Monica Malvezzi

Francesco Chinello

Domenico Prattichizzo

Claudio Pacchierotti

Design of personalized wearable haptic interfaces to account for fingertip size and shape

The size and shape of fingertips vary significantly across humans, making it challenging to design wearable fingertip interfaces suitable for everyone. Although deemed important, this issue has often been neglected due to the difficulty of customizing devices for each different user. This paper presents an innovative approach for automatically adapting the hardware design of a wearable haptic interface for a given user. We consider a 3-DoF fingertip cutaneous device, composed of a static body and a mobile platform linked by three articulated legs. The mobile platform is capable of making and breaking contact with the finger pulp and re-angle to replicate contacts with arbitrarily-oriented surfaces. We analyze the performance of this device as a function of its main geometrical dimensions. Then, starting from the user's fingertip characteristics, we define a numerical procedure that best adapts the dimension of the device to (i) maximize the range of renderable haptic stimuli, (ii) avoid unwanted contacts between the device and the skin, (iii) avoid singular configurations, and (iv) minimize the device encumbrance and weight. Together with the mechanical analysis and evaluation of the adapted design, we present a MATLAB script that calculates the device dimensions customized for a target fingertip as well as an online CAD utility for generating a ready-to-print STL file of the personalized design.

I. INTRODUCTION

Wearable haptic interfaces for the fingertips are growing interest in the field of haptics [START_REF] Pacchierotti | Wearable haptic systems for the fingertip and the hand: Taxonomy, review, and perspectives[END_REF]. All these devices have been designed for users with certain fingertip characteristics, without considering the large differences in fingertip's size and shape across humans [START_REF] Dandekar | 3-D finite-element models of human and monkey fingertips to investigate the mechanics of tactile sense[END_REF], [START_REF] Courtney | Hong Kong female hand dimensions and machine guarding[END_REF]. These physical differences can significantly distort the perception of haptic feedback provided by fingertip haptic devices (see Fig. 1). Although this problem has been widely acknowledged [START_REF] Pacchierotti | Wearable haptic systems for the fingertip and the hand: Taxonomy, review, and perspectives[END_REF], [START_REF] Pacchierotti | Displaying sensed tactile cues with a fingertip haptic device[END_REF], little work has been done to address it and no easy-to-use or automatic technique is available to adapt the design of a wearable device for a target user. One example has been presented by Young et al. [START_REF] Young | Compensating for fingertip size to render tactile cues more accurately[END_REF], where the rendering algorithm of a fingertip device is adapted to account for the fingertip size and shape. However, no hardware/design adjustment is considered.

This paper introduces an automatic technique to personalize the structure and dimensions of a wearable fingertip device for a given fingertip. As a representative example, we consider the popular wearable fingertip device of Chinello et al. [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF], shown in Fig. 2. Starting from the geometrical characteristics of the user's fingertip, we define a numerical procedure that automatically adapts the dimensions of the static body, mobile platform, and articulated legs to i) reach all the parts of the fingertip needed for the given interaction, ii) avoid undesired contacts between the device and the finger (e.g., lateral contacts), iii) avoid kinematic singularities in all the 1 Dept. Information Eng. and Mathematics, Univ. Siena -Siena, Italy. 2 Dept. Advanced Robotics, Istit. Italiano di Tecnologia -Genova, Italy. 3 Dept. Business Dev. and Tech., Aarhus Univ. -Herning, Denmark. 4 CNRS, Univ Rennes, Inria, IRISA -Rennes, France. * , ‡ These two couples of authors contributed equally to this work. Fig. 1. Problem: the same fingertip haptic device will elicit different sensations on fingertips having different size and shape. Our personalization approach optimizes the device design for a target fingertip, so as to always elicit the desired haptic sensation.

operative configurations, iv) reduce as much as possible the dimension, encumbrance, and weight of the device. We present the mechanical analysis and theory behind this procedure, together with a MATLAB script to easily calculate the personalized dimensions. Finally, we also prepared an online tool for the Computer-Aided Design (CAD) software OnShape. Inputting the dimensions of the target fingertip and the target performance characteristics, the tool automatically adjusts the design of the wearable device and generates an STL file ready to be 3D printed.

II. DEVICE DESCRIPTION We demonstrate our personalization technique for a representative 3-DoF wearable fingertip device, shown in Fig. 2.

The device is a parallel mechanism composed of a static upper body and a mobile platform (end-effector), connected by three articulated legs. The upper body and the motors are placed on the nail side of the finger, while the mobile endeffector is placed in contact with the finger pulp. The upper body and the end-effector are connected by three legs, each composed of two rigid links connected to each other, the body, and the end-effector according to a RRS kinematic chain. The revolute joints close to the upper body are actuated by 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. Therefore, the mobile platform has 3 DoF w.r.t. the body. We use Hitech HS5035hd motors and a MicroMaestro (Pololu) control board.

A preliminary version of this device, designed without taking into account any user's specific characteristic, has been presented in [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF] and in https://youtu.be/g7w5ejPa0sI. With respect to that system, our design has been modified to be suitable for personalization, as detailed in the following. A detailed analysis of the device in terms of control and dynamics response is reported in [START_REF] Chinello | A modular wearable finger interface for cutaneous and kinesthetic interaction: control and evaluation[END_REF].

IEEE Transactions on Haptics, 2021

III. DEVICE ANALYSIS AND PERSONALIZATION A. Problem introduction and main definitions

In [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF], [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF], [START_REF] Chinello | A modular wearable finger interface for cutaneous and kinesthetic interaction: control and evaluation[END_REF], we already summarized the main aspects of the device statics and kinematics model, following standard analysis procedures [START_REF] Tsai | Robot analysis: the mechanics of serial and parallel manipulators[END_REF]. In this paper, we revise the modeling to motivate, parametrize, and evaluate the design choices of our device. The goal is to personalize the main geometrical characteristics of the device for a given fingertip and interaction. The criteria to take into account for choosing this optimized design are four-fold and listed in Sec. I. The scheme of the 3RRS parallel mechanism representing the wearable fingertip device is shown in Fig. 3 [START_REF] Li | Inverse kinematics and dynamics of the 3-rrs parallel platform[END_REF].

Let us indicate with B i , i = 1, 2, 3 the centers of the spherical joints on the mobile platform, and with S 1 = O 1 , x 1 , y 1 , z 1 the reference frame fixed on it, in which the origin O 1 and the axes are chosen as shown in Fig. 3. In each leg, the links are connected to each other through a revolute joint, whose axis is parallel to the one of the revolute joint fixed to the upper body. Let us indicate with u i the unit vector identifying, for each leg, the direction of the revolute joint axes. We can then define the plane π i passing through B i and perpendicular to u i . The joint axes that intersect this plane in A i and D i correspond to the joint connecting each leg to the upper body and the middle joint, respectively. Let S 0 = O, x, y, z be a reference frame on the upper body, in which the origin O and the axes are chosen as shown in Fig. In general, the position and orientation of the mobile platform can be described by the vector r = [r x , r y , r z ] T and Roll(ψ)-Pitch(θ )-Yaw(φ ) angles ϕ = [ψ, θ , φ ] T , respectively. As shown in [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF], since the platform has 3 DoF, we can select three of these six variables and evaluate the remaining ones [START_REF] Chinello | A modular wearable finger interface for cutaneous and kinesthetic interaction: control and evaluation[END_REF]. Let us indicate with ξ a six-dimensional vector containing the mobile platform configuration (position and orientation): ξ = r T , φ T T . Let us assume that the fingertip surface is known w.r.t. S 0 , that it is convex and can be described by the function z = f f (x, y). For example, if the fingertip is represented as a three-dimensional semi-ellipsoid with semiaxes e 1 , e 2 , and e 3 , the corresponding representation is

z = e 3 1 - x 2 e 2 1 - y 2 e 2 2 . (1)
The device end-effector should be able to touch any point inside a given portion of the fingertip surface, indicated with C . The dimension and shape of C can be evaluated on the basis of the target fingertip dimension, envisioned interaction, and device performance requirements, e.g., intended roll and pitch angles, vertical displacement.

