Lorenzo Gagliardini
email: lorenzo.gagliardini@irt-jules-verne.fr

Stéphane Caro
email: stephane.caro@irccyn.ec-nantes.fr

Marc Gouttefarde
email: marc.gouttefarde@lirmm.fr

Philippe Wenger
email: philippe.wenger@irccyn.ec-nantes.fr

Alexis Girin
email: alexis.girin@irt-jules-verne.fr

A Reconfigurable Cable-Driven Parallel Robot for Sandblasting and Painting of Large Structures

published or not. The documents may come

Introduction

Over the last decades, several companies faced the necessity to manufacture novel large industrial structures. Surface finishing, e.g. painting and sandblasting, can be part of the manufacturing process of those structures. According to the different structures, painting and sandblasting are usually performed by human operators, with the support of non-automatic machines. Alternative methods can improve the efficiency of these operations and release human operators from their unpleasant tasks. Cable Driven Parallel Robots (CDPR) are one of the possible solutions. By definition, CDPRs are parallel robots composed of a platform connected to a fixed base by cables (in this paper, the connection points between the cables and the base will be referred as anchor points). Sandblasting and painting tools can be embarked on the CDPR platform, which will follow the profile of the structure to be painted according to an off-line planned strategy.

Advantages of CDPRs are their wide workspace, the possibility to carry heavy loads and the simplicity of their mechanical components [START_REF] Gouttefarde | Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots[END_REF]. However, a limitation of CDPRs is the possible interferences between cables as well as between cables and the surrounding environment. Furthermore, the non-rigid nature of CDPR links requires a rigorous study of the force transmission characteristics.

The potentialities of CDPRs have already been proved in different industrial contexts [START_REF] Bostelman | Applications of the NIST RoboCrane[END_REF], [START_REF] Holland | Cable array robot for material handling[END_REF]. Other research studies are being performed in the framework of the European project CableBot [5]. Most of the previous works are dedicated to CD-PRs with a fixed architecture and a fixed geometry (cable layout). This type of robots cannot always guarantee good performances when installed in cluttered environments. In this context, Reconfigurable Cable-Driven Parallel Robots (RCDPR) should represent a better solution. Indeed, they can modify their geometric parameters in order to adapt their characteristics or to avoid cable collisions.

One of the first works related to CDPR reconfigurability was part of the NIST RoboCrane project [START_REF] Bostelman | Cable-based reconfigurable machines for large scale manufacturing[END_REF]. Further studies on reconfigurability have been performed by Zhuo et al. [START_REF] Zhou | Analysis framework for cooperating mobile cable robots[END_REF], as well as by Izard et al. [START_REF] Izard | A reconfigurable robot for cabledriven parallel robotic research and industrial scenario proofing[END_REF] and Rosati et al. [START_REF] Rosati | On the design of adaptive cable-driven systems[END_REF]. Rosati suggested to add additional DoF to a classical CDPR (e.g., moving the cable anchor points on a rail) and optimize analytically the robot properties, such a the payload capability. This method has been proved to be efficient for planar robots. However, it cannot be easily applied to three-dimensional case studies, where the analytic solution of the problem is very difficult to define.

The research work presented in this paper focuses on the design of a RCDPR for sandblasting and painting of a three-dimensional tubular structure represented in Fig. 1. These operations are performed by appropriate tools embarked on the robot platform. The robot platform approaches each external side of the structure and the tools perform their work. Due to the structure complexity, reconfigurability is required in order to avoid cable collisions. Each external side of the structure is sandblasted and painted through a different configuration of the cable anchor points. To reconfigure the CDPR from one side of the structure to another one, one or several cables are disconnected from their current anchor points and moved to new ones. This procedure is repeated until all the sides of the structure are sandblasted and painted. The variables of the corresponding design problem are thus the Cartesian coordinates of the anchor points of the three required configurations associated to the paths P 1 , P 2 and P 3 illustrated in Fig. 2.

In the present work, we aim at minimizing the total number of anchor points on the base, selecting the anchor point locations that can be shared between two or more configurations. Thereby, during a configuration change, not all the cable anchor points need to be modified. Furthermore, we also aim at minimizing the robot overall size. The feasibility of each configuration has to be guaranteed: cable interferences as well as cable collisions with the structure are not permitted. Moreover, a minimum platform pose precision is required.

This paper is organized as follows. Section 2 briefly introduces the industrial context and the problem at hand. Section 3 presents the RCDPR geometric, static and elastostatic models used in this paper. Section 4 provides a description of the selected design strategy. Section 5 presents the achieved results. Section 6 concludes this article.

Context and Problem Description

The structure selected for the given case study is 20 m long, with a cross section of 10 m x 10 m. The number of tubes to be painted is equal to twenty. Their diameter, φ s , is equal to 0.8 m. The sandblasting and painting operations are realised indoor. The structure lies horizontally in order to reduce the dimensions of the painting workshop. The whole system can be described with respect to a fixed reference frame, F b , of origin O b and axes x b , y b , z b , as illustrated in Fig. 2.

Sandblasting and painting tools are embarked on the RCDPR mobile platform. The CoM of the platform follows the profile of the structure tubes and the tools perform the required operations. The paths to be followed, P 1 , P 2 and P 3 , are represented in Fig. 2. They are located at a distance of 2 m from the structure tubes. No path has been assigned to the lower external side of the structure, since it is sandblasted and painted from the ground.

In order to avoid collisions between the cables and the structure, the reconfigurability of the robot anchor point positions is necessary. Each external side of the structure should be painted by one and only one robot configuration. Three configu- rations are necessary to work at the exterior of the structure: configuration C i being associated to path P i , i = 1, 2 and 3. This requirement is demanded in order not to interrupt the painting and sandblasting operations during their execution. Passing from a configuration to another, one or more cables are disconnected from their anchor points and connected to other anchor points located elsewhere. For each configuration, the locations of the cable exit points are defined as variables of the design problem. In the present work, the dimensions of the platform as well as the position of the cable connection points on the platform are fixed. They will be both detailed in Sec. [START_REF] Bouchard | On the ability of a cable-driven robot to generate a prescribed set of wrenches[END_REF].

A suspended and a fully constrained 8-cable CDPR architecture are considered. The suspended architecture is inspired by the CoGiRo CDPR prototype [START_REF] Lamaury | Dual-space adaptive control of redundantly actuated cable-driven parallel robots[END_REF]. For the fully constrained configuration, note that 8 cables is the smallest possible even number of cables that can be used for the platform to be fully constrained by the cables. In the suspended architecture, the static equilibrium of the mobile platform is obtained thanks to the gravity force that plays the role of an additional cable pulling the mobile platform downward.

The RCDPR should be as cheap and simple as possible. For this reason, the minimization of the total number of cable anchor points is required. Consequently, the number of anchor point locations, shared by two or more configurations, should be maximized. The size of the robot is minimized as well, in order to reduce the dimensions of the sandblasting and painting workshop.

Since the sandblasting and painting operations are performed at low speed, the motion of the CDPR platform can be considered to be quasi-static. Hence, only the static equilibrium of the robot mobile platform will be considered. Collisions between the cables as well as collisions between the cables and the structure tubes should be avoided. Besides, the platform positioning precision is constrained as detailed in Sec. 4. Here, the cable mass is not considered.

RCDPR Kinetostatic Modeling

A RCDPR is mainly composed of a mobile platform connected to the base through a set of cables, as illustrated in Fig. 3. The connection points of the i-th cable on the platform are denoted as B i,c , where c represents the configuration number. The position of each point B i,c is expressed by the vector b p i,c with respect to a local reference frame F p , attached to the platform and of origin O p and axes x p , y p and z p . O p is the platform Center of Mass (CoM). For the c-th configuration, the anchor point of the i-th cable is denoted by A i,c , i = 1, . . . , 8. The Cartesian coordinates of each point A i,c , with respect to F b , are given by the vector a b i,c . The pose of the platform, with respect to F b , is defined by the vector p = [t, Φ] T . The vector t represents the Cartesian coordinates of the platform CoM. The platform orientation is defined by the vector Φ, through the Euler angles φ , θ and ψ corresponding to rotations around z b , x b and y b , respectively.

For a given configuration c, the vector directed along the cable from B i,c to A i,c , expressed in F b , is defined as follows:

l b i,c = a b i,c -t -Rb p i,c i = 1, . . . , 8 (1)
where R is the rotation matrix defining the platform orientation:

R = R z (φ )R x (θ )R y (ψ) =   cφ cψ -sφ sθ sψ -sφ cθ cφ sψ + sφ sθ cψ sφ cψ + cφ sθ sψ cφ cθ sφ sψ -cφ sθ cψ -cθ sψ sθ cθ cψ   (2)
The unit vector d i,c associated to each vector l i,c is given by:

d b i,c = l b i,c l i,c b 2 , i = 1, . . . , 8 (3)
The i-th cable exerts on the platform a wrench w i . This wrench is produced by a positive cable tension τ i . All the cable tensions are collected in the vector τ = [τ 1 , ..., τ 8 ] T . The static equilibrium of the platform is described by the following equation:

Wτ + w e = 0 ( 4
)
where W is the wrench matrix, defined as follows:

W = d b 1,c d b 2,c . . . d b 8,c Rb p 1,c × d b 1,c Rb p 2,c × d b 2,c . . . Rb p m,c × d b 8,c (5)
The vector w e is the external wrench. It describes the wrench transmitted by the sandblasting or painting tools to the RCDPR platform and the weight of the platform and of the embarked tools. The weight of the platform and the embarked tools is considered to be equal to 60 Kg. w e = f, m

T = f x , f y , f z , m x , m y , m z T ( 6
)
The forces transmitted along the axes x b , y b and z b are represented by the components f x , f y and f z , respectively. The maximum intensity of these components are considered to be equal to 50 N. The maximum values of the transmitted torques m x , m y and m z , are equal to 7.5 Nm.

