6-DoF Full Robotic Calibration based-on 1-D Interferometric Measurements for Micro and

Nano-Scales Applications Houari Bettahar, Olivier Lehmann, Cédric Clévy, Nadège Courjal and Philippe Lutz

Abstract-This paper proposes an original approach for robotic calibration that is based on measurements along a single direction (1-D). Among all applications, the field of micro and nano robotics has been chosen as case-study because of the strong needs for high positioning accuracy (10-100 nm typically) while measuring with sufficient resolution along multi-DoF (Degrees-of-Freedom) is still a fully open question. 1-D measurements relying on FP (Fabry-Perot) interferences is used and the proposed modelling of a 6-DoF nanopositioning robot enables to derive the measurement strategy as well as the identification procedure for both extrinsic and intrinsic parameters. Experimental investigations demonstrate that the approach is easy to implement, low cost and enables to understand what are the main influential parameters onto positioning accuracy. They also conduct to very high accuracy in 6 DoF positioning: a positioning accuracy estimate of 50 nm and 0.004 • has notably been obtained for the full pose (position and orientation respectively) and can be held during several hours after the measurements.

Note to Practitioners-The motivation of this work is to

give an answer to the growing needs for micro nanopositioning robots having a very high precision for applications in microassembly, in the characterization of micro nano components or biological elements, or for minimally invasive surgery. The key contribution of the proposed work relies in the method proposed that enables to efficiently calibrate a serial 6 DoF robot using only 1-D interferometric measurements which overcomes the need for multi DoF, small size, high resolution sensors missing in commercial offers. Moreover, the behavior of such novel robotic solutions is not well known, difficult to model and there is a clear lack of knowledge about main influential parameters. The method proposed in this paper notably enables to achieve the full calibration of the robot (all intrinsic and extrinsic parameters identified) to reach the best positioning accuracy. This first part takes times and the paper shows that it is then possible to adopt a less time taking procedure by only re-identifying extrinsic parameters, and thus to hold these performances over long periods, typically a week.

Index Terms-Micro-Nano Robotics, Nano-positioning, positioning accuracy, robot calibration, Fabry-Perot interferences, optical alignment.

I. INTRODUCTION

N owadays, positioning accuracy is one of the most im- portant performance criteria in many application fields in order to successfully perform complex tasks. This is all H. Bettahar, O. Lehmann, C. Clévy, N. Courjal, P. Lutz are with FEMTO-ST Institute, Univ. Bourgogne Franche-Comté, UFC/CNRS/ENSMM, 24 rue Savary, 25000 Besanc ¸on, France, (e-mails: houari.bettahar@femto-st.fr, olivier.lehmann@femto-st.fr, cclevy@femto-st.fr, philippe.lutz@femto-st.fr, nadege.courjal@femto-st.fr) the more true for fastly emerging applications at small scales and/or when robots are required in small free spaces such as micro-assembly [START_REF] Liu | Sensing and control for simultaneous precision peg-in-hole assembly of multiple objects[END_REF] [2] [START_REF] Xing | Efficient insertion of partially flexible objects in precision assembly[END_REF], manipulation [START_REF] Fu | Active learning-based grasp for accurate industrial manipulation[END_REF] [5] [START_REF] Wen | Nanorobotic manipulation system for 360 • characterization atomic force microscopy[END_REF], characterization of biological tissues and minimally invasive inspection and surgery [START_REF] Li | Development of a magnetic microrobot for carrying and delivering targeted cells[END_REF] [START_REF] Wei | A survey of force-assisted robotic cell microinjection technologies[END_REF]... Most of these tasks require to control very accurately the relative position and/or trajectories between a sample (for example, component to handle, tissue or living cell) and a tool used for manipulation or characterization purposes. At small scales, micro and nanopositioning robots are widely used, because of their capability to generate highresolution motions with high repeatability (typically better than 10 nm for most of commercially available devices). However, positioning accuracy is not well known and difficult to guarantee, because of intrinsic geometric errors accumulations of the built micro-nanopositioning robots, which induces key drawbacks for many applications. This led to develop control laws in closed loop by integrating many sensors, which are complex and costly.

For this sake, research about calibration of micronanopositioning robots is getting more and more attention, in order to fulfill high accurate micro-manipulation tasks in many application fields [START_REF] Yao | High-accuracy calibration of a visual motion measurement system for planar 3-dof robots using gaussian process[END_REF] [10] [START_REF]Camera-robot calibration for the da vinci robotic surgery system[END_REF].

Works done in [START_REF] Tan | Accuracy quantification and improvement of serial micropositioning robots for in-plane motions[END_REF] targeted to quantify the positioning accuracy of a XYθ serial micro-positioning robot and to identify the main influential parameters after calibration. Experiments show that positioning accuracy can be improved by more than 35 times from 96 µm to 2.5 µm by identifying geometric parameters. However, measurement at the micro-scale is a very challenging issue, especially in 3-D. Micro-scale measurement requires sensing devices with high resolution (e.g., a few nanometers) and accuracy (e.g., tens of nanometers) [START_REF] Nubiola | Comparison of two calibration methods for a small industrial robot based on an optical cmm and a laser tracker[END_REF]. State-of-the-art highlights approaches relying on multi-DoF sensing to control micro-nanopositioning robots in multi-DoF but, there is a clear lack of commercially available sensors satisfying multi-DoF measurement and resolution required [START_REF] Andre | Sensing one nanometer over ten centimeters: A micro-encoded target for visual in-plane position measurement[END_REF] [START_REF] Clévy | Signal measurement and estimation techniques for micro and nanotechnology[END_REF].

In order to overcome the measurement issues, some researchers investigated constrained robot calibration methods, such as point-point position constraint and point-surface position constraint. The constraints in the two approaches can be done either with contact [START_REF] Lembono | Scalar: Simultaneous calibration of 2-d laser and robot kinematic parameters using planarity and distance constraints[END_REF] or virtually [START_REF] Wang | A point and distance constraint based 6r robot calibration method through machine vision[END_REF]. Such approaches demonstrate their potential interest for small scale applications, notably [START_REF] Guelpa | Accurate 3d-positioning in a sem through robot calibration[END_REF] proposed a geometric calibration of 6-DoF robot using virtual constraint method in a Scanning Electron Microscope environment. A visual servoing control was used to maintain the object held by the robot in the center of the image. This work reached a positioning accuracy of 10 µm which is still not satisfying enough for most applications at the micro-nano scales. Moreover, only a small volume of the robot's workspace can be explored that can lead to nonobservability or poor estimation of some parameters. To eliminate this kind of limitations, several calibration methods based on partial specified pose measurements were raised, leading to other robot calibration methods based on relative position error model [START_REF] Liao | Parameter identification and non-parametric calibration of the tri-pyramid robot[END_REF] [START_REF] Xie | Calibration of 6-dof industrial robots based on line structured light[END_REF] or based on relative distance error model [21] [22]. In this latter, the relative distance error of any two poses in robot workspace is applied to calibrate the robot position accuracy [START_REF] Zhenhua | A distance error based industrial robot kinematic calibration method[END_REF]. It uses a set of distance measurements either directly achieved by different measurement systems have been used such as mechanical coordinate-measuring machines (CMM)s [START_REF] Driels | Full-pose calibration of a robot manipulator using a coordinate-measuring machine[END_REF], theodolites [START_REF] Sultan | Simplified theodolite calibration for robot metrology[END_REF], laser trackers [START_REF] Zhang | A simple and rapid calibration methodology for industrial robot based on geometric constraint and two-step error[END_REF], and ballbars [START_REF] Li | A calibration method for overconstrained spatial translational parallel manipulators[END_REF]. However, it positioning accuracy relies strangely on the relative distance measurement accuracy and the developed calibration model. Getting accurate measurements remains a key lock, which is not trivial to achieve, notably, at microscale.

In this scope, previous works we did for the assembly of micro-optical components, the FP interferometry happening during the active alignment of optical elements is exploited as propreoceptive measurement tool. It demonstrated the high accuracy of this 1-D interferometric measurement principle [START_REF] Bettahar | Photorobotic positioning for integrated optics[END_REF] and the high interest for relative distance-based measurements to achieve the identification of extrinsic parameters [START_REF] Bettahar | Photorobotic extrinsic parameters calibration of 6-dof robot for high positioning accuracy[END_REF]. In these works, a positioning accuracy of 390 nm was notably demonstrated for translational motions which is interesting for several applications but still not sufficient for a number of others.

