Francesco Chinello
email: chinello@btech.au.dk

Claudio Pacchierotti
email: claudio.pacchierotti@irisa.fr.

Monica Malvezzi
email: malvezzi@diism.unisi.it.

Domenico Prattichizzo
email: prattichizzo@diism.unisi.it.

A Three Revolute-Revolute-Spherical wearable fingertip cutaneous device for stiffness rendering

Keywords: Haptic interfaces, wearable haptics, cutaneous devices, fingertip devices, softness rendering ✦

We present a novel three Revolute-Revolute-Spherical (3RRS) wearable fingertip device for the rendering of stiffness information. It is composed of a static upper body and a mobile end-effector. The upper body is located on the nail side of the finger, supporting three small servo motors, and the mobile end-effector is in contact with the finger pulp. The two parts are connected by three articulated legs, actuated by the motors. The end-effector can move toward the user's fingertip and rotate it to simulate contacts with arbitrarily-oriented surfaces. Moreover, a vibrotactile motor placed below the end-effector conveys vibrations to the fingertip. The proposed device weights 25 g for 35×50×48 mm dimensions. To test the effectiveness of our wearable haptic device and its level of wearability, we carried out two experiments, enrolling thirty human subjects in total. The first experiment tested the capability of our device in differentiating stiffness information, while the second one focused on evaluating its applicability in an immersive virtual reality scenario. Results showed the effectiveness of the proposed wearable solution, with a JND for stiffness of 208.5 ± 17.2 N/m. Moreover, all subjects preferred the virtual interaction experience when provided with wearable cutaneous feedback, even if results also showed that subjects found our device still a bit difficult to use.

INTRODUCTION

W EARABLE haptics is recently gaining great attention in the haptics and robotics fields. The demand for lightweight, compact, and unobtrusive wearable interfaces challenges researchers to pursue innovative solutions to make existing technologies more portable and wearable. Commercially-available wearable devices, such as the Apple Watch, the Motorola Moto 360, and the Microsoft Band, already provide simple vibrotactile haptic feedback to the wearer. For example, the Apple Watch embeds a linear actuator that can make the watch vibrate. It is used whenever the wearer receives an alert or notification, or to communicate with other Apple Watch owners. There are also applications being specifically developed to exploit the haptic capabilities of these devices. For example, the application "Feel The Wear", available in the Google PlayStore, enables the user to create custom vibration patterns by simply tapping the screen; and the application "Touch Room", available in the Apple's AppStore, enables two users that are far away to feel each other's touch through the screen of the device.

However, although quite interesting and promising, the haptic stimuli provided by these devices are still limited to vibrations, reducing the possibility of simulating rich contact sensations. Toward more compelling interactions, researchers have recently focused on wearable fingertip devices providing tactile stimuli through moving tactors, which are able to translate, rotate, and orient to simulate haptic interaction with different surfaces. Frisoli et al. [START_REF] Frisoli | A fingertip haptic display for improving curvature discrimination[END_REF] presented already in 2008 a fingertip haptic display for improving curvature discrimination using a moving platform. The device is designed to bring a plate into contact with the fingertip at different orientations, defined by the normal to the virtual surface at the point of contact. The system is composed of a parallel platform, actuating a translation stage for positioning the plate relatively to the fingerpad, and of a serial wrist, in charge of adjusting its orientation. The device is actuated via sheathed tendons. A more portable and improved design solution of the same concept has been later developed in [START_REF] Solazzi | Design of a cutaneous fingertip display for improving haptic exploration of virtual objects[END_REF], [START_REF]Design of a novel finger haptic interface for contact and orientation display[END_REF]. A voice-coil actuator was introduced for simulating fast contact transition, and the overall system mobility was reduced to 3-degrees-of-freedom (3-DoF): two degrees of freedom for the orientation and one linear degree of freedom to control the contact force at the fingertip. Gabardi et al. [START_REF] Gabardi | A new wearable fingertip haptic interface for the rendering of virtual shapes and surface features[END_REF] further improved the above design by replacing sheathed tendons actuation with DC motors mounted directly on the joints. Moreover, they increased the portability and wearability of the system by reducing the overall weight and dimensions. The total weight of this device is now only 30 g for 66 × 35 × 38 mm dimensions.

Similarly, Prattichizzo et al. [START_REF] Prattichizzo | Towards wearability in fingertip haptics: a 3-dof wearable device for cutaneous force feedback[END_REF] presented a wearable 3degrees-of-freedom (3-DoF) cutaneous device for the fingertip. It consists of two platforms: one is located on the back of the finger, supporting three small DC motors, and the other one is in contact with the volar surface of the fingertip. The motors shorten and lengthen three cables to move the platform toward the user's fingertip and re-angle it to simulate contacts with arbitrarily oriented surfaces. Tsetserukou et al. [START_REF] Tsetserukou | Linktouch: A wearable haptic device with five-bar linkage mechanism for presentation of twodof force feedback at the fingerpad[END_REF] developed a 2-DoF wearable fingertip cutaneous device. It is composed of two DC motors driving a five-bar linkage mechanism mounted at the sides of the fingertip. Similarly to [START_REF] Minamizawa | Gravity grabber: wearable haptic display to present virtual mass sensation[END_REF], when motors rotate in the same direction the linkage slides tangentially on the finger pad. On the other hand, when motors rotate in the same direction, the linkage moves towards or away from the fingertip. More recently, Leonardis et al. [START_REF] Leonardis | A wearable fingertip haptic device with 3 dof asymmetric 3-RSR kinematics[END_REF] presented a 3RSR wearable skin stretch cutaneous device for the fingertip. An asymmetrical 3RSR configuration allowed compact dimensions with minimum encumbrance of the hand workspace and minimum inter-finger interference. Girard et al. [START_REF] Girard | Haptip: Displaying haptic shear forces at the fingertips for multi-finger interaction in virtual environments[END_REF] developed a wearable haptic device able to simulate 2-DoF shear forces at the fingertip. It is composed of a parallelogram structure actuated by two DC motors able to move a peg responsible for the shear feedback. It weights only 22 g for a total dimension of 20×34×35 mm.

The above mentioned devices have been used for the rendering of shapes, forces, and compliance. In the last couple of years, the rendering of softness/compliance have became a popular topic in haptics research. Softness represents indeed one of the most fundamental haptic properties [START_REF] Tiest | Cues for haptic perception of compliance[END_REF], and it plays a crucial role for task accomplishment in many scenarios and applications. For example, De Rossi [START_REF] Rossi | Wearable kinesthetic systems and emerging technologies in actuation for upperlimb neurorehabilitation[END_REF] integrated electroactive polymeric materials into wearable garments to endow them with sensing and actuation properties, for applications in post-stroke rehabilitation.

Mueller [START_REF] Mueller | Hug over a distance[END_REF] proposed an air-inflatable vest that can be remotely triggered to create a sensation of being hugged. Bau et al. [START_REF] Bau | Bubblewrap: a textile-based electromagnetic haptic display[END_REF] developed a matrix of electromagnetic actuators enclosed in fabric, able to expand and shrink. Sahoo et al. [START_REF] Sahoo | Tablehop: An actuated fabric display using transparent electrodes[END_REF] presented a tabletop display providing controlled self-actuated deformation to an elastic fabric surface. The surface is composed of a highly-stretchable pure spandex fabric, which is electrostatically actuated by nine electrodes. More recently, Bianchi et al. [START_REF] Bianchi | A fabric-based approach for wearable haptics[END_REF], [START_REF] Bianchi | A wearable fabric-based display for haptic multi-cue delivery[END_REF] proposed a wearable softness display for the fingertip. It controls the stretching state of a fabric to reproduce different stiffness levels, and it can convey, at the same time, softness information, tangential cues, and enable both passive and active haptic exploration. It weights 100 g for 100×60×36 mm dimensions. The same group also applied a similar fabric-based rendering principle at the forearm [START_REF] Bianchi | Design and preliminary affective characterization of a novel fabric-based tactile display[END_REF] and arm [START_REF] Casini | Design and realization of the cuff-clenching upper-limb force feedback wearable device for distributed mechano-tactile stimulation of normal and tangential skin forces[END_REF].

