Bilal Komati

Kanty Rabenorosoa

Cédric Clévy

Member, IEEE Philippe Lutz

Automated Guiding Task

Keywords: Microassembly, hybrid force/position control, automated task, flexible micropart, compliant micropart, twosensing-finger, microgripper, gripping force, lateral contact, microrobot control, microrobotics

I. INTRODUCTION

Nowadays, miniaturized systems which integrate intelligence and functionalities are more and more required. These systems are either micromechanisms (micro ball bearings, microgears, micromotors), micro-optical systems (switches, lasers) or hybrid Micro-Opto-Electro-Mechanical Systems (MOEMS) like microscanners, microspectrometers [START_REF] Aljasem | Scanning and tunable micro-optics for endoscopic optical coherence tomography[END_REF], [START_REF] Aljasem | Fiber optic tunable probe for endoscopic optical coherence tomography[END_REF], [START_REF] Waldis | Arrays of high tilt-angle micromirrors for multiobject spectroscopy[END_REF]. The integration of MEMS (Micro-Electro-Mechanical Systems) and MOEMS (Micro-Opto-Electro-Mechanical Systems) technology in commercial products is growing especially in the field of telecommunication and sensor technologies [START_REF] Tolfree | Commercializing Micro-Nanotechnology Products[END_REF]. The microfabrication limitations have helped the growth of the microassembly field. The main purpose of microassembly

The authors are with FEMTO-ST Institute, UMR CNRS 6174 -UFC / ENSMM / UTBM, Automatic Control and Micro-Mechatronic Systems Department, 25000 Besancon, France, (e-mail: bilal.Komati@femto-st.fr, kanty.rabenorosoa@femto-st.fr, cclevy@femto-st.fr, philippe.lutz@femtost.fr.) is to assemble microparts produced from various fabrication processes into one complex product. The use of robotic workstations equipped with micropositioning stages, a microgripper and vision systems is commonly practiced at the microscale.

Automated robotic microassembly is the final objective which is usually carried out by precise positioning [START_REF] Das | µ 3 : Multiscale, deterministic micro-nano assembly system for construction of on-wafer microrobots[END_REF], [START_REF] Tamadazte | Robotic micromanipulation and microassembly using monoview and multiscale visual servoing[END_REF], [START_REF] Sariola | Hybrid microassembly combining robotics and water droplet self-alignment[END_REF] but it is not sufficient for all microassembly tasks [START_REF] Lu | A force-feedback control system for micro-assembly[END_REF]. Dual finger microgrippers with feedback are used to automate some microassembly tasks [START_REF] Tamadazte | Robotic micromanipulation and microassembly using monoview and multiscale visual servoing[END_REF], [START_REF] Xie | Three-dimensional automated micromanipulation using a nanotip gripper with multi-feedback[END_REF]. The feedback could be vision, position or force feedback.

Most of the work deals with vision-based control [START_REF] Tamadazte | Robotic micromanipulation and microassembly using monoview and multiscale visual servoing[END_REF], [START_REF] Wang | Automated 3-d micrograsping tasks performed by vision-based control[END_REF], [START_REF] Anis | Automated selection and placement of single cells using vision-based feedback control[END_REF]. It mainly enables position control and rarely takes into account the interaction forces like gripping forces and contact force between the grasped micropart and the substrate. Especially at the microscale, interaction forces have to be taken into account due to the predominance of adhesive forces. It is notably manifested by pull-off force which can be 84 times the 100µm x 1000µm x 1000µm silicon micropart weight [START_REF] Rabenorosoa | Measurement of pull-off force for planar contact at the microscale[END_REF]. Another important reason to take the forces into consideration is the fragility of the components (grippers, parts, etc). Indeed, the microgrippers may also easily be broken if the gripping forces are not taken into consideration. In addition, the integration of micropositioning sensors in the microassembly station is hampered by the size of sensors [START_REF] Lu | A force-feedback control system for micro-assembly[END_REF], [START_REF] Clévy | Signal Measurement and Estimation Techniques for Micro and Nanotechnology[END_REF].

