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http://hdl.handle.net/10985/6483
Approximation par des B-Splines de solutions optimales pour des problèmes LQ : une estimation a posteriori de l’erreur
AUQUIERT, Philippe; GIBARU, Olivier; PERRUQUETTI, Wilfrid
Nous proposons une alternative à l’équation de Riccati lors de la résolution de systèmes linéaires quadratiques en contrôle optimale. Une transformation de l’équation d’état basée sur la forme de Brunoswski de ce système permet de mettre en évidence une représentation sous la forme de sorties dites plates. Le système ainsi transformé nous permet d’exprimer le problème de contrôle optimal sous la forme d’un problème variationnel. Une approximation par une B-Spline des sorties plates est proposée ainsi que la majoration a posteriori de l’erreur commise. L’intérêt de cette majoration d’erreur est qu’elle permet d’optimiser le placement des noeuds de la B-Spline afin de satisfaire une tolérance donnée.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10985/64832006-01-01T00:00:00ZAUQUIERT, PhilippeGIBARU, OlivierPERRUQUETTI, WilfridNous proposons une alternative à l’équation de Riccati lors de la résolution de systèmes linéaires quadratiques en contrôle optimale. Une transformation de l’équation d’état basée sur la forme de Brunoswski de ce système permet de mettre en évidence une représentation sous la forme de sorties dites plates. Le système ainsi transformé nous permet d’exprimer le problème de contrôle optimal sous la forme d’un problème variationnel. Une approximation par une B-Spline des sorties plates est proposée ainsi que la majoration a posteriori de l’erreur commise. L’intérêt de cette majoration d’erreur est qu’elle permet d’optimiser le placement des noeuds de la B-Spline afin de satisfaire une tolérance donnée.Toward on-line robot vibratory modes estimation
http://hdl.handle.net/10985/11406
Toward on-line robot vibratory modes estimation
DELPOUX, Romain; BEAREE, Richard; OLABI, Adel; GIBARU, Olivier
This paper is concerned with preliminaries results on robot vibratory modes on-line estimation. The dominating oscillatory mode of the robot arm is isolated by comparing the robot position given by the motors encoders and an external measure at the tool-tip of the robot arm. In this article the external measurement is provided by a laser tracker. The isolation of the oscillation permits to identify the vibratory mode, i.e. the natural frequency and the damping ratio of the undesired phenomena. Here we propose a comparison between the algebraic method and the sliding modes for the parameter identification. This comparison is motivated by the fact that both methods provide finite time convergence. Experimental identifications are proposed on a 6 degrees of freedom (DOF) manipulator robot, St¨aubli RX-170B.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/114062014-01-01T00:00:00ZDELPOUX, RomainBEAREE, RichardOLABI, AdelGIBARU, OlivierThis paper is concerned with preliminaries results on robot vibratory modes on-line estimation. The dominating oscillatory mode of the robot arm is isolated by comparing the robot position given by the motors encoders and an external measure at the tool-tip of the robot arm. In this article the external measurement is provided by a laser tracker. The isolation of the oscillation permits to identify the vibratory mode, i.e. the natural frequency and the damping ratio of the undesired phenomena. Here we propose a comparison between the algebraic method and the sliding modes for the parameter identification. This comparison is motivated by the fact that both methods provide finite time convergence. Experimental identifications are proposed on a 6 degrees of freedom (DOF) manipulator robot, St¨aubli RX-170B.LNE Activies in Nanometrology: flatness reference calibration algorithm
http://hdl.handle.net/10985/7755
LNE Activies in Nanometrology: flatness reference calibration algorithm
LAHOUSSE, Ludovic; BORIPATKOSOL, Siriwan; LELEU, Stéphane; DAVID, Jean-Marie; DUCOURTIEUX, Sébastien; COOREVITS, Thierry; GIBARU, Olivier
The Laboratoire National de Métrologie et d’Essais (LNE) has developed an innovative ultra precision coordinate measuring machine [LAH07] traceable to the national length standard to measure three-dimensional objects with nanometric uncertainties (figure 1). The measuring range is 300 mm x 300 mm x 50 μm. The objective in term of uncertainty is to reach 30 nm in X and Y directions for a displacement of 300 mm and about few nanometers for a vertical displacement of 50 μm. On this machine, we use four capacitive sensors to measure the position along z direction. These sensors target the flat surface of cylinders (300 mm diameter) used as flatness references. To measure the shape of these aluminum references with nanometric uncertainties, we propose a measurement method based on a propagation process in which we introduce an angular measurement to compensate the curvature error inherent in this method. The measurement process uses the same sensor technology (capacitive sensor) we use on the machine. This paper presents the measurement method, its validation and the first results.