A more extensive review of the literature on wearable cutaneous devices for the fingertip can be found in [START_REF] Pacchierotti | Cutaneous haptic feedback in robotic teleoperation[END_REF], [START_REF] Pacchierotti | Wearable haptic systems for the fingertip and the hand: taxonomy, review, and perspectives[END_REF].

This paper presents a the application of a 3RRS wearable fingertip device (see Fig. 1) to render the softness of a surface. It is composed of a static upper body and a mobile end-effector: the upper body is located on the nail side of the finger, supporting three small servo motors, and the mobile end-effector is in contact with the finger pulp. The two parts are connected by three articulated legs, actuated by the motors. The end-effector can move toward the user's fingertip and rotate it to simulate contacts with arbitrarily-oriented surfaces. Moreover, a vibrotactile motor placed below the end-effector conveys vibrations to the fingertip. The device was preliminarily introduced in [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF], [START_REF] Chinello | A novel 3rrs wearable fingertip cutaneous device for virtual interaction[END_REF]. However, these two works mainly focused on its mechatronic design, mechanical analysis and design, and position control system. In this paper, we will show how the device can be used to render the softness of a surface and, in particular, we will focus on its stiffness control system.

The paper is organized as follows. Section 2 introduces the device and summarizes its main features, and in particular some details on the device mechanical model and on the evaluation of the Jacobian matrix, necessary to evaluate the equivalent stiffness matrix in the actuated joint space. Section 4 describes the main outcomes of device kinematics model and proposes a position control system in which the stiffness can be regulated to render the compliance of a virtual surface. Section 5 shows some experiments in which the proposed control scheme is exploited. Finally, Sec. 6 discusses the obtained results.

DEVICE DESCRIPTION

As previously introduced, the wearable fingertip device proposed in this paper has a 3-DoF parallel structure, in which each leg connecting the end-effector to the upper body is composed of two rigid links constrained to each other, the body, and the endeffector, according to a RRS (Revolute-Revolute-Spherical) kinematic chain (see Fig. 2a and2b). Specifically, three spherical (S) joints connect the distal links of the legs to the end-effector, one revolute (R) joint connects the distal and proximal links of each leg, and another revolute (R) joint connects the proximal link of each leg to the body. The three revolute joints between the proximal links and the body are actuated by the servo motors. In each leg, the axes of the two revolute joints are parallel, so that it constitutes a 2-DoF planar articulated mechanism, constraining the motion of the center of each spherical joint on a plane fixed w.r.t. the body. The mobile end-effector has therefore 3-DoF w.r.t.

Control System Atmega328

Operating Voltage range 4.8 to 6.0 V Operating Joints Speed 0.2 s/60 With respect to the cable-driven fingertip devices presented in [START_REF] Prattichizzo | Towards wearability in fingertip haptics: a 3-dof wearable device for cutaneous force feedback[END_REF], [START_REF] Pacchierotti | Cutaneous haptic feedback to ensure the stability of robotic teleoperation systems[END_REF], [START_REF] Pacchierotti | Cutaneous feedback of fingertip deformation and vibration for palpation in robotic surgery[END_REF], this device solves the indeterminacy due to the underactuation of the platform. In fact, the platform is moved through three articulated legs, constraining its motion in a threedimensional subspace [START_REF] Merlet | Parallel robots[END_REF]. This mechanical structure decouples position and force control problems, simplifying the control structure with respect to the solution proposed in [START_REF] Prattichizzo | Towards wearability in fingertip haptics: a 3-dof wearable device for cutaneous force feedback[END_REF]. The fingertip device is wired to an arm band on the upper arm, that hosts a Raspberry Pi Model B, an Arduino Nano, and two 2 Ah batteries. The arm band is in charge of providing the required power to the device and to manage the wireless communication between the device and an external computer.

For our prototype, shown in Fig. 2a and 1b, we used three HS-5035HD servomotors by Hi-Tech Motors and one 304-101 vibration motor by Precision Microdrives. The stall torques provided by each servomotor allow us to reach a maximum force of 4.7 N at the end-effector. The overall performance and operative parameters of our device are summarized in Table 1.

DEVICE ANALYSIS

In this section, we summarise some details on the device mechanical model, in particular on the evaluation of the Jacobian matrix and of the equivalent stiffness matrix, necessary to simulate the contact with surfaces of different compliance values. Further details on the device mechanical analysis, including some numerical simulations, and manipulability evaluation, are available in [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF]. In this section, we summarise the main elements of the device mechanical model, necessary to develop the stiffness control system we adopted in the remaining of the paper. A complete analysis of the device kinematics and dynamics is out of the scope of this work; however, we have reported some necessary details in the following, regarding, in particular, the evaluation of the complete Jacobian matrix.

The meaning of the main symbols adopted in this section, representing device geometrical properties, are shown in Fig. 2b. Coherently with the model presented in [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF], let us indicate with B i , i = {1, 2, 3} the centers of the spherical joints on the mobile platform. They define a plane on which we fix the origin O 1 of the frame S 1 = O 1 , x 1 , y 1 , z 1 . Let us then indicate with u i the unit vectors identifying, for each leg, the direction of the revolute joint axes, and with A i and D i , the points indicating the joints connecting each leg to the upper body, and to the middle joint, respectively. On the upper body, we also define a reference frame

S 0 = O 0 , x, y, z .
The mobile platform will move w.r.t. the upper body according to the rotations imposed by the actuators to the joints passing through A i and according to the kinematic constraints imposed by the mechanical structure. In particular, since the axes of the revolute joints of each leg are parallel, each B i and D i points move on the respective plane, that we indicate with π i . The overall six dimensional motion of the platform is the composition of a translational and rotational motion, that can be represented by a three dimensional vector p = [p x , p y , p z ] T , containing the coordinates of O 1 w.r.t. S 0 , and another three dimensional vector ϕ = [ψ, θ , φ ] T , containing the roll (ψ), pitch (θ ) and yaw (φ ) angles that describe the relative orientation between frames S 1 and S 0 . From this, we can define a vector ζ = [p T , ϕ T ] T collecting all the six parameters necessary to define position and orientation of the mobile platform with respect to the upper body.

Inverse kinematics

As previously introduced, each leg connecting the mobile part of the device with the part fixed on the finger, is composed of two links connected to form a RRS (revolute-revolute-spherical) kinematic chain. The mechanism that constitutes the device is therefore 3-DoF, and we can choose three variables to describe its configuration. Since the device has been designed to render the shape and stiffness of virtual and remote objects, a convenient choice for the independent variables includes the displacement in the z direction, p z , and the roll (ψ) and pitch (θ ) angles. Let us collect those variables in the vector ξ = [p z , ψ, θ ] T . Recalling the rotation matrix expression as a function of the roll/pitch/yaw (RPY) angles, the geometrical dimensions of the device, and the constraints imposed by the legs, we can evaluate the other configuration variables, i.e., yaw angle φ , and p x and p y components of O 1 coordinates, as

φ = arctan (b -b h ) sin θ sin ψ b h (cos θ + cos ψ) , (1)
p x = b h (cos φ cos θ -sin φ sin θ sin ψ -cos φ cos ψ) , (2)
p y = -b sin φ cos θ , (3)
where b and b h are the geometrical parameters of the mobile platform, as shown in Fig. 2a.

