). The agreement is further improved by employing a three-dimensional timedependent Gross-Pitaevskii equation. Here, we use the imaginary time propagation to produce the steady-state, and then excite the condensate via a rapid change in the trapping frequency. A split-operator method is used at both stages.

Summary and discussion. In this Rapid Communication, we obtain an analytic expression for an empirically relevant scale-invariance-breaking correction to the frequency of a two-dimensional Bose gas in a pancakeshaped trap and compare it with both the experimental data and numerical simulations; the correction is due to a weak deviation of the state of the condensate along the third, confined, dimension from the ground vibrational state. The relative correction to the scale-invariancedictated monopole frequency (Ω B ) 0 = 2ω r is of the order of the ratio between the two-dimensional chemical potential µ and the energy of transverse confinement: ∆Ω B /(Ω B ) 0 ∼ µ/ ω z ∼ na 3D ãz (see Eq. 11).

For typical experimental conditions, the threedimensional effect we study in this Rapid Communication dominates over the purely two-dimensional genuine, quantum anomaly [9]. However, observation of the later is not out of reach. The requirement that the frequency shift caused by the quantum anomaly, (∆Ω B ) anomaly /(Ω B ) 0 = (1/(4 √ π)) (a 3D /ã z ), exceeds the shift (11) leads to the following upper bound on the number of atoms:

N < 1 16 (c 2 ) 2 π 5/2 ω z ω r 2 a 3D ãz ( 12
)
≃ 3.3 ω z ω r 2 a 3D
ãz .

Consider as an example an ensemble of rubidium 87 atoms (a 3D = 5.3 nm) in a pancake trap with the transverse and in-plane frequencies ω z = 2π × 12 kHz and ω r = 2π × 25 Hz respectively. For this set of parameters, the genuine quantum anomaly becomes detectable for atoms numbers belonging to the following window:

4 ≪ N < 3 × 10 4 .
While the upper bound is the numerical value of the bound in (12), the lower bound stems from the additional requirement that the Thomas-Fermi approximation be applicable: gN ≫ 1. For instance, a group of N = 10 4 atoms would constitute a Thomas-Fermi cloud whose breathing frequency will experience a quantum anomaly shift that will exceed the third-dimension-induced shift (11) by approximately a factor of √ 3. We are grateful to Eric Cornell, Vanja Dunjko, and Vincent Lorent for enlightening discussions on the subject, and to Aurélien Perrin for assistance on the absorption imaging. Laboratoire de physique des lasers is UMR 7538 of CNRS and Paris 13 University. We acknowledge support from the Institut Francilien de Recherche sur les Atomes Froids (IFRAF). M.O. was supported by grants from the Office of Naval Research (No. N00014-12-1-0400) and the National Science Foundation (No. PHY-1019197).

2 |c 2

 22 , and g 3D = 4π 2 a 3D /m. The first two orders of the expansion of µ(n) in the powers g 1D read |n 2 + . . ., where

  FIG.1:(Color online) Frequency of the breathing excitation of a two-dimensional gas, as a function of the chemical potential. The filled squares (red online) with error bars correspond to the experimental data. The leftmost point at α = 0.122 is an average over two experimental realizations: one that uses a resonant excitation scheme, and another that uses a quench (see the body of the paper). The error bars are the statistical error. The open circles (black online) with error bars represent an ab initio zero-temperature three-dimensional Gross-Pitaevskii calculation; the error bars are the numerical error. The connecting line is a one-parametric exponential fit that crosses the ΩB = 2 ωr line at α = 0 and reaches an ΩB = 10/3 ωr plateau at α → ∞. The thick dashed line (green online) is given by the perturbative expression(11) that describes the effect of a weak "spilling" of the condensate wave function along the confined dimension. The upper black horizontal dot-dashed line is the frequency 2 ωr predicted by scale invariance. The lower one, 10/3 ωr, is the limit of a large chemical potential, µ ≫ ωz, where the Thomas-Fermi profile in the confined direction is reached. The short thin solid horizontal line (blue online) reflects the effect of the quantum anomaly[9]-a genuinely two-dimensional effect originating from the microscopic contributions to the macroscopic equation of state. Note that the two-dimensional chemical potential µ(n) will differ from the full chemical potential µ3D = µ(n) + 1 2 ωz by the confinement ground-state energy.


Jérôme Franc

Thibault Cholez

Thomas Engel

CCN Traffic Optimization for IoT

recently received a lot of attention thanks to its elegant way to optimize content diffusion at the scale of Internet. However, communications occurring at the edge of Internet, in particular the Internet of Things (IoT), are also a vivid research topic. Even if CCN was not initially designed to optimize the specific traffic pattern of the IoT, it can be improved to better support these new applications. In this paper, we propose to optimize the traffic within a CCN for IoT network where information is created and consumed at different frequencies. The simulations show that our solution outperforms the vanilla CCN architecture for this generic scenario.

I. INTRODUCTION

Network protocols for the Internet-of-Things (IoT) are still a very active field of research. Even if 6LoWPAN/RPL [START_REF] Montenegro | Transmission of ipv6 packets over ieee 802[END_REF] is currently well established, some disruptive research works [START_REF] Carzaniga | Content-based publish/subscribe networking and information-centric networking[END_REF], [START_REF] Saadallah | CCNx for Contiki: implementation details[END_REF], [START_REF] Oh | Content centric networking in tactical and emergency MANETs[END_REF] apply the new Information-Centric Networking (ICN) paradigm, designed to improve the core of the Internet, to other usages at the edge of the Internet, like the IoT. ICN is however not optimized by design for IoT communications which exhibit different properties (push-based, short-lived, small contents).

In this context, our approach optimizes the diffusion of information requested at different sampling rates and sent by sensors within the network using the Content-Centic Networking (CCN) architecture. More precisely, we describe how a node in the path between a data producer and some consumers can maintain states to transmit the produced upstream data toward the downstream links with a limited overhead.

The rest of the paper is organized as follows: Section II presents the advantages of using CCN for the IoT. Section III presents our optimization reducing the number of messages as well as its evaluation through simulations. Finally, we present the related work in Section IV and conclude in Section V.

II. CCN-BASED IOT

A. IoT requirements

The IoT enables smart services through the interconnection of things having computational resources. Smart applications usually rely on contextual information like the geographical location or other physical sensors. Therefore, a core component of the IoT are the sensors or, in a more general way, "information producers". WSNs (Wireless Sensor Networks) are usually connected to the Internet through gateways [START_REF] Steenkamp | AFRICON[END_REF]. The information may be produced in two different modes: either on demand when another entity requests it, or proactively sent to multiple subscribers.

Similarly to WSNs, the IoT undergoes scalability and low power efficiency challenges. For efficient information in WSNs, two major routing approaches [START_REF] Boukerche | A Taxonomy of Routing Protocols in Sensor Networks[END_REF] can be identified: data-centric and hierarchical protocols. Hierarchical approaches, as for example [START_REF] Soro | Cluster head election techniques for coverage preservation in wireless sensor networks[END_REF], try to cluster nodes and to elect a leader serving as a kind of proxy. Data-centric routing, like [START_REF] Intanagonwiwat | Directed diffusion: a scalable and robust communication paradigm for sensor networks[END_REF], advocates for a name based routing where data follows the reverse path of the corresponding query by a hop by hop mechanism.

We promote the usage of CCN for IoT due to existing implementations for computers and smartphones, CCNx [START_REF][END_REF], but also for sensors running Contiki [START_REF] Saadallah | CCNx for Contiki: implementation details[END_REF]. Moreover, CCN combines the advantage of the data-oriented approach and hierarchical routing, by leveraging a scalable hierarchical naming scheme, and integrates security mechanisms and caching by design.