B. Constraints based on the user-specific features

The device design is defined by three set of dimensions, that we seek to personalize: the dimensions of a) the mobile platform (end-effector), b) the static platform, and c) the articulated legs. The personalization process considers these three sub-problems in sequence:

• mobile platform (end-effector) dimensions are defined on the basis of the user's finger dimensions and the device target workspace, i.e., the surface of the finger that will be involved in the cutaneous stimulation. • static platform dimensions are consequently defined so that, during the cutaneous stimuli application, only the mobile platform interacts with the fingertip and no undesired contacts with the legs occur. • articulated legs lengths are defined to avoid kinematic singularities in any of the device operative configurations. In the following, we provide a mathematical description of each step, constituting the basis for the automatic personalization procedure described in Sec. IV.

1) Preliminary constraints, symmetry: For fingertip devices, it is reasonable to assume that the device is symmetric with respect to the longitudinal plane (plane xz). Concerning the mobile platform, we can therefore assume

B 1 B 2 = B 1 B 3 = b l and B 2 B 3 = b d .
The geometrical parameters b d , b, and b h , indicated in Fig. 3, define the shape of the mobile platform. In a generic configuration of the platform, indicating with r the coordinates of O 1 w.r.t. S 0 and with R the rotation matrix between S 1 and S 0 , the coordinates of B i w.r.t. S 0 can be evaluated as b i = r + Rb 1 i . Since B i points move on the three fixed planes π i and according to the geometric dimensions indicated in Fig. 3, 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 . (2)
Eq. (2) introduces three constraints that limit the generic six-dimensional motion of the mobile platform to three DoF. Moreover, since points B i have to move on fixed planes π i , the following constraints on the upper static platform dimension hold a d a = b d b = r p , where r p is an aspect ratio defining platform proportion between lateral and longitudinal direction. In particular, if r p = √ 3, the platform has an equilateral structure; if r p < √ 3, the platform is thinner in the lateral direction than in the longitudinal one.

2) Mobile platform dimension, contact with the fingertip: The dimensions of the mobile platform are evaluated on the basis of the first requirement reported in Sec. I, namely: i) reach all the parts of the fingertip needed for the given interaction. The mobile platform applies cutaneous stimuli to the fingertip. We call C the portion of the fingertip surface we want the mobile platform to reach. For simplicity, at this phase, we consider the theoretical single-point contact between the platform and the finger, i.e., we neglect the complex finger skin deformation caused by this interaction. For any configuration in which the platform is tangent to the fingertip in the generic point P ∈ C , whose coordinates w.r.t. S 0 are p = [p x , p y , p z ] T , B i have to belong to the plane tangent to the fingertip surface in P. For this reason, the coordinates of B i are related by three linear relationships:

b i,z = c 1 b i,x + c 2 b i,y + c 3 (3)
where i = 1, 2, 3 , and a, b, c are three coefficients that depend on the fingertip surface parameters and platform orientation:

c 1 = ∂ f f ∂ x | p x ,p y , c 2 = ∂ f f ∂ y | p x ,p y c 3 = - ∂ f f ∂ x | p x ,p y p x - ∂ f f ∂ y | p x ,p y p y (4)
Three additional constraints are given by the distance between points B i , which is constant

(b i,x -b j,x ) 2 + (b i,y -b j,y ) 2 + (b i,z -b j,z ) 2 = B i B j 2 (5)
with i, j = 1, 2, 3, i = j. Eqs. ( 2), (3), (5) represent a 9×9 nonlinear system of equations whose solution gives the coordinates of the mobile platform vertexes B i for a given contact point P.

The device works properly if, for any point P ∈ C , P is also inside the triangle defined by B i points (i.e., it is reachable by the mobile platform). We can impose a constraint on the dimension of the mobile platform by checking that, for any platform configuration, point P is inside the triangle defined by points B 1 , B 2 , and B 3 . This constraint sets the lower bounds for the dimensions of the mobile platform. This constraint can only be indirectly verified: for a given fingertip shape and platform dimensions, we can only verify if the platform is able to reach every point of C , so that the procedure has to be implemented iteratively. A simplified, yet approximated, solution can be obtained by choosing b and b d so that the triangle that these parameters define is the minimum area triangle containing the C surface rectified on the xy plane. This simplified solution has been implemented in the MATLAB script submitted as supplemental material.

3) Static platform dimension, contact with finger lateral surface, aspect ratio: Once the mobile platform is defined, the dimensions of the static platform are evaluated to satisfy the second requirement introduced in Sec. I, specifically: ii) avoid undesired contacts between the device and the finger (e.g., lateral contacts). During haptic interaction, only the mobile platform should contact the fingertip, and any other contact between the articulated legs and the lateral surface of the fingertip should be avoided. To guarantee this behavior, we must ensure that, in any configuration of the platform, the lines connecting A i and B i do not intersect the fingertip surface. This constraint sets lower bounds for the dimensions of the static upper platform, which is defined by parameters a and a d (see Fig. 3). However, if the dimension of the mobile platform, as defined in the previous Sec. III-B.2, is very small, this constraint can lead to quite a large static platform. To obtain a better proportion between the two platforms, we can set an additional constraint on the device aspect ratio, defined as r d = a/b, imposing that it must fall within a fixed range, i.e., r d,min < r d < r d,max .

4) Articulated leg dimensions:

The dimensions of the articulated legs are evaluated to satisfy the third requirement in Sec. I, specifically: iii) avoid kinematic singularities in all the operative configurations. A configuration of the mobile platform can be defined by a vector r and a rotation matrix R, corresponding to the contact with a generic point P ∈ C . In any of these configurations, the device should be sufficiently far from singularities.

For any platform configuration ξ , the inverse kinematics procedure allows to evaluate corresponding rotations q = [q 1 , q 2 , q 3 ] T of the revolute joints in A i [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF]. In other terms, the objective of the inverse kinematics is the definition of a function f IK : R 3 → R 3 that allows to evaluate q = f IK (ξ ).

In particular, if the coordinates of B i w.r.t. S 0 are known, the actuator rotation angles q i can be evaluated as q i = π -(α i + δ i ), where

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 | ,
with s i = b i -a i , and l 1 = |D i A i | and l 2 = |B i D i | are the lengths of the proximal and distal link of each leg, respectively. The solution of the inverse kinematics problem is widely exploited in parallel mechanism analysis, and it is at the basis of our device position control [START_REF] Chinello | Design and development of a 3rrs wearable fingertip cutaneous device[END_REF]. In this paper, we use the results of the inverse kinematics to get insight for the design of the device dimensional parameters.

To avoid singular configurations during the motion, the "knee" angle β i has to ideally be comprised between 0 and π. Specifically, values of β i exactly equal to 0 or π correspond to singular configurations of the mechanism, while values close to such limits lead to configurations in which motors are required to apply high torques, degrading the device performance. The criteria introduced in the previous Sections allow to define the dimensions of the mobile and static platforms, i.e., parameters a, a d , b, b d . Angles β i depend on these values and on the mechanism configuration, in particular on the magnitude of s i and on lengths l 1 and l 2 . This new constraint β min < β i < β max leads to a system of non-linear inequalities whose solution provides indications on how to define l 1 and l 2 . For example, considering a, a d , a h , b, b d , and b h as reported in Fig. 2, filled areas in Fig. 4 show the subspace of (l 1 , l 2 ) pairs satisfying the constraints for different values of β min and β max . Simply avoiding singular configurations does not provide a unique solution for l 1 and l 2 , but rather a subspace of possible values. Among all the possible values of (l 1 , l 2 ) satisfying the constraints, we selected a solution that limits the overall device size and guarantees a suitable level of wearability and comfort, so as to satisfy the fourth requirement in Sec. I, namely: iv) reduce as much as possible the dimension, encumbrance, and weight of the device. In particular, we chose to keep l 1 as small as possible, so as to minimize motor torques for a given force to convey, as indicated with a red star in Fig. 4. Finally, since this criterion could lead to small l 1 values, which are difficult to manufacture, we considered an adjustable lower bound l 1,min . The red star marker in Fig. 4 (a), located at l 1 = 11 mm, l 2 = 28 mm, indicates the design parameters of the device summarized in Fig. 2.