When controlling the platform, according to the interaction between the fingertip and the environment, we set a reference value for the device platform configuration, ξ d . Using the relationships in eqs. ( 1), ( 2) and (3), we can then evaluate the overall platform configuration corresponding to the desired values of the independent parameters, i.e.,

ζ d = [p T d , ϕ T d ] T .
Through the inverse kinematics, we can then evaluate the corresponding reference values for the actuator rotation angles, collected in the vector q d = [q 1,d , q 2,d , q 3,d ] T . For this type of parallel manipulator, the solution of the inverse kinematics problem is straightforward, differently from the direct kinematics one, that, in general, admits multiple solutions.

The coordinates of each

B i point, i = {1, 2, 3}, w.r.t. S 0 , collected in the three dimensional vectors b i = [b i,x , b i,y , b i,z ] T , can be evaluated as b i = p + Rb 1 i , (4)
where b 1 i represents the vectors containing the coordinates of B i points w.r.t. the reference frame S 1 , defined on the mobile platform. Since B i points move on three fixed planes π i (see Fig. 2b), the following constraint equations hold

b 1,y = 0, b 2,x = 2b h b d b 2,y , b 3,x = - 2b h b d b 3,y . (5)
Eq. ( 5) introduces three constraints that limit the generic sixdimensional motion of the mobile platform. In particular, since three independent constraints have been introduced, the mobile platform will have three degrees of freedom.

Let us assume that the independent variables ξ = [p z , ψ, θ ] T are defined, and that we need to evaluate the corresponding rotations q = [q 1 , q 2 , q 3 ] T of the actuated revolute joints in A i . For a given ξ , it is possible to evaluate, through the constraint equations eq. ( 1), [START_REF] Solazzi | Design of a cutaneous fingertip display for improving haptic exploration of virtual objects[END_REF], and (3), the vector p and the rotation matrix R, completing the representation of the mobile platform configuration. Then, from eq. ( 4), it is possible to evaluate the coordinates of B i w.r.t. S 0 . Finally, angles q i can be evaluated by solving the triangles A i B i D i , in which three edges are known. In particular, the actuator rotation angles q i can be evaluated as

q i = α i + δ i , (6)
where angles α i and δ i are as follows

α i = arctan   s iz s 2 ix + s 2 iy   , δ i = arccos l 2 1 + s 2 i -l 2 2 2l 1 |s i | , (7)
where l 1 and l 2 are the lengths of the proximal and distal link of each leg, respectively, i.e., l 1 = |D i A i |, and l 2 = |B i D i |, and

s i = b i -a i .

Velocity analysis

We can express the velocities of the B i points, i = {1, 2, 3}, as

v B i = v + ω × (b i -p), ( 8
)
where v is the velocity of O 1 and ω is the angular velocity of the mobile platform, expressed w.r.t. the S 0 reference frame. Since the B i points move on planes perpendicular to the respective u i directions, which identify the direction of revolute joint axes, the following relationship holds

u i • v B i = 0, which leads to u T i v -u T i S(b i -p)ω = 0, (9)
where the operator S(•), applied to a generic three dimensional vector, gives the corresponding skew matrix. Eq. ( 9) constitutes an homogeneous linear system with three equations and six unknowns,

Uν = 0, (10)
where ν = [v T , ω T ] T represents the twist of the device mobile platform, and matrix U ∈ R 3×6 is defined as

U =      u T 1 -u T 1 S(b 1 -p) u T 2 -u T 2 S(b 2 -p) u T 3 -u T 3 S(b 3 -p)      . ( 11
)
The solutions of this homogeneous system represent, at a given configuration, all the possible twists that can be imposed to the platform.

Since the system has three degrees of freedom, we can express the twist of the platform as a function of three independent velocity components. Similarly to the position analysis described in Sec. 3.1, in our device we want to control the components v z (component of the velocity in the direction perpendicular to the platform), ω x (roll velocity), and ω y (pitch velocity), collected in the vector χ = [v z , ω x , ω z ] T . We collect the remaining components in the vector χ

= [v x , v y , ω z ] T . It is now clear that ν = T   χ χ   , ( 12
)
where T ∈ R 6×6 is a matrix that changes vector component order, specifically

T =              0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1              . ( 13
)
It is worth to observe that, in general, χ = ξ , and ν = ζ . The approximation χ ∼ = ξ is possible only if rotation angles ψ and θ are small. We can then rearrange the system in eq. ( 10) as

U χ χ +U χ χ = 0, (14)
with

U χ ,U χ ∈ R 3×3 . Assuming that U χ is non-singular, we can then express χ = -U -1 χ U χ χ, (15)
and, therefore, we can express the device platform twist as a function of the controlled components of the velocity,

ν = Hχ, ( 16
)
where H ∈ R 6×3 is a matrix whose components depend on platform configuration, specifically

H = T   I -U -1 χ U χ   . (17)
The velocities of B i points can also be evaluated considering the articulated mechanism of each leg, as follow

v Bi = ω i × (d i -a i ) + ω ′ i × (b i -d i ), (18)
where ω i = qi u i are the angular velocities of the links connected to the upper body, actuated by the motors, and ω ′ i are the angular velocities of the links connected to the mobile platform, that are not actuated (passive joints). The directions of both ω i and ω ′ i are parallel to u i (see Fig. 2). From eq. ( 8) and [START_REF] Casini | Design and realization of the cuff-clenching upper-limb force feedback wearable device for distributed mechano-tactile stimulation of normal and tangential skin forces[END_REF], dot multiplying both sides by (b id i ), we get

(b i -d i ) T v -(b i -d i ) T S(b i -p)ω = (b i -d i ) T S(d i -a i )ω i . (19)
Collecting the actuator angular velocity magnitudes in a vector q = [ q1 , q2 , q3 ] T , eq. ( 19) can be written in matrix form as

Eν = F q, ( 20
)
where E ∈ R 3×6 and F ∈ R 3×3 are defined as

E = (b i -d i ) T (b i -d i ) T S(b i -p) F = diag (b i -d i ) T S(d i -a i )u i , i = 1, 2, 3.
If F is invertible, recalling eq. ( 16), it is possible to evaluate the actuator velocities q as a function of the platform twist ν, i.e., q = Jν,

where J = F -1 E ∈ R 3×6 is the complete Jacobian matrix.

If we consider also the constraint in eq. ( 9), we can define the constrained Jacobian matrix J = JH = F -1 EH ∈ R 3×3 , relating the actuator angular velocities to the independent twist components, i.e., q = Jχ. [START_REF] Chinello | A novel 3rrs wearable fingertip cutaneous device for virtual interaction[END_REF] If the mechanism is not in a singular configuration, i.e., if J is full-rank, eq. ( 22) can be inverted to solve the direct differential kinematic problem, i.e. χ = J -1 q.

Statics

Let us consider now the static equilibrium of the device. We indicate with w = [ f , m] T ∈ R 6 the wrench applied to the mobile platform, where f is the resulting force applied to the mobile platform and m is the resulting moment evaluated w.r.t. O 1 . This wrench represents the resultant of the interaction between the platform and the fingertip, dependent on the fingertip skin deformation. The skin deformation and the stress distribution are related by an impedance relationship that is non-linear and dependent on several parameters [START_REF] Provancher | Contact location display for haptic perception of curvature and object motion[END_REF], [START_REF] Wang | In vivo biomechanics of the fingerpad skin under local tangential traction[END_REF], [START_REF] Adams | Finger pad friction and its role in grip and touch[END_REF], [START_REF] Wiertlewski | Mechanical behavior of the fingertip in the range of frequencies and displacements relevant to touch[END_REF].

Let us indicate with τ = [τ 1 , τ 2 , τ 3 ] T the torques applied by the actuators to the links connected to the upper body.