In order to achieve automated microassembly and to avoid the destruction of microparts, a control of the gripping force is often used [START_REF] Carrozza | Towards a force-controlled microgripper for assembling biomedical microdevice[END_REF], [START_REF] Reddy | Miniature compliant grippers with vision-based force sensing[END_REF], [START_REF] Rakotondrabe | Development and force/position control of a new hybrid thermo-piezoelectric microgripper dedicated to micromanipulation tasks[END_REF]. The detection of contact and the control of the impact force are performed in [START_REF] Volpe | A theoretical and experimental investigation of explicit force control strategies for manipulators[END_REF], [START_REF] Zhou | Fusing force and vision feedback for micromanipulation[END_REF]. There are some tasks which are carried out by using force control like insertion [START_REF] Wason | Multiprobe micro-assembly[END_REF], [START_REF] Lu | A force-feedback control system for micro-assembly[END_REF] and pushing [START_REF] Zesch | Alignment of microparts using force controlled pushing[END_REF]. In these works, AFM probes are often used or grippers with one sensing fingers and one actuated finger. The use of two-sensing-finger allows to detect the side of contact [START_REF] Rabenorosoa | Study of forces during microassembly tasks using two-sensing-fingers grippers[END_REF] and to control the gripping forces at the same time or independently (picking of a micropart). Such a system brings suitable information about the contact, provides more dexterity of the grasp and ensures more safety to not break microparts. In addition, the use of two-sensing-finger microgripper simplifies the pick of the micropart because the contact from the two sides will be easily detected.

In our previous work [START_REF] Bargiel | Towards micro-assembly of hybrid moems components on a reconfigurable silicon free-space micro-optical bench[END_REF], we designed RFS-MOB (Reconfigurable Free Space Micro-Optical Benches) that are based on generic components (holders and substrates). This principle can be easily used to design various MOEMS (µ spectrometer, coupling system, µ-confocal microscope, etc) and test benches (characterization of micro-optical devices). These holders include flexible structures (springs). However, flexible microparts are of great interest for microassembly [START_REF] Popa | High yield automated mems assembly[END_REF]. To automatically assemble microproducts such as RFS-MOB and achieve fine positioning, it is required to pick the holder to be assembled, to guide it along a rail and to release it. This guiding task is studied in this paper. In a previous paper [START_REF] Rabenorosoa | Active force control for robotic micro-assembly: Application to guiding tasks[END_REF], the guiding task of a rigid micropart was studied. In this paper, the guiding task of a flexible micropart in rail will be studied (see Fig. 1). In our case, the automated guiding task (see Fig. 1) requires the control of both the gripping force applied by finger 1 and 2 on the micropart and the contact force between the micropart and the rail. For the considered micropart scale, interaction forces (gripping force, contact force, pull-off force) have to be taken into account and few tens of µN forces have to be controlled.

The objective of this paper is to study automated guiding tasks at the microscale and to investigate a suitable control scheme. Therefore, the integration of force sensors and axis of correction in the microassembly station is discussed and an experimental setup is proposed to achieve automated guiding tasks (Section II). The stability of the grasp, the two-sensingfinger microgripper modeling and the guiding strategy are investigated in section III. Section IV presents the proposed control scheme based on hybrid force/position control with an observer to estimate the contact force. Section V presents the experimental results of automated guiding tasks. Finally, section VI concludes this paper.

II. GUIDING SYSTEM CONFIGURATION

A. Integration of force sensors in the microassembly station

The development of force sensors for the microscale has been investigated by many researchers [START_REF] Cappelleri | A two dimensional visionbased force sensor for microrobotic applications[END_REF], [START_REF] Arai | Integrated microendeffector for micromanipulation[END_REF], [START_REF] Shen | Contact and force control in microassembly[END_REF], [START_REF] Beyeler | Monolithically fabricated microgripper with integrated force sensor for manipulating microobjects and biological cells aligned in an ultrasonic field[END_REF] especially for micromanipulation and/or microassembly. Their integration in microrobotic systems is a very interesting approach because it provides the information about the contact when it happens and it prevents from breaking components (gripper, microparts, etc). During microassembly, there are some interaction forces: (i) between a microgripper and a grasped micropart, (ii) between a manipulator and its environment (for example the substrate), and (iii) between a grasped micropart and its environment. The force sensors and the axis of correction can be configured in four ways:

(a) the manipulator is equipped with force sensors and the axis of correction is mounted on the workplace (location where are placed parts to assemble), (b) the manipulator is equipped with force sensors and correcting axis, (c) force sensors are mounted on the workplace and the axis of correction is on the manipulator, (d) force sensors and correcting axis are on the workplace. The choice of the configuration depends on the task constraints, technological capabilities and cost minimization. The study of hybrid force/position controlled tasks usually leads to define directions with unconstrained motion and directions with constrained motion [START_REF] Mason | Compliance and force control for computer controlled manipulators[END_REF], [START_REF] Lefebvre | Active compliant motion: a survey[END_REF]. Force control is applied on the directions with constrained motion. In our case (guiding task along X), lateral contact may happen between the grasped micropart and the rail thus motions along Y and Z are force constrained contrary to the move forward motion along X (see Fig. 1). If we consider that the depth of the rail is enough to ensure no mechanical contact between the micropart and the rail, the motion along Z becomes unconstrained. The chosen configuration has to enable the measurement of the lateral contact force for ensuring its control during the task. To measure both gripping forces and the lateral contact force with minimum number of force sensors, configurations (a) and (b) can be chosen. The axis of correction generates a relative displacement between the grasped micropart and the substrate so there is no difference between (a) and (b), in terms of control. For this study, we will use a two-sensing-finger microgripper to achieve automated guiding tasks so we choose configuration (a) that provides a better sepsfness of the robot structure and a better stability for handling the micropart since in this case the soft micropart can be held by the microgripper with a constant clamping force.