IV. DESIGN AND ANALYSIS PROCEDURE

All the above-described criteria can be implemented in a numerical procedure that, given the user's finger characteristics and some hardware/manufacturing constraints, allows to dimension the device. We provide a MATLAB implementation of this procedure as a supplemental material. Moreover, a video, available as supplemental material and at https://youtu.be/FdTRPPIUJi8, summarizes the procedure.

One needs to provide the finger dimensions e 1 , e 2 , e 3 (see Fig. 5), the maximum roll angle ψ max , the maximum pitch angle θ max , the maximum vertical displacement z max , and a fixed offset h between the finger and the static platform. This last input can be considered to model the thickness of the static platform as well as the presence of a layer of soft material reducing the pressure on the top of the finger (e.g., foam). In the script, for the sake of simplicity, platform aspect ratio r p has been considered constant and the device ratio r d has not been constrained as described in Sec. III-B.3. Nonetheless, both aspects can be easily considered as further design/input variables in the optimization procedure.

The procedure for defining the optimal device dimensions is divided in three main parts: the first one sets the dimension of the mobile platform (see Sec. III-B.2), the second part defines the dimensions of the static platform (see Sec. III-B.3), and the third part allows to define the optimal length of the device legs (see Sec. III-B.4). The outputs of this procedure are the optimized dimensions of the device, i.e., a, a d , b, b d , l 1 , l 2 . Examples of outputs for four representative fingertips are shown in Tab. I. Fig. 6 shows, for the same four fingertips, the contact patch C rectified on the xy plane and the optimized mobile platform as evaluated by our procedure. The filled areas in Fig. 6 represent, as in Fig. 4, the set of (l 1 , l 2 ) pairs that avoid kinematic singularities in all the operative configurations of the device. The red stars represent the (l 1 , l 2 ) pair chosen by the automatic personalization procedure. As we can see, in all cases but 7a, the procedure chooses the pair minimizing l 1 , so as to reduce as much as possible the torque required from the actuators. In case 7a, following this approach would provide an l 1 too small (l 1 < l min ), so the procedure settles for l 1 = l min . Fig. 8 shows, for the same four representative fingertips, a front view (yz plane) of the finger wearing its personalized device. The distance between the fixed platform and the finger was h = 8 mm for all the configurations. It is interesting to notice that the procedure does not provide a mere scaling of the device, but instead a more complex personalization and optimization of the device structure and kinematics.

For each representative finger, we also calculated the ratio between the device and finger volumes, r v . The former is approximated as the volume of the polyhedron defined by points A i , B i and D i , while the latter is approximated as the union between a semi-ellipsoid with semi-axes e 1 , e 2 , and e 3 and a cylinder with an elliptical base with semi-axes e 1 and e 2 and height e 3 (in red in Fig. 5). As expected, this ratio varies in the different configurations: it is higher for small fingers, due to the fixed constraints that were imposed (e.g., l 1min and h), and it tends to decrease as the dimension of the finger increases. Finally, we also calculated the same device/fingertip volume ratio, r v,no , assuming that all the fingers wear the same device, i.e., the largest one (so that it fits everyone). In this case the ratio has a much wider variability. This analysis shows the importance of our personalization. If we design a platform that is too small, we cannot reach all the fingertip surface; conversely, if we design a platform that is too big, we ask the user to wear an unnecessarily bulky device. Finally, these parameters can be used in any CAD software to get the solid model of the optimized device. As an example, we have prepared a parametric CAD design on the online software OnShape. Starting from the optimized dimensions of the device as described above, the design automatically adjusts and generates a solid model ready to be 3D-printed. The resource is available at https://tinyurl.com/yx8ucceo. A user needs to register to OnShape (free of charge) and then copy the workspace so as to be able to edit it. Variables can be modified in the tab named "VARIABLES," while the adjusted design can be seen in the tab named "assembleddevice." As the user modifies the dimension variables in the first tab, the design modifies accordingly. Finally, the design can be exported in different formats (e.g., STL) and realized using any additive manufacturing technology, as for instance a standard 3D printer. We have included the device STEP files as supplemental material.

V. USE CASE We carried out a preliminary evaluation aimed at showing an effect in using a personalized vs. a general-purpose device.

The experimental setup is composed of a Leap Motion tracking system, one wearable fingertip device, and a virtual environment composed of a 3-dimensional sphere. Subjects are required to wear the fingertip device on the right index finger and interact with the virtual environment. The subjects hand pose is tracked using the Leap Motion, and a virtual hand mimicked the hand pose in the virtual environment. Every time the index finger came in contact with the virtual sphere, the wearable device applied a suitable amount of force to the fingertip (similarly to what we did in [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF], [START_REF] Meli | Wearable haptics and hand tracking via an rgb-d camera for immersive tactile experiences[END_REF]). Users were able to see the virtual environment through a screen placed in front of them. The Leap Motion was placed on a table between the user and the screen. Seven participants (5 males, 2 females) took part to the experiment. The task consisted of interacting with the virtual environment for two 5-minutes periods: once wearing a general-purpose wearable device (G), with the same dimensions described in Sec. II and Fig. 2, and once wearing a personalized device (P) generated following our procedure, presented in a randomized order. Users could interact with the sphere as they liked, e.g., poking, throwing, squeezing, or juggling it.

We evaluated the experience through 4 Likert-type questions, asking users to rate the "coherence of the haptic feedback with respect to the virtual environment (Q1)," the "quality of the haptic feedback received (Q2)," the "wearability of the system (Q3)," and "the comfort of the system (Q4)" in p = 0.016 p = 0.018 Fig. 9. Virtual Reality (VR) interaction: results. Mean and 95% confidence interval of the answers to the questionnaire when using the general-purpose device (G) vs. the personalized device (P). Higher is better.

the two conditions (general-purpose vs. personalized device, G vs. P). Each assertion is rated with a score from 1 ("completely disagree" with the assertion) to 9 ("completely agree"). To determine whether the answers for the conditions differed, we ran one Wilcoxon signed-rank tests (a = 0.05) per question, see Fig. 9. The personalized device showed significantly increased performance regarding the coherence (Q1) and quality (Q2) of the interaction, while no significant difference was registered for the wearability (Q3) and comfort (Q4). The latter is probably due to the fact that the personalized devices were, depending on the user, sometimes larger and sometimes smaller than the general-purpose one.

VI. DISCUSSION AND CONCLUSION

We presented a novel approach for personalizing a wearable haptic device for a target fingertip, taking into account its specific geometrical characteristics as well as some target performance metrics.