Considering a virtual displacement of the mobile platform, δ ζ , generated by a small variation of actuator joint angles, δ q, according to the Principle of Virtual Works, the following relationship can be written

δ ζ T w = δ q T τ. ( 23
)
The components of δ ζ are not independent, since the device has 3-DoF. Recalling the constraint relationships in eq. ( 16) and eq. ( 22), we get

δ χ T H T w = δ χ T J T τ. (24)
Since δ χ components are independent, this relationship holds for any δ χ only if

H T w = J T τ, (25)
and, consequently, if the Jacobian matrix J is invertible, i.e., if the device is in a nonsingular configuration,

τ = J -T H T w. ( 26
)

DEVICE CONTROL

Equivalent stiffness evaluation

The objective of our stiffness control system is to simulate contact with a surface of given stiffness, represented by the matrix K d . Indicating with

K p = diag(k x , k y , k z ), K ϕ = diag(k ψ , k θ , k φ ), (27)
the desired translational stiffness and the desired rotational stiffness, respectively, the desired stiffness matrix is defined as

K d = diag(K p , K ϕ ). ( 28
)
When the platform is in a generic configuration ζ , the corresponding wrench that has to be applied to the fingertip is given by w

= K d ∆ζ , (29)
where ∆ζ = ζ -ζ 0 and ζ 0 is an initial configuration corresponding to w = 0. ∆ζ is related to a variation of the independent variables ∆ξ through the relationships in eq. ( 1), (2), and (3). For small values of ∆ζ , we can use the approximation

∆ζ = H∆ξ , (30)
ξ d

(1),( 2) and ( 3)

ζ d Inverse kinematics q d q _ K q D q
_ τ Device and finger interaction q . q J, H K d Fig. 3: Position control of the platform with adaptable contact stiffness simulation. The proportional gain matrix K d is evaluated as a function of the stiffness that has to be simulated and the platform configuration, through the Jacobian matrix J and the matrix H, relating dependent and independent components of platform configuration vector.

where H is defined in eq. ( 16). Assuming for the device actuator an impedance (stiffness) control system, the torque applied by device actuators, necessary to balance the wrench -w that the fingertip exerts on the platform, can be expressed as

τ = K q ∆q, (31)
where ∆q = qq 0 and q 0 represents the joint configuration corresponding to ζ 0 . For small values of ∆q we can use the approximation

∆q = J∆ξ . ( 32
)
where J is defined in eq. [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF]. By substituting eq. ( 29), ( 30), [START_REF] Mason | Haptic modeling of a street intersection using the novint falcon[END_REF], and (32) in eq. ( 26), we get

K q J∆ξ = J -T H T K d H∆ξ . (33)
Since this relationship holds for any ∆ξ , whose components can be set independently, the following matrix equality can be set

K q J = J -T H T K d H. ( 34
)
Finally, assuming again a non-singular configuration and that the Jacobian matrix J is invertible, we can right-multiply both sides of eq. ( 34) by J -1 . We then obtain the expression that allows to evaluate the stiffness matrix in the joint space, K q , corresponding to a given stiffness matrix in the operative space of the device platform, K d :

K q = J -T H T K d HJ -1 . (35)
It is worth to observe that K q components depend on the stiffness K d that has to be rendered, but also on the platform configuration, that affects the values of matrices J and H.

Control system description

Let us consider a Virtual Reality (VR) scenario, in which we haptically render the stiffness of different virtual surfaces, e.g., grasping and interacting with surfaces that have different mechanical properties. For the sake of clarity, let us consider only one cutaneous device. However, thanks to the wearability of our system, this framework can be easily extended to multi-contact interactions (see the multi-contact experience of Sec. 5.2). Let us also assume the availability of a hand motion capture system, able to measure the configuration (position and orientation) of the {S 0 } frame, introduced at the beginning of Sec. 3. This measure is adopted to render the position and orientation of the user's fingertip avatar in the VR environment. A contact detection algorithm is then used to recognize the interactions between the haptic-equipped fingertip and the virtual objects, i.e., the desired configuration of the device's platform ξ d with respect to {S 0 }. Let us assume K d to be the stiffness matrix of the simulated contact surface. The complete position and orientation vector ζ d is evaluated by means of eqs. ( 1), (2), and (3). Reference values for the device actuators angular positions q d can be evaluated by applying the inverse kinematic procedure detailed in Sec. 3. These reference values q d are then compared with the angles measured by the actuator encoders, q = [q 1 , q 2 , q 3 ] T , and their difference is sent to a position controller with a proportional-derivative (PD) scheme. The proportional term K q is dynamically evaluated to simulate the stiffness of the virtual surface, as a function of the desired stiffness K d and of the platform configuration, i.e., matrices H and J, according to eq. ( 35). Moreover, the derivative term D q ∈ R 3×3 is set to have a suitable damping in system dynamical behavior. In future developments of this work, also D q ∈ R 3×3 will be dynamically regulated to simulate a viscous behaviour in the interaction with the virtual environment. Finally, the torque τ generated by actuators is evaluated as

τ = K q (q d -q) + D q ( qd -q) . (36)
A simplified block diagram of the proposed stiffness control algorithm is shown in Fig. 3.

EXPERIMENTAL EVALUATION

We carried two experiments to test the effectiveness of our wearable haptic device and its level of wearability. In the first experiment we aimed at evaluating the effectiveness of our wearable haptic device in rendering stiffness information, while in the second experiment we focused on the evaluation of its immersiveness and wearability.

Experiment #1: stiffness discrimination experiment

In order to test the effectiveness of our wearable haptic device in rendering stiffness information, we carried out a stiffness discrimination experiment using the same-different procedure of TSD (theory of signal detection) [START_REF] Gescheider | Psychophysics: the fundamentals[END_REF]. This technique enables us to evaluate the differential stiffness threshold for our device. The differential threshold can be defined as "the smallest amount of stimulus change necessary to achieve some criterion level of performance in a discrimination task" [START_REF] Gescheider | Psychophysics: the fundamentals[END_REF]. It gives us information about how different two displacements provided with our device need to be in order to be perceived as different by a human user. This threshold is often referred to as just-noticeable difference or JND. The differential threshold of a perceptual stimulus reflects also the fact that people are usually more sensitive to changes in weak stimuli than they are to similar changes in stronger or more intense stimuli. The German physician Ernst Heinrich Weber proposed the simple proportional law JND = kI, suggesting that the differential threshold increases with increasing the stimulus intensity I. Constant k is thus referred to as "Weber's fraction".

Setup

The experimental setup is composed of two wearable fingertip devices attached to the end-effectors of two 3-DoF Falcon haptic interfaces (Novint Technologies, USA), as shown in Fig. 4. The Falcon interfaces are placed so that the centers of their endeffectors are at a distance of 13 cm in the nominal position, and the wearable devices are mounted to have the end-effectors of the devices facing each other. Each Falcon has a workspace of 11×12.5×13 cm and a tracking accuracy of 0.06 mm [START_REF] Mason | Haptic modeling of a street intersection using the novint falcon[END_REF]. Subjects were blindfolded and asked to wear the two wearable fingertip devices on the thumb and index finger of their right hand.

Methods

Eighteen participants (15 males, 3 females, age range 22 -37) took part to the experiment, all of whom were right-handed. Nine of them had previous experience with haptic interfaces. None of the participants reported any deficiencies in their perception abilities and they were all naïve as to the purpose of the study.

We evaluated the differential threshold for stiffness discrimination using the same-different procedure [START_REF] Gescheider | Psychophysics: the fundamentals[END_REF]. Each trial involved interacting, in succession, with two virtual spheres rendered between the two wearable devices (see Fig. 4). Subjects were asked to judge, on each trial, if the stiffness of the two virtual spheres was different or the same. The hit rate p h corresponded to the percentage of correct responses given by a subject ("yes, the spheres are different") when the two objects had different stiffness, while the false alarm rate p f corresponded to the percentage of incorrect responses ("yes, the spheres are different") when the stiffness of the two objects were the same [START_REF] Gescheider | Psychophysics: the fundamentals[END_REF]. No visual feedback on the virtual sphere was provided.