B. CCN

CCN is well suited for distributed environments where each node plays a role in the routing decisions. A node interested in a given content (consumer) sends an interest request which is forwarded until another node can satisfy it (producer) by sending a data message using the reverse path. Each CCN node maintains three vital types of information:

• the Pending Interest Table (PIT) tracks the forwarded

interests not yet satisfied,

• the Forward Information Base (FIB) maintains the next hop information used to forward interests,

• the Content Store (CS) indexes the content which is actually stored or cached on the local node.

In CCN, a face is anything serving as medium for transmitting and receiving messages. So, when a content c is requested by an interest i on a current node n, received from another node on the face f , the steps are as follows:

1) if c is available locally (c is in the CS), n sends it by a data message on the face f 2) if no match for c exists in the CS but exists in the PIT, this means that n already forwarded an interest for c. Hence, no message is emitted. If the new interest i is coming from a new face f , the latter is added to the list of faces associated to c in the PIT, 3) if no match exists in the PIT and in the CS, i is forwarded to another node using the FIB except if no route exists towards c, and the corresponding entry in created in the PIT.

The data message sent by the content provider is forwarded back hop-by-hop using the different PIT entries on the path as they contain the faces from where this content was requested.

More precisely, CCN leverages a hierarchical naming scheme such that data can only "satisfy" Fig. 1: A CCN enabled IoT Network a specific interest whose content name is a prefix of the data message. For example, a content named ccnx:/uni.lu/videos/intro.avi defines several levels separated by /. To fill out the FIBs, nodes have to announce their content which is propagated to all other nodes with a limited overhead using aggregation. A typical example is the router of an organization which does not announce individual content but only a prefix like ccnx:/uni.lu.

C. Problem definition

A common IoT deployment is composed of communicating things in a dedicated network. Thanks to gateways, such a network is interconnected to the Internet. However, things tends also to be more and more directly connected, especially using cellular networks, like smartphones or connected cars.

We promote the use of CCN for low power devices. CCN considers every node as a router and so enhances direct neighbor to neighbor communications as in Figure 1. In addition, CCN is designed to be incrementally deployed beside IP which is necessary for traversing non-CCN paths.

However, this paper focuses on the low power devices at left hand in Figure 1. As highlighted before, CCN is well designed for distributed environments. Data-centric approaches are helpful for saving resources while the issue of a flat naming scheme is addressed with CCN. In addition, the mechanisms of CCN can route interests in parallel on multiple paths and faces (and so communication medium) which thus helps to improve the QoS (opportunistic routing). Besides, the meaningful naming scheme enables new context-aware routing features [START_REF] Jacobson | Networking named content[END_REF].

These low power networks are composed of information producers (like sensors) requested by low power devices (like actuators) and other Internet devices (servers, smartphones, etc). Therefore, a single information producer may have several information consumers desiring different granularities. As an example, a temperature sensor can send information to a fire detection system at a high frequency, every 10 seconds, but such an information provided only every 5 minutes is enough for automatically adjusting a heating system. Therefore, the information should not be multi-casted to every consumer at the same regularity to limit the communication overhead. Sending information temperature every 10 seconds during five minutes represents an overhead of 29 useless messages which can be forwarded through multiple paths and so consume even more resources.

The general scenario is depicted in Figure 2 where there is an intermediate CCN node R i which has to forward the information from M producers transmitted by a previous router R i-1 towards K destinations which are accessible through other downstream nodes like R i+1 . The upstream and downstream routers can be also other producers or consumers as highlighted before. To reduce the number of messages forwarded by R i , we consider a sub problem qualified as local regarding one router and one producer. Resolving the more general problem with multiple producers consists in resolving multiple times the previous problem.

Formally, the problem is defined as follows. Assuming (1) an intermediate node, a router R i , (2) one producer P able to send an information inf every x seconds, (3) N consumers C = c 1 , . . . , c N and (4) that each consumer c i is interested to have inf every x×i i seconds where i i ∈ N (sampling period), the goal is to minimize the number of messages sent by R i . Since each sensor node has a limited capacity, this optimization can only use a limited number of additional resources Cap i . This assumes that a proportion of resources is already reserved for the common CCN operations.

III. SAMPLING OPTIMIZATION

A. Basic Forwarding strategies

In the following discussions, the targeted router for sampling optimization purposes is R i and the considered producer is P . For sake of clarity, only one content is supposed for this producer, named P content , but the approach can be easily applied in parallel to different contents.

By definition, CCN nodes are stateful and only forward data on the back path if an interest was emitted beforehand. Therefore, a basic usage of CCN requires that information consumers directly request producers as illustrated in figure 3(a). This strategy is called pull and allows CCN to send data only when needed (on demand delivery) but the initial interest packet represents an overhead. However, an interest is not forwarded if a previous similar one has been already sent, and a given data message is sent only once per face which is then multi-casted by design. The producer also needs to initialize the FIB of the CCN nodes by announcing the hosted content. Such a step is not considered in the overhead computation because it is required only once.

Pushing data over CCN was envisioned in [START_REF] Carzaniga | Content-based publish/subscribe networking and information-centric networking[END_REF] which describes potential solutions and finally ends up designing a publish-subscribe mechanism where a node interesting in a certain content can subscribe for it, but in this case the diffusion is still based on IP. In this paper, we consider a strategy, push where data is directly transmitted using the FIB. In fact, the subscription is done in the same way that the registration of contents populating the FIB and the sensors' data dissemination is similar to the propagation of interests. In particular, sensors'data are not cached and corresponds to a one-way message. To do so, a simple option is to disseminate such very small and ephemeral data directly inside interests like for example /roomA/temperature/ts=10/value=20 assuming that the temperature sensor has registered the content /roomA/temperature/. Such an interest is forwarded using the FIB but without creating any entry in the PIT, since no data will be sent back. This can be easily done using a flag in the content name or in the interest header. However, a main advantage of creating an entry in the PIT, in the common usage More recent data will be forwarded while older obsolete ones will be discarded, thus avoiding loops and saving bandwidth.

Hence, we assume our aforementioned mechanism. This corresponds to data messages forwarded in Figure 3(b). However, since the information is transmitted regularly and independently of the demands, each value out of the sampling period (i i ) of a consumer c i is dropped and represents an overhead of useless messages. Such a mechanism is comparable to use IP multi-cast where data is forwarded to all subscribers.

B. Optimal Forwarding strategy

To reduce the message overhead in an optimal way, the goal is to combine the advantage of both pulling and pushing modes. The router should only forward data to C i in pushing mode at the period t only if C i has expressed its interest regarding this period: t is a multiple of the sampling period i i . Hence, when the consumers subscribe, they have to specify their sampling period such that R i can keep track of it thanks to a dedicated counter. This is shown in Figure 4(a) where C 1 subscribes to P name whit i 1 = 2. As highlighted, the counter is directly inserted in the FIB and updated each time a message of the subscribed data arrives.

However, this optimal strategy needs one counter per subscription. The additional resources Cap i are considered in terms of number of available counters, independently of the implementation. To limit the number of messages, identical messages are combined into one. Assuming i 1 = 2 and i 2 = 3, the sixth produced message is not forwarded twice as D 1 and D 2 but only once as D 1+2 meaning that this data serves both C 1 and C 2 . The different notations of the same message just help in identifying the purpose of the message. In fact, all these messages are exactly the same and will be forwarded to both consumers thanks to the propagation mechanism of CCN, which makes feasible the use of a single message D 1+2 . This simple mechanism is also applied to the other strategies described in the next section.