-50

N = f min ≤ f x , f y , f z ≤ f max = 50 N (7) -7.5 Nm = m min ≤m x , m y , m z ≤ m max = 7.5 Nm (8)
Cable tensions can be computed from Eq. ( 4):

τ = τ n + τ 0 = W † w e + λ N τ ≥ 0 (9)
W † is the Moore-Penrose generalized inverse of W, λ ∈ R 2 and N is the null space of W [START_REF] Roberts | On the inverse kinematics, statics, and fault tolerance of cable-suspended robots[END_REF]. The elastostatic model defines the relationship between the infinitesimal change δ p in the platform pose and the corresponding infinitesimal change of the external wrench δ w e :

δ w e = Kδ p [START_REF] Holland | Cable array robot for material handling[END_REF] The expression of the stiffness matrix

K is [1] K = m ∑ i=1 k i d i,c d T i,c d i,c d T i,c bb i,c T bb i,c d i,c d T i,c bb i,c d i,c d T i,c bb i,c T + - m ∑ i=1 τ i l i   -I 3,3 + d i,c d T i,c -I 3,3 + d i,c d T i,c bb i,c T bb i,c -I 3,3 + d i,c d T i,c bb i,c -I 3,3 + d i,c d T i + bb i,c T bb i,c   (11)
where k i denotes the i-th cable longitudinal stiffness, I 3x3 denotes the 3 × 3 identity matrix, bb i,c and di,c represent the cross product matrices of vectors b b i,c and d i,c , respectively. For a generalized 3-dimensional vector r = [r x , r y , r z ] T , the cross product matrix is defined as follows:

r =   0 -r z r y r z 0 -r x -r y r x 0   (12)
4 Design Procedure

The design problem aims at identifying the locations of points A i,c for the configurations C 1 , C 2 and C 3 . The number of cables, m, the cable properties and the dimensions of the platform are given in Sec. 4.1. Those parameters are the same for the three robot configurations. At first, in order to identify the set of feasible locations for the anchor points A i,c , the three robot configurations are parameterized and analysed separately in Secs. 4.2, 4.3 and 4.4. A set of anchor points will be considered feasible if the design constraints are satisfied along the whole path to be followed by the CoM of the platform. The design constraints are listed in Sec. 4.5. Note that each path P i , i = 1, . . . , 3 is discretized into 38 points P j,i , j = 1, . . . , 38 i = 1, . . . , 3

Once the set of feasible solutions have been obtained for each configuration, i.e., for each path, a list of robots with a minimum number of anchor points, n c , is extracted from the list of feasible robots. Finally, the most compact robots from the list of robots with a minimum number of anchor points are optimal solutions.

Design parameters

The RCDPR developed in this paper is composed of steel cables. The Young Modulus, E, is equal to 100 GPa. Their diameter, φ c is equal to 4 mm, the stiffness coefficient, k i , is equal to 252 KN/m. The maximum allowed tension in the cables, τ max , is equal to 34 950 N:

0 < τ i ≤ τ max , ∀i = 1, . . . , 8 (13)
l p , w p and h p denote the length, width and height of the platform, respectively: l p = 30 cm, w p = 30 cm and h p = 60 cm. The design (constant) parameter vector q is expressed as:

q = [m, φ c , k i , τ max , l p , w p , h p ] T (14)

Configuration C 1

A fully constrained architecture has been assigned to the configuration C 1 . As shown in [START_REF] Gagliardini | Optimal design of cabledriven parallel robots for large industrial structures[END_REF], this type of robot architecture can assure the robot static equilibrium while minimizing its size. The anchor points A i,1 have been arranged in a parallelepiped layout. The edges of the parallelepiped are aligned with the axes of frame F b . This layout can be fully described by means of five variables: u 1 , u 2 and u 3 define the Cartesian coordinates of the parallelepiped centre; u 4 and u 5 represent the halflengths of the parallelepiped along the axes x b and y b , respectively. Therefore, the Cartesian coordinates of the anchor points A i,1 are expressed as follows:

a b 1,1 = [u 1 + u 4 , u 2 + u 5 , -u 3 ] T a b 2,1 = [u 1 + u 4 , u 2 + u 5 , u 3 ] T ( 15
)
a b 3,1 = [u 1 -u 4 , u 2 + u 5 , -u 3 ] T a b 4,1 = [u 1 -u 4 , u 2 + u 5 , u 3 ] T ( 16
)
a b 5,1 = [u 1 -u 4 , u 2 -u 5 , -u 3 ] T a b 6,1 = [u 1 -u 4 , u 2 -u 5 , u 3 ] T (17)
a b 7,1 = [u 1 + u 4 , u 2 -u 5 , -u 3 ] T a b 8,1 = [u 1 + u 4 , u 2 -u 5 , u 3 ] T (18)
The layout of the first robot configuration is described in Fig. 4. The design variables of the design problem at hand are collected into the vector x 1 :

x 1 = [u 1 , u 2 , u 3 , u 4 , u 5 ] T (19)
The Cartesian coordinates of the connection points B i,1 of the cables to the platform are expressed as:

b b 1,1 = 1 2 [l p , w p , h p ] T , b b 2,1 = 1 2 [l p , w p , -h p ] T (20) b b 3,1 = 1 2 [-l p , w p , h p ] T , b b 4,1 = 1 2 [-l p , w p , -h p ] T (21) b b 5,1 = 1 2 [-l p , -w p , h p ] T , b b 6,1 = 1 2 [-l p , -w p , -h p ] T (22) b b 7,1 = 1 2 [l p , -w p , h p ] T , b b 8,1 = 1 2 [l p , -w p , -h p ] T (23)
A discretized set of design variables have been considered. The lower and upper bounds as well as the number of values for each variable are given in Tab. 1. 18225 robot configurations have been generated with those values. It turns out that 4576 configurations satisfy the design constraints expressed in Sec. 4.5 along the 38 discretized points of path P 1 .

Configuration C 2

A suspended architecture has been attributed to the configuration C 2 in order to avoid any possible collision with the tubular structure. The selected architecture is based on CoGiRo, a suspended CDPR designed and built in the framework of the ANR CoGiRo project [START_REF] Lamaury | Dual-space adaptive control of redundantly actuated cable-driven parallel robots[END_REF], [11]. An advantage of this architecture is the possibility to balance efficiently the external wrench throughout a very large part of the robot footprint. The anchor points A i,2 have been arranged in a parallelepiped layout. The Cartesian coordinates a i,c are defined as follows:

a b 1,2 = a b 2,2 = [v 1 -v 4 , v 2 -v 5 , v 3 ] T ( 24
)
a b 3,2 = a b 4,2 = [v 1 -v 4 , v 2 + v 5 , v 3 ] T (25) a b 5,2 = a b 6,2 = [v 1 + v 4 , v 2 + v 5 , v 3 ] T (26) a b 7,2 = a b 7,2 = [v 1 + v 4 , v 2 -v 5 , v 3 ] T ( 27
)
Variables v 1 = 1, . . . , 5 assume the same geometric roles assigned to variables u 1 = 1, . . . , 5. The layout of this configuration is illustrated in Fig. 5. The design variables of configuration C 2 are collected into the vector x 2 :

x 2 = [v 1 , v 2 , v 3 , v 4 , v 5 ] T (28)
Note that this architecture is composed of couples of anchor points theoretically connected to the same locations: {A 1,2 , A 2,2 }, {A 3,2 , A 4,2 }, {A 5,2 , A 6,2 } and {A 7,2 , A 8,2 }. From a technical point of view, in order to avoid any cable interference, the coupled anchor points should be separated by a distance at least greater than cable diameter. For the design problem at hand, this distance has been fixed to 5 mm.

The Cartesian coordinates of points B i,2 are defined as:

b b 1,2 = 1 2 [l p , -w p , h p ] T , b b 2,2 = 1 2 [-l p , w p , -h p ] T (29) b b 3,2 = 1 2 [-l p , -w p , h p ] T , b b 4,2 = 1 2 [l p , w p , -h p ] T (30) b b 5,2 = 1 2 [-l p , w p , h p ] T , b b 6,2 = 1 2 [l p , -w p , -h p ] T (31) b b 7,2 = 1 2 [l p , w p , h p ] T , b b 8,2 = 1 2 [-l p , -w p , -h p ] T (32)
Table 1 describes the lower and upper bounds as well as the number of values considered for the configuration C 2 . Combining these values, 22275 configurations have been generated. Amongst these configurations, only 5579 configurations are valid.

Configuration C 3

The configuration C 3 follows the path P 3 . This path is symmetric to the path P 1 with respect to the plane y b Oz b , O, y b and z b being the origin, the y-axis and the zaxis of the base frame. Considering the symmetry of the tubular structure, the robot architecture used for the configuration C 1 has been assigned to the configuration C 3 . The discretized set of design variables chosen for the configuration C 3 is described in Tab. 1. The design variables for the configuration C 3 are collected into the vector x 3 :

x 3 = [w 1 , w 2 , w 3 , w 4 , w 5 ] T (33)
where the variables w i amount to variables u i described in Sec. 4.2. Therefore, the Cartesian coordinates of the anchor points A i,3 are expressed as follows:

a b 1,3 = [w 1 + w 4 , w 2 + w 5 , -w 3 ] T a b 2,3 = [w 1 + w 4 , w 2 + w 5 , w 3 ] T (34) a b 3,3 = [w 1 -w 4 , w 2 + w 5 , -w 3 ] T a b 4,3 = [w 1 -w 4 , w 2 + w 5 , w 3 ] T (35) a b 5,3 = [w 1 -w 4 , w 2 -w 5 , -w 3 ] T a b 6,3 = [w 1 -w 4 , w 2 -w 5 , w 3 ] T (36) a b 7,3 = [w 1 + w 4 , w 2 -w 5 , -w 3 ] T a b 8,3 = [w 1 + w 4 , w 2 -w 5 , w 3 ] T (37)

Constraints

The static equilibrium of the robot should be assured during the entire task execution, balancing any possible external wrench w e , according to the limits specified in Eq. ( 7) and Eq. ( 8). This condition is verified for all the points P i , i = 1, . . . , 3. The set of required external wrenches consists of a hyperrectangle, defined as [w] r .