B. Experimental setup

In this section, the experimental setup is proposed to perform guiding tasks (see Fig. 2). It is based on two force sensors FT-S270 from FemtoTools with a measuring range of 2000µN and a resolution of 0.4µN. Each force sensor comprises a probe, of 3mm of length and 50µm of thickness, that moves along its main direction (Y according to Fig. 2) once a force is applied at its tip. The displacement is converted into a voltage thanks to a capacitive variation measured by a dedicated circuit. They work like a jaw of the microgripper and are mounted on x 1 y 1 z 1 linear stages for Finger 1 and x 2 y 2 z 2 for Finger 2. The position control of fingers along Y enables to open/close the resulting microgripper and apply the necessary force to pick the micropart. The manipulated micropart is 50 x 50 x 2000µm 3 in size. The rail is mounted on a microrobotic structure (workplace) composed of x s y s z s coarse positioning, y p large range but fine positioning, x n y n z n fine positioning, and θ rotation. The large range positioning stage is a P625.1CD from Physik Instrumente with 500µm of travel range and 1.4nm in resolution. The fine positioning stage is a P-611.3 NanoCube with 100µm range and 1 nm in resolution. A rotation stage is a SmarAct SR-3610-S with 1.1 µ o in resolution is used to adjust the alignment between the rails and the axis of the Nanocube. These three devices are sensorized and closed loop controlled. The rail width is adjustable from 0µm to 1mm enabling set up of the axial play between the grasped micropart and the rail.

Considering the pick of the micropart, initial gripping forces are applied by each finger onto the micropart. They are named preload and noted F y10 , F y20 (Subscripts 1 & 2 refer to finger 1 and 2 respectively. Subscript 0 refers to the constant preload applied, once the micropart is grasped). The displacement along X enables to position the micropart to the desired position into the rail. When the contact between the rail and the micropart appears, the rail position along Y has to be modified to cancel or reduce the force generated by the contact in order to preserve the stability and the reference frame of the micropart. This force is named thereafter lateral contact force. It has three components: F x , F y , F z and we consider F x and F z smaller than F y because they are the friction components of the lateral contact force.

In the following, the microgripper remains fixed with the grasped micropart and the center of the microgripper is defined by a coordinate frame O m X m Y m Z m . The guiding task is performed by actuating x n to move forward and by moving y n for correcting when the contact happens (see Fig. 3). y p is used during the validation for creating a known perturbation to test the control strategy proposed. O rail X rail Y rail Z rail is the coordinate frame of the rail. w r is the rail width and w m is the micropart width (w m ≤ w r ).

III. GUIDING STRATEGY FOR STABLE GRASP

Given the objective of the paper to achieve an automated guiding task, a guiding strategy is proposed in this section. For this purpose, the pull-off forces effect is investigated, the effect of perturbations along X, Y and Z are detailed, the model of the two-sensing-finger microgripper and the evolution of the gripping forces in presence of lateral contact force are investigated. This model will then be used to achieve automated guiding tasks in Section V.

A. Pull-off forces

During a microassembly process, contacts between surfaces often happen. Surface force being predominant at the microscale, it is required to evaluate the influence of surface forces during a microassembly process. To automatically achieve guiding tasks at the microscale, pull-off force, which is the necessary force to break a contact due to sticking effect, has predominant role notably when a contact between the micropart and the rails happens.

It was shown in [START_REF] Rabenorosoa | Measurement of pull-off force for planar contact at the microscale[END_REF] that the pull-off force can reach 196µN for a planar 50µm x 50µm silicon surface size of contact that can typically happen in the present case. During the guiding task, the breaking of the lateral contact may induce a pull-off force for each side of the contact. In this case, the evolution of the lateral contact force according to the position of the micropart can follow curves in Fig. 4, i.e once a contact (micropart/rail) happens, the pull-off force acts as a sticking effect. In Fig. 4, the micropart is supposed to be at point O M . While moving the micropart, it could approach from a sidewall until a contact happens at point A or C and the lateral contact force increases as the object still move in the same direction along Y. To break the contact, the micropart should be moved in the opposite direction until the point A or C. At points A and C, the lateral contact forces are zero but the contact remains due to adhesive force. The contacts are broken at B and when enough forces are applied in balance to the adhesive force.