The optimal strategy (one counter per content per consumer) cannot be applied with a fixed Cap i value because the number of subscriptions can be very large and the sensors' resources are very limited. While not being practical, this strategy is considered as the baseline for evaluating the performances of the other ones.

C. Smart Forwarding strategies

Assumes a fixed maximal number of counters Cap i , the goal of a smart forwarding strategy is to refine the pushing mode while limiting the number of forwarded messages. The worst case considers a single counter which serves to all subscribed periods. For example, with multiples like i 1 = 2 and i 2 = 4, a unique counter looping between 1 and 2 is enough and does not entail additional messages. This can be extended using the Greatest Common Divisor (GCD) (strategy gcd). With i 1 = 4 and i 2 = 6 as in Figure 4(b), the unique counter loops over gcd(4, 6) = 2 which thus avoids to forward message at every period. However, there is an overhead of useless messages like the first forwarded message D 1+2 which is then transferred by other routers as D 1 or D 2 before being dropped by the consumers. Moreover, there is a high risk that with numerous subscriptions, the global GCD reaches 1 which so does not represent any improvement compared to the basic pushing forwarding scheme.

With more counters, i.e. Cap i > 1, this can be extended by selecting Cap i values, G = {g 1 , . . . , g Capi }, such that: Again, this will entail some message overhead but it is better than having considered the unique GCD which is one.

∀C i ∈ C, ∃g k ∈ G, α ∈ N, g k × α = i i
After having filtered identical intervals and those being multiple of others, the smart forwarding strategy affects one counter per unique remaining sampling interval G ′ = {g 1 , . . . , g M }. If the number of needed counters is acceptable, i.e. |G ′ | ≤ Cap i , the algorithm stops and G = G ′ . Otherwise it iterates until this condition is reached by merging at each step two counters, g merge = gcd(g i , g j ), (g i , g j ) ∈ G ′ × G ′ , g i = g j . These counters are selected to maximize the GCD in order to limit the message overhead:

∀(g k , g l ) ∈ G ′ ×G ′ , (g k , g l ) = (g i , g j ), gcd(g j , g i ) ≥ gcd(g k , g l )

D. Evaluation

For evaluation purposes, a dedicated simulator has been developed which implements the only necessary functions of CCN which are used in our approach. The number msg s of messages forwarded by R i is considered regarding the chosen strategy s (among pull, push, optimal, gcd or smart) and a configuration defined by:

• M AX T : the maximal length of the sampling interval that a consumer can subscribe to,

• N = |C|: the number of consumers which subscribes to a unique sampling interval. The latter is chosen randomly between 1 and M AX T ,

• #counters: the number of available counters (only impacts the smart forwarding strategy),

• #steps is the number of simulation steps assuming that the length of a step is defined by the initial sampling period at which the sensor can produce data.

We measured the number of messages because it is clearly correlated to the energy consumption which is one of the main criteria for designing protocols for WSNs. Based on preliminary experiments, #steps was fixed to 5 × M AX T , which guarantees that every consumer has received data at least five times during the discrete events simulation. As previously said, the optimal strategy is used as the baseline to compute an overhead ratio defined as:

f s = msg s msg optimal (1)
We always calculate the average of f over 10 experiments. The number of consumers affects our performances by increasing the number of different sampling periods and is therefore expressed as a proportion p of M AX T .

The number of consumers is evaluated in figure 5(a) where M AX T = 3000 and #counters = 100. The vanilla CCN architecture (pull) highlights a ratio of 2 which is coherent since every data is sent after an initial interest. When p increases, all other curves tend to one because the optimal strategy also requires to forward more messages as there are more customers. In particular, when p increases, the chance to have a consumer C i having subscribed with an interval i i = 1 is higher which thus leads to forward a message at every step. Due to the same mechanism, the benefit of smart forwarding compare to the push mode is reduced. Therefore, using optimization has logically a higher impact when the number of subscribed intervals is low. However, the worst case for smart routing is for p = 0.08 representing 240 distinct intervals which are handled by the 100 counters. As highlighted, the gcd strategy leads to the same result that the simple push strategy which forwards every data message because the overall GCD computation reaches always 1 even with p = 0.05 due to the probability to have randomly selected one of the 430 prime numbers between 1 and 3000. Besides, as previously highlighted, the push mechanism is similar to IP multicast, which thus allows to compare our approach with the latter.

The smart forwarding strategy proposed in this paper always exhibits a ratio significantly lower than the classical CCN approach. It varies between 1 and 1.67. When p is very small, there are enough counters to be optimal and starting at p = 4%, the optimization starts by sharing the counters for multiple intervals which entails a message overhead. Around 0.1, the optimal strategy has to forward many messages which thus highly impacts on the denominator in equation (1).

In figure 5(b), the number of counters for the smart forwarding strategy varies on x-axis and different maximal sampling intervals have been tested. The number of uniquely subscribed intervals is set to 5% of M AX T and so varies between 100 and 1500 depending on the configuration. When the number of usable counter increases, the overhead is logically reduced, even faster if there are less subscribed intervals (lower M AX T ). Such an experiment helps to choose the right tradeoff between message overhead and hardware/software additional resources (number of counters). Then, depending on the communication medium and the hardware, it would be possible possible to select the most efficient number of counters in terms of energy consumption. For instance, assuming that the maximal acceptable overhead is expressed as f = 2, the proper number of counters can be chosen regarding the number of uniquely subscribed intervals.

IV. RELATED WORK

As mentioned, an important missing feature to use CCN for IoT is a push-based mechanism for communications. Instead of probing a sensor regularly, which consumes energy, a better way would be to let the sensor transmit its data when needed. Doing this in CCN is not natural but yet feasible. Van Jabobson et al. solved a similar issue to enable CCNbased conversational communications for voice over IP [START_REF] Jacobson | VoCCN: voice-over content-centric networks[END_REF]. They propose a solution based on two properties of CCN: on-demand publishing to request content that has not been published yet, which simulates a rendez-vous point, and a deterministic algorithm followed by the two parties to find this service name. The approach in [START_REF] Carzaniga | Content-based publish/subscribe networking and information-centric networking[END_REF] handles small ephemeral messages, more precisely events communication typically produced by IoT. This allows CCN to support publish/subscribe communications by adding a new unicast forwarding table and a new set of dedicated messages: "one way" messages for event notifications that can follow the path of subscriptions up to the subscribers. In [START_REF] Saadallah | CCNx for Contiki: implementation details[END_REF], a full CCN layer is provided for Contiki which enables CCN usage for low power devices and IoT.

Our paper also deals with the problem of efficient dissemination of event notifications in a sensor network. Some papers are close to this topic even if they do not optimize the diffusion of information according to fixed sampling rates. For example, the authors in [START_REF] Mao | Sampling frequency optimization in wireless sensor network-based control system[END_REF] used non-linear optimization theory to optimize the rate at which sensors can be probed by a control system under network limitations. Another way to save network resources in WSNs is to rely on in-network aggregation techniques which have been largely investigated through different strategies [START_REF] Fasolo | In-network aggregation techniques for wireless sensor networks: a survey[END_REF], even secured ones [START_REF] Yu | Secure continuous aggregation via sampling-based verification in wireless sensor networks[END_REF]. This solution is particularly efficient when data is gathered by a few sinks while we envision in our case a more neighbor-toneighbor communication pattern between sensors.

V. CONCLUSION

In this paper, CCN is leveraged for distributed IoT communications, especially in the context of producers regularly updating information sent to multiple consumers. A new pushbased mechanism was designed and optimized. Even under strict resource constraints, the nodes optimize the forwarding of messages based on the update frequencies required by the different consumers. Compared to the optimal but unrealistic approach, the results show a limited overhead, always under the regular CCN pull approach. Our future work will focus on improving our approach for multiple-content producers.