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/77552008-01-01T00:00:00ZLAHOUSSE, LudovicBORIPATKOSOL, SiriwanLELEU, StéphaneDAVID, Jean-MarieDUCOURTIEUX, SébastienCOOREVITS, ThierryGIBARU, OlivierThe Laboratoire National de Métrologie et d’Essais (LNE) has developed an innovative ultra precision coordinate measuring machine [LAH07] traceable to the national length standard to measure three-dimensional objects with nanometric uncertainties (figure 1). The measuring range is 300 mm x 300 mm x 50 μm. The objective in term of uncertainty is to reach 30 nm in X and Y directions for a displacement of 300 mm and about few nanometers for a vertical displacement of 50 μm. On this machine, we use four capacitive sensors to measure the position along z direction. These sensors target the flat surface of cylinders (300 mm diameter) used as flatness references. To measure the shape of these aluminum references with nanometric uncertainties, we propose a measurement method based on a propagation process in which we introduce an angular measurement to compensate the curvature error inherent in this method. The measurement process uses the same sensor technology (capacitive sensor) we use on the machine. This paper presents the measurement method, its validation and the first results.Feedrate planning for machining with industrial six-axis robots
http://hdl.handle.net/10985/8155
Feedrate planning for machining with industrial six-axis robots
BEAREE, Richard; OLABI, Adel; GIBARU, Olivier; DAMAK, Mohamed
Nowadays, the adaptation of industrial robots to carry out high-speed machining operations is strongly required by the manufacturing industry. This new technology machining process demands the improvement of the overall performances of robots to achieve an accuracy level close to that realized by machine-tools. This paper presents a method of trajectory planning adapted for continuous machining by robot. The methodology used is based on a parametric interpolation of the geometry in the operational space. FIR filters properties are exploited to generate the tool feedrate with limited jerk. This planning method is validated experimentally on an industrial robot.
The authors want to thank Stäubli for providing the necessary information of the controller, Dynalog for its contribution to the experimental validations and X. Helle for its material contributions.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/81552010-01-01T00:00:00ZBEAREE, RichardOLABI, AdelGIBARU, OlivierDAMAK, MohamedNowadays, the adaptation of industrial robots to carry out high-speed machining operations is strongly required by the manufacturing industry. This new technology machining process demands the improvement of the overall performances of robots to achieve an accuracy level close to that realized by machine-tools. This paper presents a method of trajectory planning adapted for continuous machining by robot. The methodology used is based on a parametric interpolation of the geometry in the operational space. FIR filters properties are exploited to generate the tool feedrate with limited jerk. This planning method is validated experimentally on an industrial robot.On Algebraic Approach for MSD Parametric Estimation
http://hdl.handle.net/10985/10131
On Algebraic Approach for MSD Parametric Estimation
OUESLATI, Marouene; THIERY, Stéphane; GIBARU, Olivier; BEAREE, Richard; MORARU, George
This article address the identification problem of the natural frequency and the damping ratio of a second order continuous system where the input is a sinusoidal signal. An algebra based approach for identifying parameters of a Mass Spring Damper (MSD) system is proposed and compared to the Kalman-Bucy filter. The proposed estimator uses the algebraic parametric method in the frequency domain yielding exact formula, when placed in the time domain to identify the unknown parameters. We focus on finding the optimal sinusoidal exciting trajectory which allow to minimize the variance of the identification algorithms. We show that the variance of the estimators issued from the algebraic identification method introduced by Fliess and Sira-Ramirez is less sensitive to the input frequency than the ones obtained by the classical recursive Kalman-Bucy filter. Unlike conventional estimation approach, where the knowledge of the statistical properties of the noise is required, algebraic method is deterministic and non-asymptotic. We show that we don't need to know the variance of the noise so as to perform these algebraic estimators. Moreover, as they are non-asymptotic, we give numerical results where we show that they can be used directly for online estimations without any special setting.