In this paper, the calibration of a 6 DOF robot based on the identification of the extrinsic and intrinsic parameters is addressed. For this sake, a relative distance error calibration model based on 1-D propreoceptive Fabry-Perot measurements has been developed and validated experimentally. This paper is organized as follows. Section II notably explains the FP interferometry principle used for measurements. Section III provides the geometric modelling of the 6-DoF robot while Section IV enables to derive the method for intrinsic and extrinsic parameters identification and Section V the related experimental procedure for parameters identification. Section VI presents the experimental setup and Section VII investigates the performances of the calibrated robot comparing its behavior when the robot is fully calibrated (all intrinsic and extrinsic parameters identified) with when the robot has only its extrinsic parameters identified. Section VIII conclude the paper contribution.

II. 1-D RELATIVE MEASUREMENTS BASED ON FP

INTERFEROMETRY

Interferometric sensors are widely used in laboratories as well as in industry fields because of their extremely accurate measurements, high resolution, wide measuring range and bandwidth. These interferometric sensors operate based on different interferometric principles such as Michelson and FP interferences.

Interferences of multiple light beams from the same light source in an optical free-space cavity induces FP interferences as shown in Figure 1. As a result, the light intensity varies periodically with the optical path difference between the beams [START_REF] Hariharan | Basics of interferometry[END_REF]. Active alignment of a mirror relative to the optical fiber yields FP interferences phenomenon. In this case, the concerned surfaces are the fiber extremity (R 1 ) in one hand and the mirror surface (R 2 ) in the other hand. Each time the light comes across one of the surfaces, a portion of it is transmitted out, and the remaining part is reflected back. The net effect is to split a single beam into multiple beams which interfere with each other. Based on FP interferences principle, when the reflective surface (R 2 ) moves along the optical axis (Z-axis), the FP cavity length (L) changes and modifies the reflected light signal accordingly. Therefore, there is a correlation between the FP cavity length L and the interferences figure. A slight variation of the FP cavity length can be identified on the interferences figure.

The periodicity of the irradiance signal directly depends on the wavelength of the laser signal (λ = 1560 nm). If p is a natural number, the distance between two resonances peaks can be written as in equation 1 (see Figure 1), i.e. the distance variation between two peaks (δL) is a multiple of half wavelength λ of the laser irradiance, such as:

δL = λ 2 • p with p ∈ N (1)
This FP interferences principle is used in order to achieve 1-D measurements and it is used also for validation after full 6-DoF robot calibration.

For validation, if the mirror is perpendicular to the optical fiber, then the expected displacement of the mirror perpendicular to the optical axis induces no cavity distance variation. Consequently, it induces constant reflected light irradiance versus time. But, if the mirror has a small perpendicularity error with respect to the fiber optical axis, then the expected translation of the mirror perpendicular to the optical axis induces a cavity distance variation δL. Consequently, it generates an oscillating reflected light irradiance at the same time. This principle is used to evaluate positioning accuracy after full robot calibration. The proposed robotic calibration approach is based on the robot geometric model that is presented in the next section.

III. 6-DOF ROBOT GEOMETRIC MODELING

Geometric model relates the joint and the operational coordinates (coordinates with respect to the world reference frame), by involving robot geometric parameters. Geometric model permits to establish the robot DGM (Direct Geometric Model) and IGM (Inverse Geometric Model), which are successively used to control the robot. These models includes intrinsic parameters that can be identified to calibrate the robot.

Khalil and Kleinfinger representation is one of the most used conventions for the geometric modeling [START_REF] Khalil | A new geometric notation for open and closed-loop robots[END_REF]. However, in the case of nearly parallel neighboring axes, the common normal is poorly defined and the calibration is ill-conditioned. For this case, Hayati introduced an extra rotational parameter β i about the Y i-1 axis [START_REF] Hayati | Improving the absolute positioning accuracy of robot manipulators[END_REF]. Therefore, the modified version by Khalil and Kleinfinger with additional Hayati parameter β i is used to establish the transformation matrix between two successive links based on two main assumptions: the links are perfectly rigid and the joints are ideal in a sense that there is neither backlash nor elasticity.

For these works, a serial robot is studied because it is of widespread use at small scales. A serial robot is composed of a sequence of n links and n joints where link 0 is the base of the robot and link n is the terminal link. Joint i connects the link i to the link i -1. A frame R i is attached to each link i with [START_REF] Khalil | Modeling, identification and control of robots[END_REF]:

• The Z i axis is located along the axis of joint i;

• The X i axis is located along the common normal between the Z i and Z i+1 axes. If Z i and Z i+1 axes are parallel or collinear, the choice of X i is not unique: considerations of symmetry or simplicity then allow a rational choice; • The Y i axis is located using the right-hand rule to form (X i , Y i , Z i ) coordinate system. The transformation matrix from frame R i-1 to frame R i is expressed using the following four geometric parameters (Figure 2):

• Joint parallelism: β i is the angle around the axis Y i-1
between the axes Z i-1 and Z i-1 ; • Link twist: α i is the angle around the axis X i-1 and between the axes Z i-1 and Z i ;

• Link length: d i is the distance along the axis X i-1
between the axes Z i-1 and Z i ; • Joint angle:θ i is the angle around the axis Z i between the axes X i-1 and X i ; • Link offset: r i is the distance along the axis Z i between the axes X i-1 and X i .

The variable of the joint i denoted by q i is θ i if i is rotational and r i if i is prismatic. Hence

q i = θ i (1 -ρ i ) + r i ρ i , (2)
where Two rotations are required to relate

ρ i = 0, for rotational joint 1, for prismatic joint . ( 3
)
𝑍 𝑖 𝑌 𝑖 𝑋 𝑖 𝑍 𝑖-1 𝑋′ 𝑖-1 𝑑 𝑖 𝛼 𝑖 𝛽 𝑖 Link 𝑖 Link 𝑖 -1 Joint 𝑖 Joint 𝑖 -1 𝑂 𝑖-1 𝑂 𝑖 𝑑 𝑖+1 𝑟 𝑖 𝜃 𝑖 Joint 𝑖 + 1 𝛽 𝑖 𝛼 𝑖 𝑍′ 𝑖-1 𝑍 𝑖 𝑍 𝑖-1 𝑌 𝑖-1
Z i-1 to Z i : a rotation β i about Y i-1 maps Z i-1 to Z i-1 and X i-1 to X i-1 . Hence, X i-1 axis is located along the common normal between the Z i-1 and Z i axes. A second rotation α i about X i-1 maps Z i-1 to Z i . The angle θ i is now from X i-1 to X i about Z i .
The transformation matrix defining the frame R i in the frame R i-1 is given by

i-1 T i = Rot Yi-1 (β i ).Rot X i-1 (α i ).T rans X i-1 (d i ) .Rot Zi (θ i ).T rans Zi (r i ). (4)
The matrices associated with this equation are:

Rot Yi-1 (β i ) =     Cβ i 0 Sβ i 0 0 1 0 0 -Sβ i 0 Cβ i 0 0 0 0 1     ; (5)
Rot X i-1 (α i ) =     1 0 0 0 0 Cα i -Sα i 0 0 Sα i Cα i 0 0 0 0 1     ; (6)
T rans

X i-1 (d i ) =     1 0 0 d i 0 1 0 0 0 0 1 0 0 0 0 1     ; (7)
Rot Zi (θ i ) =     Cθ i -Sθ i 0 0 Sθ i Cθ i 0 0 0 0 1 0 0 0 0 1     ; (8)
T rans Zi (r i ) =     1 0 0 0 0 1 0 0 0 0 1 r i 0 0 0 1     , (9)
where Cγ stands for cos γ and Sγ stands for sin γ. Thus, the general transformation matrix between two frames with consecutive parallel joints becomes:

i-1 T i =     A 11 A 12 A 13 A 14 B 11 B 12 B 13 B 14 C 11 C 12 C 13 C 14 0 0 0 1     (10)
where

A 11 = Cβ i Cθ i + Sα i Sβ i Sθ i A 12 = Sα i Sβ i Cθ i -Cβ i Sθ i A 13 = Cα i Sβ i A 14 = d i Cβ i + r i Cα i Sβ i B 11 = Cα i Sθ i B 12 = Cα i Cθ i B 13 = -Sα i B 14 = -r i Sα i C 11 = Sα i Cβ i Sθ i -Sβ i Cθ i C 12 = Sβ i Cθ i + Sα i Cβ i Sθ i C 13 = Cα i Cβ i C 14 = r i Cα i Cβ i -d i Sβ i
The direct geometric model for a serial-chain manipulator defines the pose (position and orientation) of the end-effector relative to the base given the values of the joint variables and the geometric link parameters. It can be solved by calculating the transformation between the end-effector frames and the base frame. This transformation can be obtained by concatenating the transformations between the frames of the adjacent links:

0 T n = 0 T 1 . 1 T 2 . . . n-2 T n-1 . n-1 T n . ( 12
)
The inverse problem is to calculate the joint coordinates corresponding to a given operational coordinates of the endeffector. When exists, the form that gives all the possible solutions (there is rarely a single solution) is the IGM.