Fig. 2 :Fig. 3 :

 23 Fig. 2: Optimization problem

Fig. 4 :

 4 Fig. 4: Sampling optimization (Dotted lines represents possible multiple hops)

Figure 4 (

 4 Figure 4(c) considers two counters and so introduces a specific structure, the Information Sampling Table (IST), which keeps track of them. With three consumers and i 1 = 9, i 2 = 12 and i 3 = 5, R i will forward every 3 and 5 data messages.Again, this will entail some message overhead but it is better than having considered the unique GCD which is one.

Fig. 5 :

 5 Fig. 5: Message overhead evaluation

Acknowledgement: This work was partly funded by BUT-LER and IoT6 FP7 EU projects under the grant agreements 287901 and 288445.


Vincent Weistroffer
email: vincent.weistroffer@mines-paristech.fr

Alexis Paljic
email: alexis.paljic@mines-paristech.fr

Lucile Callebert
email: lucile.callebert@mines-paristech.fr

Philippe Fuchs
email: philippe.fuchs@mines-paristech.fr

A Methodology to Assess the Acceptability of Human-Robot Collaboration Using Virtual Reality

Keywords: I, 2, 9 [Artificial Intelligence]: Robotics-Manipulators; H, 5, 2 [Information Interfaces and Presentation]: User Interfaces-Ergonomics, Evaluation/methodology

Robots are becoming more and more present in our everyday life: they are already used for domestic tasks, for companionship activities, and soon they will be used to assist humans and collaborate with them in their work. Human-robot collaboration has already been studied in the industry, for ergonomics and efficiency purposes, but more from a safety than from an acceptability point of view. In this work, we focused on how people perceive robots in a collaboration task and we proposed to use virtual reality as a simulation environment to test different parameters, by making users collaborate with virtual robots. A simple use case was implemented to compare different robot appearances and different robot movements. Questionnaires and physiological measures were used to assess the acceptability level of each condition with a user study. The results showed that the perception of robot movements depended on robot appearance and that a more anthropomorphic robot, both in its appearance and movements, was not necessarily better accepted by the users in a collaboration task. Finally, this preliminary use case was also the opportunity to guarantee the relevance of using such a methodology -based on virtual reality, questionnaires and physiological measures -for future studies.

INTRODUCTION

Robots are becoming more and more present in our everyday life. Some robots can already handle domestic tasks autonomously, others are used as companions for the youth or the elderly, or even as guides in museums. In a near future, robots will be able to handle more complicated tasks, to assist humans in their everyday work and to collaborate with them.

Human-robot collaboration has already been studied for many years in the industry: specific robots are used to assist workers on difficult tasks, for example on assembly lines. The assets of this collaboration are improved ergonomics for the workers and improved competitiveness for the industry. For now, the main issue being studied has been safety: since physical interaction between robots and workers is needed, the safety of people around robots has to be guaranteed. This issue has been dealt with thanks to the development of new sensors placed directly on robots or in their environments, in order to detect intrusion in a safety perimeter and avoid collision if necessary.

However, another issue, less studied but nonetheless important, is the acceptability of such a collaboration between humans and robots. From the users' point of view, the introduction of robots in their everyday work may be perceived and accepted differently than expected. This acceptability is difficult to evaluate and may be influenced by several factors that are hard to determine. This is where virtual reality may provide interesting insights and functionalities to study the acceptability of human-robot collaboration. By making users collaborate with virtual robots under different conditions, it should be possible to evaluate the influence of different factors on this acceptability, in a more practical way than if the experiments were performed with real robots.

In our work, we propose to use virtual reality as a simulation environment to study different scenarios of human-robot collaboration and to evaluate their acceptability from the users' point of view. We provide a methodology to assess the acceptability of humanrobot collaboration systems, based on questionnaires and physiological measures. This methodology was applied to a preliminary use case to evaluate the impact of robot appearance and movements on the users' perception. A user study was performed to assess the relevance of our methodology in this particular use case.

In Section 2, we describe related work on the acceptability of human-robot collaboration, the methodologies used to evaluate it and the need to use virtual reality in this context. In Section 3, we present the tools we developed to set up our methodology, dedicated to the simulation environment and the acceptability criteria. In Section 4, we describe the design of the use case we implemented to study human-robot collaboration and we explain the user study we performed. Finally, in Section 5, we present the results and the analysis of this user study before concluding on the relevance of our methodology and our future work in Section 6.

RELATED WORK

Human-robot collaboration has been studied for a long time, both in the fields of service robotics, for example with the Care-O-bot [START_REF] Parlitz | Careo-bot 3 -rationale for human-robot interaction design[END_REF], and industrial robotics, with European projects such as PiSA [START_REF] Krüger | Flexible assembly systems through workplace-sharing and time-sharing human-machine cooperation (PISA)[END_REF] and SMErobot [START_REF] Nillson | Productive robots and the SMErobot project[END_REF]. Studies on human-robot collaboration have often focused on safety: since physical interaction between humans and robots is needed, the safety of this interaction has to be guaranteed. In that context, several improvements have been made in safe obstacle avoidance [START_REF] Pedrocchi | Safe obstacle avoidance for industrial robot working without fences[END_REF], in the safety evaluation of robots [START_REF] Haddadin | Safety evaluation of physical human-robot interaction via crash-testing[END_REF] or in intrusion detection [START_REF] Lenz | Context-aware human-robot collaboration as a basis for future cognitive factories[END_REF].

If the safety of collaborative robots is nowadays well studied, another issue is being less considered: the acceptability of such a collaboration between humans and robots. The notion of acceptability is not easy to define. Nielsen [START_REF] Nielsen | Usability engineering[END_REF] proposed a model in which acceptability is divided between social acceptability and practical acceptability, the latter gathering the notions of utility and usability. We tried to apply this abstract definition to our specific context: human-robot collaboration. Social acceptability concerns how the society perceives robots in everyday life, while practical acceptability relates to how people perceive robots when interacting directly with them. In our work, we were especially interested in the practical acceptability of robots from the users' point of view: we tried to study the usability and the satisfaction of people when collaborating with robots.

The study of the acceptability of human-robot collaboration focuses on several parameters: robot appearance [START_REF] Goetz | Matching robot appearance and behavior to tasks to improve human-robot cooperation[END_REF], robot movements [START_REF] Nonaka | Evaluation of human sense of security for coexisting robots using virtual reality. 1st report: evaluation of pick and place motion of humanoid robots[END_REF][START_REF] Kulić | Affective state estimation for human-robot interaction[END_REF][START_REF] Huber | Humanrobot interaction in handing-over tasks[END_REF][START_REF] Kupferberg | Biological movement increases acceptance of humanoid robots as human partners in motor interaction[END_REF], robot behavior, robot speed, robot safety distance [START_REF] Karwowski | Worker selection of safe speed and idle condition in simulated monitoring of two industrial robots[END_REF]... When dealing with only one kind of parameter or with a specific system, the implementation of experiments in a real environment with a real robot is the usual way to proceed and may be sufficient. However, if the experiments become more complicated (using several robots for comparison, testing several parameters), the implementation becomes impossible for practical and cost reasons. That is why the use of virtual reality is interesting in that context: it can ease the implementation of the study and enable a large number of test parameters.