B. Grasp stability

The study of the grasp stability is considered. While guiding the micropart in the rail (see Fig. 3) a contact may appear along X, Y or Z at a distance (see Fig. 5). When a contact appears, the grasp is perturbed due to the contact force. As a result, the micropart may slip through the fingers, rotate, be lost or broken. We separately consider each component of the contact force F : F x , F y , and F z and we determine the gripping force to apply according to the contact force for ensuring the stability of the grasp. 1) Stability according to a F z perturbation (Fig. 5): Based on the Coulomb friction, the sliding does not happen if the tangential forces applied by the fingers are important enough to overcome F z . The condition is 2µ F yi ≥ F z with F y1 = F y2 = F yi where µ is the friction coefficient and F yi is the preload force applied along Y by finger i. The friction coefficient depends on the roughness of the contact surface and the type of the materials.

2) Stability according to a F x perturbation (Fig. 5): F x induces a torque that may cause the rotation of the micropart. To prevent rotation, the admissible force F x can be approximated. The surface in contact (between fingers and micropart) is square with 50µm of side. We consider the circle (R: radius) with the equivalent surface S, F yi the applied force by the finger to the micropart, P the uniform pressure induced by F yi , dS the elementary contact surface, → dN and → dT the elementary normal and tangential force vector respectively (Fig. 6). Note that is the distance of the applied force F x to the center of the rotation and → n is the normal unit vector. Fig. 6. Detailed scheme used to determine the maximum force Fx before rotation.

F yi = P.S (1)
→

dN = P.dS. → n (2)
The condition of non sliding at the considered point P i is:

→ dT ≤ µ.P.dS. → n (3)
According to the elementary torque dC, the integration on the complete surface gives the torque for one finger:

dC = ρ → dT => C = 2 3 F yi µR ( 4
)
Where ρ is the distance between the point P i and the axis of the F y1 in Fig. 6. The condition of the stability is then:

F x limit ≤ 4F yi µR 3 (5)
With Eq. ( 5), the limit force F x limit to ensure the stable grasp according to F y10 = F y20 = 1200µN, µ = 0.3, =400µm and R=28.2µm is estimated to be F x limit ≤ 27.07µN. µ is the friction coefficient. Then,

F y limit X ≤ F x limit µ (6)
where F y limit X refers to the limit of F y induced by the conditions of stability along X axis. Finally,

F y limit X = 90µN (7)
3) Stability according to a F y perturbation (Fig. 5): The force F y induces the displacement (linear displacement + deflection + rotation) of the micropart between the two fingers but the micropart is maintained. The maximum admissible force F y corresponds to the breaking of the fingers due to the generated torque. It will be a great interest to study the evolution of the gripping forces F y1 and F y2 in function of the contact lateral force F y , in order to determine a limit contact force to ensure that the gripping forces are in the safe range in order not to break the microgripper fingers.

The model of the microgripper shown in Fig. 7 is used to study the evolution of the gripping forces in function of the lateral contact force F y . Our previous studies showed the evolution of the gripping force evolution in the presence of lateral contact force for a rigid micropart. It was shown that the evolution of the gripping forces follows two steps, according to the contact between the microgripper fingers and the rigid micropart: planar contact and edge/vertex contact [START_REF] Rabenorosoa | Study of forces during microassembly tasks using two-sensing-fingers grippers[END_REF]. The planar contact is characterized by the linear displacement of the micropart and the edge/vertex contact by the combined linear translational displacement of the micropart along Y for small F y force and rotation around X for higher F y . For that, a system of 5 non linear equations based on the contact force F y enables to determine the evolution of gripping force. This model has been established for a rigid micropart and experimentally validated. Based on that knowledge, Fig. 8 displays the experimental behavior for a flexible micropart. These Experimental results of gripping forces evolution F s1 and F s2 according to Fy with F y10 = F y20 = 1200µN, =500µm: (1) rigid micropart, (2) flexible micropart curves show that the gripping force on the two fingers are not equal when the lateral contact force is applied. The finger on the opposite side of the contact applies the biggest force to the micropart. Consequently, the side of the contact can be distinguished thanks to a two-sensing-finger microgripper.