The DGM and the IGM are used to control the proposed 6-DoF robot. For this sake, reference frames have been assigned to the 6-DoF robot building stages. For simplification, we choose the same origin for all the frames, which corresponds to the real rotational center of the robot (intersection of joint 4 and 5) when q 1 = q 2 = q 3 = q 4 = q 5 = q 6 = 0. The world (base) frame R w is assigned to be aligned with the first frame when q 1 = 0. The assignment of frames is shown in Figure 3, which represents the robot geometric model and the nominal geometrical parameters are given in Table I.

By replacing variables from equation (10) using Table I, The transformation matrix between frame R i and frame R i-1 is given as follows:

W T1 =    1 0 0 0 0 1 0 0 0 0 1 q1 0 0 0 1    , 1 T2 =    0 1 0 0 0 0 1 q2 1 0 0 0 0 0 0 1    2 T3 =    0 1 0 0 0 0 1 q3 1 0 0 0 0 0 0 1    , 3 T4 =    Cq4 -Sq4 0 0 Sq4 Cq4 0 0 0 0 1 0 0 0 0 1    , q 1 q 2 q 3 q 4 q 6 Y w Z w X w q 5 Z 2 Y 5 Z 6 X 4 X 3 X 1 X 5 X 6 Z 1 Z 4 Z 3 Y 4 Y 1 Y 6 Z 5 X 2 Y 3 Y 2 Figure 3. Robot kinematic model.

Table I NOMINAL PARAMETERS OF ROBOT DIRECT GEOMETRIC MODEL (DGM)

FOLLOWING THE HAYATI MODIFIED CONVENTION OF KHALIL AND KLEINFINGER.

Link

ρ i β i α i d i θ i r i 1 1 0 0 0 0 q 1 2 1 0 -90 0 -90 q 2 3 1 0 -90 0 -90 q 3 4 0 0 0 0 q 4 0 5 0 0 -90 0 q 5 -90 0 6 0 0 -90 0 q 6 0 4 T5 =    Cq5 Cq5 0 0 0 0 1 0 Cq5 -Sq5 0 0 0 0 0 1    , 5 T6 =    Cq6 -Sq6 0 0 0 0 1 0 -Sq6 -Cq6 0 0 0 0 0 1    .
The transformation between the world frame and measurement system frame or the transformation between the endeffector frame and the measurement system frame use the extrinsic geometric parameters. The DGM and the IGM use the intrinsic parameters. A referenced robot control uses extrinsic transformation between world and measurement system frames and the IGM together. Hence, high accurate extrinsic and intrinsic parameters lead to high accurate control of the 6-DoF robot. For this sake, in the next section, the 6-DoF robot extrinsic and intrinsic geometric parameters identification based on a the proposed robotic approach is presented.

IV. 6-DOF ROBOT EXTRINSIC AND INTRINSIC GEOMETRIC PARAMETERS IDENTIFICATION

In order to achieve the full robot geometric calibration (both intrinsic and extrinsic parameters) based on relative distance measure in 1-D, a new calibration model is proposed. The distance measure is achieved based on very high accurate FP interferometric principle measurements as presented in section II. In order to develop the geometrical model of the robot, the main reference frames are defined as schematically shown in Figure 4. R f is assigned to the fiber frame, its origin, labeled O f , is defined as the intersection point between the optical axis and the outer surface of the fiber. R e corresponds to the robot end-effector frame, its origin, labeled O e , corresponds to the real rotational center of the robot (intersection of joint 4 and 5). The ---→ O e X e , ---→ O e Y e and ---→ O e Z e are the expected motion directions of the robot, where R e = R 6 . R t corresponds to the tool frame, its origin, labeled O t , is defined as the intersection between the ---→ O e Z e and the mirror plane (Y t O t X t ). R w is assigned to the world frame, its origin, labeled O w , corresponds to the real rotational center of the robot (intersection of joint 4 and 5) when all axes are at zero (initial configuration), with the same directions as the first stage axes R 1 .

DOF robot

Fiber

Mirror The vector ---→ O e Z e is assumed to be collinear with the vector ---→ O w Y w . Thus, the homogeneous transformation matrix from the world frame to the fiber frame is given in equation [START_REF] Nubiola | Comparison of two calibration methods for a small industrial robot based on an optical cmm and a laser tracker[END_REF], and the transformation matrix from the end-effector frame to the tool frame is given in equation ( 14).

𝑅 𝑓 𝑅 𝑡 𝑂 𝑒 𝑂 𝑤 Z 𝑤 X 𝑤 Y 𝑤 X 𝑒 Y 𝑒 Z 𝑒 𝑅 𝑒 𝑅 𝑤 Z 𝑓 X 𝑓 Y 𝑓 O 𝑓 𝑃 𝑟 𝑂 𝑡 𝑍 𝑡 𝑌 𝑡 𝑋 𝑡 𝒘 𝑻 𝒇 𝒆 𝑻 𝒕

End-effector

w T f = T ransX w (x wf ).T ransY w (y wf ).T ransZ w (z wf )

.RotX w (β wf ).RotZ w (θ wf ) =    Cθ wf -Sθ wf 0 x wf Cβ wf Sθ wf Cθ wf Cβ wf -Sβ wf y wf Sβ wf Sθ wf Cθ wf Sβ wf Cβ wf z wf 0 0 0 1    (13)
where x wf , y wf and z wf are the translational coordinates of the origin of the fiber frame O f with respect to the world frame, along X w , Y w and Z w axis respectively. β wf is the angle between Y f and Z w around X w axis and θ wf is the angle between X f and X w around Z w axis.

e T t = T rans Ze (Z et ).Rot Xe (β et ).Rot Ye (θ et ) =     Cθ et 0 Sθ et 0 Sθ et Sβ et Cβ et -Cθ et Sβ et 0 -Cβ et Sθ et Sβ et Cθ et Cβ et Z et 0 0 0 1     (14)
where Z et is the translational coordinate of the origin of the mirror O t with respect to the end-effector frame, along Z e axis. β et and θ et are the rotational coordinates of X t and Y t axes of the mirror with respect to the end-effector frame, around the X e and Y e respectively.

P r is the reflection point projection of the laser spot on the mirror plane (Y t O t X t ). w P r ( w P rx , w P ry , w P rz ) is the reflection point projection in the world frame R w . t P r ( t P rx , t P ry , 0) is the reflection point in the tool frame R t .

The proposed extrinsic and intrinsic parameters identification uses the optical axis 3-D parametric equation and the plane equation of the mirror.