The procedure tackles four sub-tasks sequentially: symmetry and aspect ratio, customization of the mobile platform (i.e., definition of b and b d parameters), customization of the static platform, (i.e., definition of a and a d parameters), and definition of the articulated leg lengths l 1 and l 2 . This approach does not consider the process as a global optimization problem and, for this reason, it could lead to suboptimal results -but it also presents some advantages. First, the proposed process can be directly managed by the user, who can easily add or remove constraints and features without significantly impacting the overall algorithm structure. For instance, if the user decides to produce different devices with the same static platform (e.g., to speed up the manufacturing process), the proposed personalization procedure can be easily modified to act on the mobile platform and articulated legs only. Second, since each sub-task has been solved in an analytic way, its software implementation is straightforward, does not need any specific optimization tool, and can also be integrated in parametric CAD systems. Together with the mechanical analysis and evaluation of the adapted design, we present an automatic procedure to calculate the personalized device dimensions as well as an online CAD utility for generating a ready-to-3D-print STL file of the adapted design. Any user can design a personalized version of our device using this technique.

Our analysis can be completed by assessing the device kinematics, quasi-static modeling, and manipulability, extending the formulation presented in [START_REF] Chinello | A three revolute-revolute-spherical wearable fingertip cutaneous device for stiffness rendering[END_REF]. Of course, it is always important to know that a device should consider its target application. Toward this objective, from our parametric analysis, researchers can further adjust the design to their specific needs, to achieve different target performance and wearability levels according to the field of application. Another point to highlight is that, of course, the shape of a fingertip is not exactly that of an ellipsoid, and discrepancies between our ellipsoidal model and the actual fingertip might result in suboptimal choices for the design.

In the future, we will focus on the evaluation of this method, analyzing in depth the difference in performance and comfort between using a general-purpose device and one personalized through our procedure.

Fig. 2 .

 2 Fig.2. The considered wearable haptic device. It is a 3-DoF cutaneous module, composed of a static upper body (A) and a mobile platform (B): the body is located above the nail, supporting three servo motors (C), while the mobile platform contacts the finger pulp. Three legs (D) 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. Specifications and dimensions (w.r.t. Fig.3) are reported on the right side.

3 .

 3 Let us indicate with a i = [a ix , a iy , a iz ] T and b i = [b ix , b iy , b iz ] T the coordinates of A i and B i , respectively, both expressed w.r.t. the S 0 frame, and with b 1 i = [b 1 ix , b 1 iy , b 1 iz ] T the coordinates of B i expressed w.r.t. the S 1 .

Fig. 3 .

 3 Fig. 3. Kinematic scheme of the 3-DoF cutaneous device. The structure of each leg is RRS (Revolute-Revolute-Spherical).

Fig. 4 .

 4 Fig. 4. Choice of l 1 and l 2 . Filled areas represent possible values of l 1 and l 2 considering different β min and β max . Red curves represent equation β = β min , blue curves represent equation β = β max . The red star marker in case (a) represents the l 1 and l 2 values used for the prototype shown in Fig. 2.

Fig. 5 .

 5 Fig. 5. The numerical procedure to optimize the device design uses these fingertip geometric characteristics as inputs.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Rectified contact patch C and mobile platform profile for the four representative fingertips and configurations (a), (b), (c), (d) of Tab. I.

Fig. 8 .

 8 Fig. 8. Front views of the finger (pink dashed ellipse) and thimble structure for the four representative fingertips and configurations (a), (b), (c), (d) of Tab. I. Red line represents the front view of the fixed platform, blue line the mobile platform, black lines the legs. Cyan dots represent the surface (projected on the yz plane) that the device can reach. The device is represented in the reference configuration.

TABLE I EXAMPLE

 I OF DEVICE CHARACTERISTICS AS EVALUATED BY OUR PROCEDURE (DIMENSIONS IN mm. VALUES IN BOLD ARE PROVIDED BY THE USER. THE OTHER INPUTS ARE SET TO ψ max = θ max = 30 • , z max = 10 mm , h = 8 mm, l 1min = 8 mm.

			Ex.	e 1	e 2	e 3	a	a d	b	b d	l 1	l 2	r v	r v,no	Figs.
			(a)	5.5	5	11	20	35	10	17	11	28	7.08	16.68	6a, 7a, 8a
			(b)	7.5	7	16	16	28	10	17	11	29	2.27	6.00	6b, 7b, 8b
			(c)	9.5	8.5	18	17	30	11	20	12	34	1.88	3.46	6c, 7c, 8c
			(d)	13.5	11	23	21	37	16	27	16	44	1.47	1.47	6d, 7d, 8d
	8
	6
	4
	2
		Q1	Q2		Q3			Q4
	0	G P	G P		G P		G P


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Techno-Economic Comparison of Total Cost of Ownership of Electric and Diesel Vehicles

Keywords: diesel vehicle, life cycle cost, total cost of ownership, sensitivity analysis

Despite their low environmental impact, electrical vehicles have low penetration in the automotive market. Consumers are reluctant for technical reasons (limited driving range and long charging time) but also for an economic reason (high investment costs). Electric vehicle total cost of ownership (TCO) is often perceived as higher than for a thermal car, especially in Europe where diesel cars have a lower TCO than gasoline cars. Accurate TCO estimations are critical, but most of the techno-economic studies of electrified vehicles are based on very simplified energy models. In this paper, a techno-economic model is developed using an accurate technical model of an electric vehicle and a diesel car of the same segment. These technical models are validated by experimental measurements on real cars using real driving cycles. These models are then coupled to economic models to calculate TCO for a French case study. The total cost of ownership of the studied electric car is lower than for the equivalent diesel car by about 1000¿ for a 5-year ownership period. Of particular importance is the finding that using real driving cycles instead of standard driving cycles decreases the TCO of electric cars while simultaneously increasing the TCO of diesel vehicles. This has implications for techno-economic models, suggesting that the typical TCO approach that uses manufacturer-reported standard cycle data may be systemically biased towards thermal vehicles. In order to understand how TCO may change in different locations, a sensitivity analysis varies different technical and economic factors. Government subsidy, ownership duration, and vehicle depreciation are the most important factors for the TCO of electric vehicles. However, TCO of the electric cars can be lower than the TCO of equivalent diesel cars under a wide range of reasonable inputs.

I. INTRODUCTION

Air pollution and greenhouse gas emissions are important challenges for the transport sector. Electric vehicles (EVs) with zero-emission energy sources have great potential for reducing harmful emissions [START_REF] Van Mierlo | Comparative environmental assessment of alternative fueled vehicles using a life cycle assessment[END_REF], [START_REF] Mou | Achieving low carbon emission for dynamically charging electric vehicles through renewable energy integration[END_REF]. According to the International Energy Agency [START_REF] Global | Towards Cross-Modal Electrification[END_REF], a scenario that limits global warning to 2 • C is possible with 150 million EVs on roads by 2030. Efficiency of transport systems are an important parallel effort to reduce pollutant emissions [START_REF] Saponara | Electric drives and power chargers: Recent solutions to improve performance and energy efficiency for hybrid and fully electric vehicles[END_REF].

Many cities around the world expect to replace conventional vehicles by electrified vehicles [START_REF]C40 Cities Organization. Fossil Fuel Free Streets Declaration[END_REF], [START_REF] Bloomberg | A Dead End for Fossil Fuel in Europe's City Centers[END_REF]. For example, 40 cities plan to ban thermal cars by 2030 [START_REF]C40 Cities Organization. Fossil Fuel Free Streets Declaration[END_REF]. However, The associate editor coordinating the review of this manuscript and approving it for publication was Jesus Felez . drivers are generally reluctant to adopt electric vehicles due to some technical reasons (limited driving range and long charging time) but mainly for economic reasons (initial purchase costs) [START_REF] Junquera | Analyzing consumer attitudes towards electric vehicle purchasing intentions in spain: Technological limitations and vehicle confidence[END_REF], [START_REF] Habib | A comprehensive study of implemented international standards, technical challenges, impacts and prospects for electric vehicles[END_REF]. Government subsidies can have a strong effect on EV economics [START_REF] Yan | The economic and environmental impacts of tax incentives for battery electric vehicles in Europe[END_REF], but cost declines and better cost of ownership information also support EV adoption. It is difficult for a consumer to understand the economic viability of EVs in comparison with thermal cars, which is different for each driver. To achieve a high-quality estimation that accounts for a driver's individual situation, an economic model must use technical tools that produce accurate and personalized energy consumption estimates of different vehicles.