In order the robot to be in a static equilibrium in a given posture, the hyperrectangle of the required external wrench should be included inside the zonotope of the admissible wrench, [w] a , as follows:

∀w e ∈ [w] r , ∃τ ∈ [τ] such that [w] r ∈ [w] a Wτ + w e = 0 (38)
[w] a represents the possible external wrenches that the platform can balance.

[w] a depends on the robot geometry and the cable tension limits, defined by Eq. ( 13). Any mobile platform pose respecting the previous condition is said to be wrench feasible.

The set of wrench feasible poses represents the Wrench Feasible Workspace (WFW) of the given robot.

In [START_REF] Gouttefarde | Characterization of parallel manipulator available wrench set facets[END_REF], Gouttefarde et al. improved the wrench feasibility verification procedure defined by Bouchard et al. in [START_REF] Bouchard | On the ability of a cable-driven robot to generate a prescribed set of wrenches[END_REF]. Both the procedures lead to a set of inequalities:

Cw ≤ d, ∀w ∈ [w] r (39)
Cable interferences have to be avoided. The interference between the i-th cable and the j-th cable is verified analysing the distance d cc i, j between them. The cables have been modelled as linear segments, neglecting the mass and elastic effects on the sagging phenomenon. A fast computation of d cc i, j is realised through Lumelsy's approach [START_REF] Lumelsky | On fast computation of distance between line segments[END_REF]. For the constraint to be satisfied, distance d cc i, j should be greater than the diameter of the cables, φ c , i.e.,

d cc i, j ≥ φ c ∀i, j = 1, . . . , m, i = j (40)
The same approach is used to detect collisions between the cables and the tubular structure. The collision between the i-th cable and the k-th structure tube does not occur when their distance d cc i,k is greater than the sum of the cable and tube radii:

d cs i,k ≥ (φ c + φ s ) 2 ∀i = 1, . . . , m, ∀k = 1, . . . , 12 (41)
The RCDPR should respect a prescribed pose accuracy along all the paths. Inside the limits defined by the required wrench set, the maximum mobile platform linear displacements δt x , δt y and δt z along the x b , y b and z b axes should be lower than 5 cm:

-5 cm ≤ δt x , δt y , δt z ≤ 5 cm (42)

The rotation displacements of the platform δ r x , δ r y and δ r z about axes x b , y b and z b should not be higher than 0.1 rad:

-0.1 rad ≤ δ r x , δ r y , δ r z ≤ 0.1 rad (43)

The linear and rotational displacements of the mobile platform are computed from Eq. ( 10).

Objective Functions

In Secs. 4.2, 4.3 and 4.4, the feasible robot configurations associated to paths P 1 , P 2 and P 3 have been identified. For each path, a configuration is selected, aiming at minimizing the total number of anchor points required by the RCDPR to complete the task. These optimal solutions have been computed in two phases. At first, the 4576 feasible robot configurations for path P 1 are compared with the 5579 feasible robot configurations for path P 2 . The sets of robot configurations that minimize the number, n c , of required anchor points along the three paths are selected.

Then, the problem aims to minimize the size of the robot, defined as the convex hull of the robot anchor points. The Cartesian coordinates of anchor point A i,c are defined as a i,c = [a x i,c , a y i,c , a z i,c ] T . The variables s x , s y and s z denote the smallest Cartesian coordinates of the robot anchor points along the axes x b , y b and z b , respectively:

s x = min a x i,c , ∀i = 1, ..., 8, c = 1, ..., 3 (44)
The upper bounds on the Cartesian coordinates of the RCDPR anchor points, along the axes x b , y b , z b , are denoted by sx , sy and sz , respectively.

sx = max a x i,c , ∀i = 1, ..., 8, c = 1, ..., 3 (47)
sy = max a y i,c , ∀i = 1, ..., 8, c = 1, ..., 3 (48)
sz = max a z i,c , ∀i = 1, ..., 8, c = 1, ..., 3 (49)
Hence, the objective function related to the size of the robot is expressed as follows:

V 2 = ( sx -s x )( sy -s y )( sz -s z ) (50)

Design Problem Formulation

The design problem of the CDPR is formulated as follows:

minimize V 1 = n c V 2 = ( sx -s x )( sy -s y )( sz -s z ) over x 1 , x 2 , x 3 subject to: ∀P m,n , m = 1, . . . , 38 n = 1, . . . , 3                      Cw ≤ d, ∀w ∈ [w] r d cc i, j ≥ φ c ∀i, j = 1, . . . , 8, i = j d cs i,k ≥ (φ c + φ s ) 2 ∀i = 1, . . . , 8, ∀k = 1, . . . , 12 -5 cm ≤ δt x , δt y , δt z ≤ 5 cm -0.1 rad ≤ δ r x , δ r y , δ r z ≤ 0.1 rad (51)
5 Results

Following the procedure described in Sec. 4, a set of feasible configurations have been identified for C l , l = 1, . . . , 3. 16516 triplets of configurations minimize the total number of anchor points. A generic CDPR composed of 8 cables requires 8 anchor points A i = 1, . . . , 8 on the base. It is the case for the fully-constrained configuration C 1 described in Sec. 4.2. The suspended CDPR proposed in Sec. 4.3 presents 4 coincident couples of anchor points. Hence, the maximum total number of anchor points of the RCDPR is equal to 20. The best results provide a reduction of 4 points. Regarding the configurations C 1 and C 2 , points A 5,2 and A 7,2 can be coincident with points A 3,1 and A 5,1 , respectively. Alternatively, points A 5,2 and A 7,2 can be coincident with points A 1,1 and A 7,1 . As far as configurations C 2 and C 3 are concerned, points A 1,2 and A 3,2 can be coincident with points A 8,3 and A 2,3 , respectively. Likewise, points A 1,2 and A 3,2 can be coincident with points A 4,3 and A 6,3 , respectively.

The total volume of the robot has been computed for the 16516 configurations minimizing the total number of anchor points. 96 RCDPRs amongst the 16516 robot configurations have the smallest size, this minimum size being equal to 5104 m 3 . An optimal solution is illustrated in Fig. 6. The corresponding optimal design parameters are given in Tab. 2. Fig. 7 illustrates the minimum degree of constraint satisfaction introduced in [9] and defined thereafter along the paths P 1 , P 2 and P 3 , which is discretized into 388 points.

It turns out that mobile platform is in a static equilibrium along all the paths because the minimum degree of constraint satisfaction remains negative. The degree of constraint satisfaction s j,i is the signed distance from the j-th vertex w e, j of [w] r to the i-th face of [w] a . s j,i is negative when a pose is wrench feasible. Configurations C 1 and C 3 maintain their degree of satisfaction lower than the 400 N. On the contrary, configuration C 2 is often close to 0. The poses where s vanishes require that two cables of the suspended CDPR are slack. This paper dealt with the design of a Reconfigurable Cable Driven Parallel Robot (RCDPR) for sandblasting and painting of large structures. A tubular structure of 20 m long and 10 m wide was considered. The design problem aimed at determining the optimal locations of the cable anchor points such that the number of anchor points is minimized and the RCDPR is as small as possible. The problem solving led to 96 optimal solutions. A RCDPR was required in order to complete a given task in a complex environment. Unfortunately, the design strategy introduced in this paper is very time consuming. The whole procedure, performed on a Intel Core TM i7-3630QM 2.40 GHz, required 19 h of computation, on Matlab 2013a. Therefore, the development of more efficient strategies for the design of RCDPRs will be part of our future work. Moreover, the mass of the cables should be taken into account.

Fig. 1

 1 Fig. 1 Case study model. The structure is 20 m long, with a cross section of 10 m x 10 m.

Fig. 2

 2 Fig. 2 Definition of the desired paths, P 1 , P 2 and P 3 of the platform CoM.

Fig. 3

 3 Fig.3Geometric model of a generic RCDPR. In this example, the anchor points are connected to a four-beam structure. Two configurations are illustrated. The anchor point A 1,1 , belonging to the first configuration, is exchanged for the position A 1,2 , belonging to the second configuration.

Fig. 4

 4 Fig. 4 Design variables parametrizing the configuration C 1 .

Fig. 5

 5 Fig. 5 Design variables parametrizing the configuration C 2 .

  s y = min a y i,c , ∀i = 1, ..., 8, c = 1, ..., 3 (45) s z = min a z i,c , ∀i = 1, ..., 8, c = 1, ..., 3

Fig. 6

 6 Fig. 6 Optimal Reconfigurable Cable-Driven Parallel Robot.

Fig. 7 Table 2

 72 Fig. 7 Minimum degree of constraint satisfaction. The analysis has been performed by discretizing the paths P 1 , P 2 and P 3 into 388 points.