The 3-dimensional parametric form of the equation of optical axis line is defined by a point on the optical axis line O f and its direction vector -→ Z f . The point O f (x wf , y wf , z wf ) is a point with respect to the world frame R w through which the optical axis line passes. The unit vector -→ Z f (a wf , b wf , c wf ) is the direction vector of the optical axis line with respect to the world frame R w . Therefore, the 3-dimensional parametric equations of the line carrying the vector ---→ O f Z f (optical axis) can be written as follows:

   x = a wf L + x wf y = b wf L + y wf z = c wf L + z wf , ( 15
)
where a 2 wf + b 2 wf + c 2 wf = 1. The intersection point between the mirror plane (Y t O t X t ) and the line carries the vector ---→ O e Z e is O t (x wt , y wt , z wt ). The mirror plane is defined by the point O t (x wt , y wt , z wt ) in the plane with respect to the world frame and the normal unit vector to the plane -→ Z t (a wt , b wt , c wt ). If M (x, y, z) is any other point which belongs to the mirror plane, then the equation of the mirror plane can be written as follows:

---→ O t M • ---→ O t Z t = 0. (16)
This yields:

a wt (x -x wt ) + b wt (y -y wt ) + c wt (z -z wt ) = 0. ( 17
)
By considering d wt = -a wt x wt -b wt y wt -c wt z wt , then:

a wt x + b wt y + c wt z + d wt = 0, (18)
where: a 2 wt + b 2 wt + c 2 wt = 1. From the other hand, the columns of a rotation matrix are orthogonal unit vectors along X, Y and Z axes respectively. Hence, the third column of a rotation matrix represents the unit vector along Z-axis. Accordingly, the transformation matrix w T t of the tool frame in the world frame can be written using the unit vector Z t (a wt , b wt , c wt ) with respect to the world frame as follows:

w T t (q, , β et , θ et , Z et ) = w T e (q, ). e T t (β et , θ et , Z et ) =    
r r a wt x wt r r b wt y wt r r c wt z wt 0 0 0 1

    (19)
The label r is appointed to the matrix elements that are not required in the development of our approach. w T e is Direct Geometric Model (DGM), is the vector of the real (unknown intrinsic) parameters of the geometric errors, and q is the joint coordinates vector.

From the other side, the mirror plane equation given in equation [START_REF] Guelpa | Accurate 3d-positioning in a sem through robot calibration[END_REF], can be deduced from the transformation matrix between the world frame and the tool (mirror) frame given in equation. [START_REF] Liao | Parameter identification and non-parametric calibration of the tri-pyramid robot[END_REF], where:

a wt = w T t (1, 3), b wt = w T t (2, 3), c wt = w T t (3, 3), x wt = w T t (1, 4), y wt = w T t (2, 4), z wt = w T t (3, 4).
The direction vector -→ Z t (a wt ,b wt , c wt ) is orthogonal to the mirror plane and passes through the origin O t (x wt ,y wt , z wt ) of the tool frame (mirror frame).

The new mirror plane equation after new pose with respect to the world frame is given as follows:

a wt x + b wt y + c wt z + d wt = 0, (20)
where a wt , b wt , c wt and d wt are the coefficients of the mirror plane equation after the new pose. As shown in Figure 5, the fiber is fixed, which means that the optical axis equation stays unchanged. From the other side, displacing the mirror from one pose to another yields two plane equations (before and after the new pose).

The mirror plane equations before and after the new pose are given as follows:

a wt x + b wt y + c wt z + d wt = 0 a wt x + b wt y + c wt z + d wt = 0 . ( 21
)
Using the optical axis line equation given in equation ( 15). The intersection of the optical axis line with the mirror plane before the new pose gives: awt(a wf L+x wf )+bwt(b wf L+y wf )+cwt(c wf L+z wf )+dwt = 0.

(

) 22
The intersection of the optical axis line with the mirror plane after the new pose gives:

a wt (a wf L +x wf )+b wt (b wf L +y wf )+c wt (c wf L +z wf )+d wt = 0.

Then, L and L can be calculated respectively as follow:

L = -(a wt x wf + b wt y wf + c wt z wf + d wt ) a wt a wf + b wt b wf + c wt c wf , (24)
The mirror displacement along the optical axis after the new pose can be deduced as follows:

dL = L -L = (a
where:

d wt = -a wt . w T t (1, 4) -b wt . w T t (2, 4) -c wt . w T t (3, 4), a wt = w T t (1, 3), b wt = w T t (2, 3), c wt = w T t (3, 3), d wt = -a wt . w T t (1, 4) -b wt . w T t (2, 4) -c wt . w T t (3, 4).
And at the same time, this mirror displacement along the optical axis after the new pose is measured from the FP interferometric measurements. This displacement dL, can be written as a function of robot intrinsic and extrinsic geometric parameters as follows: dL = f (q, , θ et , β et , a wf , b wf , c wf , x wf , y wf , z wf , Z et ).

(27) Equation 27 represents the model for extrinsic and intrinsic parameters identification. Displacing the mirror in different poses using the 6 DoF robot, will lead to form a system of non-linear equations, where the unknowns are the intrinsic and the extrinsic geometric parameters. The system of equations can be solved using different optimization algorithms (it is detailed in the next section).

When the intrinsic and the extrinsic parameters of the robot are identified, the point of intersection between the optical axis and the plane of the mirror with respect to the world frame can be deduced by calculating the distance L between the mirror and the fiber using equation [START_REF] Driels | Full-pose calibration of a robot manipulator using a coordinate-measuring machine[END_REF] and then calculating the Cartesian coordinates of the reflection point w P r ( w P rx , w P ry , w P rz ) in the world frame using the following equation:

   w P rx = a wf L + x wf w P ry = b wf L + y wf w P rz = c wf L + z wf . ( 28
)
At the initial mirror pose (q 1 = q 2 = q 3 = q 3 = q 4 = q 5 = q 6 = 0), the Direct Geometric Model (DGM) transformation matrix is written as a function of intrinsic parameters errors w T e (q = 0, ).

By replacing the already deduced vector w P r and the transformation matrices e T t and w T e , the vector t P r can be deduced as follows:

t P r = e T -1 t . w T -1 e . w P r . ( 29
)
After having developed the robotic model for extrinsic and intrinsic parameters identification, this model combines 6-DoF robot motion with a high accurate 1-D FP measurements in order to identify the extrinsic and the intrinsic parameters of the robot. In order to detail the robotic calibration approach, the next section presents the experimental procedure for robot extrinsic and intrinsic parameters identification.

V. EXPERIMENTAL PROCEDURE OF ROBOT EXTRINSIC AND INTRINSIC PARAMETERS CALIBRATION

The whole procedure of the full robot calibration (both intrinsic and extrinsic parameters identified) includes measurement, identification, parameters correction and validation step.

A. Measurement strategy

In order to cover all the robot workspace and to achieve a high accurate measurement. The proposed measurement strategy consists of 2 steps:

• The mirror held on the robot was put in a cubical workspace with 15 nodes is chosen as shown in Figure 6. For each node, three continuous rotations of the mirror are applied, around X w , Y w , Z w . Rotation of [-3

= (0 • , 3 • )), Rot Zw (q 5 = (0 • , 3 • )) and Rot Yw (q 6 = (0 • , 90 • )), 2 3
angular combinations are obtained. For each angular combination (each orientation), three translations are applied along X w , Y w and Z w (3 equations), thus yields 24 equations. Translation of [-150 + 150] µm is applied along X w and Z w and [-20 + 20] µm along Y w with translational velocity control. Wavelength scan distance measure is used based on FP interferometry before and after each translation along X w and Z w axes in order to determine the sign of dL. The two previous measurement steps can give 69 equations. This non-linear minimization problem can be solved using various algorithms. The Levenberg-Marquardt method is most often cited and used in the literature. Such a method makes a compromise between the gradient method (launch of the algorithm far from the minimum) and Newton's method (neighborhood of the solution, acceleration of convergence). In addition, such a method frees itself from the problems of singularities of the Hessian matrix. Levenberg-Marquardt method is used for the identification of the robot extrinsic and intrinsic parameters.

B. 6-DoF Nanopositioning robot control after full calibration

The 6-DoF Nanopositioning robot control after full calibration is shown in the scheme in Figure 7. The control scheme of the robot uses the identified extrinsic and intrinsic parameters of the robot. The inverse kinematic model of the robot is calculated based on the identified intrinsic parameters of the robot. The two transformation matrices between the end-effector and the tool and then between the tool and the reflection spot P r are calculated based on the identified extrinsic parameters. The experimental setup used to validate the proposed calibration approach is presented in the next section.