The two Falcon haptic interfaces were only used to track the position of the fingers and did not provide any external force to the user, i.e., they were programmed to provide only gravity compensation. We decided to use these grounded interfaces, instead of, e.g., a wireless motion tracking system, to enable a more precise tracking of our devices. We will focus on the evaluation of the wearability and portability of our system in the experiment of Sec. 5.2.

We evaluated the differential threshold for stiffness discrimination when employing (S) cutaneous feedback provided only by the servo motors of the wearable device (no vibrations), (V) cutaneous feedback provided only by the vibrotactile motor of the wearable device (platform not moving), (SV) cutaneous feedback provided both by the servo motors and the vibrotactile motor of the wearable device.

In condition S, the servo motors move the end-effector to render the contact with the virtual sphere, and the vibrotactile motor is not active. The interaction is designed according to the god-object model [START_REF] Zilles | A constraint-based god-object method for haptic display[END_REF], and the magnitude of the force applied at the fingertip is evaluated as

f S = k S ∆x, ( 37
)
where ∆x is the penetration of the finger inside the virtual object and k S is the simulated stiffness constant. More in detail, in this experiment the desired translational stiffness matrix K p introduced in eq. ( 27) is defined as K p = k S I 3×3 , where I 3×3 identifies the three dimensional identity matrix. The same numerical values were assumed for the sake of simplicity also for the K ϕ matrix introduced in eq. ( 27), even if its values are represented with different units. Once the desired stiffness K d matrix is set as in eq. ( 28), the equivalent K q matrix can be evaluated according to eq. ( 35).

In condition V, the vibrotactile motor provides a 100-ms vibration burst when the finger contacts the virtual sphere. The amplitude A V of the vibration is proportional to the stiffness of the virtual sphere [START_REF]4 mm vibration motor -11 mm type -operating voltage 3 V (model 304-101)[END_REF], i.e.,

A V = k S 1500 + 0.4 G, ( 38
)
where G is the acceleration from gravity. In this case, the servo motors are not active, and the mobile platform always contacts the fingertip. Providing a vibration burst of fixed duration on making/breaking contact events has been proved to improve the performance of several (tele)manipulation tasks [START_REF] Cipriani | Humans can integrate feedback of discrete events in their sensorimotor control of a robotic hand[END_REF], [START_REF] Hussain | Using the robotic sixth finger and vibrotactile feedback for grasp compensation in chronic stroke patients[END_REF], [START_REF] Pacchierotti | Steering and control of miniaturized untethered soft magnetic grippers with haptic assistance[END_REF], [START_REF] Meli | Experimental evaluation of magnified haptic feedback for robot-assisted needle insertion and palpation[END_REF]. Moreover, amplitude (and frequency) of the contact vibration has been proved to generally increase with increasing stiffness of the touched object [START_REF] Okamura | Vibration feedback models for virtual environments[END_REF]. Finally, in condition SV, cutaneous feedback is provided both by the servo motors and the vibrotactile motor, as indicated in eqs. [START_REF] Meli | Experimental evaluation of magnified haptic feedback for robot-assisted needle insertion and palpation[END_REF] and [START_REF] Okamura | Vibration feedback models for virtual environments[END_REF].

Each subject carried out three series of trials, in which the virtual sphere stiffness k S assumed two different values, k S = k a, * Each series consisted of 36 repetitions of the stiffness discrimination task, with 12 trials for each feedback condition. The entire experiment lasted approximately 35 minutes.

On each repetition of each series, two virtual spheres with random stiffness (k a, * or k b ) were rendered, i.e., the probability of interacting with a pair of objects with same (different) stiffness was 0.5. The order of presentation of the sequence of series and conditions was different for each subject, in order to minimize learning and fatigue effects.

Results

False alarm and hit rate were converted to z scores of the normal distribution [START_REF] Gescheider | Psychophysics: the fundamentals[END_REF], [START_REF] Stanislaw | Calculation of signal detection theory measures[END_REF]. The sensitivity index d ′ was then calculated as the difference

d ′ = z h -z f .
According to the criterion commonly adopted [START_REF] Frisoli | A fingertip haptic display for improving curvature discrimination[END_REF], [START_REF] Prattichizzo | Towards wearability in fingertip haptics: a 3-dof wearable device for cutaneous force feedback[END_REF], [START_REF] Gescheider | Psychophysics: the fundamentals[END_REF], the discrimination threshold can be defined as the difference between the stiffness for which d ′ = 1. The threshold was computed for each subject for each condition S, V, and SV, assuming a linear proportionality between the values of d ′ .

The overall JND was then computed as the mean of the values obtained for all the subjects. Fig. 5 shows the average JND and 95% confidence interval for each condition. The collected data of each condition passed the Shapiro-Wilk normality test and the Mauchly's test of sphericity. A repeated-measures ANOVA showed a statistically significant difference between the means of the three feedback conditions (F 2,34 = 47.153, p < 0.001, a = 0.05). Post-hoc analysis (Games-Howell post-hoc test) revealed statistically significant in S vs. V (p < 0.001) and V vs. SV (p < 0.001), while S vs. SV fell short of significance (p = 0.154). Time needed to complete the given tasks was recorded as well. No statistically significant difference was found.

In addition to the quantitative evaluation reported above, we also measured the users' experience. Immediately after the experiment, subjects were asked to report the effectiveness of each feedback condition in completing the given task using bipolar Likert-type nine-point scales. Condition S scored 6.7 out of 9, condition V scored 3.7 out of 9, and condition SV scored 7.6 out of 9. Although we registered no significant difference between conditions S and SV, subjects appreciated the capability of the vibrotactile bursts to effectively notify the making contact with the virtual surface.

Experiment #2: interaction with a virtual immersive environment

In order to test the level of wearability of our cutaneous device, we carried out a second experiment, where subjects are requested to interact with a virtual immersive environment. This experience has been inspired by the experiments carried out in [START_REF] Scheggi | Touch the virtual reality: using the leap motion controller for hand tracking and wearable tactile devices for immersive haptic rendering[END_REF], [START_REF] Meli | Wearable haptics and hand tracking via an rgb-d camera for immersive tactile experiences[END_REF]. Since here we focus on the wearability aspect of our system, we Fig. 6: Experimental setup. Subjects were asked to interact with the virtual environment while wearing two wearable cutaneous devices, one on the thumb and one on the index finger. The virtual environment is composed of a baseball (being grasped in the picture) and a teddy bear. Interaction forces in the virtual environment are provided to the user by the cutaneous device as indicated in Sec. 4. substituted the two Falcon interfaces with the unobtrusive Leap Motion tracking system. The interaction forces are still computed according to the stiffness rendering algorithm of Sec. 4.

Setup and Methods

The experimental setup is composed of a Leap Motion controller, one wearable fingertip device, and a virtual environment. The Leap Motion controller is a small USB peripheral device that uses two monochromatic IR cameras and three infrared LEDs to track the position of the fingertip in 3-D space. It observes a hemispherical area up to a distance of 1 m with an average accuracy of 0.7 mm [START_REF] Weichert | Analysis of the accuracy and robustness of the leap motion controller[END_REF]. Subjects are required to wear two fingertip devices on the thumb and index finger of their right hand, and interact with the virtual environment (see Fig. 6). The subjects hand pose is tracked using the Leap Motion controller and a virtual hand mimicked the subjects hand pose in the virtual environment. Every time the index finger comes in contact with a virtual object, the cutaneous device applies a suitable amount of force to the fingertip. Interaction forces in the virtual environment are computed using a virtual proxy approach [START_REF] Ruspini | Haptic interaction in virtual environments[END_REF] and were provided by the cutaneous device as indicated in Sec. 4. The virtual environment is composed of a baseball and a teddy bear, as shown in Fig. 6.