Table 1

 1 Design variables associated with configurations C 1 , C 2 and C 3 .

		Variables Lower Bounds Upper Bounds Number of values
		u 1	5.5	7.5	9
		u 2	8.0	12.0	9
	C 1	u 3	6	10	5
		u 4	0.5	2.5	9
		u 5	10	14	5
		v 1	-1	1	9
		v 2	8.0	12.0	5
	C 2	v 3	7	11	9
		v 4	5	7.5	11
		v 5	10	14	5
		u 1	-7.5	-5.5	9
		u 2	8.0	12.0	9
	C 3	u 3	6	10	5
		u 4	0.5	2.5	9
		u 5	10	14	5

Acknowledgements This research work has been supported by the IRT Jules Verne, Bouguenais, France (Project CAROCA, Evaluation des CApacités de la RObotique à C Âbles dans un contexte industriel).


Nicolas Roux

Baptiste Vrigneau

Olivier Sentieys

Estimating Power Loads from Partial Appliance States

come

• Smartsense deployment and data collection are imminent.

• Smartsenseis expected to yield accurate environmental data but inaccurate appliance states matrix. • Next challenges to address are the algorithm robustness to this kind of errors, and association between NILM algorithms and environmental data instead of electrical data.

Nicolas Roux (nicolas.roux@inria.fr), Baptiste Vrigneau, Olivier Sentieys

Estimating Power Loads from Partial Appliance States

General scope

Knowing the plug-level power consumption of each appliance in a building can lead to significant savings in energy consumption, as well as giving a deep insight of a building power consumption. A critical information is the knowledge of the characteristic power consumptions of an appliance.

The problem can be stated as an optimization problem as follows :

Non-Intrusive Load Monitoring (NILM)

SmartSense

Comparison with "blind" algorithms

Conclusion

Main power of a building is disaggregated to isolate single appliance power consumptions. This ensures a better understanding of the energy consumption in a building. Most of the current NILM methods have an a priori knowledge of the individual signatures or are trained on single appliances.

Dataflow States detection and estimation accuracy

Future work

• An estimation algorithm based on environmental sensing has been proposed.

• SmartSense, a sensor network with a wide range of sensors is introduced.

• Promising results are displayed in terms of complexity and prediction error, but the algorithm showed significant variations according to the nature of the appliance power time series.

• w i,j the steady state power value j for appliance i • x tot the main aggregated power of all appliances • N the total number of monitored appliances Lighting circuit appliance states count This consists in solving (1) with a linear optimization tool. We used GNU Math Programming Language

Steady states values errorbars for various REDD appliances

	100 %
	80 %
	60 %
	40 %
	20 %
	0
				23000	65000	84600
	dishwasher	lighting	microwave lighting bis	Window length (seconds) 16800

• M i the states count for appliance i • s i,j a boolean which indicates if appliance i is in state j • d a given norm.


Eric Deville

Tania Marsset

Simon Courgeon

Romain Jatiault

Jean-Pierre Ponte

Estelle Thereau

Gwenael Jouet

Stéphan J Jorry

Laurence Droz

Active fault system across the oceanic lithosphere of the Mozambique Channel: Implications for the Nubia-Somalia southern plate boundary

Keywords: Active faults, Mozambique Channel, plate boundary, Nubia plate, Somalia plate

Seismic reflection and multibeam echosounder data were acquired in the Mozambique Channel in 2014 and 2015 during the PTOLEMEE, PAMELA-MOZ02 and -MOZ04 marine surveys aboard the RV Atalante and Pourquoi Pas? These data revealed that an active fault system is deforming the oceanic lithosphere of the Mozambique Basin which has developed during Jurassic-Cretaceous times.

The correlation between the fault system and the arrangement of earthquake epicenters suggests that this tectonically active zone directly connects northward with the southern part of the eastern branch of the East African Rift System which corresponds to the seismically active graben system bounding the northern part of the Davie ridge. The fault zone extends southwestward of the Mozambique Ridge along the same trend as the Agulhas-Falkland transform fault zone. The general organization of the fault zone shows the characteristics of an extensional system north of the Mozambique Channel (north of the Europa Island) and a right-lateral transtensional system with coeval normal faults and strike-slip EPSL 2 faults south-west of Europa. This tectonic activity is associated with volcanic activity since at least Late Miocene times. Our findings emphasize that the eastern branch of East African Rift System is extending largely toward the south, not only in continental domains but also through the oceanic lithosphere of the Mozambique basin. This fault zone is participating to the complex plate boundary between the main African continent (Nubia Plate) and Madagascar (Somalia Plate).

Introduction

The East African Rift System (EARS), originally described by [START_REF] Suess | Die Bruche des ostlichen Africa[END_REF], corresponds to the northern part of the divergent plate boundary system between the Nubian (West African) and Somali (East African) plates. This rift system is connected northward to the Afar hot spot which is related to the opening of the Red Sea and the Gulf of Aden, which began being active about 30 Ma ago. However, it is considered that the EARS began to be active only later, starting 24 Ma ago in the Afar area [START_REF] Chorowicz | The East African rift system[END_REF]. Although the EARS is commonly considered as the modern archetype of rifted plate boundaries, the current Nubia-Somalia kinematics is among the least well-known of all the major plate boundaries [START_REF] Calais | Structure and Evolution of the Rift Systems Within the Afar Volcanic Province, Northeast Africa[END_REF][START_REF] Stamps | A kinematic model for the East African Rift[END_REF]. The plate boundary between Nubia and Somalia developed over thousands of kilometers across the eastern part of Africa during Late Oligocene and Neogene times [START_REF] Chorowicz | The East African rift system[END_REF][START_REF] Ebinger | Evolution of the Cenozoic East African Rift System: Cratons, plumes, and continental breakup[END_REF][START_REF] Mcgregor | History of the development of the East African Rift System: a series of interpreted maps through time[END_REF]. The location of the plate boundaries is well-defined along the continental branches of the EARS which include a western branch and an eastern branch (Fig. 1). The eastern branch (Gregory Rift) is characterized by high volcanic activity (including Mount Kilimanjaro, the highest point of Africa) and the western branch (Albertine Rift) is characterized by a moderate volcanic activity relative to the eastern branch and by deeper basins, containing lakes and sediments.

The Great Lakes (Albert, Tanganyika, Rukwa, Malawi) are located in highly rifted basins bounded by normal and strike-slip faults of the western branch of the EARS. The two branches of the EARS delineate major relatively poorly deformed blocks: Victoria and Rovuma [START_REF] Hartnady | Earthquake hazard in Africa: perspectives on the Nubia-Somalia boundary[END_REF][START_REF] Calais | Structure and Evolution of the Rift Systems Within the Afar Volcanic Province, Northeast Africa[END_REF][START_REF] Stamps | A kinematic model for the East African Rift[END_REF][START_REF] Stamps | Current kinematics and dynamics of Africa and the East African Rift System[END_REF][START_REF] Epsl Fernandes | Re-evaluation of the kinematics of Victoria Block using continuous GNSS data[END_REF][START_REF] Saria | Present-day kinematics of the East African Rift[END_REF]Fig. 1). The eastern branch of the EARS extends off Tanzania and in the northern part of the Mozambique offshore, bounding notably the Davie Ridge (Mougenot et al., 2005;Mahanjane et al., 2014 a & b;[START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF][START_REF] Mulibo | The seismotectonics of Southeastern Tanzania: Implications for the propagation of the eastern branch of the East African Rift[END_REF].

But south of the Davie Ridge in the eastern branch and south of the Machaze epicentral area in the western branch (Fig. 1 & 2), the exact location of the EARS still remains a topic of discussion. Scattered extensional structures associated with seismic activity are found onshore in Mozambique, Swaziland and South Africa [START_REF] Foster | Source parameters of large African earthquakes: Implications for crustal rheology and regional kinematics[END_REF][START_REF] Yang | Earthquakes along the East African Rift System: A multiscale, system-wide perspective[END_REF][START_REF] Fonseca | MOZART: A Seismological Investigation of the East African Rift in Central Mozambique[END_REF][START_REF] Domingues | Ambient noise tomography of the East African Rift in Mozambique Geophys[END_REF] and also along the Comores and Mayotte islands and within Madagascar (Grinison and Chen, 1988;[START_REF] Bertil | Seismotectonics of Madagascar[END_REF][START_REF] Kusky | The Great Rift Valley of Madagascar: an extension of the Africa-Somali diffuse plate boundary?[END_REF][START_REF] Kusky | Active tectonics of the Alaotra-Ankay Graben system, Madagascar: possible extension of Somalian-African diffuse plate boundary[END_REF][START_REF] Michon | The volcanism of the Comoros Archipelago integrated at a regional scale[END_REF]Fig. 1). Active tectonics across Madagascar has been interpreted as a possible extension connected to the East African Rift System [START_REF] Kusky | The Great Rift Valley of Madagascar: an extension of the Africa-Somali diffuse plate boundary?[END_REF]2010). It forms a segment running through Comores, across Madagascar and finally extends to the Southwest Indian spreading ridge. This extension is associated to Neogene-Quaternary alkaline volcanic activity associated with active hot springs. It also causes high and young topography and seismic activity and it is probably associated to mantle rise under Madagascar [START_REF] Kusky | Active tectonics of the Alaotra-Ankay Graben system, Madagascar: possible extension of Somalian-African diffuse plate boundary[END_REF]. Earthquakes have also been recorded within the Mozambique Channel [START_REF] Hartnady | Earthquake hazard in Africa: perspectives on the Nubia-Somalia boundary[END_REF]Stamp et al., 2008) but prior to this study no data were available to characterize structural evidence for recent to active deformation within the Mozambique Channel (Fig. 1). Marine geophysical surveys carried out in 2014 and 2015 provided evidence for a recent/active fault system running crossing the Mozambique Basin (Fig. 4). This paper aims providing an analysis of the spatial distribution of active faults as well as faults sealed by recent sediments within this area. We notably present some examples of bathymetric data and seismic lines showing these structures and we discuss the significance of this fault system in the plate tectonics framework of the East African offshore.