VI. EXPERIMENTAL SETUP

The proposed experimental setup for 6-DoF robotic calibration based on 1-D interferometric measurements is shown in Figure 8. The mirror is held by a 6-DoF serial robot to control its poses. The fiber ferrule is held by an other XYZ manual positioner which is fixed in front of the 6-DoF robot, it is used to pre-position the fiber ferrule. The experimental setup is placed on an anti-vibration table. The 6-DoF robot is assembled with minimum geometric errors based on one (XYZ) nanopositioning stage followed by a bracket support, which is fabricated specifically to join the (XYZ) translation stage (q 1 , q 2 , q 3 ) to a set of two gomiometers (q 4 , q 5 ) and then a rotary positioner (q 6 ) (see Figure 8). The two gomiometers are used for rotation around X w -axis and Z w -axis and the rotary positioner for rotation around Y waxis. A XYZ prepositioner is placed after the rotary positioner for coarse adjustment of the rotation center of the whole assembled 6-DoF robot.

XYZ passive prepositioner

The (XYZ) nanopositioning stage is a PIMars P-563.3CD, its resolution is 0.5 nm. It is controlled via a E-712 controller. The two goniometers are SGO-60.5 and SGO-77.5, their resolution is 0.57 µ • . They use the stick-slip principle and are controlled by MCS-3D unit. The SGO-60.5 goniometer's center of rotation is 60.5 mm. The SGO-77.5 goniometer's center of rotation is extended to 77.5 mm. The rotary positioner is SR-3610-S, its resolution is 1.1 µ • . It uses the piezo principle and is controlled by MCS-3D unit. E-712 controller and MCS-3D unit are controlled via Matlab.

The optical fiber is connected to an optical set up. This optical setup consists in a laser light source (wavelength λ = 1560 nm). This latter is connected to a circulator and then to the fiber ferrule. The reflected optical irradiance from mirror through the fiber ferrule is the feedback information for the 6-DoF robot control loop. This set up enables the acquisition of the reflected optical irradiance signal from the mirror surface, coming back through the fiber ferrule and then through the beam circulator.

The next section studies the optical performances after robot extrinsic and intrinsic parameters identification.

VII. EXPERIMENTAL RESULTS

A. Performances after full 6-DoF robot calibration

Figure 9 represents the optical irradiance during a rotation q 6 around Z 6 axis before calibration. Figure 10 represents the optical irradiance during a circular translation on the mirror plane before calibration. The fringes (peaks) on the optical irradiance are due to FP cavity variation along the optical axis. This proves the strong influence of geometric errors, that can be extrinsic and/or intrinsic. The robot calibration aims to reach a 6-DoF positioning that does not induce a FP cavity variation along the optical axis i.e, applying rotations and translations along the mirror plane without inducing a distance change along the optical axis (the reflection point on the mirror plane is kept fixed).

The method presented in previous sections conducts to identify both intrinsic and extrinsic parameters whose identified values are provided in Table II and Table III respectively. Figure 11 represents the obtained results after identification of both extrinsic and intrinsic parameters of the 6-DoF robot for 3 rotations around Z f , for the reflection point projection on the mirror P r (141.1, 116.34), calculated from equation ( 29).

Link ρ i β i ( • ) α i ( • ) d i (µm) θ i ( • ) r i (µm) 1 1 0 0 0 0 q 1 2 1 0 -90.13 0 -89.22 q 2 3 1 0 -90.29 0 -89.47 q 3
4 0 -0.26 0.25 -4.20 q 4 -0.07 0 5 0 0 -89.45 -2.21 q 5 -90.49 0 6 0 0 -90.57 0 q 6 + 0.14 0

For rotations around Z f , the corresponding optical irradiance, the 3 translational joints and the 2 rotational joints (joint 4 and 5) are plotted. 11. Rotation q 6 around Z f axes in operational coordinates when the reflection point projection is in Pr(141.1, 116.34), after robot extrinsic and intrinsic parameters identification.

Results show that, after full robot calibration, the joints intervene in order to move the rotation center of the robot to the reflection point of the laser spot P r and maintains it at that point (reflection point P r ) during rotations in operational coordinates. For example, for a rotation q 6 around Z f , the translational and rotational joints intervene in order to maintain the rotation at the reflection point P r , where the optical irradiance is constant until the saturation of at least one translational joint, the frequency of the fringes (peaks) increase, which represents an increase in FP cavity variation during the rotation.

Figure 12 shows the optical irradiance corresponding to a circular translation along the optical fiber plane before calibration, after extrinsic parameters identification, and after extrinsic and intrinsic parameters identification. Results shows many fringes on the optical signal before calibration. After only extrinsic parameters identification, there is still almost half of FP peak. After extrinsic and intrinsic parameters identification, the irradiance is constant and it is maximum compared with the two others cases. It is also important to note that the maximum irradiance obtained is largely improved when the positioning robot is calibrated. This demonstrates that there is no FP cavity variation during the circular translation along the optical fiber plane.

B. Full calibration durability and parameters behavior investigation

At micro-scale and more generally in precision robotics, drift often happens. For this reason, the durability of the obtained performances needs to be studied. In order to evaluate the durability of the calibrated extrinsic and intrinsic parameters of the 6-DoF robot, a circular translation along the optical fiber plane is applied every 2 hours for 14 hours after the end of the full calibration (which defines time "T 0 ").

Figure 13 shows the obtained optical irradiance for each circular translation along the optical fiber plane for each 2 hours from the end of the full (extrinsic and intrinsic) calibration at T 0 . The optical irradiance remains constant during the 8 first hours and it starts to derive after 10 hours and then it derives increasingly after 12 and 14 hours.

In order to study the parameters changes to drifts, two robot extrinsic and intrinsic parameters identifications are repeated (the sequence of all experiments done is detailed in Fig. 16). The first one is done one day after the first full robot calibration, and the obtained identified extrinsic and intrinsic parameters are shown in column one of Table IV and Table V respectively. The second one is done two days after the full calibration and the obtained identified extrinsic and intrinsic parameters are shown in column two of Table IV and Table VI respectively. From the obtained identified parameters, all robot extrinsic parameters change from one day to another and only one intrinsic parameter that changes, which is β 4 . θ 6 is dependent to θ et , therefore it can be fixed. After 7 days from the first full robot calibration, only robot extrinsic parameters calibration is done, the obtained identified extrinsic parameters are shown in column three of Table IV. The obtained optical irradiance which corresponds to the circular translation along the optical lamella plane is highlighted in red color in Figure 14.

Link ρ

i β i ( • ) α i ( • ) d i (µm) θ i ( • ) r i (µm) 1 1 0 0 0 0 q 1 2 1

Link ρ

i β i ( • ) α i ( • ) d i (µm) θ i ( • ) r i (µm) 1 1 0 0 0 0 q 1 2 1

Link ρ

i β i ( • ) α i ( • ) d i (µm) θ i ( • ) r i (µm) 1 1 0 0 0 0 q 1 2 1
The obtained optical irradiance which corresponds to the circular translation along the mirror plane is not maximum and is not constant, which means that there is small FP cavity variation. Hence, we can conclude that during the 7 days, some intrinsic parameters were slightly changing. In order to verify that some intrinsic parameters are changing, a full extrinsic and intrinsic robot parameters is identified one day after (8 days from the first full robot calibration). The obtained identified extrinsic and intrinsic parameters are given in column four of Table IV In order to estimate the positioning accuracy, after identification of both intrinsic and extrinsic parameters, a translation along Y f axis (parallel to the plane of the fiber) is applied after having modified the identified parameter β et by adding each time 0.002 • (misaligning the mirror from the fiber plane). In summary, full (extrinsic and intrinsic parameters) robot can be maintained for about 8 hours, without parameters change. Optical irradiance derivation starts after 10 hours. All robot extrinsic parameters change from one day to another and only one intrinsic parameter that changes, which is β 4 . Therefore, the optical irradiance derivation is because of extrinsic geometric parameters change. Doing extrinsic parameters calibration after 7 days from full parameters calibration demonstrates that intrinsic parameters were changing slowly with time.

VIII. CONCLUSION

Positioning accuracy is one of the most important performance criteria ore especially for nanopositioning robots. However, there are many extrinsic and intrinsic parameters that induce inaccuracy. In this paper, these extrinsic and intrinsic parameters were identified to calibrate the nanopositioning robot studied, in order to improve its positioning accuracy.