In the literature, very few people made use of virtual reality tools to study human-robot collaboration. Most studies used real scenarios where the users only observed robots and did not interact with them. Those were scenarios in which the robots performed specific movements or tasks in front of the users, such as moving from point to point [START_REF] Shibata | Psychological evaluations of robot motions[END_REF] or manipulating objects close to the users [START_REF] Kulić | Affective state estimation for human-robot interaction[END_REF]. Some studies did involve the users in an interaction task with real robots [START_REF] Huber | Humanrobot interaction in handing-over tasks[END_REF], but they were often performed to assess the efficiency of the system, and not the acceptability. The only experiments that used virtual reality to study human-robot collaboration took little advantage of its interaction functionalities. Nonaka et al. [START_REF] Nonaka | Evaluation of human sense of security for coexisting robots using virtual reality. 1st report: evaluation of pick and place motion of humanoid robots[END_REF] and Inoue et al. [START_REF] Inoue | Comparison of human psychology for real and virtual mobile manipulators[END_REF] used virtual robots (with head-mounted displays or CAVE systems) to evaluate the effect of robot movements and robot proximity on the users, but did not study any interaction and collaboration between them. On a different topic, De Santis et al. [START_REF] Santis | A virtual-reality-based evaluation environment for wheelchair-mounted manipulators[END_REF] used virtual reality to evaluate the usability of different (virtual) robotic arms mounted on a wheelchair, but this was especially for efficiency purposes. Our aim is to benefit from all the functionalities of virtual reality (immersion and interaction), by implementing interactive scenarios in which users collaborate with virtual robots, and by evaluating the acceptability of that collaboration.

The main issue when dealing with acceptability is how to evaluate it. This question is not easy since acceptability is a subjective notion that people often seek to measure in an objective way. The most common tool to evaluate acceptability is to use questionnaires. Different kinds of questionnaires exist in the literature: some of them focus on the robot's attributes [START_REF] Shibata | Psychological evaluations of robot motions[END_REF] (humanlike, pleasant, interesting...), while others focus on the user's emotions [START_REF] Nonaka | Evaluation of human sense of security for coexisting robots using virtual reality. 1st report: evaluation of pick and place motion of humanoid robots[END_REF] (surprise, fear...). Bartneck et al. [START_REF] Bartneck | Measurement instruments for the anthropomorphism, animacy, likeability, perceived intelligence, and perceived safety of robots[END_REF] performed a complete review on questionnaires about human-robot interaction and proposed their own questionnaires intended to be used by the community of robot developers. Even if questionnaires can be analysed directly, they rely on subjective impressions of the users and their results should be correlated with more objective measures. One solution is user observation during the interaction: Kanda et al. [START_REF] Kanda | Development and evaluation of interactive humanoid robots[END_REF] defined an evaluation score based on body movements, Kooijmans et al. [START_REF] Kooijmans | Accelerating robot development through integral analysis of humanrobot interaction[END_REF] implemented a software to record and analyse data from video clips, Minato et al. [START_REF] Minato | Does gaze reveal the human likeness of an android? In Development and Learning[END_REF] tried to analyse eye gaze during the interaction. Those studies showed that defining an objective way to observe and evaluate the user's behavior is definitely not an easy method. Another solution is to evaluate the user's affective state thanks to physiological measures. The main idea in the literature [START_REF] Rani | Online stress detection using psychophysiological signals for implicit human-robot cooperation[END_REF][START_REF] Sarkar | Psychophysiological control architecture for human-robot coordination -concepts and initial experiments[END_REF][START_REF] Kulić | Affective state estimation for human-robot interaction[END_REF] was to use multiple physiological signals (such as heart rate, skin conductance, facial muscle contraction) in order to infer human physiological states (stress, anxiety) and enable the robot to react appropriately. The same idea could be used to assess the user's acceptability towards human-robot collaboration.

As a summary, the scope of our work is to study the acceptability of human-robot collaboration from the users' point of view. Our approach is to use virtual reality to make users collaborate with virtual robots and gather their impressions for different conditions. We propose to use a combination of questionnaires and physiological measures to evaluate the acceptability of the collaboration in an objective way.

METHODOLOGY TOOLS

In this section, we describe the tools that we developed and used to set up our methodology. Since our approach was to use virtual environments to study human-robot collaboration, a large part of this section is dedicated to explaining how to model and control virtual robots. We also describe the criteria we chose to evaluate the acceptability of human-robot collaboration: questionnaires for subjective impressions and physiological measures for estimating human affective state.

Simulation Environment

Robot Models

In our work, we focused on robotic articulated arms: their structure is often represented by a series of rigid bodies linked to each other by joints. We considered only rotational joints: the state of a joint is represented by an angle around a specific axis. The adaptation of this representation to virtual robots is straightforward: the virtual robot is modelled as a hierarchy of 3D frames (the joints of the robot) and 3D objects as their specific children (the rigid bodies). Thanks to this hierarchy, rotating a specific joint moves the entire arm from this joint to the end-effector. An example of a virtual robotic arm is presented in Figure 1.

Robot Kinematics

Before collaborating with robots in virtual environments, it is necessary to know how to control them. By modifying directly the joints states of a robotic arm, it is easy to find the cartesian state (position, orientation) of its end-effector(s). This process is called forward kinematics. Even if forward kinematics is the most direct way to control a robotic arm, it is not the most usual and practical way to proceed: end-effectors are often assigned target positions that they have to follow. Therefore, given the cartesian states of the targets, the joints states of the arm have to be computed to give the correct positions to the end-effectors. This process is called inverse kinematics.

Inverse kinematics have been well studied both in the fields of animation (for human arms and skeletons) and robotics. Several methods have been proposed to solve this complex problem, that can be classified between analytical and numerical solutions. Analytical solutions are difficult to produce and depend largely on the structure of the arm [START_REF] Kucuk | Robot Kinematics: Forward and Inverse Kinematics, chapter 4[END_REF]. Numerical solutions, based on optimisation or jacobian methods, are easier to implement and can be generalised to different robotic arm structures. Buss and Kim [START_REF] Buss | Selectively damped least squares for inverse kinematics[END_REF] presented a complete review on the methods using jacobians and provided their source code online 1 .

As Buss' algorithms are dedicated to control multibodies for computer graphics, with multi-targets and in real time, we decided to use them and to integrate them in our system to control virtual robotic arms. Buss' model uses a tree to represent the structure of a rigid multibody (such as a robotic arm): the nodes of the tree represent the joints, while the leaves are the end-effectors (see Figure 1). Each node of the tree gathers all the needed data about the corresponding joint: joint state (angle of rotation, axis of rotation), cartesian state (absolute position, relative position to the former joint). The states of the nodes are updated in real time according to the targets' positions, thanks to inverse kinematics algorithms based on jacobian methods.

In our system, each of our robot models is coupled with a tree structure in real time. This tree structure is first built according to the robot's hierarchy (initialisation phase). The robot's hierarchy (series of joints, joints initial positions and axes) is stored in a text file (identification file) that is used as a parameter for the construction of the tree. The nodes data are then updated in real time depending on the targets' positions. The joints states are finally sent to the robot's model for graphical update (mapping phase). With this principle, the core of the inverse kinematics algorithms is done in the tree and the robot's model is only updated according to the nodes data.

We used this architecture with several robots. Each robot had a different identification file, since each robot had a different structure and thus was coupled with a different tree. This system was tested successfully with predefined trajectories, with targets generated and controlled by a mouse cursor, and finally with targets generated by users in a virtual environment: thanks to motion capture, the users were able to guide the end-effectors of robotic arms with their hands, in real time (see Figure 2). With this principle, it was possible to give different behaviors to robots by generating different movements profiles with the targets.

Acceptability Criteria

One of the aims of our methodology was to find the relevant criteria for the evaluation of acceptability that enabled to show that a certain situation was better accepted than others. In that context, we chose to use questionnaires, for subjective impressions, and physiological measures, for correlation with the questionnaires through the estimation of human affective state.