Geodynamic and geological framework

North of the Mozambique Channel, the southern extension of the eastern branch of the EARS off Tanzania and Mozambique (eastern boundary of the Rovuma block) has been wellestablished by seismic reflection data [START_REF] Mougenot | Seaward extension of the East African Rift[END_REF]Mahanjane, 2014a;[START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF], earthquake slip vector data and GPS data [START_REF] Calais | Structure and Evolution of the Rift Systems Within the Afar Volcanic Province, Northeast Africa[END_REF][START_REF] Stamps | A kinematic model for the East African Rift[END_REF][START_REF] Saria | Present-day kinematics of the East African Rift[END_REF], and spatial distribution of earthquake focal mechanisms [START_REF] Grimison | Earthquakes in Davie Ridge-Madagascar region and the southern Nubian-Somalian plate boundary[END_REF][START_REF] Yang | Earthquakes along the East African Rift System: A multiscale, system-wide perspective[END_REF]Delvaux and Barth, 2010;[START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF]. The offshore segment of the eastern branch of the EARS is characterized from north to south by Neogene extension tectonics overimposed on former strike-slip structures of the Tanzaniannorthern Mozambique transform margin which have developed during Mid Jurassic-Cretaceous times in relation with the drift of Madagascar with respect to Africa [START_REF] Rabinowitz | The separation of Madagascar and Africa[END_REF][START_REF] Coffin | Reconstruction of Madagascar and Africa: Evidence from the Davie Fracture Zone and Western Somali Basin[END_REF][START_REF] Storey | Timing of hot spotrelated volcanism and the breakup of Madagascar and India[END_REF][START_REF] Reeves | The position of Madagascar within Gondwana and its movements during Gondwana dispersal[END_REF][START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF]. Regarding the current kinematics of the plate boundary between Nubia and Somalia, [START_REF] Chu | Evidence for motion between Nubia and Somalia along the Southwest Indian Ridge[END_REF] analysis placed the pole of rotation of Nubia versus Somalia in the offshore of southeastern cost of South African, in the Mozambique Ridge or south of the Mozambique basin (Fig. 1), which imply that south of the rotation pole, the southern part of the Nubian-Somali plate boundary is a diffuse zone of convergence (up to ~2mm yr -1 ). This interpretation is consistent with subsequent work integrating seismicity studies [START_REF] Horner-Johnson | Plate kinematic evidence for the existence of a distinct plate between the Nubian and Somalian plates along the Southwest Indian Ridge[END_REF] and coupled seismicity-GPS studies [START_REF] Calais | Structure and Evolution of the Rift Systems Within the Afar Volcanic Province, Northeast Africa[END_REF][START_REF] Stamps | A kinematic model for the East African Rift[END_REF][START_REF] Argus | The angular velocities of the plates and the velocity of Earth's center from space geodesy[END_REF][START_REF] Demets | Geologically current plate motions[END_REF][START_REF] Saria | Present-day kinematics of the East African Rift[END_REF][START_REF] Stamps | Current kinematics and dynamics of Africa and the East African Rift System[END_REF]Fig. 1).

Clusters of earthquake epicenters are located in continental Africa [START_REF] Fonseca | MOZART: A Seismological Investigation of the East African Rift in Central Mozambique[END_REF]. In addition, evidence for volcanism and tectonic activity characterized by earthquakes has been reported along faults in the Comoros and Mayotte [START_REF] Emerick | Age progressive volcanism in the Comores Archipelago, western Indian Ocean and implications for Somali plate tectonics[END_REF][START_REF] Michon | The volcanism of the Comoros Archipelago integrated at a regional scale[END_REF] and Madagascar [START_REF] Kusky | The Great Rift Valley of Madagascar: an extension of the Africa-Somali diffuse plate boundary?[END_REF]2010). This seismic activity shows that the deformation between the Nubian and Somali plates is distributed over a wide area, in several segments. In this complex tectonic setting, the exact location and the processes of deformation related to plate tectonics movements in the area of the Mozambique Channel remain poorly understood. West of the Mozambique Channel, surface structural evidence for rifting appears to stop around 22°S, south of the Lake Malawi and the Inhaminga fault, in the Machaze epicentral area (Fig. 1), whereas seismic activity at depth extend farther to the south in Swaziland and South Africa [START_REF] Fonseca | MOZART: A Seismological Investigation of the East African Rift in Central Mozambique[END_REF]. On the other hand, east of the Mozambique Channel, the presence of active volcanism, recent faults, and seismic activity suggest that active deformation running through wide parts of Madagascar might correspond to the western boundary of the Somali plate [START_REF] Kusky | The Great Rift Valley of Madagascar: an extension of the Africa-Somali diffuse plate boundary?[END_REF][START_REF] Kusky | Active tectonics of the Alaotra-Ankay Graben system, Madagascar: possible extension of Somalian-African diffuse plate boundary[END_REF][START_REF] Stamps | A kinematic model for the East African Rift[END_REF][START_REF] Saria | A new velocity field for Africa from combined GPS and DORIS space geodetic solutions: Contribution to the definition of the African reference frame (AFREF)[END_REF]. Several authors have proposed the presence of a dominantly oceanic Lwandle block (name derived from the Xhosa word for ocean) extending south of the Rovuma block in the Mozambique Channel between southern Mozambique and Madagascar [START_REF] Hartnady | Earthquake hazard in Africa: perspectives on the Nubia-Somalia boundary[END_REF][START_REF] Horner-Johnson | Plate kinematic evidence for the existence of a distinct plate between the Nubian and Somalian plates along the Southwest Indian Ridge[END_REF][START_REF] Stamps | A kinematic model for the East African Rift[END_REF][START_REF] Stamps | A Geodetic Strain Rate Model for the East African Rift System[END_REF][START_REF] Saria | Present-day kinematics of the East African Rift[END_REF].

The dimension and precise boundaries of this block are very poorly constrained at this stage. Kinematic models proposed by [START_REF] Stamps | A kinematic model for the East African Rift[END_REF] and [START_REF] Saria | Present-day kinematics of the East African Rift[END_REF] invoke a possible extensive/transform zone in the Mozambique channel distributed along a NE-SW trend crossing the channel (Figs. 1 and2). Between Africa and Madagascar, the deep water area of the Mozambique basin is characterized by the development of an oceanic lithosphere which began to develop during the Mid Jurassic-Cretaceous drift of Antarctica with respect to Africa [START_REF] Rabinowitz | The separation of Madagascar and Africa[END_REF]Coffin and Rabinowitz, 1988). The oceanic domain of the Mozambique basin is largely invaded by sediments forming the turbidite system connected to the sediment supply coming from the Zambezi River [START_REF] Walford | Solid sediment load history of the Zambezi Delta[END_REF]. The main channel of this turbidite system shows locally strong evidence of erosion [START_REF] Kolla | Morphology and Quaternary Sedimentation of the Mozambique Fan and Environs, Southwestern Indian Ocean, in Deep-Water Turbidite Systems[END_REF]. The Mozambique Channel is also characterized by the presence of the Davie ridge which runs NNW-SSE west of Madagascar and which delimits the eastern part the oceanic domain of the Mozambique Channel. It corresponds to the extinct transform fault system along which Madagascar separated from the future Somali plate between 160-115 Ma ago. Dredge samples collected along the Davie Ridge show that isolated blocks of Precambrian basement and volcanics are preserved along this paleo-transform ridge. These volcanics include Late Cretaceous and Cenozoic lava flows [START_REF] De Wit | Madagascar: Heads It's a Continent, Tails It's an Island[END_REF][START_REF] Courgeon | Growth and demise of Cenozoic isolated carbonate platforms: New insights from the Mozambique Channel seamounts (SW Indian Ocean)[END_REF][START_REF] Courgeon | Impact of tectonic and volcanism on the Neogene evolution of isolated carbonate platforms (SW Indian Ocean)[END_REF]. The oceanic domain of the Mozambique Channel is also the site of volcanic edifices forming seamounts covered by Neogene carbonate deposits forming locally modern reefs and emerged lands at Bassas da India and Europa [START_REF] Jorry | Modern sediments and EPSL 21 Pleistocene reefs from isolated carbonate platforms (Iles Eparses, SW Indian Ocean): A preliminary study[END_REF][START_REF] Courgeon | Growth and demise of Cenozoic isolated carbonate platforms: New insights from the Mozambique Channel seamounts (SW Indian Ocean)[END_REF][START_REF] Courgeon | Impact of tectonic and volcanism on the Neogene evolution of isolated carbonate platforms (SW Indian Ocean)[END_REF]. The average elevation of the Mozambique basin is anomalously high with respect to its age even taking into account the sedimentary and volcanic input [START_REF] Castelino | Anomalous bathymetry and palaeobathymetric models of the Mozambique Basin and Riiser Larsen Sea[END_REF] and this anomalously shallow area extends largely southwesterly to the southwest offshore of South Africa [START_REF] Nyblade | The African Superwell[END_REF]. This topographic anomaly, as well as the significance of the volcanism discovered in this area remained both largely unexplained before this study.