A robotic approach was proposed for 6-DoF nanopositioning robot calibration. This approach uses 1-D relative distance measurements in order to identify extrinsic and intrinsic geometric parameters, through a new reliable robotic calibration model and a dedicated measurement strategy for high measurement accuracy. The 1-D relative distance measurements is based on 1-D FP interferometric measurements.

After full 6-DoF robot calibration, no FP fringes appear on the optical irradiance for rotations around X f , Y f and Z f axes, neither for circular translation along the mirror plane. A translational and rotational positioning accuracy estimate of about 50 nm and 0.004 • have been obtained respectively.

Moreover works shown that this level of performances can be held during several hours.

The alignment of the mirror with respect to the fiber is easily reachable after full robot calibration. Moreover, two complementary approaches can be used: the full calibration of the robot (all extrinsic and intrinsic parameters identified) and a partial calibration where only the extrinsic parameters are reidentified. These two approaches demonstrated that extrinsic parameters change the most with time/drift and then their reidentification enable to reach again a very high positioning accuracy. Combining these two approaches, it is possible to hold a high level of performances over long periods, typically a week, which appears particularly promising for a wide scope of applications and more especially at the micro and nano scales.

FP

Figure 1 .

 1 Figure 1. Schematic diagram representing the interferences in a FP optical cavity, with reflected irradiance versus FP cavity length L, at wavelength λ = 1560 nm .

Figure 2 .

 2 Figure 2. Khalil and Kleinfinger with additional Hayati parameter β i about Y i-1 is used for nearly parallel axes.

Figure 4 .

 4 Figure 4. The robotic positioning scheme with frames assignment.

Figure 5 .

 5 Figure 5. Mirror before the new pose and after the new pose.

  wt x wf + b wt y wf + c wt z wf + d wt ) a wt a wf + b wt b wf + c wt c wf .

  wL x wf + b wL y wf + c wL z wf + d wt ) a wt a wf + b wt b wf + c wt c wf -(a wt x wf + b wt y wf + c wt z wf + d wt ) a wt a wf + b wt b wf + c wt c wf ,

Figure 6 .

 6 Figure 6. Measurement strategy for robot calibration.

Figure 7 . 6 -

 76 Figure 7. 6-DoF Nanopositioning robot control after full calibration.

  Goniometers(𝒒 𝟒 , 𝒒 𝟓 ) Rotary positioner (𝒒 𝟔 ) Nanopositioning stage XYZ (𝒒 𝟏 , 𝒒 𝟐 , 𝒒 𝟑 )

Figure 8 .

 8 Figure 8. Robotic experimental platform.

2 )Figure 9 .

 29 Figure 9. Optical signal (irradiance) when a rotation q 6 around Z 6 axis is done before calibration.

Figure 10 .

 10 Figure 10. Circular translation on the mirror plane before calibration.

Figure 12 .

 12 Figure 12. The optical irradiance corresponding to a circular translation on the mirror plane before robot calibration, after robot extrinsic parameters calibration and after robot extrinsic and intrinsic parameters calibration.

Figure 13 .

 13 Figure 13. Durability evaluation of the fully calibrated robot (both extrinsic and intrinsic parameters) by applying circular translation on the optical fiber plane every 2 hours without recalibration for 14 after the end of the full calibration (the full calibration ends at time T 0 ).

Figure 14 .

 14 Figure 14. The obtained optical irradiance for circular translation on the optical lamella plane for only robot extrinsic parameters calibration, after 7 days from the first full calibration.

2 )Figure 15 .

 215 Figure 15.Experimental estimation of angular accuracy when a small compensation error of βet parameter is created.

Figure 16

 16 Figure 16 summarize the experimental protocol for full calibration durability and parameters behavior investigation.In order to estimate the positioning accuracy, after identification of both intrinsic and extrinsic parameters, a translation along Y f axis (parallel to the plane of the fiber) is applied after having modified the identified parameter β et by adding each time 0.002 • (misaligning the mirror from the fiber plane).(β et ) set = (β et ) identif ied + ε, such that 0.002 • ≤ ε ≤ 0.012 • .The obtained optical irradiance for each translation is shown in Figure15and highlights that the optical irradiance starts to derive after having modified β et by 0.004 • , which is an estimate of the rotational positioning accuracy. The same optical irradiance can be estimated to 1/8 of half oscillation period, which corresponds approximately to a translational positioning accuracy estimate of 50 nm.

Figure 16 .

 16 Figure 16 summarize the experimental protocol for full calibration durability and parameters behavior investigation.In order to estimate the positioning accuracy, after identification of both intrinsic and extrinsic parameters, a translation along Y f axis (parallel to the plane of the fiber) is applied after having modified the identified parameter β et by adding each time 0.002 • (misaligning the mirror from the fiber plane).(β et ) set = (β et ) identif ied + ε, such that 0.002 • ≤ ε ≤ 0.012 • .The obtained optical irradiance for each translation is shown in Figure15and highlights that the optical irradiance starts to derive after having modified β et by 0.004 • , which is an estimate of the rotational positioning accuracy. The same optical irradiance can be estimated to 1/8 of half oscillation period, which corresponds approximately to a translational positioning accuracy estimate of 50 nm.

Table II IDENTIFIED

 II ROBOT INTRINSIC PARAMETERS.

Table III IDENTIFIED

 III EXTRINSIC PARAMETERS. Values 0.768 • -0.613 • 0.721 • -0.533 • 1.61 µm 113.40 µm 916.1 µm 115.3 µm 155.5 µm -3.82 µm -109.78 µm

	Parameters	βet	θet	β wf	θ wf	Zet	x wf	y wf	z wf	w Prx

w Pry w Prz

Table IV IDENTIFIED

 IV EXTRINSIC PARAMETERS AFTER, 1, 2, 7 AND 8 DAYS FROM THE FIRST FULL ROBOT CALIBRATION. Prz -109.08 µm -109.87 µm -106.54 µm -107.53 µm

	Parameters After 1 day After 2 days After 7 days After 8 days
	βet	0.781 •	0.785 •	0.802 •	0.811 •
	θet	-0.615 •	-0.619 •	-0.710 •	-0.702 •
	β wf	0.729 •	0.725 •	0.784 •	0.763 •
	θ wf	-0.561 •	-0.565 •	-0.591 •	-0.561 •
	Zet	1.42 µm	1.52 µm	2.1 µm	2.3 µm
	x wf	112.9 µm	112.3 µm	112.4 µm	113.3 µm
	y wf	917.2 µm	917.8 µm	920 µm	918.8 µm
	z wf	115.7 µm	116.4 µm	113.1 µm	112.2 µm
	w Prx	154.8 µm	154.4 µm	149.2 µm	148.7 µm
	w Pry	-3.75 µm	-3.61 µm	-3.4 µm	-3.54 µm

w

Table V IDENTIFIED

 V ROBOT INTRINSIC PARAMETERS, ONE DAY AFTER THE FIRST FULL ROBOT CALIBRATION.

  and TableVIIrespectively and shows that some intrinsic parameters are changing slowly with time.

ACKNOWLEDGMENT

These works have been funded by the Franche-Comté region, the EUR EIPHI Graduate School (ANR-17-EURE-0002), ANR CEPAGE (ANR-16-CE24-0024) and by the French RENATECH network through its FEMTO-ST technological facility.


Clara Rigaud
email: clara.rigaud@sorbonne-universite.fr

From the Makerspace to the Web: Creating Knowledge Resources from Fabrication Activities

Keywords: Human-centered computing → HCI theory, concepts and models; fabrication, documentation, tutorial, portfolio, workshop, maker culture, DIY

This paper presents an overview of the research I am conducting as part of my PhD studies. The goal of my research is to describe and better understand the barriers to the creation and reuse of fabrication knowledge resources and to explore technological interventions to remove these barriers.