Fig. 8 shows that the evolution of the gripping forces for the rigid (sepsfness around 1000N/m) and flexible (10N/m) microparts are quite similar in terms of contact force but different in terms of displacement. Some conclusions could be made:

• The evolution of the gripping forces follows also two steps, according to the contact between the microgripper fingers and the flexible micropart: planar contact and edge/vertex contact. • A better gripping stability can be induced. Indeed, the displacement along Y before the rotation of the flexible micropart is bigger than for the rigid micropart. In addition, the limit of the contact force before the rotation of the object around X is F y limit Y (F y limit Y refers to the limit of F y induced by the conditions of stability along Y axis). F y limit Y is quite bigger for the flexible micropart (50µN for the flexible micropart and 41.42µN for the rigid micropart). • The evolution of the gripping forces does not follow a slope in the planar contact. In fact, the evolution of the gripping forces is quite non linear in the planar contact. This non linearity is caused by the deflection of the flexible micropart. Otherwise, once the contact force F y is greater than 50µN, the micropart starts to rotate and then switches to the edge/vertex contact. • The slope in the flexible micropart case (≈ 21.9) is smaller than that for the rigid micropart (≈ 28.14) one during the edge/vertex contact. These results show that the contact between the micropart and the microgripper fingers switches to the edge/vertex contact when F y exceeds 50µN. Once the switching to the edge/vertex contact happens, the evolution of the gripping forces in function of the contact force F y increases rapidly. Thus, a limit contact force F y limit Y should be defined in order to prevent the gripping forces for being bigger than 2mN (which is the sensing range of the microgripper fingers given by the manufacturer).

C. Guiding strategy

To achieve automated guiding tasks, it is necessary to establish a strategy. Two important parameters have been considered: the stability of the grasp (III-B) and the microscale specificities (III-A). The limits defined in the two previous sections will be considered in the guiding strategy.

The micropart motion is composed of an unconstrained displacement along X with a fixed velocity and a constrained displacement along Y. When the contact appears, three strategies exist to achieve the task:

• Stop the motion along X and correct the trajectory along Y in order to break the contact. After that, the manipulator can be moved forward freely along X again. • Move forward along X and correction along Y are performed simultaneously. In that case, the gripping force must comply the condition in Eq. ( 5). This strategy is often used for the automated guiding tasks in macroscale. • Stop the motion along X and correct the trajectory along Y for ensuring the stability in the Eq. ( 5) without breaking the contact. First strategy may induce the presence of the pull-off force and a remaining contact even for Fy = 0 µN. It will be difficult to locate the contact break because the pull-off force is not constant, it indeed depends on many parameters [START_REF] Rabenorosoa | Measurement of pull-off force for planar contact at the microscale[END_REF]. Second and third strategies could be applied. Thus, an hybrid strategy of these two strategies is chosen. When a contact happens, F y is small so V x could be maximum. When F y is big (bigger than 90µN see Eq. ( 7)), the motion along X have to be stopped in order to prevent breaking or loosing the micropart. When F y is between 50µN and 90µN, the contact between the gripping fingers and the micropart switches to the edge/vertex contact and then the evolution of the gripping forces increases rapidly. In addition, uncertainties on the distance and the friction coefficient µ could change the limit defined in (7) (F Y limit X = 90µN ). Stopping the contact at 60µN ensures that F Y limit X remains bigger than 60µN even with the uncertainties concerning the friction coefficient and the distance and then the stability along the X axis is ensured. Thus, F y =60µN has been chosen as limit force before switching OFF the motion along X because when F y lim = 60µN , the gripping forces F y1 and F y2 will increase 28% of their preload values. Such increase in gripping forces is accepted and the condition of stability along X given by the Eq. 7 remain valid. The gripping forces stay, as well, far away from the limit before breaking the microgripper fingers 2mN. The guiding strategy is summarized in Fig. 9.

IV. HYBRID FORCE/POSITION CONTROL WITH FORCE ESTIMATION

In this section, an hybrid force/position control is proposed to achieve the control strategy developed in section III-C. For this purpose, a force estimator is developed to estimate the lateral contact force F y .

A. Estimation of the lateral contact force by a two-sensingfinger microgripper

As seen in III-C, the guiding strategy depends on the lateral contact force F y . For that, F y should be estimated. To estimate the lateral contact force F y , we use the force equilibrium along Y (Eq. ( 8)) by using the information from two-sensing-finger in quasi-static mode (see Fig. 7).