Questionnaires

As a starting point for our questionnaires, we focused on the 'Godspeed questionnaires' proposed by Bartneck et al. [START_REF] Bartneck | Measurement instruments for the anthropomorphism, animacy, likeability, perceived intelligence, and perceived safety of robots[END_REF]. Those are five consistent questionnaires using semantic differential scales, on the topics of anthropomorphism, animacy, likeability, perceived intelligence and perceived safety of robots, based on empirical studies and dedicated to robot developers. Those questionnaires were adapted to the use cases we wanted to study and were mainly focused on anthropomorphism, perceived intelligence and safety.

Physiological Measures

In the literature, studies with physiological measures for humanrobot interaction usually used heart rate and skin conductance. Kulić and Croft [START_REF] Kulić | Affective state estimation for human-robot interaction[END_REF] also used facial muscle contraction but they concluded that it was not a good indicator for estimating human affective state.

Skin conductance level (SCL) measures the skin sweating activity of the user and is directly related to his stress level: a higher SCL usually means a higher level of stress. Since SCL differs between users, it is necessary to always compare it to an average or control value (specific to each user). Skin conductance responses (SCR) may also occur: they are peaks in SCL that happen spontaneously one to three times per minute (depending on users) or directly after a stimulus [START_REF] Dawson | Handbook of Psychophysiology[END_REF]. The amplitude of SCR may be related to the strength of the reaction to the stimulus. Heart rate activity is usually more difficult to analyse, since it can be influenced by several factors (physical state, fatigue, body position).

For our studies, the average SCL, the frequency of SCR and the average heart rate (HR) seemed to be the relevant criteria to estimate human affective state and to evaluate acceptability in a collaboration task. It was also important to use physiological signals that were simple to handle, whose measurements were non-invasive and allowed the users to move and interact in a virtual environment, which is the case with HR and SCL.

PRELIMINARY STUDY

We applied the methodology described in Section 3 to a preliminary use case. The aim of this study was to evaluate the effect of robot appearance and movements on the acceptability of a simple collaboration task.

Use Case Design 4.1.1 Collaboration Task

A simple use case was implemented for collaboration between a user and a robot. We wanted this use case to be interactive, to give specific roles to both the robot and the user, but also to be simple enough to allow the user to look at the robot's appearance and movements (and not to focus on the task only). It was also important that this use case could be related to a real industrial task.

In our study, we took inspiration from an industrial task in which a robot may have to hand mechanical parts to a worker on an assembly line. For abstraction purposes, this task was simplified into a cubes exchange process between a user and a robot (see Figure 3). The user and the robot were on each side of a table. Eight cubes (four red and four blue) were positioned in front of the robot (unreachable by the user), while storage areas were placed in front of the user (unreachable by the robot). The robot had to take cubes one by one and give them to the user, who had to store them in the correct area, depending on the color of the cubes (blue on the left or red on the right).

The robot was controlled thanks to the IK process exposed in Section 3.1.2: the effector of the robot followed a specific target in the virtual environment. The movements of the target were trajectories between a neutral position P n , the cubes positions P c1 ...P c8 and an interaction position P i from which the cubes were exchanged with the user (see Figure 3). The movements were divided in two steps: P n → P c → P i (taking a cube and waiting for the user to grab it), and P i → P n (coming back to the neutral position).

To give some challenge to the collaboration task, the placement of the cubes on the table was randomised, so as the order in which they were taken by the robot. The task was considered done when all the cubes were put in the storage areas.

Robots Conditions

Different robots were used to perform the collaboration task (see Figure 4). We chose industrial robots whose appearances differed in

Movements Conditions

We wanted each robot to move with different movements profiles: machinelike [M1] and humanlike [M2]. Usually, humanlike movements are expected to have different trajectories, different speed profiles, but also more variability when repeating actions and reaching positions. It seemed interesting to study the effect of humanlike movements on the acceptability of the collaboration task.

Since each robot was controlled thanks to inverse kinematics (IK) algorithms, M1 and M2 movements were generated by giving different profiles to the IK target's movements. The M1 movements were straight lines at constant speed between the specified positions. To generate the M2 movements, we recorded the hand trajectories and speed of a real user performing the specific movements in a virtual environment: the user was placed on the robot side of the table and performed a pointing task between the specified positions. For this recording phase, P n and P i were represented as virtual spheres in the environment: the sphere for P n was 5cm wide, while the sphere for P i was 20cm wide to give the movements some variability in the reaching position. A complete set of 16 movements was recorded (2 steps for each cube) and could be replayed at any moment in the virtual environment (see Section 4.1.4 for more details on the implementation). These movements were applied to the inverse kinematics targets so that the robots could follow them in real time. The speed of M1 movements were adapted to match the average speed of M2 movements.

Since robot R3 had two arms, slightly different movements were generated for this model. The same collaboration steps than for the other robots were used, except that the cubes on the right side of the table were taken by the right arm, while the cubes on the left side were taken by the left arm. In order to prevent the arms from colliding with each other, a slight offset was given to the positions of P n and P i : 5cm on the right and on the left, for each arm respectively. A different set of M2 movements was also recorded for this robot, taking the offset positions of P n and P i into account.

The main challenge when recording the M2 movements was to reduce the transition effects between each step: since each movement was recorded separately, the transitions between them could occur in a non-smooth manner during playback. This was overcome by always coming back to the same neutral position P n and by recording the same step several times and choosing the best.

Use Case Implementation

This use case was implemented thanks to 3DVIA Virtools software 2 . The virtual environment was rendered on a back-projected wall (3.1m × 1.7m), with active stereoscopy. We used infrared ART 3 cameras for motion capture: both the head and the dominant hand of the user were tracked in real time thanks to passive targets. The motion capture data were sent to the Virtools software through VRPN 4 . Specific implementations were performed inside the Virtools software: virtual robots' control through inverse kinematics, movements recording and movements playback (the VRPN stream was recorded/replayed thanks to VRPN logging and playback functionalities). Figure 5 shows the entire settings of this use case.

User Study Design

The aim of our work was to study the influence of robot appearance and robot movements on the acceptability of the collaboration task, from the users' point of view. First, we wanted to know what was the impact of robot appearance between R1, R2 and R3. Secondly, we wanted to know if the users perceived a difference between M1 and M2, if this difference was the same for each robot and in which way it influenced acceptability.

In order to compare each condition, we performed a user study on the collaboration task. The independent variables were robot appearance (R1, R2, R3) and robot movements (M1, M2). A withinsubject design was chosen: each subject tested the 6 conditions. For each condition, the collaboration task was repeated three times.

The different steps of our user study were the following (see Table 1 for an example). For each subject, the test began with a training phase with robot R0 and movement M1 to let the user familiarise with the collaboration task. The test was then divided in three steps corresponding to each robot condition: for each step, the user was shown a specific robot and had to complete the collaboration task with both movements conditions. The order of robots conditions was randomised, and the order of movements conditions was randomised for each robot as well. At the end of each step, the user was asked to fill out a questionnaire [Q M ] to assess the perceived differences between both movements. Finally, at the end of the whole test, the user was asked to fill out an additional questionnaire [Q R ] to assess the perceived differences between the robots' appearances.

This design was chosen to enable the users to compare directly the movements conditions for a specific robot: since the differences between M1 and M2 could be subtle, it was better to group those conditions next to each other and to ask the Q M questions directly after the robot condition, in order to help user memory. The Q R questions were asked at the end of the test once the user had seen each robot.

User Study Measures

Questionnaires

Two questionnaires were used: one to compare the two movements types for a given robot (Q M , see Table 2), one to compare the robots' appearances (Q R , see Table 3). For both questionnaires, we used five questions for which the users had to rank each condition on a 6-point Likert scale. The questions with anthropomorphism, competence, relaxation, safety and impression.