CONTEXT AND MOTIVATION

Makerspaces and more generally fabrication workshops are places that gather people around machines, tools and materials to design, build, repair, prototype and invent things [START_REF] Dougherty | The Maker Movement[END_REF]. In parallel of the different projects and activities happening inside these places, makers create, share, search and use knowledge about fabrication methods, tips, techniques and previous DIY projects [START_REF] Kuznetsov | Rise of the expert amateur: DIY projects, communities, and cultures[END_REF]. These knowledge exchanges happen directly when people talk, share tips between each others, get curious about one's project. But a big part, however, happens indirectly, often digitally by the mean of project documentations, portfolios, social networks or tutorials, or when makers leave traces for themselves to reuse later [START_REF] Wolf | Sharing is Sparing: Open Knowledge Sharing in Fab Labs[END_REF]. Creating and using a fabrication knowledge resource is a complex activity. It takes place in parallel of a fabrication activity, happening before, during and after a project, while the maker can be in different places inside or outside the workshop. The knowledge resources can be of different forms and consequently require the use of different tools to capture, edit, transmit and use or display the resource.

Therefore, providing tools to support makers during this whole process is crucial. While a number of systems and tools have been already proposed to support makers in specific situations, there are still many situations where these tools are not well adapted. Indeed, there is a the wide variety of activities happening in a space like fabrication workshops and different reasons and manners to create content about a fabrication project. It remains a challenge to propose approaches generic enough yet effective to realistically be considered as a widely fitting solution to support all makers. The goal of my project is to study this thematic of knowledge about fabrication and DIY activities, by focusing on how it happens inside the fabrication workshop. I intend to understand the ways makers work in these places, their methods and objectives for producing and using knowledge and to explore which approaches could fit the peculiar space of fabrication workshop. This would help with the process of leaving traces of one's work, support the creation and sharing of knowledge and bring back existing knowledge inside the place. To do this, I consider the variety of profiles of makers and the different kind of activities they can do in a fabrication workshop, as well as the whole set of reasons for creating and using fabrication and DIY knowledge.

BACKGROUND AND RELATED WORK 3.1 Understanding DIY knowledge and makers

With the wide availability of internet access, DIY culture has taken a new dimension with people forming communities on forums to exchange tips and hacks online [START_REF] Dougherty | The Maker Movement[END_REF][START_REF] Kuznetsov | Rise of the expert amateur: DIY projects, communities, and cultures[END_REF]. Today, people share their DIY projects on their personal websites, on dedicated platforms such as Instructables and on social networks, with a variety of motivations such as enabling others to reuse these resources to get inspired, apply some parts of an idea to their own project or reproduce a method or an object [START_REF] Kuznetsov | Rise of the expert amateur: DIY projects, communities, and cultures[END_REF][START_REF] Lafreniere | Looks cool, I'll try this later![END_REF][START_REF] Rosner | Learning from IKEA Hacking[END_REF][START_REF] Torrey | Learning how: the search for craft knowledge on the internet[END_REF][START_REF] Tseng | Product versus process: representing and appropriating DIY projects online[END_REF]. More generally, makers create knowledge resources about their fabrication projects to keep track of their work for themselves [START_REF] Schoffelen | Sharing is caring. Sharing and documenting complex participatory projects to enable generative participation[END_REF][START_REF] Wolf | Sharing is Sparing: Open Knowledge Sharing in Fab Labs[END_REF], or to share a technique or a method with others. Their motivations can be altruistic as part of the philosophy of open knowledge, to gain recognition, visibility and feedback from peers, or to gain money [START_REF] Kurti | The Philosophy of Educational Makerspaces Part 1 of Making an Educational Makerspace[END_REF][START_REF] Lafreniere | Looks cool, I'll try this later![END_REF][START_REF] Peppler | Maker Movement Spreads Innovation One Project at a Time[END_REF][START_REF] Torrey | How-To pages: Informal systems of expertise sharing[END_REF]. Sometimes, the fabrication places can demand that makers produce knowledge from their projects as a support of learning or to enable assessment [START_REF] Dalsgaard | Reflective design documentation[END_REF][START_REF] Desjardins | Exploring DIY tutorials as a way to disseminate research through design[END_REF][START_REF] Keune | Maker Portfolios as Learning and Community-Building Tools Inside and Outside Makerspaces[END_REF][START_REF] Sheridan | Learning in the Making: A Comparative Case Study of Three Makerspaces[END_REF], or because it's part of the policy of the place, for example in the case of Fablabs [START_REF] Gershenfeld | How to Make Almost Anything[END_REF]. However, producing knowledge resources from one's physical activity is not a easy task. During the fabrication, it requires to switch focus from the actual work to the knowledge capture, and thus is costly and can be forgotten [START_REF] Wolf | Sharing is Sparing: Open Knowledge Sharing in Fab Labs[END_REF]. In addition, while working, makers are busy with their hands and it can be difficult to hold a camera to take a picture or a video [START_REF] Carter | Tools to support expository video capture and access[END_REF]. The process of creating knowledge support also happens after the activity, and makers have to retrieve their content, use many tools to edit and to author a support that will be reusable by themselves or others [START_REF] Tseng | Product versus process: representing and appropriating DIY projects online[END_REF]. Due to these difficulties, the resulting resource can lack details or quality, making it difficult to reuse for reproducing a method [START_REF] Wakkary | Tutorial Authorship and Hybrid Designers: The Joy (and Frustration) of DIY Tutorials[END_REF]. Sometimes they do not include the different attempts that are important to get feedback along the project [START_REF] Tseng | Product versus process: representing and appropriating DIY projects online[END_REF] in some contexts or even not made at all [START_REF] Wolf | Sharing is Sparing: Open Knowledge Sharing in Fab Labs[END_REF].

Designing for DIY knowledge and makers

Different approaches have been explored to support makers when creating knowledge resources. Some of them focus on integrating the gathering of content during the activity, for example in the case of assembly. Some systems tend to automate the capture of the fabrication process by the mean of sensors on the pieces [START_REF] Tseng | Replay: a selfdocumenting construction kit[END_REF], computer vision [START_REF] Gupta | DuploTrack: a real-time system for authoring and guiding duplo block assembly[END_REF], or augmented reality to author tutorials [START_REF] Whitlock | AuthAR: Concurrent Authoring of Tutorials for AR Assembly Guidance[END_REF]. However, these approaches are very specific to the material used. For example, it would be difficult to use the same approaches with activities for which the objects are unknown, and imply more complex manipulations such as soldering or doing circuitry on a breadboard. Some systems are aimed to be installed as "documentation stations" inside the workshop, providing cameras to capture an object [START_REF] Keune | DIY Documentation Tools for Makers[END_REF][START_REF] Tseng | Spin: a photography turntable system for creating animated documentation[END_REF], a series of steps [START_REF] Tsukada | FabNavi: Support system to assemble physical objects using visual instructions[END_REF], or include a modular toolkit to take pictures and videos from different angles [START_REF] Gourlet | DoDoc: a Composite Interface that Supports Reflection-in-Action[END_REF]. These approaches have the advantage of freeing the hands of the maker and to make the knowledge capture less inclined to be forgotten, but these solutions are limited to rather small objects or workbench activities. Other systems imply to equip the maker with sensors to capture or recognize the activity [START_REF] Lukowicz | Recognizing Workshop Activity Using Body Worn Microphones and Accelerometers[END_REF][START_REF] Schoop | Drill Sergeant: Supporting Physical Construction Projects through an Ecosystem of Augmented Tools[END_REF] or even the expertise of the maker [START_REF] Gong | Instrumenting and Analyzing Fabrication Activities, Users, and Expertise[END_REF], or with head mounted cameras to capture from the first person point of view [START_REF] Carter | Tools for online tutorials: comparing capture devices, tutorial representations, and access devices[END_REF].

If not questioning the invasive and privacy aspects of those approaches, equipping all the makers in the space with such systems can be very expansive and maybe not suited to many fabrication workshops. Producing knowledge resources happen during a whole project that can often take weeks or months, and some approaches developed tools aimed to facilitate the integration of the captured content inside a document, automating some parts of the editing process [START_REF] Sánchez Milara | Document-while-doing": a documentation tool for Fab Lab environments[END_REF], enabling feedback along the project [START_REF] Tseng | Making Make-throughs: Supporting Young Makers Sharing Design Process[END_REF] or generating step by step web-based documents or videos [START_REF] Carter | Tools for online tutorials: comparing capture devices, tutorial representations, and access devices[END_REF]. These approaches are promising but often limit the maker to the use of the platform itself, although they might want to publish their work in different platforms, already popular among a particular community [START_REF] Peppler | It helps create and enhance a community": Youth motivations for making portfolios[END_REF].