Methodology

In this paper, we present seismic reflection data coupled with multibeam echosounder acquisitions. Geophysical data were acquired in the Mozambique Channel in 2014 and 2015 during the PTOLEMEE [START_REF] Jorry | PTOLEMEE cruise[END_REF], PAMELA-MOZ02 (Robin and Droz, 2014) and PAMELA-MOZ04 [START_REF] Jouet | PAMELA-MOZ04 cruise[END_REF] marine surveys aboard the RV L'Atalante and Pourquoi Pas? The seismic source used for the seismic acquisitions was 2 GI air guns (105/105 ci, 45/45 ci). The streamer had 48 seismic traces with inter-traces of 6.25 m and 4 hydrophones SFH with a spacing of 0.78 m per trace. The total length of the streamer was 531.6 m. Acquisition time was 9 seconds and the sampling frequency was 1 kHz. The seismic acquisition system was a SEAL 428, V1.1 Patch 23. Seismic data were processed using Ifremer QC-Sispeed software and integrated in Kingdom Suite software for the interpretation of seismic profiles. A map of the fault zone was produced (Fig. 2), encompassing the spatial distribution of active faults (i.e. faults expressed up to the seafloor) and sealed faults (i.e. faults covered by sediments). Bathymetric data were acquired using the multibeam echosounders Kongsberg EM122 (Frequency of 12 kHz) and EM710 (Frequency bandwidth of 71-100 kHz). The data were processed using Ifremer Caraïbes software and integrated in ArcGis software for morphobathymetric analysis of seafloor features. The map of the fault zone based on seismic data was compared with morphobathymetric analysis.

In order to provide a reliable mapping of the fault zone, we compared the morphologic features visible on bathymetric data and the visible structures on the seismic lines (Fig. 3), in order to distinguish notably linear sedimentary features (e.g. dunes crests) and structural lineaments (active faults; Fig. 3). The map of fault zone was completed for active faults whose linear extent and orientation are visible on the bathymetric profiles (Fig. 3).

Results and interpretation

Spatial distribution of the faults

Several seismic profiles, especially around the Bassas da India and Europa islands, show the presence of a wide system of faults (Fig. 2,3). Some of the most characteristic lines illustrating this fault system are presented in figure 4, 5, 6, and 7. The penetration in the sediments is slightly than 1.5 s TWT (Two Way Travel time) and deepest observations reach 5.5 s TWT.

The results of the bathymetry-seismic reflection correlation are synthetized in Fig. 3 and examples of the most characteristic bathymetric data showing morphologic expressions at the seabedrelated to fault activity are shown along seismic lines of the Fig. 5 and6. The comparison between the morphological features visible on bathymetric data and the structures visible on the seismic lines shows a good fit concerning the location of the fault system (Fig. 2,5,6). It also allows estimating the main strikes of the faults which is not possible with the seismic data alone because the density of the available seismic data does not allow correlating faults from one line to another. This combined approach using bathymetry and seismic data allows defining the main fracturing zones within the Mozambique Channel. This work shows that between latitudes 18°S and 20°S, the fault zone merges with the active fault system adjacent to the northern part of the Davie Ridge which has been described in recent papers [START_REF] Mahanjane | The Davie Fracture Zone and adjacent basins in the offshore Mozambique Margin-A new insights for the hydrocarbon potential[END_REF][START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF]; Fig. 3), including notably, N-S trending faults found along the Sakalaves Mounts (Courgeon et al., 2018;Fig. 3). From the Davie ridge, the fault zone develops to the southwest across the Mozambique Channel. This fault zone, more than 200 km-wide, crosses the seamounts of Europa, Bassas da India, and Hall bank (Fig. 2,4) and joins the northern part of the Mozambique Ridge to the southwest. Two main trends of fault strikes have been observed, one trending N160-180°, the other N45-80° (Fig. 2). This confirms the results of a recent study of the Mounts Sakalaves and the Bassas de India-Jaguar-Hall banks, which showed the existence of faults trending NE-SW that can be tracked on bathymetric data affecting the carbonates of the seamounts, some of these faults being associated with volcanic activity [START_REF] Courgeon | Growth and demise of Cenozoic isolated carbonate platforms: New insights from the Mozambique Channel seamounts (SW Indian Ocean)[END_REF][START_REF] Courgeon | Impact of tectonic and volcanism on the Neogene evolution of isolated carbonate platforms (SW Indian Ocean)[END_REF]Fig. 4). In the vicinity of the seamounts which include volcanic edifices, acoustic masks prevent these faults from being imaged under volcanic rocks (probably related to the contrast of the high seismic velocity of the volcanics compared to the seismic velocity of the sediments around; Fig. 7) but apart from seamounts, faults are clearly visible on the seismic reflection lines. The fault system is trending toward the southwest of the Mozambique Basin as a continuation of the Agulhas major fracture zone (Fig. 1), which extends largely westward along the Falkland fault zone in Southern Atlantic.

EPSL 10

On some of the seismic lines considered approximately perpendicular to the strike of the faults, depth-conversion with an average velocity of 2000 m/s (mean velocity deduced from refraction studies and ODP drilling in the area, ODP leg 25, wells 242, 248, 250; see Supplementary Material, Figs. S2 andS3) shows that most of these faults, north of the Europa island, correspond to normal faults. Indeed, these faults have apparent conjugated dips showing absolute values between 50° and 70° (Fig. 4, 5, 6, i.e. compatible with conjugated normal faults). In the south of Europa Island, to the southwest, the faults tend to be steeper and many of them are almost vertical (Fig. 7). As such, the fault system of this SW area is different from the characteristic conjugated systems of normal faults present in the northern part of the Mozambique Channel and the presence of nearly vertical faults suggests a strikeslip activity. In addition, well-expressed and localized depressions forming traps for the sediments of the Mozambique turbidite system may correspond to pull-apart basins associated with strike-slip activity. This interpretation is consistent with the fact that some border faults systems of these depressions show clear evidence for the development of en-échelons systems of faults probably related to right lateral strike-slip component (Fig. 9). The general characteristics of the fault geometries in the southwestern part of the Mozambique Channel can be regarded as related to transtensional structures.

The most recent faults affect all sedimentary series down to the penetration window and are well-expressed in the seabed topography with fault scarps up to 50 ms TWT visible on both the seismic lines and multibeam data. It is therefore likely that these faults were active during Quaternary times and some of them are probably active and contemporaneous with the most recent volcanism events. The fault zone described here is indeed still partly active as shown by the seismicity data in the Europa and Bassas da India area (Fig. 1; see discussion below). The profile L4 in figure 6 shows a major syn-sedimentary fault with very high amplitude reflectors in the shallow layers. The syn-tectonic character of this fault is demonstrated by the presence of syn-tectonic pinch-out clearly visible on the seismic line (Fig. 6). This fault, well-expressed in the topography of the sea bottom, is probably an active fault. Throughout the study area, the major faults affect the sedimentary series down to the penetration limit of the seismic data.

In addition to the faults that affect the uppermost sedimentary series many faults do not reach the seabed. The interpretation of the timing of activity of these buried faults is questionable. They can either correspond to sealed faults which were active in the past and then became inactive after or, depending on the rheological properties of the sedimentary series, some faults may be expressed at depth (brittle deformation), while deformation is accommodated by continuous creeping in shallower layers. The observed offsets of the sealed faults seem to be lower than the one of the active faults (maximum ~ 30 ms TWT, ~ 20 m) but these faults are much more numerous than the recent faults (Fig. 5,6,7). This suggests that early deformation was more diffuse and widely distributed and that, overtime, deformation tended to be more localized. Some of these faults are hardly detectable (if at all) in a poorly reflective interval (Fig. 5,6,7). This could be related to the rheological properties of these levels which can correspond to relatively plastic clays-rich horizons. On the other hand, many faults are sealed by the uppermost sedimentary series and partly by volcanic flows (Fig. 5, 6, 7).

Chronostratigraphic framework of fault activity

The picking of these faults shows that they are not always sealed at the same level but, depending of the cases, the throw of the fault stops at different stratigraphic layers (Fig. 4). In addition, in some cases, the values of the fault throw are higher at depth with some values above 100 ms TWT. This suggests a relatively long duration of fault activity (since the Miocene). It is worth noting that sealed faults are also observed on the inactive part of the Davie Ridge (southernmost area of this ridge) as evidenced by the draping of faults by the sediments (Fig. 5).

In order to propose a timing of the beginning of the fault activities, we picked some characteristic horizons which are interpreted as time lines (Fig. 4, 5, 6, 7). The ages proposed for these horizons are consistent with the interpretations of [START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF] in the northern part of the Mozambique Channel and Mahanjane et al. (2014b) and [START_REF] Ponte | La marge africaine du Canal du Mozambique (le Système turbiditique du Zambèze) : une approche « Source to Sink[END_REF] from well calibration located on Zambezi platform (yellow marker: near top Miocene, orange marker: near top Oligocene, red marker: near top Eocene). According to this interpretation, it appears that all the faults affect Miocene and older sediments but some being sealed at the top of the Miocene whereas, as mentioned previously, others affect the whole stratigraphic series up to the sea-bottom. Accordingly, we deduced that the global period of faulting lasted from late Miocene to present-day.

Discussion

Structural trends within the fault zone

Between the Davie Ridge and the Mozambique Ridge, the fault system developed within the oceanic lithosphere of the Mozambique Basin (see Fig. 10, with location of the oceanic crust from [START_REF] Konig | Advanced insights into magmatism and volcanism of the Mozambique Ridge and Mozambique Basin in the view of new potential field data[END_REF][START_REF] Leinweber | The Jurassic history of the Africa-Antarctica corridornew constraints from magnetic data on the conjugate continental margins[END_REF][START_REF] Davis | New Somali Basin magnetic anomalies and plate model for the early Indian Ocean[END_REF][START_REF] Mueller | Geophysical evidence for the crustal and distribution of magmatism along the central coast of Mozambique[END_REF]. In this area, the tectonic style is different from the dominant one north of 20°S which corresponds to rift-related structures including the tilt of wide continental crustal blocks [START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF]. South of 20°S, the fault zone forms a wide area (> 200 km wide) characterized by a diffuse deformation made of a relatively dense system of faults with moderate throws. These faults are mostly straight (planar), whereas the main faults are mainly listric north of 20°S [START_REF] Franke | The offshore East African Rift System: Structural framework at the toe of a juvenile rift[END_REF]. This may be due to the fact that the oceanic lithosphere does not includes decoupling layers like the lower thick continental crust, the faults being here rooted deeply within the oceanic lithosphere.