Twelve participants (10 males, 2 females, age range 21 -35) took part to the experiment, all of whom were right-handed. Eight of them had previous experience with haptic interfaces. None of the participants reported any deficiencies in their perception abilities and they were all naïve as to the purpose of the study.

The task consisted of interacting with the two virtual objects for 5 minutes, either wearing two wearable cutaneous devices (condition C, as in Fig. 6) or barehanded (condition N).

Results

We evaluated the immersiveness of the haptic-enabled virtual reality scenario through the Usefulness, Satisfaction, and Ease of use (USE) questionnaire [START_REF] Lund | Measuring usability with the use questionnaire12[END_REF], asking subjects to compare the experience while wearing the wearable devices vs. bare hand. Our USE questionnaire is composed of 21 Likert-type questions. It contained a set of assertions, where a score of 9 was described as "completely agree" and a score of 1 as "completely disagree" with the assertion. Questions and results are reported in Table 2. The first set of questions (QA in Table 2) considered the usefulness of having the wearable cutaneous devices (C) with respect to not having any force feedback (N). The other three sets of questions (QB, QC, and QD in Table 2) were asked separately for both conditions. In order to determine whether the data registered in sets B, C, and D differ between the two feedback conditions, we ran seventeen Wilcoxon signed-rank tests (significance level alpha = 0.05), one for each question. The Wilcoxon signed-rank test is the non-parametric equivalent of the more popular paired t-test. The latter is not appropriate here since the dependent variable was measured at the ordinal level. The analysis revealed significant statistical difference between answers QB5 (p = 0.050), QB6 (p = 0.013), QB7 (p = 0.012), QC1 (p = 0.003), QC2 (p = 0.016), QD1 (p = 0.010), QD2 (p = 0.015), and QD4 (p = 0.005). Answers that resulted statistically significantly different are reported in red in Table 2.

We also asked which condition the subjects preferred. All subjects preferred the condition where they were wearing the wearable cutaneous devices. However, four subjects out of twelve complained that, while wearing the wearable devices, the tracking of the fingertip seemed less accurate with respect to interacting with the environment barehanded.

DISCUSSION AND CONCLUSIONS

This work presented the application of a 3RRS wearable fingertip device for stiffness discrimination. Three servo motors move a mobile end-effector toward the user's fingertip and re-angle it to simulate contacts with arbitrarily oriented surfaces. Moreover, a vibrotactile motor conveys vibrations to the fingertip. The device was preliminary introduced in [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF], [START_REF] Chinello | A novel 3rrs wearable fingertip cutaneous device for virtual interaction[END_REF]. In this paper, we have extended the analysis and evaluation of the device with a novel stiffness control system and an in-depth kinematics analysis. Moreover, in order to test the effectiveness and wearability of our wearable haptic device, we carried out two experiments.

Stiffness discrimination experiment. The first experiment tested the capability of our device in differentiating stiffness information. We considered three feedback conditions: cutaneous feedback provided only by the servo motors (S), only by the vibrotactile motor (V), and both by the servo motors and the vibrotactile motor (SV). In the best condition, SV, subjects were able to differentiate values of stiffness different by 208.5 ± 17.2 N/m (mean ± 95% confidence interval). Surprisingly, adding vibrotactile feedback did not significantly improved the performance of the stiffness discrimination task. However, subjects appreciated the capability of the vibrations to effectively notify the making contact with the virtual surface. The Weber fraction (JND/I, see Sec. 5.1.2) for conditions S, V, and SV is 31.5%, 39.0%, and 23.2%, respectively, which is in agreement with previous results in the literature. For example, Lècuyer et al. [START_REF] Lecuyer | Pseudo-haptic feedback: can isometric input devices simulate force feedback?[END_REF] used a passive isometric input device, together with visual feedback, to provide the operator with pseudo-haptic feedback. The Weber Fraction for stiffness between a real spring and a spring rendered using the isometric input device was 16%. Genecov et al. [START_REF] Genecov | Perception of a haptic jamming display: Just noticeable differences in stiffness and geometry[END_REF] presented a tactile display capable of simultaneously and independently controlling its stiffness and geometry via particle jamming and pneumatic actuation. The Weber Fraction for stiffness was also 16%. Gurari et al. [START_REF] Gurari | Stiffness discrimination with visual and proprioceptive cues[END_REF] compared the Weber fraction for human perception of stiffness among three conditions: vision, proprioceptive motion feedback, and their combination. Results gave average Weber fractions of 5.6% for vision, 3.6% for proprioception, and 3.9% for their combination. As expected, our performance is sligthly worse with respect to [START_REF] Lecuyer | Pseudo-haptic feedback: can isometric input devices simulate force feedback?[END_REF], [START_REF] Genecov | Perception of a haptic jamming display: Just noticeable differences in stiffness and geometry[END_REF] and significantly worse than [START_REF] Gurari | Stiffness discrimination with visual and proprioceptive cues[END_REF]. This can be justified by the fact that we are using wearable tactile interfaces with limited actuation and sensing capabilities, and no visual feedback was provided.

In this experiment, to precisely track the position of the fingers, we used two Falcon interfaces (see Fig. 4), able to guarantee a high tracking accuracy (i.e., more than 10 times higher than the Leap Motion used in the second experiment). However, of course, this choice severely reduced the workspace of the system and did not enable us to evaluate the portability and wearability of our system, which is one of the main points of our work. Moreover, the Falcon interfaces, even when commanded to provide no external force, shows an internal stiffness and friction that is unwittingly displayed to the user. However, since this effect was present in all the considered comparisons, we expect it to have negligible effect in the final computation of the differential thresholds.

Immersive environment experiment. The second experiment tested the effectiveness of our device in an immersive virtual reality scenario, focusing on its wearability and portability. All subjects preferred the experience while being provided with cutaneous feedback. Moreover, cutaneous feedback made the interaction more satisfactory (question QD1), more fun to use (QD2), and more "wonderful" (QD4). On the other hand, as expected, wearing the two devices made the task more difficult to learn (QB5, QC1, QC2). Indeed, most of the subjects had no previous experience with wearable interfaces, and they had to get used to wearing them before starting to truly appreciate the additional information provided. In fact, as mentioned above, after this initial setback, all subjects preferred using the system with the cutaneous devices. Finally, subjects complained that the fingertip tracking worked better when using the system barehanded (QB6). These results show that the proposed wearable solution is definitely wellreceived and well-appreciated. However, there is still some work to be done to improve the wearability of these systems and the quality of the tracking.

Future Work. In the next future, we are planning to integrate our fingertip device with a compact and lightweight finger exoskeleton, able to provide kinesthetic feedback to the PIP and DIP joints. In order to improve the tracking of fingers wearing cutaneous devices, we will also consider using more sophisticated tracking systems, such as the V:120 Trio by OptiTrack, or placing the devices on other parts of the hand. A promising solution is moving the device from the fingertip to the proximal phalanx, similarly to what has been done in [START_REF] Pacchierotti | The hring: a wearable haptic device to avoid occlusions in hand tracking[END_REF], [START_REF] Hussain | A wearable haptic ring for the control of extra robotic fingers[END_REF], [START_REF] Maisto | Evaluation of wearable haptic systems for the fingers in augmented reality applications[END_REF]. Moreover, we are also considering the possibility of including an Inertial Measurement Unit (IMU) unit directly on the cutaneous device, in order to combine the information coming from the external tracker (e.g., a Leap Motion) together with the information captured by the IMU. A similar approach is currently being used by the company GoTouchVR for their wearable fingertip device [START_REF] Pacchierotti | Wearable haptic systems for the fingertip and the hand: taxonomy, review, and perspectives[END_REF]. Finally, to improve the immersiveness of the virtual environment, we will consider using a Virtual Reality headset, such as an Oculus Rift Head-Mounted Display (HMD). We are also interested in studying how amplitude and duration of vibration bursts affect the sensation of making and breaking contact with virtual objects in wearable haptics.