Discussion and positioning

We saw in the previous section that researchers have gone a long way studying the phenomena of knowledge creation and sharing in the context of fabrication, identifying problems at different levels and providing approaches to support makers confronted to these problems. However, it appears that much of the approaches and systems I found in literature tend to focus on a specific community of practices (such as crafters, hobbyists, electronics, learners...), on a specific kind of activity (3d printing, assembly,...), or a specific kind of purpose in knowledge creation (tutorials, assessment portfolios, project documentation). While these approaches may address the issues found in the specific context in which they were developed, they are difficult to generalize to more generic forms.

People do a broad range of different activities in the workshop going from soldering, to programming, computer aided design, ceramics, to laser cutting. During their journey, they can move a lot, changing from a workstation to the other, sometimes dealing with messy environments or having their hand dirty. This can impact their way to interact with the tools they use to create content while working. Moreover, the activities themselves can lead to different approaches regarding the type of content to capture, for example sometimes video is the best way to illustrate a process rather than pictures [START_REF] Carter | Tools to support expository video capture and access[END_REF]. Makers may not use the same tools to capture small manipulations on a workbench and painting a table. Some work have been exploring the way workshop are physically organised [START_REF] Annett | Exploring and Understanding the Role of Workshop Environments in Personal Fabrication Processes[END_REF] and the impact of object size on the best way point of view from which to capture visual content [START_REF] Carter | Tools for online tutorials: comparing capture devices, tutorial representations, and access devices[END_REF]. The vast majority of the tools to support knowledge creation inside the workshop tend however to focus on a specific kind of fabrication activity or context. In addition, some of these systems make use of technologies that might be expansive, or maybe make people feel uncomfortable or invading their privacy. I think that literature is missing a closer look on how people actually capture content or make records depending on the activities they are doing in the workshop, and that an analysis of the different aspects that matter when capturing or recording might help designing better systems.

On a higher level, I found a lot of published articles studying habits and designing tools for knowledge resources, but most of them are focusing on specific cases of fabrication knowledge resources like tutorials, documentations, portfolios. Makers can have different objectives to create and use knowledge resources, and depending on the reasons to make a support, the way to build it and then reuse it might differ. Most of the systems to support makers acknowledge issues regarding one specific objective for creating knowledge resources but are not suited for other purposes. Also, I found that a big part of the systems aimed to support makers on knowledge creation are not made to be used for other purposes. At the end, all of these knowledge resources have in common that they are a representation of a fabrication activity and have at some point to be made inside the workshop, leading to overlapping challenges for the makers. I think that by better understanding the objectives of the different knowledge resources and identifying the challenges related to them we can inform the design of better systems for fabrication workshops.

THESIS STATEMENT

Exploring the habits and providing tools generic enough inside the workshop to fit different activities and purposes in knowledge creation might lead to more effective approaches for the work of all makers, and help them to create richer and more reusable content and resources. From that statement I highlighted 4 research questions that I am exploring during my PhD.

• Which tools and media makers use currently when they capture their work and how does this vary across activities? • What are the objectives and challenges when creating and using fabrication knowledge resources? • What are the different dimensions to consider when designing systems to capture content from fabrication activities? • What kinds of properties of a system influence the practices in the creation of knowledge resources in fabrication workshops ?

DISSERTATION STATUS

To explore these questions, I have adopted different methodologies including an online study, a literature survey, a framework, and the design of a prototype. The projects summarized in subsection 5.1, subsection 5.2 and subsection 5.3 are currently under review for publication.

Which tools and media makers use currently when they capture their work and how does this vary across activities?

In 2021, we ran an online study resulting in 60 responses among makers from all around the world. The purpose of this questionnaire was twofold. The first part was made of 19 questions aimed to gather insights from the current habits of makers when capturing content while working inside a makerspace. Participants had first to pick the activities they are used to do in a workshop (woodworking, CAD, 3D printing, ...) and were asked about general habits regarding documenting. They were then asked questions about the two activities they create the most frequently content from and asked about the tools, habits, advantages and problems they could encounter while capturing content while doing these activities. Results showed for instance that makers will create different kinds of records depending on the activity they do, as shown in [Figure 1].

What are the objectives and challenges when creating and using fabrication knowledge resources?

To explore this question, we made a literature survey and extracted the objectives and challenges associated with knowledge resources in fabrication workshops. Through an analysis of the different types of knowledge resources, we identified 4 objectives [Figure 2]:

• Represent a fabrication project, which is common to all We explored this questions with two approaches. First, we identified different dimensions describing the capture of fabrication related content from literature, and provided a framework to illustrate these dimensions. We made our analysis with the 5W+H, enabling us to describe the capture of content according to:

• Why: the different reasons to capture content • What: the kind of data to capture, such as images, videos, sound, contextual information or metadata • How: the devices or sensors used to capture • When: the moment when the capture is made, before when planning or sketching, during the activity or after. • Where: the location from which to capture (user attached, environment or tool) • Who: The degree of automation of the capture control Based on the dimensions we had identified, we created a concept of modular actuated units based on connected cameras that we illustrated with sketches and animations in a video [Figure 3]. This concept is a fleet of cameras that are connected to a local repository and offer different options, enabling the mobility of the maker or not by being wore on the head or being fixed on the machine and offering different options such as tracking and following a tool.

On a second part of the previously mentioned online study (subsection 5.1), we showed the video to participants and asked them feedback about it. The second part of the questionnaire was made of 19 questions including some focused on one specific activity (the one participants said creating the most frequently visual content about). This work was made during the quarantine episode, making it impossible for us to make a real evaluation of a set of prototypes in situ. However, results and feedbacks from participants were useful as a formative study, informing the design of a prototype that would come later.

What kinds of properties of a system

influence the practices in the creation of knowledge resources in fabrication workshops?

On my last 1.5 year, I plan to refine and elaborate my prototypes mentioned in subsection 5.3 for capturing content from fabrication activities based on the insights I gathered from the online formative study [Figure 4]. Then I will explore the impact of this system on the makers workflow by installing it in my local Fablab, and maybe offer a new tool for fabrication workshops and designers. To do that, I plan to run interviews among makers willing to use the system during their projects to gather feedback on their experiences alongside weekly observations of the makers inside the Fablab with the system in place. I will as well interview managers of the workshop to gather their opinion on such a system inside their place. In addition, if possible, I would try to measure the impact of such a system on the knowledge resources by comparing the ones made with and without the system. Ideally, I would compare them according to the different objectives and challenges I identified in subsection 5.2.

CONCLUSION

In my work, I study the creation and reuse of fabrication knowledge resources, by better understanding 1) the objectives of makers in the creation and use of fabrication knowledge resources, 2) their habits and difficulties when creating these resources and 3) how these habits and difficulties can vary across situations such as activities or fabrication workshops By doing that, I intend to understand which properties of a system aimed to be installed in a fabrication workshop would succeed in helping and supporting makers in the creation of knowledge resources. I'm hoping that this article will generate discussions around the different objectives behind fabrication knowledge resources and provide feedback on the general approach. I'm also hoping to raise discussions around automation, the impact and suitability of technology inside the peculiar space of fabrication workshops.

Figure 1 :

 1 Figure 1: We ran an online survey resulting in 60 responses to better understand the practices of makers when capturing or recording content while doing different activities in the fabrication workshop. This visualisation illustrates responses to the question what kind of records participants generated depending on fabrication activity.

Figure 2 :

 2 Figure 2: This graph shows how the creation of knowledge resources can be understood as Objectives instead of Terminologies.

Figure 3 :

 3 Figure 3: A design concept based on a fleet of actuated units based on connected cameras was inspired from the different dimensions of our framework to capture visual content from a variety of activities and situations.

Figure 4 :

 4 Figure 4: A first generation of prototypes inspired by our design of connected camera-based units is intended to be evaluated with a user study in the field

ACKNOWLEDGMENTS

This work was supported by a grant from Agence Nationale de Recherche (ANR-17-CE33-0001).