Many techno-economic studies of EVs have been completed for different countries and with different time perspectives [START_REF] Faria | A sustainability assessment of electric vehicles as a personal mobility system[END_REF]- [START_REF] Abas | Technoeconomic analysis and environmental impact of electric vehicle[END_REF]. Generally, the economic model is well developed, but is usually coupled with a simplistic technical model [START_REF] Abas | Technoeconomic analysis and environmental impact of electric vehicle[END_REF]- [START_REF] Letmathe | A consumer-oriented total cost of ownership model for different vehicle types in Germany[END_REF]. For example, a common approach for vehicle energy consumption is to use a fixed kWh/km or l/km, regardless of driving conditions or behavior [START_REF] De Clerck | How total is a total cost of ownership?[END_REF], [START_REF] Desai | Heterogeneity in economic and carbon benefits of electric technology vehicles in the US[END_REF]. However, there are a few exceptions where the technical vehicle model is more sophisticated. In [START_REF] Neubauer | Sensitivity of battery electric vehicle economics to drive patterns, vehicle range, and charge strategies[END_REF], the authors deal with a techno-economic study and a well-to-wheel analysis of electrified vehicles. The vehicle model is realized on the FASTSim software from NREL (US National Renewable Energy Laboratory). The vehicle consumption is calculated using NEDC, a standard driving cycle. In [START_REF] Cox | Life cycle environmental and cost comparison of current and future passenger cars under different energy scenarios[END_REF], a vehicle simulation tool is used to calculate the energy consumption for different vehicles for a Life Cycle Assessment and an economic study. The vehicle models are not presented, but are calibrated with the NEDC driving cycle. However, [START_REF] Fontaras | Fuel consumption and CO 2 emissions from passenger cars in Europe-Laboratory versus real-world emissions[END_REF] shows that the NEDC underestimates the energy consumption of thermal cars. Consequently, that error in the consumption estimation has an impact on any economic calculations. In [START_REF] Michaelides | Thermodynamics and energy usage of electric vehicles[END_REF], a technical model of an EV is developed for a well-to-wheel analysis of the vehicle. Then, an economic model is used to compare the energy cost of an EV and a thermal vehicle. However, the technical model of the vehicle traction developed in this study is a static model, not accounting for acceleration. These transient effects are important for high-quality estimation of the energy consumption of a vehicle [START_REF] Mayet | Comparison of different models and simulation approaches for the energetic study of a subway[END_REF]. Thus, there is a gap in the existing literature, as researchers have not yet brought together a high-quality technical model using realistic driving cycles with an economic model to understand how actual driving cycle patterns affect the total cost of ownership (TCO).

The objective of this paper is to propose a more realistic TCO comparison between an electric vehicle and a diesel car of the same segment. Towards that goal, two accurate technical models will be used for a more precise estimation of driving consumption. These accurate vehicle models have been developed for a first comparison of the pollutant emissions of both vehicles [START_REF] Noura | Comparison of the energy consumption of a diesel car and an electric car[END_REF]. Because no experimental validation of these technical models was performed, this work improves the prior research with a model update and a comparison using driving tests of real vehicles. These verified technical models are then coupled with an economic model, which evaluates the TCO of vehicle operations [START_REF] Desai | Heterogeneity in economic and carbon benefits of electric technology vehicles in the US[END_REF].

The contribution of the paper is to link accurate and validated vehicle models using a real driving cycle with detailed economic models to improve total cost of ownership estimates. This new capability allows comparison between the standard driving cycles (ex. WLTC) that have historically been used in techno-economic analysis with actual driving cycles. It also allows direct comparison between technical and economic features (such as between driving style and interest rate on vehicle loan).

In order to give real-life results, actual driving cycles from commuters at our university are considered instead of classical driving cycles. This first step produces a base case that allows for sensitivity analysis with different technical and economic inputs, which can represent the scenarios in other locations.

Section II presents the technical model for both vehicles, which are validated with real measurements. In section III, the economic model is established. Section IV presents the techno-economic comparison based on real commuting trips. Finally, the impact of the accurate technical models and real trips on the techno-economic metrics are discussed under different scenarios.

II. TECHNICAL MODEL OF THE VEHICLES

The simulation tools of diesel and electric vehicles are developed respectively in part A and B. In part C, the energy consumption of both vehicles is compared with standard consumption estimation approaches found in literature. This comparison shows the importance of using accurate technical models instead of standard fixed values. In part IV, the two models are used in an economic model to produce the techno-economic results that account for more accurate energy consumption estimates.

A. SIMULATION OF THE DIESEL VEHICLE 1) MODELING OF THE DIESEL VEHICLE

The diesel vehicle is based on a Renault Clio (Figure 1) [START_REF] Clio | [END_REF]. The parameters of the vehicle are given by Table 1. The Internal Combustion Engine (ICE) is connected to the wheels through a manual gearbox and a differential.

A classical consumption map is used to model the engine fuel consumption as a function of the engine torque and its rotation speed (Figure 2).

The gearbox torque T gb is given as a function of the engine torque T ice , the gearbox ratio k gb , and the efficiency η gb . The last two variables can change as a function of the 5 gears of the manual gearbox (Table 2). At each step, the gear ratio is chosen as a function of the velocity of the vehicle. The speed of the gearbox gb depends on the wheel speed wh and the gearbox ratio:

T gb = k gb T ice η k g gb gb = k gb wh with k g = 1 if T gb wh ≥ 0 -1 if T gb wh < 0 (1)
The wheels are considered as an equivalent wheel. The wheel force F wh is calculated as a function of the gearbox torque T gb , the wheel radius R wh , and the differential ratio

k diff :      F wh = k diff T gb R wh wh = k diff v dv R wh (2)
The total force F tot depends on the wheel force F wh and the braking force F br :

F tot = F wh + F br (3)
Newton's second law gives the vehicle velocity v dv as a function of the total force F tot , the resistive force F res , and the mass of the vehicle M veh :

M veh dv dv dt = F tot -F res ( 4
)
The resistive force F res is composed of the road resistance F road , the aerodynamic resistance F aero , and the slope resistance F slope :

F res = F road + F aero + F slope (5)

2) ORGANIZATION OF THE MODEL

The model of the diesel vehicle is described using Energetic Macroscopic Representation (EMR) [START_REF] Bouscayrol | Graphic formalisms for the control of multi-physical energetic systems[END_REF]. EMR is a graphical formalism that organizes different models of multi-physical systems. Moreover, a control loop can be deduced directly from the EMR by inverting each element. The EMR of the diesel vehicle (Figure 3) is composed of a mechanical source represented by the ICE (green oval), two conversion elements for the gearbox and the wheel (orange squares), a coupling element to couple the brake and the wheel (double orange square), an accumulation element for the chassis (crossed orange rectangle), and a mechanical source for the road. All modelling equations are integrated in the pictograms.

The control scheme is deduced from the EMR. The accumulation elements need a closed-loop control of the velocity of the vehicle (light blue crossed parallelogram). The other elements are directly inverted. A strategy level gives the gearbox ratio as a function of the car velocity to optimize the fuel consumption. Moreover, this strategy allows the decoupling of the mechanical brake from the propulsion part of the model.

3) VALIDATION

A real extra-urban trip was recorded with the diesel vehicle. The trip was 21 km long for a duration of 26 min in a city. The velocity profile (Figure 4 a) and the fuel consumption were measured. The velocity is measured with a GPS and depends on the speed limitations and the traffic conditions during the car trip. The consumption is measured on the CAN Bus of the vehicle with an OBD dongle.