Within this fault zone affecting the oceanic lithosphere of the Mozambique Basin, two main strikes of fault were observed, N160-180° and NE-SW. The N160-180° trends are predominant in the northern area (north of Bassas da India), while fault trends from the southern area are mostly oriented NE-SW. These different trends are possibly controlled by inherited fracture zones within the oceanic lithosphere, the N160-180° trends being probably controlled mainly by transform fracture zones parallel to the Davie Ridge transform system (Fig. 10), and the NE-SW trends being possibly influenced by fractures which are parallel to the magnetic anomalies of the oceanic crust (normal faults from the oceanic accretion period; Fig. 10).

Active earthquakes along the fault zone

A correlation exists between the area of recent faulting evidenced within the Pliocene-Quaternary sediments and the location of the earthquakes (Fig. 10). Indeed, the most significant earthquakes (Mw > 4) recorded within the Mozambique Channel are trending mostly along the zones where the faults described in this paper are reaching the sea floor (Fig. 2). Only a few isolated and relatively shallow earthquakes (focal depths < 25 km) occurred south of this fault zone in the deep water part of the Mozambique Basin south of 26°S (Fig. 10, see also supplementary material Fig. S1, Table S1). These isolated earthquakes show focal mechanisms consistent with a NW-SE extension (Fig. 10), while earthquake focal mechanisms north of Mozambique Channel along the Davie Ridge are consistent with EPSL 14

roughly a E-W extension with focal depths mostly shallower than 25 km, some being between 25 km and 50 km [START_REF] Foster | Source parameters of large African earthquakes: Implications for crustal rheology and regional kinematics[END_REF][START_REF] Yang | Earthquakes along the East African Rift System: A multiscale, system-wide perspective[END_REF][START_REF] Saria | Present-day kinematics of the East African Rift[END_REF]Fig. 2, 3). The 4 larger earthquakes (Mw 5.0 to 5.7) over the last 50 years were recorded between 1980 and 1983, in the Europa/Bassas da India region. In 1951 and 1950, earthquake magnitudes reached Mw 6.1 and 6.2 in the area of the Davie Ridge (Fig. 2). South of 20°S, the Davie Ridge is mostly tectonically inactive (no recorded earthquake > Mw 3 and no evidence of recent tectonics on the seismic lines as shown by the fault sealing of the Ridge; Fig. 2). As mentioned above, to the southwest, the studied active fault zone seems to be aligned with Agulhas-Falkland fault zone where important earthquakes have been mentioned, notably one Mw 6.8 located offshore of Durban in the Natal valley (point A in Fig. 1), which occurred December 31 st , 1932 (focal depth 15 km). This area of the Natal valley is possibly associated with volcanic seamounts which might be related to the EARS extension tectonics [START_REF] Wiles | Anomalous sea floor mounds in the northern Natal Valley, southwest Indian Ocean: Implications for the East African Rift System[END_REF]. The active fault system described in this paper which is associated to seismic activity is clearly distinct from the deformation trend onshore Mozambique which is associated to seismic activity characterizing an E-W extension or local strike-slip movements (Fig. 10). It is also clearly distinct from the deformation processes recorded within Madagascar which are associated to scattered earthquakes some of them being compressional (Fig. 10).

Fault zone and volcanism

As described in previous works, the carbonate seamounts of the Mozambique Channel have developed either on crystalline basement rocks or on volcanic systems [START_REF] Bassias | Petrological and geochemical investigation of rocks from the Davie fracture zone (Mozambique Channel) and some tectonic implications[END_REF][START_REF] Courgeon | Growth and demise of Cenozoic isolated carbonate platforms: New insights from the Mozambique Channel seamounts (SW Indian Ocean)[END_REF][START_REF] Courgeon | Impact of tectonic and volcanism on the Neogene evolution of isolated carbonate platforms (SW Indian Ocean)[END_REF]. Faults are expressed at the seabed even in the most recent carbonate deposits covering the volcanic edifices (Figs. 4 and7). The main volcanic edifices trending along the fault zone described in this work were most likely developed during Mid-Miocene but volcanism went on to be active until very recent times forming dykes and lava flows visible at the sea bottom [START_REF] Courgeon | Growth and demise of Cenozoic isolated carbonate platforms: New insights from the Mozambique Channel seamounts (SW Indian Ocean)[END_REF][START_REF] Courgeon | Impact of tectonic and volcanism on the Neogene evolution of isolated carbonate platforms (SW Indian Ocean)[END_REF]. The acoustic masks below the volcanics around Bassas da India, Europa Islands and Hall Bank being located along the fault zone, we can assume that the volcanic mounts are rooted on deep faults that cannot be imaged from the seismic data because of the acoustic mask under the volcanics. In the peripheral areas of the Mozambique Channel, the end of the Miocene corresponds to a period of significant volcanism, probably the major episode in the region [START_REF] Roberts | Initiation of the western branch of the East African Rift coeval with the eastern branch[END_REF].

Therefore, some of the faults were probably already active as soon as Miocene times which is consistent with the tectonic framework of the EARS [START_REF] Chorowicz | The East African rift system[END_REF][START_REF] Mcgregor | History of the development of the East African Rift System: a series of interpreted maps through time[END_REF].

Significance of the fault zone in the framework of plate tectonics

In terms of global plate tectonics and location of deformation zones between the Nubian and Somali plates, this study shows that one of the branches of this complex plate boundary (the eastern branch of the EARS) can be followed at least as south as 25°S trending toward the area where most of the kinematic studies locate the pole of rotation between Nubia and Somalia plates (see discussion above § 2; Fig. 1). As such, this study shows that the eastern branch of the East African Rift System is extending much further south than previously demonstrated with facts, not only in continental domains but also across the oceanic lithosphere of the Mozambique basin. As it is the case along the eastern branch of the EARS north of the studied area [START_REF] Mulibo | Mantle transition zone thinning beneath eastern Africa: Evidence for a whole-mantle superplume structure[END_REF], the zone of lithospheric divergence presented in this paper, with a transform component toward the south, is probably responsible for the thinning and the rise of the mantle below which may be the cause of partial melting in the mantle sourcing the volcanic systems associated with the fault zone. This oceanic mantle rise is also probably responsible for the regional uplift linked with the anomalously high topography of the northern part of the Mozambique basin mentioned previously.

Conclusion

This the Davie Ridge and the Mozambique Ridge. This interpretation is also compatible with earthquake focal mechanisms (Fig. 10) and recently published kinematic models [START_REF] Stamps | A kinematic model for the East African Rift[END_REF]2014[START_REF] Ponte | La marge africaine du Canal du Mozambique (le Système turbiditique du Zambèze) : une approche « Source to Sink[END_REF][START_REF] Saria | Present-day kinematics of the East African Rift[END_REF]. The fault zone activity is associated with volcanic activity controlling the development of the seamounts present within the Mozambique Channel. This active extensional process taking part of the EARS is probably associated with mantle rise that might be responsible for the anomalously high topography of the northern part of the Mozambique basin due to the presence of relatively hot rising mantle at depth.

With active deformation onshore Africa, notably along the Inhaminga fault zone, and also along the Comoros-Mayotte and Madagascar system, the active fault zone of the Mozambique Channel is participating to the complex plate boundary between the African main continent (Nubia Plate) and Madagascar (Somalia Plate). Tensor database [START_REF] Ekström | The global CMT project 2004-2010: Centroid-moment tensors for 13,017 earthquakes[END_REF]. Pink arrows: relative motions between plate tectonic blocks from [START_REF] Saria | Present-day kinematics of the East African Rift[END_REF]. Elevation/bathymetry grid from GEBCO. In red: main volcanic systems. Location of the oceanic crust and oceanic fracture zones compiled from [START_REF] Konig | Advanced insights into magmatism and volcanism of the Mozambique Ridge and Mozambique Basin in the view of new potential field data[END_REF], [START_REF] Leinweber | The Jurassic history of the Africa-Antarctica corridornew constraints from magnetic data on the conjugate continental margins[END_REF], [START_REF] Davis | New Somali Basin magnetic anomalies and plate model for the early Indian Ocean[END_REF] and [START_REF] Mueller | Geophysical evidence for the crustal and distribution of magmatism along the central coast of Mozambique[END_REF]. Magnetic anomalies are from [START_REF] Davis | New Somali Basin magnetic anomalies and plate model for the early Indian Ocean[END_REF]. COB: Continent-Ocean Boundary.

  study has shown that the eastern branch of the EARS extends offshore across the Mozambique Channel from the Davie Ridge to the Mozambique Ridge, where it is characterized by a zone of densely distributed faults, trending NNE-SSW and deforming the oceanic lithosphere of the Mozambique channel that developed much earlier, during Jurassic-Cretaceous times. The fault zone is well characterized within the sediments of the Mozambique basin and shows that faults have been active since at least the Miocene times and some of them are still seismically active (Fig. 10). Earthquakes with magnitude reaching Mw 6.1 around the Davie Ridge and Mw 5.7 around the Europa-Bassas da India Islands occurred along the fault zone during the last decades. The focal depths of the earthquakes are deeper than the sedimentary accumulations, probably within the mantle of the oceanic lithosphere of the Mozambique Basin. The fault zone structure is compatible with a purely extensional deformation around the Davie Ridge and a dextral transtensional system between

FiguresEPSLFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. Spatial distribution of faults in the Mozambique Channel. (A) Map showing the main

Fig. 3 .Fig. 4 .

 34 Fig. 3. Sunshaded bathymetry (A) and interpretative structural sketch-map (B) showing the

Fig. 5 .