In order to simplify the questionnaire process during the user study, the questions were displayed on the screen (one by one) and the user had to give his answers verbally to the coordinators.

Physiological Measures

To strengthen the questionnaires results, our methodology focused on estimating human affective state by measuring heart rate and skin conductance. We used a physiological monitoring system from Biopac Systems 5 with a Bionomadix PPG (Photoplethysmogram) and EDA (Electrodermal Activity) amplifier. PPG signal provides information on the subject's heart rate, while EDA signal measures the skin conductance level (SCL). Those signals were measured on the fingertips of the non-dominant hand of the users (keeping the dominant hand available for interaction). The system was wireless: a small transmitter was placed on the user's forearm and sent the data to a receiver (connected to a computer through ethernet) for storage and later analysis.

PPG and EDA signals were sampled at 250Hz, and were recorded and analysed thanks to AcqKnowledge software (from Biopac Systems). Skin conductance responses (SCR) were detected thanks to this software: they were peaks in SCL with a maximum duration of 5s and a minimum amplitude of 0.02µS. Events (condition start, task start and stop) were marked by the experimentators in real time, with a key press, and stored with signal curves. Those events markers simplified the offline segmentation of the signals.

For each condition, the physiological criteria we chose to measure were: the average heart rate (HR), the average skin conductance level (SCL), the frequency of skin conductance responses (SCR). Those criteria were computed for each task of the test. To allow comparison between all the users, those criteria were normalised (between 0 and 1) according to the subject's corresponding minimum and maximum values over all the tasks of the test. For a specific condition, the average over the three corresponding tasks was taken as the final value for each criterion.

USER STUDY RESULTS

A total of 20 subjects participated in the user study. The average age of the participants was 26. For each subject, the test duration 5 http://www.biopac.com/ was approximately 45 minutes, including the questionnaires. We first present the results and analysis of the questionnaires. Then, we describe the correlation of those results with the physiological measures.

Questionnaires

Robot Appearance

The Q R questions on robot appearance were asked at the end of the test, once the subject had completed the collaboration task with each robot. The robots' appearances were scored on 6-point Likert scales, on the following criteria: anthropomorphism, competence, relaxation, safety and impression. Kruskal-Wallis (KW) tests were performed to evaluate if robot appearance was a significant factor for each criterion, and single Mann-Whitney (MW) tests were used for condition pairs analysis. The values mentioned in the following results are the average over all the users.

The main difference to be seen between the robots' appearances was the anthropomorphism dimension (see Figure 6). With its two arms, robot R3 was perceived as the most humanlike (4.8). Robot R2 was more perceived like an animal (3.8), while robot R1 was definitely seen as an industrial robot (2). A KW test confirmed that robot appearance was indeed a significant factor for anthropomorphism (KW (2) = 29.7, p < 10 -6 ) and MW tests showed that the difference was significant for each condition pair.

For the relaxation, safety and impression dimensions, robot R1 always got the lowest answers (less than 3.5), while robots R2 and R3 got similar results (more than 4.5 for each criterion). A KW test confirmed a significant influence of robot appearance on those criteria (KW (2) = 9.4, p = 0.01; KW (2) = 11.6, p = 0.003; KW (2) = 16.7, p < 10 -3 ; respectively). MW tests showed this influence was mainly due to the low scores of robot R1 but that there was no big difference between robots R2 and R3. However, it can be noted that robot R2 got slightly better results than robot R3 on those criteria (see Figure 6).

For the competence dimension, each robot was scored globally the same (between 4.1 and 4.7). No significant difference was shown by a KW test (KW (2) = 4, p = 0.14). On the whole, the results of the Q R questionnaire showed that robot R1 was the least appreciated by the users. According to the users' comments, its tough structure did not inspire trust or safety compared to the other robots. Robots R2 and R3 were globally rated similarly. It is to be noted that even if robot R3 was perceived as the most humanlike (with its two arms), this was not necessarily a good point for the other criteria: working with a humanoid robot on the collaboration task was often perturbing, and the relevance to use two arms for this task was often questionned. In matters of relaxation, safety or global impression, robot R2 was often preferred to robot R3 because it was better adapted to the task. Therefore,

Step

Training

Step 1

Step 2

Step 3 increased anthropomorphism does not necessarily imply a better acceptability.

Condition R0M1 R3M1 R3M2 Q M R1M2 R1M1 Q M R2M2 R2M1 Q M Q R Repetitions 1 3 3 3 3 3 3

Robot Movements

The Q M questions on robot movements were asked once the users had completed the collaboration task with both movements conditions for a specific robot. The users were asked to focus on the robot's movements and to answer the questionnaire according to the difference(s) they might have perceived. For analysis and comparison between each robot, we subtracted the scores of M1 movements (straight uniform) to the scores of M2 movements (human motion capture). For each criterion (anthropomorphism, competence, relaxation, safety and impression), each robot was therefore given a score ∆ (negative or positive) to assess the difference in movements perception. As for the questionnaire on robot appearance, KW and MW tests were performed to analyse the results. First, on the average of all the users, the ∆ scores for anthropomorphism were positive for each robot, meaning that M2 movements were consistently perceived as more humanlike than M1 movements. However, the amplitude of ∆ was not the same for each robot (1.4 for R1, 0.45 for R2 and 0.2 for R3): the difference was perceived more strongly for robot R1 than for the others (see Figure 7). The physical appearance of robot R1 probably made the difference between M1 and M2 more obvious than for the other robots, whose appearance was more anthropomorphic. A KW test showed indeed a significant influence of robot appearance on movements perception for anthropomorphism (KW (2) = 4.5, p = 0.1).

A second interesting point was about the global impression dimension, for which a significant impact was found (KW (2) = 5.9, p = 0.05). On the whole, the more the robot was anthropomorphic, the less the M2 movements were appreciated (see Figure 7). Actually, M2 movements were preferred to M1 movements only in the case of robot R1 (∆ = 0.35), while robots R2 and R3 were preferred with M1 movements (∆ = -0.1 and -0.75, respectively). Since robot R1 was perceived as an industrial robot, adding humanlike movements to its behavior was appreciated, whereas it was perturbing with robots R2 and R3, whose appearance was already perceived as humanlike.

No significant difference was shown for the other criteria. However, it can still be noted that, on the average of all the users, M1 movements were perceived as more safe and more competent than M2 movements (the ∆ scores for safety and competence were negative; see Figure 7). This means that, in terms of safety and competence, more mechanical movements were better accepted than more natural ones.

Global Analysis of the Questionnaires

The results of the questionnaires showed three interesting points. The first point is on robot appearance. A difference in anthropomorphism was indeed perceived between each robot, robot R1 being the most industrial and robot R3 the most humanlike. However, robots R2 and R3 were appreciated globally on the same level, meaning that a more anthropomorphic robot is not necessarily better accepted. This may be explained by two reasons: first, robot appearance has to match its function (an industrial task in our case), as shown by Goetz et al. [START_REF] Goetz | Matching robot appearance and behavior to tasks to improve human-robot cooperation[END_REF]; secondly, a too anthropomorphic robot may fall into the uncanny valley [START_REF] Mori | The uncanny valley[END_REF], as it was sometimes the case with robot R3.

The second point is on the perception of robot movements: our study showed that the appreciation of robot movements depended on the robot's appearance. Indeed, an industrial robot (like R1) may tend to highlight the differences between M1 and M2 movements, while more anthropomorphic robots (like R2 and R3) may gather the attention of the users more on their appearance and less on their movements, thus perceiving less difference between M1 and M2.