The simulation of the vehicle is realized with Matlab/Simulink software based on the EMR organization. The measured velocity is provided as a simulation input. The instantaneous fuel consumption is calculated in the vehicle simulation (Figure 4 b). This fuel consumption is then integrated to obtain the cumulative fuel consumption (Figure 4 c.). The cumulative fuel consummation measured during the driving test is also plotted in the same figure. In order to have a more general comparison, the final consumption is reported in l/100 km. The consumption of the measured real trip is 4.88 l/100 km. The fuel consumption of the simulation is 4.91 l/100 km. That leads to an error of about 1%.

B. SIMULATION OF THE ELECTRIC VEHICLE 1) MODELING OF THE ELECTRIC VEHICLE

The electric vehicle is the Renault Zoe (Figure 5) [START_REF] Zoe | [END_REF]. It is in the same size segment as the diesel vehicle and comes from the same manufacturer. The parameters of the vehicle are given by Table 3.

The vehicle is composed of a battery, an electric drive, a gearbox, a differential, and the wheels.

The battery voltage u bat is a function of the Open Circuit Voltage (OCV) u O , the resistance of the battery, and the current i bat . The OCV depends on the State of Charge (SoC) relative to the current.

u bat = u O (SoC) -R bat i bat (6)
The electric drive is modeled with a static model that has a constant efficiency η ed = 87%, considered sufficient for such a study [START_REF] Mayet | Comparison of different models and simulation approaches for the energetic study of a subway[END_REF].

     T ed = T ed_ref i bat = T ed gb η k ed ed u bat with k ed = 1 if T ed gb < 0 -1 if T ed gb ≥ 0 (7)
The gearbox is a fixed-gear gearbox with a constant efficiency η gb = 95%.

T gb = k gb T ed η k g gb gb = k gb wh with k g = 1 if T gb wh ≥ 0 -1 if T gb wh < 0 (8)
The equations for the wheel and the chassis are the same as the diesel vehicle.

2) ORGANIZATION OF THE MODEL

The model of the EV is organized with EMR. The EMR of the EV (Figure 6) is composed as follows: the battery as a power source (green oval), the electric drive as a multi-domain conversion element (orange circle), a gearbox and wheels as mono-domain conversion elements (orange squares), the coupling of mechanical brakes with the wheels as coupling elements (overlapped orange squares) and the chassis as an accumulation element (crossed orange rectangle) for the velocity of the vehicle, and a source for the road.

The control scheme of the EV is similar to that of the diesel vehicle (blue parallelograms) deduced directly from the EMR.

A strategy element manages the use of the electric brake and the mechanical brake as a function of the total force imposed by the vehicle and the SoC of the battery. In this case, energy recovery is possible during the braking phases thanks to the reversible electrical machine.

3) VALIDATION

The Renault Zoe was driven on an extra-urban trip (Figure 7 The power at the input of the battery is calculated by the simulation (Figure 7 b). This power is integrated to find the energy consumption of the vehicle and compared with the measured energy consumption (Figure 7 c). The final simulated energy consumption is 3.53 kWh. The final measured consumption from the vehicle is 3.45 kWh. That leads to an error of about 2%.

C. COMPARISON WITH STANDARD CONSUMPTION VALUES

The energy consumption of the two vehicles calculated by the developed models are compared with a ''constant consumption'' approach based on manufacturer-reported values for the same vehicles. These constant values are used for the TCO calculation in [START_REF] Letmathe | A consumer-oriented total cost of ownership model for different vehicle types in Germany[END_REF] and [START_REF] Scorrano | Dissecting the total cost of ownership of fully electric cars in italy: The impact of annual distance travelled, home charging and urban driving[END_REF].

1) ELECTRIC VEHICLE

The ''constant consumption'' value is 20 kWh/100 km. The energy consumption of the real extra-urban trip (Figure 7) is 20% lower than the constant consumption value for the EV (Table 4). In [START_REF] Letmathe | A consumer-oriented total cost of ownership model for different vehicle types in Germany[END_REF] and [START_REF] Scorrano | Dissecting the total cost of ownership of fully electric cars in italy: The impact of annual distance travelled, home charging and urban driving[END_REF], the authors used the manufacturer-reported NEDC energy consumption value with a corrective factor of 45% which would lead to overestimation of the costs of the EV.

2) DIESEL VEHICLE

For the diesel vehicle, the ''constant consumption'' value is 3.8 L/100km [START_REF] Scorrano | Dissecting the total cost of ownership of fully electric cars in italy: The impact of annual distance travelled, home charging and urban driving[END_REF] based on the manufacturer-reported NEDC consumption. The fuel consumption based on the extra-urban trip measured with the vehicle (Figure 4 a) can be compared to this fixed value for the diesel vehicle. In this case, the relationship is reversed: the constant consumption value underestimates energy use by ∼20%, which leads to underestimation of the fuel consumption and costs of the diesel vehicle (Table 5).

3) COMPARISON DEVIATION

From these results, it should be clear that the classical techno-economical approach leads to an important misestimation. The energy consumption is overestimated for the EV and underestimated for the diesel car. This deviation will thus have an impact on the TCO estimates, biasing the results towards diesel vehicles. A more accurate technical model is thus important.

III. ECONOMIC MODEL

The economic model is developed for a vehicle purchased in France in 2020 and calculates the total cost of ownership (TCO) using a standard Net Present Value (NPV) method. The economic model takes into account the cost of the Electric Vehicle and the Diesel Vehicle, the tax policy, the salvage/resale values of the vehicles at the end of the ownership, and the energy costs. The replacement of the battery and its lifetime is not considered as newer batteries now have lifetimes approximately equal to the expected life of the vehicle [START_REF] Hossain | A comprehensive review on secondlife batteries: Current state, manufacturing considerations, applications, impacts, barriers & potential solutions, business strategies, and policies[END_REF].

The capital cost of the vehicles (CC) depends on the initial cost of the vehicle C veh , the cost of the green card (registration) C gc , and a tax policy P veh in favor of the vehicle (or disfavor in the case of the diesel):

CC = C veh + C gc -P veh (9)
The Salvage Value SV is the resale value of a vehicle at the end of its ownership. We follow the method described in [START_REF] Desai | Heterogeneity in economic and carbon benefits of electric technology vehicles in the US[END_REF] where resale value depends on the initial cost of the vehicle C veh , the tax policy P veh , and the depreciation rate A dep, and is discounted to present value using the discount rate σ and the number of years before resale n [START_REF] Faria | A sustainability assessment of electric vehicles as a personal mobility system[END_REF]. The depreciation rate follows a decelerating decline, calibrated based on actual resale values of US vehicles [START_REF] Raustad | Electric vehicle life cycle cost analysis[END_REF]. We assume that the percentage change in value over time for a vehicle in France follows the same empirical trend as the US. Moreover we assume that the same model can be used for both types of vehicles. While new technologies generally do not have the same salvage value as mature technologies, we consider that EVs will become a more mature and accepted technology in the coming years. However a sensitivity analysis will study the impact of this factor in section IV.F.