Fig. 1 :

 1 Fig. 1: The proposed 3-DoF fingertip cutaneous device. It is composed of a static upper body (F) and a mobile platform (E): the body is located above the nail, supporting three servo motors (C), while the mobile platform contacts the finger pulp. Three legs (A) connect the mobile platform with the static body. Each leg is composed of two rigid links connected to each other and then with the body and the mobile platform, according to a RRS (Revolute-Revolute-Spherical) kinematic chain. The three upper revolute joints are actuated by the servo motors, and a piezoresistive sensor (D) measures the force applied by the mobile platform to the fingertip. A vibrotactile motor (G), attached below the platform, provides additional vibrotactile stimuli to the wearer. Finally, a clamp (B) enables the user to easily wear the device on the finger.

  (a) Picture of the device. (b) Scheme of the device.

Fig. 2 :

 2 Fig. 2: Kinematic structure of the 3RRS wearable fingertip device. The servo motors move the mobile end-effector toward the user's fingertip and re-angle it to simulate contacts with arbitrarily oriented surfaces. Moreover, a vibrotactile motor placed below the end-effector conveys vibrations to the fingertip.

Fig. 4 :

 4 Fig. 4: Experimental setup. Two wearable devices are attached to the end-effectors of two Falcon interfaces, with the end-effectors facing each other. The Falcon interfaces are only used to track the position of the fingers and do not provide any external force to the user.

Fig. 5 :

 5 Fig. 5: Differential threshold for stiffness discrimination. Mean and and 95% confidence interval are plotted for condition providing cutaneous feedback only by the servo motors (S), only by the vibrotactile motor (V), and both by the servo motors and the vibrotactile motor (SV).

  and k S = k b , where k a, * and k b assumed the following numerical values: (i) k a,1 = 500 N/m and k b = 900 N/m (k a,1k b = 400 N/m) for Series 1, (ii) k a,2 = 600 N/m and k b = 900 N/m (k a,2k b = 300 N/m) for Series 2, (iii) k a,3 = 700 N/m and k b = 900 N/m (k a,3k b = 200 N/m) for Series 3.

TABLE 1 :

 1 • to 0.1 s/60 • Specifications for the proposed 3-DoF cutaneous device.

	Maximum Normal Force	4.7 N
	Maximum Roll Angle	π 5 rad
	Maximum Pitch Angle	π 6 rad
	Maximum Vertical Displacement	15 mm
	Frequency vibration range	50 -240 Hz
	Amplitude vibration range	0.05 -1 g
	the body. The proposed device weights 25 g for 35×50×48 mm
	dimensions.

TABLE 2 :

 2 Experiment #2. Usefulness, Satisfaction, and Ease of use (USE) questionnaire results.

	QA. Usefulness (condition C with respect to condition N)
	1. It helps me be more effective.		8.3 ± 0.9
	2. It helps me be more productive.		7.9 ± 1.2
	3. It is useful.			6.8 ± 1.3
	4. It makes the things I want to accomplish easier to get done.	8.1 ± 0.7
	Experiment in condition C (statistically different values in red)	Experiment in condition N (statistically different values in red)
	QB. Ease of use		QB. Ease of use
	1. It is easy to use.	3.4 ± 1.9	1. It is easy to use.		4.2 ± 2.2
	2. It is simple to use.	7.2 ± 1.5	2. It is simple to use.		6.7 ± 2.0
	3. It is user friendly.	6.3 ± 1.4	3. It is user friendly.		7.1 ± 1.9
	4. Using it is effortless.	5.5 ± 1.2	4. Using it is effortless.		5.8 ± 0.7
	5. I can use it without written instructions.	2.6 ± 1.4	5. I can use it without written instructions.	5.4 ± 1.4
	6. I don't notice any inconsistencies as I use it.	6.7 ± 7.6	6. I don't notice any inconsistences as I use it.	7.6 ± 0.8
	7. Both occasional and regular users would like it.	7.3 ± 0.6	Both occasional and regular users would like it.	5.2 ± 1.7
	8. I can recover from mistakes quickly and easily.	7.3 ± 1.2	8. I can recover from mistakes quickly and easily.	7.5 ± 1.2
	9. I can use it successfully every time.	4.1 ± 1.6	9. I can use it successfully every time.	4.4 ± 1.6
	QC. Ease of learning		QC. Ease of learning
	1. I learned to use it quickly.	4.3 ± 1.4	1. I learned to use it quickly.	6.9 ± 1.6
	2. It is easy to learn to use it.	5.9 ± 1.4	2. It is easy to learn to use it.	7.7 ± 1.3
	3. I quickly became skillful with it.	6.4 ± 0.9	3. I quickly became skillful with it.	6.8 ± 0.6
	QD. Satisfaction		QD. Satisfaction
	1. I am satisfied with it.	7.1 ± 1.4	1. I am satisfied with it.	4.8 ± 1.4
	2. It is fun to use.	8.7 ± 0.5	2. It is fun to use.		6.2 ± 1.2
	3. It works the way I want it to work.	7.3 ± 1.4	3. It works the way I want it to work.	6.7 ± 0.5
	4. It is wonderful.	7.6 ± 1.6	4. It is wonderful.		5.5± 1.5
	5. It is pleasant to use.	7.2 ± 1.3	5. It is pleasant to use.		7.1 ± 0.7

• This research has received funding from the European Union Seventh Framework Programme FP7/2007-2013 under grant n • 601165 of the project "WEARHAP -WEARable HAPtics for humans and robots," and from Rennes Métropole under the "Allocation d'Installation Scientifique (AIS) 2017" programme.

Francesco Chinello received the M.S. degree


Planet's right use through political philosophy

In this communication we wish to explore the question of the right use of the planet through the prism of major political ideas. According to Mannheim two major political ideas dominate modernity: liberalism and socialism. Each of them is subdivided into various subcurrents. Mannheim also adds conservatism, which seems to be less important, but we will examine these three political ideas. Mannheim's analysis of each of these political ideas is rather limited. For the sake of the discussion we will base our analysis of liberalism on the book of Catherine Audard ("Qu'est-ce que le libéralisme?", mainly based on a rawlsian framework), and socialism on Jacques Droz's "History of Socialism". Conservatism has been the subject of several recent books (Scruton, EHESS etc.) and does not give itself easily in the form of a single reference; we will therefore use several references including a relatively well-known author in conservative circles in France: Alain de Benoist, who wrote a famous book on ecology, with an apology of degrowth. We will also follow the method proposed by Mannheim, who suggests that political ideas can be studied only by the conflicts they generate, because they are performative concepts, aiming to reach a goal: to convince. "The planet" will be understood here as the space where life is constantly taking place.