F y = F y2 -F y1 (8)
Force sensors are generally coupled (in our case, the measurement depends on the force applied in the Y direction but also along the Z direction). The expression of the measured forces by sensorized fingers are F s1 = F y1 + αF z1 (Finger 1) and F s2 = F y2 + αF z2 (Finger 2) where α is the coupling coefficient. F s1 and F s2 are the measurement of the microgripper sensing fingers. Consequently,

F y = F s2 -F s1 -2αF z (9)
The coupling coefficient is small (α = 0.01 given by the manufacturer). F z is also small during the contact, 2αF z becomes negligible thus the contact force F y can be evaluated:

F y = F s2 -F s1 ( 10
)
To validate this model, we use the experimental setup shown in Fig. 10. The proposed microgripper is used and a third force sensor applies a known lateral contact force. Fig. 11 shows the time evolution of the measured gripping forces (F s1 , F s2 ) and the comparison of the applied contact force F y applied by an external force sensor to the estimated contact force F y estimated (using Eq. ( 10)). The estimated force is slightly equal to the applied force in static part. The relative error is calculated and estimated to be smaller than 15%. Indeed, this error is due to the drift of the force sensors. These force sensors are hightech products and they work in a very small range of forces (maximum 2 mN). This result validates the estimation of the lateral contact force which can definitely be used for the control.

B. Hybrid force/position control for achieving guiding task

To control the guiding tasks in automated mode, a control scheme of the system is established. Its objective is to maintain the lateral contact force under the fixed limit F y limit and to reach the desired position along X. The position control along the rail and the lateral contact force have to be separated. Thus, the use of hybrid control [START_REF] Raibert | Hybrid position/force control of manipulators[END_REF], [START_REF] Fisher | Hybrid position/force control: A correct formulation[END_REF] combined with an internal position control [START_REF] Volpe | A theoretical and experimental investigation of explicit force control strategies for manipulators[END_REF] is chosen. This control structure is named external hybrid force/position control and was first proposed in [START_REF] Perdereau | A new scheme for hybrid force-position control[END_REF]. In this section, a new controller based on the model proposed in [START_REF] Perdereau | A new scheme for hybrid force-position control[END_REF] and taking into consideration the microscale specificities and the force limits developed in section III-C is proposed. The proposed block diagram (Fig. 12) enables to guiding, it is required to directly detect the contact and to start the correction along the Y in order to reduce the lateral contact force under the fixed limit (F y lim = 60µN). At the same time, we keep going forward along X. The E block is an "Enable control" which stops the motion along X when the lateral contact force is bigger than the upper limit (F y lim ) in order to be able to ensure the guiding task (see III-C). The details of E are shown in Fig. 13. A strategy to achieve automated guiding tasks based on hybrid force/position control have been integrated. Position Control Laws (PCL) are Proportional Integral controllers which are internal to the positioning stages. Investigations are focused on the Force Control Law (FCL).

The use of Incremental Control is proposed to ensure the control of the contact force. It's a simple and robust controller which the correction speed could be easily controlled with ensuring stability. The use of this type of controller is a first step that guarantees the desired performances. The study is performed for different kinds of perturbations. The complete system is not considered to be linear time invariant (LTI) due to the play between the micropart and the rail and the distance of the contact ( ) uncertainty [START_REF] Rabenorosoa | Hybrid force/position control applied to automated guiding tasks at the microscale[END_REF]. Thus, conventional studies based on LTI theories are not relevant.

In the robotic field, the use of this incremental controller enables easy and fast set up of parameters and reduces the risks of breaking the microparts or the manipulator. Details of the controller structure are given in Fig. 14. It is composed of a dead zone for rejecting the sensor noise measurement (10µN), the sign operator for indicating the direction of the increment, and the memory operation for enabling the relative positioning. This nonlinear controller enables to set the velocity of the correction V corr in accordance to the sampling frequency F sampling and the increment Step incr . It can be calculated by V corr = F sampling .Step incr . The magnitude of this step has to be smaller than the play for ensuring the stability.

C. Incremental Control

The objective is to apply the incremental controller as for the Force Control Law (FCL). The control scheme is implemented on a 1104 Dspace board with a sampling frequency F sampling = 1KHz. This sampling frequency is a trade off between high speed sampling and experimental limitations.

In the following, the performance of the controller will be tested for different incremental steps Step incr . The robustness of the controller will be tested for the misalignment between the rail axis and the guiding axis but also for some perturbations on each side of the rail.