SV = 1 -A dep (C veh -P veh )(1 + σ ) -n (10)
With A dep = 6 × 10 -5 n 3 -0.0038 n 2 + 0.093 n + 0.1384 [START_REF] He | Economic and climate benefits of electric vehicles in China, the United States, and Germany[END_REF] The energy cost of the Electric Vehicle EC EV is a function of the vehicle annual mileage D veh , the annual amount of charging energy needed by the vehicle E ev , and the cost of electricity C elec : [START_REF] Abas | Technoeconomic analysis and environmental impact of electric vehicle[END_REF] The energy cost of the diesel vehicle EC DV depends on the fuel consumption of the diesel vehicle E DV , the diesel cost C D and the annual mileage of the vehicle D veh :

EC EV = E EV D veh C elec
EC DV = E DV D veh C ( 13
)
The energy cost for each vehicle EC is added to the maintenance cost C m and the insurance cost C ins to obtain the annual cost for the different vehicles AC: [START_REF] Hao | Levelized costs of conventional and battery electric vehicles in China: Beijing experiences[END_REF] The total cost of ownership (TCO) depends on the capital cost, the salvage value and the annual cost of the vehicle:

AC = EC + C m + C ins
TCO = CC -SV + n i=0 AC (1 + σ ) i ( 15
)

IV. ECONOMIC COMPARISON UNDER DIFFERENT SCENARIOS

In this part, the techno-economic model is brought together to analyze the total cost of ownership of vehicles. The techno-economic study is presented first as the link between the technical models and the economic model. Then, the study is applied to 3 different real driving cycles: an urban, an extra-urban and a highway trip. The real driving cycles represent a case study at the University of Lille, as part of the CUMIN program. The CUMIN (Campus of University with Mobility based on Innovation and carbon Neutrality) program [START_REF] Bouscayrol | Campus of university with mobility based on innovation and carbon neutral[END_REF] is focused on reducing greenhouse gas emission from thermal vehicles that come to campus. One strategy of this program is to replace thermal cars with electric vehicles. In this transition, economic tools are necessary to plan for charging stations and photovoltaic panels to provide electricity for EVs.

Commuting trips to the University of Lille are analyzed in detail to guide the selection of vehicles for campus commuters. These driving cycles represent the diversity of expected road conditions and energy consumption. The three driving cycles are compared with the standard case (WLTC) used in recent techno-economic studies. Finally, a sensitivity analysis is conducted to compare the effect of different technical and economic parameters.

A. TECHNO-ECONOMIC STUDY

A driving cycle is an input of the technical models, used to calculate the energy consumption of the vehicles. For the diesel vehicle, the fuel consumption is directly connected to the economic model. For the Electric Vehicle, the charging infrastructure efficiency is also required to estimate the true energy used to charge the vehicle and purchased by the EV owner. The charging infrastructure is considered to have an efficiency of 87% [START_REF] Apostolaki-Iosifidou | Measurement of power loss during electric vehicle charging and discharging[END_REF]. Only slow charging is considered in this study. For both vehicle types, the calculated energy consumption is an input of the economic model (Figure 8).

Other inputs of the economic model are the mileage of the vehicle, the interest rate of the vehicle loan, the electricity price, the diesel price, and the maintenance and the insurance of the vehicle. These variables are summed up in VOLUME 8, 2020 TABLE 6. Base case parameters of the techno-economic study and ranges used in sensitivity analysis. TABLE 6 with their values in 2020. Base case numbers the most current values available, while the range is based on historical variation in the variable over the last 10 years, except for the interest rate, where it is 5 years. The economic calculations give the energy cost and the TCO for the different vehicles.

The vehicle prices are the prices in 2020. The EV can be considered with two options: one has battery leasing, the second is the electric vehicle purchased with its battery. In leasing, the vehicle is sold at 23 900¿, versus 32 000¿ for the complete The leasing cost of the battery depends on the mileage and the lifetime of the vehicle and is between 530¿ and 1 490¿ per year. The diesel vehicle is sold at 19 300¿ and has no tax policy. The Electric Vehicle is considered to have a tax bonus of 8 000¿ in the base case. While the actual subsidy is higher than 8 000¿ in France [START_REF]EV Bonus in France[END_REF] or Norway [START_REF]EV Bonus in France[END_REF], it represents a typical subsidy level given by most European countries [START_REF] Global | Entering the decades?[END_REF].

B. COMPARISON OF DIESEL AND EV VEHICLES FOR AN URBAN DRIVING CYCLE

The first considered trip is a real measured urban trip with a lot of stops due to traffic lights and traffic conditions (Figure 9). The trip length is 14 km. The duration is 40 min.

The consumption is calculated for the two vehicles with the two technical models. The fuel consumption for the diesel vehicle is 5.48 l/100 km. The EV has an energy consumption of 14.16 kWh/100 km. These energy consumption estimates are scaled up for the two vehicles and used to estimate annual energy costs by assuming that the vehicle is driven 9 500 km per year on this route. The energy cost for the diesel vehicle is 754¿ per year against 204¿ per year for the EV. That leads to a reduction of 73% in the energy cost when switching to an EV under the urban driving cycle. The total cost of ownership (TCO) for the EV with and without the leasing of the battery and the diesel vehicle are compared (Figure 10). In each case, the EV has a TCO equal to or lower than the diesel vehicle. The EV saves between 72¿ and 1952¿. Between the 2 EV options, the leasing of the battery is preferred for shorter ownership duration of the vehicle. But in the long-term, it is better to buy the full EV with the battery included. This is generally expected: leasing terms are normally most favorable for shorter-term ownership of assets.

C. COMPARISON OF DIESEL AND ELECTRIC VEHICLES FOR AN EXTRA-URBAN DRIVING CYCLE

The extra-urban case was used for the validation of the EV (see Figure 7) and is also used as a scenario here. The simulation of the diesel vehicle gives a consumption of 4.72 l/100 km. The EV has a consumption of 16.64 kWh/100 km. Using this as the standard driving cycle over the year gives an energy cost of 650¿ for the diesel. The EV has an energy cost of 240¿, representing a reduction of 63%.

In this case, the TCO of the electric vehicle is not consistently dominating the diesel (Figure 13). The difference goes from -317¿ to 1563¿ of savings on the total cost of ownership for EVs. As in the urban case, the leasing of the battery is preferred in the first 5 years but not at 8 years or more.

D. COMPARISON OF DIESEL AND EV VEHICLES FOR A HIGHWAY DRIVING CYCLE

The last case is a real, measured highway-heavy trip (Figure 14). The trip has a higher average velocity and fewer accelerations than the previous driving cycles. The trip length is 19.5 km for a duration of 16 min.

The diesel vehicle has a fuel consumption of 5.73 l/100 km. The energy consumption is 22.9 kWh/100 for the EV. The annualized energy cost for the diesel vehicle, assuming that this driving cycle represents driving patterns over the year, is 789¿. The EV has an energy cost of 330¿, saving 58%. The TCO for the vehicles are presented in Figure 13. Except for the full EV with resale at 3 years, the EV has a lower TCO than the diesel vehicle. Despite having a lower percentage decrease in the annual energy cost than the Extra-urban driving cycle (58% vs. 63%), this cycle has more favorable economics for the EVs because the absolute difference in annual fuel costs is larger (459¿ versus 410¿). The leasing of the battery is preferred for 3-or 5-year lifetime but not for 8-years of ownership.

E. COMPARISON BETWEEN DIFFERENT DRIVING CYCLES

In this part, the results of the different cases are summarized and a comparison with the classical approach is provided. For the classical approach, the consumption of the two vehicles is taken from the manufacturer [START_REF] Clio | [END_REF], [START_REF] Zoe | [END_REF]. This consumption is calculated with the WLTC and represents a more traditional (and simple) method for calculating the total cost of ownership of vehicles.