In liberalism Locke and Kant are probably two cardinal references. The right use of Earth is given by what is usually called the "lockean proviso". Locke writes in the Treatise of the Government that no one can be wronged to see another person drink in a river if he leaves enough and as good water for everyone who wants to quench his thirst. He says also that what is true for water is the same for the earth, if there is enough of both (1690: chapter 5). Appropriation of land is also subject to some limitations. One of them is that ownership is given by work, which means that you cannot appropriate a surface that exceeds your work capacities. Locke says also: "The same law of nature that gives us ownership in this way [ie, by work] imposes limits on it. God has given all things in abundance. [...] All that a man can use in order to derive any benefit for his existence without wasting, is what his work can mark the seal of the property. All that goes beyond it belongs to others "(ibid.). Locke also recognizes a right to appropriate the property of others if one's vital needs are at stake. In general, it is clear to Locke that there are limits to human appropriation of the natural environment, and this for various criterias ; at the same time he sees no conflict, especially with established properties, and this mainly because one appropriates only a tiny portion of natural resources, which integrity is not threatened by human industry. On his side Kant makes a distinction between intelligible property and empirical property. Intelligible property derives from the fact that Earth is a finite sphere, and therefore every property is contiguous to another, which means that the extension of any property affects all the others. Thats' why property cannot only be "empirical", that means : legal. Rawls keeps this in mind when he says that natural talents or abilities are inappropriable and should benefit to everyone, especially the less gifted. Nowadays the situation is different and there are various adaptations of the lockean provisio. For right wing libertarians such as Nozick human rights are linked to private property: our properties have same status as our body, nobody as the tiny right to challenge one's legal entitlements. Appropriation of natural resources is private and everyone must manage alone to find resources to use and to value, without using force or threatening private property, only at the will of the owner. That is true also for the State or any collective body, whose role is only to protect life, that is : private property. Another argument is money and wealth. Locke was limiting appropriation by forbidding any waste making, and this means that I cannot appropriate what I cannot use (for exemple, to much food, to much water etc.). As Pierre Manent says: "[...] suppose that I find a way to avoid this waste, by agreeing with my fellow creatures an incorruptible equivalent of corruptible natural goods, for example gold or silver, then the accumulation can be limitless since it will no longer involve waste. Therefore, by appropriating a piece of land by my work, far from removing the common good of humanity, I add " (Manent, 1987: 98-99). For liberals, work can always add value, and therefore wealth, that's why there's no limits on appropriation. Everything relies on ingenuity and work. Paul Romer, an wel known economist, argued that there will be growth for 3 billions years, given that growth is mainly based on resources and ideas. Nuclear power is a frequent example for explaining that capital accumulation, which means also physical accumulation, is not a threat but a solution, given that without nuclear machinery uranium is useless. Capital accumulation creates wealth, litteraly, out of nothing. Every human being who owns his own work has a parcel of nature more than sufficient for his life, depending on what use he will make. Sharing is unnecessary. Scarcity is only relative. Depending on the degree of "social" in a given form of liberalism, this political idea will accept some distribution (Dworkin) or redistribution (Rawls), in order to grant some fair and equal opportunities to each member of society.

Socialism takes up most of the liberal argument, but criticizes distribution. Socialism argues that liberalism idealizes the situation, when considering that exchange is free and equal. Socialism shows that not everybody wins over free trade, which is not free. Some are exploited and others are exploiters: they are usually the owners of the means of production. The question of limits appears in three ways: as a temporary limit of the technological progress carried by capitalism, which digs its own grave, destroying the peasantry and creating an ever larger mass of workers; as ideological discourse on the part of capitalists who do not wish to share the production and thus make workers believe in the existence of limits where there is in fact only egoism; as the inability of workers to gain access to the products of their own labor, because of the propensity of capitalists to compress wages, in order to win the competition between themselves. The dominant idea of socialism, which is a modern idea, is that of a rich communism, where equality would be attained by the saturation of needs, and putting an end to scarcity; this breaks deeply with earlier communisms rather based on poverty. When socialism admits ecology, usually, it tends to lead to a Polanyian conception, pointing to the exploitation of the land and the worker; These general remarks, however, are not very clear about their consequences for political action. Polanyi himself was not criticizing the act of destruction of the commons, but only the manner it has been done; he believes it was necessary, for modernity to awake. Another difficulty is that socialism relies on workers movements, especially clasical socialism and classical marxism, as defined in the Communist Party Manifesto. It's not true for "utopian socialism", as Marx call them, which are criticized because not being based on a social movement. Even today unions and workers' movements are usually asking for more growth, as we can see in the current crisis of university. This explains that ecologism rises as a distinct political idea, and that it is still difficult to see a massive support in favor of what could be called an "ecosocialism". One source of the difficulty is alienation from capitalist or productivist system, which is dividing issues. One finds difficult to fight for another content of production when his salary depends on that production and at the same time unemployment is high. Unions now use the concept of "just transition" to underline the necessity of taking care of workers, when restructuring production. But sociologically speaking workers in developed countries rely deeply on products with high content of natural resources. They are all the time intoxicated by the system's ability to hide ecological information, which can discourage sales. Who wants to buy products that destroys Earth? Almost nobody. Therefore ecological implications of production should be hided behind a massive effort for "lift the bottlenecks that constrain the expansion of consumption". Ecologists are therefore mostly coming from the "petty bourgeoisie", with low economic capital and high cultural capital. They rely often on liberal types of working, such as entrepreneurship. Only a minority is employee or worker in big industry. Unions are often suspicious against them. Ecologists are not necessary very prone to support workers fights, given that they are not very often in line with ecologists fights. There are convergence cases such as the defence of railways. But many divergences. The idea of respect for nature is present in socialism and especially in Marx but in vague terms that do not go as far as the idea of a nature subject of right, endowed with rights. The content of this idea partly covers the idea of a harmonious society carried by socialism; but the expected or expected cosmology is often different: while ecologism is often opposed to mega-tools, socialism has often made it a condition of emancipation. Any limit in this domain is lived as a renunciation, a privation and almost a sacrilege; since the Marxian condemnation of Luddites the problem is deemed to reside first in the use of tools, not in the tools themselves.

Conservatism is more difficult to identify, as we pointed out in introduction. Either it is confused with a liberalism emphasizing national power and a traditionalism of manners (the respect of the "natural" family for example), and we thus return to a current already examined, either it covers currents of very small magnitude, thus the illiberal and anti-capitalist right of Alain de Benoist or Alain Soral. What is confusing or surprising at first glance is that the arguments are partly similar to socialism and communism, with a clear condemnation of capitalist egoism, exploitation, destruction of nature, which is why this trend feeds on writers such as Polanyi, again; but the solutions are different, based on corporatism of Vichy or Maurassian inspiration and the critique of democracy. Conservatism tends to externalise the social order, to make it inappropriate by individuals, contrary to the liberal and socialist claim of autonomy. The support of this externalisation can take all appearances, not just religion as one might think. Nature is a good candidate, if it is understood as a set of intangible laws, as an eternal essence, which does not necessarily have much to do with the empirical nature understood as a planet or biosphere. Thus the example of the "Manif pour Tous", a french movement fighting against homosexual unions, and naturalises a specific, catholic family arrangement. Culture is also a good candidate: custom also externalizes the social order. But reason can also be elevated to the rank of sacred intangible and indisputable. This is what Jacques Ellul criticized in the technology, the fact that it is depository of the sacred: so we must believe in technology (in the sense of capitalistic growth of tools) and not question it. The "ecological conservatism" embodied by Alain de Benoist however seems to us contradictory insofar as his obsession with the enemy, inside or outside, does not seem to lead him to give up the means of power, which are destructive of nature. This short discussion shows that the notion of "limit" is not intrinsically conservative, contrary to what conservatives or progressives often believe, the first to recall the limits and the second to reject them. The concept of limit derives also from the concept of justice, which can put the established order into question rather than strengthen it. This is the case of the rights of nature. The Lockean or Kantian or Rawlsian clause of the inappropriability of nature, understood in a strong way, has clearly communist implications. As everything comes from nature, no one should have more than others. This could be true for living bodies, humans or not; for past bodies, already dead ; and for bodies to come to life, in the future. An example is the discussion on climate justice; the congestion generated in the atmosphere by GHG emissions raises the question of the sharing of atmospheric space and it is no coincidence that conservative positions such as the one recently supported by Olivier Godard (2017) emphasize grandfathering as the best principle, to the extent that it comes as a long time and "consented" appropriation of the atmosphere -a custom. According to this position Godard argues that the sharing issue arose after 1990, not before, because before that date the problem was unknown. For him responsibility before 1990 does not make any sense. We can argue alternatively that emissions increase since 1900, indicating an excess compared to the carrying capacity of the biosphere, of which Arrhenius (1896) was aware. According to the cosmopolitan perspective, limits should have been imposed on polluting countries. Denying the existence of limits was deeply conservative, in this example. This can of deny can therefore be emancipatory or conservative, depending on the case.