The dead zone of the FCL is fixed to 15 µN which is slightly bigger than the range of noise (10 µN). FCL is switched on (Enable control) when the estimated contact force becomes bigger than 15 µN, the correction acts and the lateral contact force is brought back smaller than 15 µN. The move forward motion stops when the lateral contact force is bigger than 60 µN which is the upper limit defined in the guiding strategy presented in Fig. 9. The increase of velocity correction V corr induces a time reduction to cancel the perturbation. V corr must be faster than the increase of contact force velocity to prevent from stopping moving along X. Otherwise, if the increase of contact force is faster than the V corr , we may reach the upper limit F y limit and in this case, the enable bloc will stop moving along X and the FCL controller will reduce the contact force below 60µN.

V. AUTOMATED GUIDING TASKS AND EXPERIMENTAL

RESULTS

In this section, automated guiding tasks are tested and experimental investigations are performed to test the controller's performances and the guiding strategy.

A. Automated guiding task with misalignment between the rail axis and the guiding axis

To experiment the automated guiding task including a misalignment between the rail axis and the move forward axis, we introduce a ramp by moving y p . During this phase, the FCL controller is always "ON" and can directly work. Considering the perturbation displacement and the move forward displacement, an equivalent angle γ of misalignment is estimated to 32.8 • by γ = tan -1 (∆ y p /∆ xn ). Results are shown in Fig. 15 1 . It is observed that when the contact occurs, the estimated force gradually increases to the fixed limit. The controller starts the correction to maintain this force under the authorized limit (15µN). We can also observe that during the guiding task, gripping forces are maintained in the tolerable range avoids the risk of breaking microparts and guarantees the stability of the micropart between microgripper fingers. The increase of the preload is estimated to 1.9% for 15µN offset contact force. This small increase is the cause of the micropart flexibility. Indeed, a big displacement has to be applied to the micropart in order to increase the force with a relative big value. The desired position along X is reached without micropart sliding thus the task is successfully achieved.

B. Automated guiding task with step perturbation at each side of the rail

The robustness of the guiding task control is tested by introducing a step perturbation during the task. Left side contact and right side contact are successively generated during the move forward motion. The FCL controller is already "ON" at 1 Coordinate frames and positioning stages are detailed in Fig. 3 the beginning of the task. The fixed limit is also 15µN. Results are shown in Fig. 16. It was shown that the established control scheme is able to reject step perturbations that are applied at t=6s and t=17s: the move forward motion is stopped to ensure the stability of the grasp when the estimated contact force is over 60µN (Enable control effect). These results are shown for a velocity correction V corr = 10µm/s with step increment

Step incr = 10nm and F sampling = 1000Hz. The rejection time is 5s which is quite big. In order to reduce the rejection time, we have two possibilities: one is to increase the step increment, another is to increase the sampling frequency. If we increase the step increment with a big value, the velocity correction will be so fast and we won't see the effect of the perturbation. In order to calculate the response time of the controller, we have switched OFF the FCL controller once we have applied the perturbation and then we have turned it ON. Fig. 17 shows the response of the system to a step perturbation for a velocity correction V corr = 1mm/s with step increment Step incr = 1µm and F sampling = 1000Hz. Fig. 17 shows that the response time is 75ms which is near the response time of the correction stage. The desired position along X is reached without micropart sliding despite the big step perturbation displacement applied. Thus, the task is successfully achieved.

C. Behavior of the micropart during guiding task

During the guiding task, the proposed control scheme has ensured the stability of the tasks. As shown in section V-A and V-B, the performances were robust enough for the misalignment between the axis (rail axis and guiding axis) and in presence of big step perturbation. The FCL controller was able to deal with a 100µm of displacement (see Fig. 17) after the contact appears (100µN of contact force) which is a big displacement (almost the same of the rail width). Fig. 16 shows that the Enable control appears 900ms after application of the step perturbation. This is due to the flexibility of the micropart. Indeed, for a rigid micropart the limit force will be exceeded for a small contact between the rail and the micropart. Otherwise, the deflection of the flexible micropart induces a smaller variation of gripping forces than for the rigid micropart. Consequently, the automated guiding task stability increases with the flexibility of the micropart. The proposed guiding strategy is able to accomplish an automated guiding task for both a flexible and a rigid micropart. However, the rigid micropart could be lost if the limit is fixed to 60 µN because a contact force of 60 µN corresponds to an increase of 50% (see Fig. 8) on the gripping forces which will be close to the limit of the force sensors. Thus, the limit of going forward along X should be fixed carefully depending on the micropart sepsfness as shown in Fig. 18. The sepsfness of the micropart should be known or estimated before starting the experiments. Another option is to use an adaptive controller in order to estimate the sepsfness of the micropart and to use it for the controller. The influence of the sepsfness of the object on the guiding strategy is summarized in Fig. 18.