 5 Fig. 5. Seismic profiles L1 and L2 illustrating the fault zone system of the Mozambique

Fig. 6 .

 6 Fig. 6. Seismic profiles illustrating the fault zone system of the Mozambique Channel north of

Fig. 7 . 632 Fig. 8 .

 76328 Fig.7. Seismic profiles South of Bassas da India (profiles L8 and L7 located in figure2). L7

Fig. 9 . 651 Fig. 10 .

 965110 Fig. 9. Multibeam map crossing a depression along the fault zone showing en-échelons border

Acknowledgements

This work has been conducted within the framework of the PAMELA (PAssive Margin Exploration LAboratories) project leaded by IFREMER and TOTAL in collaboration with Université de Bretagne Occidentale, Université de Rennes 1, Université Pierre et Marie Curie Paris 6, CNRS and IFP Energies Nouvelles. Data acquisition was made in 2014 during the PTOLEMEE (Jorry, 2014), and PAMELA-MOZ02 (Robin and Droz, 2014) marine surveys onboard the R/V L'Atalante and in 2015 during the PAMELA-MOZ04 survey (Jouet and Deville, 2015) onboard the R/V Pourquoi Pas? We thank captains, officers, crew members and scientific teams of the PTOLEMEE, PAMELA-MOZ2 and PAMELA-MOZ4 cruises for their technical support in recovering dataset. Yannick Thomas and Pauline Dupont from Ifremer are acknowledged for their contribution in the processing of the seismic lines.

Appendix A. Supplementary data

Supplementary data to this article can be found at http://www.seanoe.org/data/00445/55634/


Alexandre Audinot

Emeric Goga

Vincent Goupil

Carl-Johan Jorgensen

Adrien Reuzeau

Ferran Argelaguet

Climb, Fly, Stack: Design of Tangible and Gesture-based Interfaces for Natural and Efficient Interaction

Keywords: H, 5, 2 [User Interfaces]: User Interfaces-Graphical user interfaces (GUI);

This paper describes three novel 3D interaction metaphors conceived to fulfill the three tasks proposed in the current edition of the IEEE VR 3DUI Contest. We propose the VladdeR, a tangible interface for Virtual laddeR climbing, the FPDrone, a First Person Drone control flying interface, and the Dice Cup, a tangible interface for virtual object stacking. All three interactions take advantage of body proprioception and previous knowledge of real life interactions without the need of complex interaction mechanics: climbing a tangible ladder through arm and leg motions, control a drone like a child flies an imaginary plane by extending your arms or stacking objects as you will grab and stack dice with a dice cup.

INTRODUCTION

This year the IEEE VR 3DUI contest required the design of interaction techniques to perform three different tasks: ladder climbing, drone flying and object stacking. This paper describes our solution, which focused on the design of tangible and gesture-based input mechanisms to resemble real-life interactions. We believe that the described techniques can inspire further research on 3DUI.

CLIMBING A VIRTUAL LADDER

The virtual climbing task required the user to climb a virtual ladder in which the user could control independently his/her feet and hands. Our goal was to provide a good matching between the user's proprioceptive information and the sensory data in order to achieve higher levels of presence [START_REF] Slater | Taking steps: the influence of a walking technique on presence in virtual reality[END_REF]. We wanted the user to feel that he/she was actually climbing a ladder. Di Loreto and al. [START_REF] Di Loreto | Simulation de travail en hauteur en réalite mixte : étude de la présence et de l'anxiété[END_REF] have already shown the effectiveness of using a physical ladder to enhance presence. However, they used a standard ladder which has a predefined number of rugs, which does not allow to climb taller virtual ladders.

VladdeR. In our system, we wanted the user to be able to climb any virtual ladder, regardless of the number of rungs. With this intention, we designed a dynamic tangible interface for climbing virtual ladders: the VladdeR (see Figure 1). Our first physical prototype consisted of a 2.5 meters high wooden structure stabilized with lateral supports and equipped with four movable rungs, one for each limb. Each rung is allowed to move vertically along two vertical rails with a span equal to the distance between two consecutive virtual rungs. An elastic mechanism brings the rung up whenever the user releases his hold of it, and a metallic contact detects when it reaches its highest position.

Climbing task control. In the user's resting position, all four rungs are brought down and the virtual hands and feet of the user are attached to their respective virtual rungs. When the user releases a rung, it is brought back up by an elastic mechanism and a contact is detected and translated into a keyboard press using a Makey Makey1 . Then, the corresponding virtual hand or foot is free to move and the user can grab/step on the rung again. Every time that the user descends a rung with any of their hands the virtual camera is raised, giving the impression that the user is hauling himself up. In addition to their head, users' hands were tracked using HTC Vive trackers.

FLYING A VIRTUAL DRONE

The drone task required the user to control a drone in order to flight through a pre-defined route (go through a set of ring-shaped objects). This section describes the main components of FPDrone, a novel navigation metaphor for First Person Drone control. Our goal was to provide a gesture-based interface which enabled the coupling of all the degrees of freedom of the drone at once, taking advantage of body proprioception.

Input Mapping. The designed navigation interface can be seen as a head-steering flying interface [START_REF] Usoh | Walking¿ walking-in-place¿ flying, in virtual environments[END_REF] in which hand motions determine roll and speed. Head tracking was provided by the HTC Vive and hands motions by two HTC Vive trackers. The drone was driven by computing (A) a target drone up-vector (defined by the head yaw and the signed difference between the left and right hand height (see Algorithm 1), (B) a support plane (π) in which the drone forward vector should lay (defined by the user's viewing direction and the global y-axis) and (C) a target thrust value (defined by the distance between both hands). Regarding the user's view, in order to reduce simulation sickness, it did not reflect the current drone orientation, the view direction was directly controlled by head motions.

Stabilization. In order to ease the drone control, the system automatically compensates for inertia and external forces (e.g. gravity and drag). The compensation system updates the target up-vector and the target thrust value. For example, when the user required the drone to stop, the system will compute an up-vector opposing the drone motion reducing the braking time. In addition, once the drone is stopped, the system will compute a thrust which will negate gravity. Automatic stabilization greatly improved the maneuvering of the drone; users had a lot of difficulties to compensate inertial forces manually. If not enabled, it resulted on the feeling of losing control of the drone, which can potentially increase the risk of motion sickness [START_REF] Stanney | Locus of user-initiated control in virtual environments: Influences on cybersickness[END_REF].

Control. Once the new target values were computed, the system computed two rotations. The first rotation aims to align the drone to the target up-vector, and the second rotation aims to align the forward vector with π. Both rotations are concatenated and a yawpitch-roll command is sent to the drone. The closed-loop control ensured smoothness and responsiveness.

Graphical User Interface. The interface (see Figure 2) provided information regarding the current state of the drone. (1) A vertical slider placed in the center of the view provided information regarding the pitch control (head pitch). ( 2) A second vertical slider, placed in the center right provided information regarding the current thrust (hand distance). (3) Two vertical lines displaying the current roll value were also displayed at the sides. The most important feedback, elevation and speed were kept at the center to ensure their visibility.

STACKING VIRTUAL OBJECTS

The stacking task required the user to be able to stack a set of objects. In order to perform this task, we propose the Dice Cup metaphor (see Figure 3). The user controls a virtual dice cup which enables to grab and stack virtual objects as if they were dice. With the Dice Cup, users can perform two operations: grab virtual objects and the release of all virtual objects previously grabbed.

Object Grab. Grabbing an object is achieved by covering the desired virtual object with the virtual cup. Upward red arrows are displayed on the cup to display a grabbing confirmation. The user can grab as many objects as desired.

Object Release. In order to release the grabbed objects, the user has to shake the virtual cup. Once the release is confirmed (blue downward arrows on the cup), the user rests the cup on the virtual table (red downward arrow displayed) and then, he lifts it to release all previously grabbed objects. The objects are released in the inverse order as grabbed. In addition, objects are not structured in a perfect stack they fell on each other following their physical properties following the y-axis of the cup.

Furthermore, in order to enable the precise control of the virtual cup and increase immersion, we provided a tangible object (plastic cup) which matched the virtual dice cup. The tangible cup was tracked using a HTC Vive tracker. Furthermore, we added small wooden objects inside the plastic cup to provide sound and tactile feedback when shaking the cup.

RESULTS AND CONCLUSION

Informal testing among the colleagues in the lab has shown the all three interfaces provides usable interfaces for the completion of the three tasks. Moreover, users with no experience are able to complete the tasks without major problems. Yet, we observed two main aspects that require additional analysis/works. First, the VladdeR cannot match perfectly the preconception of the user with his virtual situation. Indeed, when the virtual hand/feet are on different rungs, the user's hands/feet are at the same level. Second, the control of the drone at maximum thrust required moderate training. The drone is controlled by the laws of physics, thus the user must learn the limits of the drone and which maneuvers are possible.

In conclusion, although further evaluations are needed, we believe that the proposed techniques provides natural and intuitive mechanisms to perform the three proposed tasks in the IEEE VR 3DUI Contest enabling an efficient control with a limited amount of training.

Figure 1 :

 1 Figure 1: Left, the VladdeR, a tangible interface for Virtual laddeR climbing. Right-up, the hands rungs. Right-down, the feet rungs.

Figure 2 :

 2 Figure 2: Illustration of the FPDrone interface. Left, hand tracking was achieved using two HTC Vive trackers. Right, the GUI of FPDrone provided information regarding pitch (vertical slider), roll (horizontal lines) and thrust (vertical line).

Figure 3 :

 3 Figure 3: Illustration of the Dice Cup metaphor. From left to right, tracked tangible cup, grab operation, release confirmation after shaking the cup and lift of the cup revealing the stacked objects.

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