Finally, the third point is about the relevance to use humanlike movements on robots for an industrial task. Humanlike movements were better accepted in the case of robot R1 but not for more anthropomorphic robots like R2 and R3. This result shows that there could be a trade-off to establish between appearance and humanlike movements. Two main reasons may account for this fact. First, adding humanlike movements to an already anthropomorphic robot reinforced the uncanny valley effect: especially with robot R3, some users were perturbed and did not know how to consider this robot -as a human or as an industrial robot. Secondly, too much anthropomorphism increased the impression that the robots were not efficient enough: for the collaboration task, the users often preferred M1 movements since they could predict the robot's actions and adapt to the robot's behavior. They were more focused and felt more efficient.

The non-relevance to use humanlike movements (at least with robots R2 and R3) for a better acceptability may seem contradictory with other studies which showed the opposite trend [START_REF] Kupferberg | Biological movement increases acceptance of humanoid robots as human partners in motor interaction[END_REF]. However, the main difference here is about the context of the study: in our work, we focused on an interaction scenario where the users had an active role, whereas the other studies used passive scenarios where the users only observed robot movements without interaction. Therefore, the use case context has a strong impact on the results of acceptability.

Physiological Measures

We analysed the physiological measures in correlation with the results of the questionnaires. On the whole, a total of three criteria, normalised between 0 and 1, were used for each condition: HR, SCL, frequency of SCR. We performed 2-way ANOVAs (analysis of variance) to detect any significant effect of the robots and movements conditions for the different criteria. First, a slight effect of the movements conditions could be shown for heart rate (F(17, 1) = 2.75, p = 0.11; 2 subjects were not taken into the analysis for improper heart rate signal). As can be seen in Figure 8, the average heart rate was always lower for M2 movements with each robot condition. This could mean that the subjects focused more on the task when dealing with more mechanical movements (M1): this correlates with the questionnaires results which showed that M1 movements were perceived as more competent than M2 movements. This difference in heart rate activity between M1 and M2 conditions could also mean that the subjects were more relaxed with M2 movements; this is however not correlated by the questionnaires results. A second slight effect was shown between robots conditions for SCL and SCR frequency. Figure 9 shows that SCL was generally higher for robot R1 than for the other robots. This can be explained by the more industrial appearance of robot R1: the subjects were more impressed by this robot than by the others. However, the SCR frequency was higher for robots R2 and R3 than for robot R1 (see Figure 9). This should not be necessarily correlated with a higher level of stress, but rather to a specific reaction to the robots' movements: when moving, robots R2 and R3 induced more responses because of their anthropomorphic appearance. It is also to be noted that the difference in SCR between M1 and M2 for each robot followed the same pattern than the Q M questionnaire results for impression: there were more SCRs for M2 with robot R1, which was the preferred movements condition for this robot, whereas the opposite trend was seen for robots R2 and R3 (more SCRs for M1 which was the preferred condition). On the whole, some interesting results were found with physiological measures that correlate with the questionnaires results. We are conscious that those results are still subtle and that we need more knowledge about how to analyse them correctly. The main challenge of our approach was that we did not use an event-related study (analysing SCR according to specific events in the environment), but rather a study on continuous conditions. However, those first results showed that this approach seems promising.

CONCLUSION AND FUTURE WORK

The topic of our work was human-robot collaboration. We pointed out that, in the literature, the main focus was put on the physical safety of users in the environment of robots, but that less importance was given to the acceptability of collaboration between humans and robots. We were especially interested to study how people reacted to robots during a collaboration task. The need to use virtual reality in this context was relevant since several parameters had to be tested and such a study would require heavy setups with real robots and robot-specific developments. Our aim was to make users collaborate with virtual robots under different conditions and to gather their impressions.

The first step of our work was to develop and use suitable tools to set up our methodology. We first focused on the simulation environment, with the development of inverse kinematics algorithms, inspired from the literature, which enabled us to control different kinds of virtual robotic arms in a practical way. We also chose the relevant criteria to evaluate acceptability in an objective way for our use cases: using questionnaires and estimating human affective state through heart rate and skin conductance measures.

A simple use case was implemented in which users had to collaborate with virtual robots. The conditions we wanted to compare were robot appearance (three different robots) and robot move-ments (mechanical movements and movements generated from motion capture). A user study was performed to gather the users' impressions and to evaluate the acceptability of each condition.

The results of this preliminary use case showed that movements perception depended on robot appearance: an industrial robot tended to highlight the differences between mechanical and humanlike movements, whereas anthropomorphic robots gathered the attention on their own appearance. Moreover, a too anthropomorphic robot was not necessarily better accepted: humanlike movements were preferred in the case of industrial robots but not in the case of an anthropomorphic robot. This implies that a trade-off probably has to be established between appearance and humanlike movements. This trend could be due to two main reasons. First, the uncanny valley effect tended to appear when already anthropomorphic robots moved with natural movements. Secondly, too much anthropomorphism increased the impression that the robots were not efficient enough in the collaboration task. Those results were obtained in an industrial context; they would probably be different in another context, such as in service robotics.

This preliminary study was an attempt to assess the acceptability of human-robot collaboration with a simple use case. We used virtual reality as a simulation environment to implement a collaboration task and study different parameters, and questionnaires and physiological measures to estimate the users' impressions and acceptability of human-robot collaboration. We showed that this methodology was relevant to study human-robot collaboration, even if we still lack knowledge about the analysis of physiological measures. In the future, we intend to apply this methodology to more tangible scenarios, directly inspired from assembly lines in the industry, both in virtual and real environments. Those scenarios will be based on more advanced collaboration and will aim at studying alternative parameters, such as robot adaptive speed and robot safety distance, for which the use of physiological measures may be better suited. We believe that the methodology we proposed will be able to provide relevant results on those use cases.

Figure 1 :

 1 Figure 1: Left: An example of a virtual robotic arm (the 3D frames are in white color); Right: its representation as a tree structure.

Figure 2 :

 2 Figure 2: Robot control in a virtual environment using inverse kinematics and motion capture.

Figure 3 :

 3 Figure 3: The collaboration task and the robot collaboration steps.

Figure 4 :

 4 Figure 4: The robot models used for the collaboration task.

Figure 5 :

 5 Figure 5: The set up of the use case in a virtual environment.

Figure 6 :

 6 Figure 6: The average scores of each robot for the appearance questionnaire.

Figure 7 :

 7 Figure 7: The average difference between M1 and M2 for each criterion, for each robot.

Figure 8 :

 8 Figure 8: The average normalised heart rate for each condition.

Figure 9 :

 9 Figure 9: The average normalised SCL and SCR frequency.

Table 1 :

 1 An example of the different steps of the user study.

	Questions	Propositions	Answers M1 M2
	The movements seemed rather... Machinelike 1 -6 Humanlike
	The movements seemed rather... Incompetent 1 -6 Competent
	Did you feel rather...	Anxious 1 -6 Relaxed
	Did you feel rather...	Unsafe 1 -6 Safe
	What is your global impression	Dislike 1 -6 Like

Table 2 :

 2 The Q M questionnaire to grade and compare the different movements for a specific robot.

Table 3 :

 3 The Q R questionnaire to grade and compare the different robots' appearances.

http://www.acm.org/jgt/papers/BussKim05

http://www.3ds.com/products/3dvia/

3dvia-virtools/ 3 http://www.ar-tracking.com/home/ 4 http://www.cs.unc.edu/Research/vrpn/

ACKNOWLEDGEMENTS

The authors would like to thank the subjects that participated in the user study. This research benefited from the support of the Chair 'PSA Peugeot Citroën -Robotics and Virtual Reality' led by MINES ParisTech, and supported by PEUGEOT S.A.. The partners of the Chair cannot be held accountable for the content of this paper, which engages the authors' responsibility only.