VI. CONCLUSION

A study of hybrid force/position control based guiding task at the microscale is proposed in this paper. A guiding strategy and experimental validations of the automated guiding task are proposed. A flexible micropart of 50 x 50 x 2000µm 3 in size is manipulated and a few tens of µN force control is achieved in parallel to position control with a nanometer resolution stage. An experimental model of the behavior of the flexible micropart between the microgripper fingers has been established. The lateral contact force is estimated by using a two-sensing-finger microgripper and it is used in an external hybrid force/position control. A guiding strategy is proposed taking into consideration the non linearity of the system and the microscale specificities. It has been observed that the rejection time of the force control law reaches the response time of the correcting stage during the experimental measurements (≈ 75ms). The incremental controller has been validated and its robustness shown by rejecting step perturbations at each side of the rail. The controller has dealt with a relative big displacement perturbations (100µm i.e. 2 times the cross section of the manipulated object) which is near to the width of the rail. Automated guiding tasks with a misalignment angle γ of 32.8 • between the rail axis and the guiding axis have been experimentally performed. The slight increase of gripping forces (1.9% compared to preload) during the task authorizes to perform it with fragile microparts, enables to ensure fine grasping of the micropart and provides more dexterity of the grasp.

This whole study shows that the use of hybrid force/position control to achieve automated microassembly tasks constitutes a promising approach. The estimated contact force was performed for 1 DOF and an additional force or torque information will be studied to perform more complex and other delicate automated microassembly tasks like insertion.

Fig. 1 .

 1 Fig. 1. Principle of a guiding task with move forward along X and correction along Y (use of a microgripper and a robotic workstation to control the trajectory of the handled micropart).

Fig. 2 .

 2 Fig. 2. Experimental setup proposed for achieving guiding tasks: a micropart is hold by two-sensing-finger microgripper. xny n zn and y p enable guiding motions of this micropart into a rail.

Fig. 3 .

 3 Fig. 3. Guiding task based on two-sensing-finger microgripper with coordinate frames: O rail X rail Y rail Z rail and OmXmYmZm

Fig. 4 .

 4 Fig. 4. The evolution of the lateral contact force in the presence of pull-off force during left side and right side contacts in the rail.

Fig. 5 .

 5 Fig. 5. Perturbed grasp with each component of the contact force: Fx, Fy, and Fz.

Fig. 7 .

 7 Fig. 7. Microgripper model based on two-sensing-finger microgripper.

Fig. 8 .

 8 Fig. 8. Experimental results of gripping forces evolution F s1 and F s2 according to Fy with F y10 = F y20 = 1200µN, =500µm: (1) rigid micropart, (2) flexible micropart

Fig. 9 .

 9 Fig. 9. The guiding strategy proposed: Vx is the speed along X and Fy is the contact force between the micropart and the rail.

Fig. 10 .

 10 Fig. 10. Setup measurement of Fy by using an external force sensor.

Fig. 11 .

 11 Fig.11. Estimation of the contact force F y estimated by using F s1 and F s2 compared to the applied contact force F y applied .

Fig. 12 .

 12 Fig. 12. Block diagram of the external hybrid force/position control during the guiding task.

Fig. 13 .

 13 Fig. 13. Detailed of the enable control block E.

Fig. 14 .

 14 Fig. 14. Block diagram of the incremental controller (FCL).

Fig. 15 .

 15 Fig. 15. Experimental results of an automated guiding task: (1) Lateral contact force estimation Fy = F s1 -F s2 (2) gripping forces, (3) move forward motion along X with 5µm/s velocity, (4) Position of the point Om (Ym) of the micropart in Fig. 3 compared to the rail position along Y (Y rail ).

Fig. 16 .

 16 Fig. 16. Experimental results of an automated guiding task: (1) lateral contact force estimation (Fy = F s2 -F s1 ), (2) gripping forces, (3) move forward motion along X with 5µm/s velocity, (4) Position of the point Om (Ym) of the micropart in Fig. 3 compared to the rail position along Y (Y rail ).

Fig. 17 .

 17 Fig. 17. Experimental results of an automated guiding task: (1) lateral contact force estimation (Fy = F s2 -F s1 ), (2) gripping forces, (3) move forward motion along X with 5µm/s velocity, (4) Position of the point Om (Ym) of the micropart in Fig. 3 compared to the rail position along Y (Y rail ).

Fig. 18 .

 18 Fig. 18. Guiding strategy variation in function of the sepsfness of the object.

ACKNOWLEDGMENT

These works have been funded by the region Franche-Comte. We would like to acknowledge Mr. David Guibert for technical support.