The difference in annual energy costs is given by Figure 14. The largest savings for the EV in terms of energy spending is for the urban cycle (550¿ less than the energy cost for the diesel car). The difference is 410¿ for the extra urban trip and for the highway trip. Using the information provided by a standard WLTC produces the smallest savings for the EV, at 330¿ per year. This standard classical driving cycle thus underestimates the annual savings of an EV relative to any of the three measured driving cycles. However, this standard driving cycle is used, directly or indirectly through manufacturer-reported data, in essentially all techno-economic comparisons of thermal and electric vehicles [START_REF] Fontaras | Fuel consumption and CO 2 emissions from passenger cars in Europe-Laboratory versus real-world emissions[END_REF]. The Difference in TCO between EVs and diesel vehicle are given in Figure 15 for an ownership period of 5 years. In order to show the importance of the accurate technical models, TCO values calculated using a traditional techno-economic approach are also plotted. This includes the TCO using a WLTC (rather than a real driving cycle) and a TCO calculated using the ''constant consumption'' value reported by the manufacturer (see section II.C). Both the WLTC-based information from the manufacturer and the constant consumption data are more favorable to diesel than any of the real driving cycles. Relative to a diesel vehicle, the real driving cycles suggest that EVs are consistently preferred in terms of TCO. While further study is justified, this suggests that the existing economic literature may have a small but consistent bias against EVs because of the commonly used methods.

F. SENSITIVITY ANALYSIS

A sensitivity analysis is performed to compare the effects of technical variables with economic variables. This also permits consideration of other scenarios and locations than the study case.

The base case and the ranges are given in TABLE 6. The base case driving cycle is the extra-urban cycle and the base case vehicle carries only the driver. For variation in technical parameters, we change the driving cycle for the vehicle or increase the average number of passengers to For economic variation, we use historical variation in the data collected (references in TABLE 6) to get plausible ranges for the variables: electricity and diesel prices in [START_REF] Andreï | Bilan Energétique de la France pour l'année 2018[END_REF], the mileage in [START_REF] Armoogum | La Mobilité des Français, Panorama Issu de l'Enquête Nationale Transports et Déplacements[END_REF] and the interest rate in [START_REF] France | Loans to the Households[END_REF]. The bonus (government subsidy) can change quickly, and we apply a variation in either direction of 40%. A more regressive salvage value is also considered for the EV. Equation ( 16) gives a faster depreciation rate of the salvage value compared to [START_REF] He | Economic and climate benefits of electric vehicles in China, the United States, and Germany[END_REF].

A dep = -58 × 10 -10 n 5 + 10 -7 n 4 + 1, 98 × 10 -4 n 3 -0.0087 n 2 + 0.137 n + 0.1384 [START_REF] De Clerck | How total is a total cost of ownership?[END_REF] The Total cost of ownership (TCO) is calculated for both the diesel and the electric vehicle. The difference between the TCO for the diesel vehicle and the EV are calculated for each case (Figure 16). In the base case, the difference is -10¿, meaning that the TCO of the EV is essentially equal to the TCO of the diesel vehicle.

The higher (light blue) and lower (dark green) cases are represented for each variable by a bar beginning at the base case. The variables are sorted by the magnitude of the effect on TCO difference. Over the ranges selected, a faster vehicle depreciation rate for resale of the electric vehicle has the largest effect on TCO. However, this depreciation rate will likely slow down as EVs sales increase. The EV Bonus has the second-largest effect. A reduction of the EV bonus by 3 000¿ leads to a difference of 1800¿ (due to the depreciation of the EV) in favor of the diesel vehicle. The next is the mileage, where an increase of 4500 km increases the TCO difference by 860¿. Increasing the diesel price by 28% (consistent with historical fluctuations) increases the TCO difference by 800¿. The duration of ownership has a moderate impact. A highway driving cycle or an urban trip instead of the extra-urban cycle increases the difference respectively by 220¿ and 620¿. The increase of the electricity price by 30% decreases the TCO difference by 320¿. Adding two passengers into the cars increases the total cost of ownership benefit of an EV by 210¿. The interest rate is the last variable and has the smallest impact on the TCO of the vehicle because of the short lifetimes of vehicle loan payments and the historically consistent loan rates. Increasing the loan interest rate from 4.05% to 5.17% decreases the TCO difference by 40¿.

V. CONCLUSION

This work has developed a techno-economic analysis of the total cost of ownership of electric and diesel vehicles and applied it to a case study in France. The focus of the work is to bring together technical and economic models that can capture and compare the relevant factors from both domains. The technical model has been validated with real measurements and is able to provide accurate energy consumption for the two vehicles studied. This has been coupled with an economic model to assess the energy cost and total cost of ownership for the vehicles under a variety of scenarios. An accurate consumption can thus be calculated for any driving cycle and used in an economic estimation of the total cost of ownership.

The results illustrate a TCO advantage for EVs in France that is dependent on the currently favorable tax bonus but is otherwise relatively robust. In general, the economic variables have a stronger effect on TCO than the technical variables. The depreciation rate and governmental incentives are the main factors for the TCO of EVs. Importantly, this work highlights a general issue with standard driving cycles, which consistently underestimate the benefits of EVs for the three measured driving cycles we used.

There is potential to apply or extend this research in several directions. For an economic study of a dedicated area, we can offer precise estimations to commuters about the cost of ownership of their vehicle options and calculate the amount of charging infrastructure needed to charge a fleet of EVs. The analysis can be extended to other vehicle segments and technologies and the effect of climate conditions and driver behavior on the TCO can be assessed.

FIGURE 1 .

 1 FIGURE 1. Renault Clio used for validation tests.

FIGURE 2 .

 2 FIGURE 2. Consumption map of the diesel engine.

FIGURE 3 .

 3 FIGURE 3. EMR of the diesel vehicle.

FIGURE 4 .

 4 FIGURE 4. a) Measured velocity profile for the diesel vehicle b) Instantaneous fuel consumption of the ICE c) Comparison of the measured and simulated cumulative fuel consumption.

FIGURE 5 .

 5 FIGURE 5. Renault Zoe used for validation test.

FIGURE 6 .

 6 FIGURE 6. EMR of the electric vehicle.

  a) of 21 km and a duration of 27 min. The velocity profile is measured with a GPS and the energy consumption is measured on the vehicle CAN Bus with an OBD dongle.VOLUME 8, 2020

FIGURE 7 .

 7 FIGURE 7. a) Measured velocity profile for the evaluation of the EV b) Simulated battery power c) comparison of the simulated and measured cumulative energy consumption of the EV.

FIGURE 8 .

 8 FIGURE 8. Techno-economic model coupling for the study.

FIGURE

  FIGURE Urban driving cycle.

FIGURE 10 .

 10 FIGURE 10. TCO of vehicles for the urban case, for the diesel car and electric vehicles with and without the battery leasing.

FIGURE 11 .

 11 FIGURE 11. TCO for the extra-urban case, for diesel vehicle and electric vehicles with and without the battery leasing.

FIGURE 12 .

 12 FIGURE 12. Highway driving cycle.

FIGURE 13 .

 13 FIGURE 13. TCO for the highway driving cycle, for the diesel vehicle and electric vehicles with and without the battery leasing.

FIGURE 14 .

 14 FIGURE 14. Annual energy costs savings achieved by switching from the diesel to the electric vehicle under four driving cycles.

FIGURE 15 .

 15 FIGURE 15. TCO benefit of selecting an electric rather than a diesel vehicle, under five driving cycle scenarios.

FIGURE 16 .

 16 FIGURE 16. Sensitivity analysis.

TABLE 1 .

 1 Critical parameters of the Renault Clio.

TABLE 2 .

 2 Gear ratio for the gearbox of the diesel vehicle.

TABLE 3 .

 3 Critical parameters of the Renault Zoe.

TABLE 4 .

 4 Comparison of the energy consumption for an EV.

TABLE 5 .

 5 Comparison of the energy consumption for a diesel vehicle.

 VOLUME 8, 2020

VOLUME 8, 2020

This work was supported in part by the Framework of the TESS Project of the CUMIN Program of University of Lille from the I-SITE Université de Lille Nord Europe, the Métropole Européenne de Lille, and Region Hauts-de-France, and in part by the Framework of the PANDA Project from the European Union's Horizon 2020 Research and Innovation Program under grant agreement 824256 (PANDA).