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/101312011-01-01T00:00:00ZOUESLATI, MaroueneTHIERY, StéphaneGIBARU, OlivierBEAREE, RichardMORARU, GeorgeThis article address the identification problem of the natural frequency and the damping ratio of a second order continuous system where the input is a sinusoidal signal. An algebra based approach for identifying parameters of a Mass Spring Damper (MSD) system is proposed and compared to the Kalman-Bucy filter. The proposed estimator uses the algebraic parametric method in the frequency domain yielding exact formula, when placed in the time domain to identify the unknown parameters. We focus on finding the optimal sinusoidal exciting trajectory which allow to minimize the variance of the identification algorithms. We show that the variance of the estimators issued from the algebraic identification method introduced by Fliess and Sira-Ramirez is less sensitive to the input frequency than the ones obtained by the classical recursive Kalman-Bucy filter. Unlike conventional estimation approach, where the knowledge of the statistical properties of the noise is required, algebraic method is deterministic and non-asymptotic. We show that we don't need to know the variance of the noise so as to perform these algebraic estimators. Moreover, as they are non-asymptotic, we give numerical results where we show that they can be used directly for online estimations without any special setting.Leap Motion pour la capture de mouvement 3D par spline L1
http://hdl.handle.net/10985/7897
Leap Motion pour la capture de mouvement 3D par spline L1
HERNOUX, Franck; BEAREE, Richard; GAJNY, Laurent; BANCALIN, Julien; NYIRI, Eric; GIBARU, Olivier
Afin d’accroître leur compétitivité les entreprises ont recours de plus en plus à des systèmes robotisés pour realiser différentes tâches complexes. Ces robots sont très attractifs par leur coût mais nécessitent d’introduire des capteurs externes afin de garantir une plus grande précision de mouvement. Un enjeu majeur concerne la co-activité avec l’homme. Fort de l’acquisition très récente du système de vision low-cost, Leap Motion, qui présente des caractéristiques de précision inégalées à ce coût, nous proposons un premier travail d’apprentissage, par un système robotisé, de la gestuelle d’un opérateur. L’objectif est de reproduire des tâches complexes en 3D sans contraintes pour l’opérateur. Cette interaction permet d’engendrer un nuage de points et de directions très précises. Afin de garantir une bonne répétabilité du mouvement sur notre robot UR10, nous réalisons une interpolation de ces données par des splines polynomiales minimisant la norme L1. Ce formalisme développé récemment présente une complexité de calcul linéaire avec les données et permet de conserver la forme des données même lorsque le pas de discrétisation n’est pas uniforme en espace.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/78972013-01-01T00:00:00ZHERNOUX, FranckBEAREE, RichardGAJNY, LaurentBANCALIN, JulienNYIRI, EricGIBARU, OlivierAfin d’accroître leur compétitivité les entreprises ont recours de plus en plus à des systèmes robotisés pour realiser différentes tâches complexes. Ces robots sont très attractifs par leur coût mais nécessitent d’introduire des capteurs externes afin de garantir une plus grande précision de mouvement. Un enjeu majeur concerne la co-activité avec l’homme. Fort de l’acquisition très récente du système de vision low-cost, Leap Motion, qui présente des caractéristiques de précision inégalées à ce coût, nous proposons un premier travail d’apprentissage, par un système robotisé, de la gestuelle d’un opérateur. L’objectif est de reproduire des tâches complexes en 3D sans contraintes pour l’opérateur. Cette interaction permet d’engendrer un nuage de points et de directions très précises. Afin de garantir une bonne répétabilité du mouvement sur notre robot UR10, nous réalisons une interpolation de ces données par des splines polynomiales minimisant la norme L1. Ce formalisme développé récemment présente une complexité de calcul linéaire avec les données et permet de conserver la forme des données même lorsque le pas de discrétisation n’est pas uniforme en espace.CALIBRATION OF CAPACITIVE SENSORS AND ELECTRONIC LEVELS FOR THE STRAIGHTNESS MEASUREMENTS USING MULTIPROBE METHOD
http://hdl.handle.net/10985/7746
CALIBRATION OF CAPACITIVE SENSORS AND ELECTRONIC LEVELS FOR THE STRAIGHTNESS MEASUREMENTS USING MULTIPROBE METHOD
BORIPATKOSOL, Siriwan; LELEU, Stéphane; COOREVITS, Thierry; GIBARU, Olivier
In this work, the straightness length 300 mm measurement under nanometer uncertainty. The proposed methodology represents a process known as propagation using the assumption of small displacement which leads to solving an overdetermined linear system. The experimental studies were carried out on the capacitive sensors and electronic levels. The least squares mathematic method is apply to calculate the optimal solution. This method requires taking into account the uncertainties of the two different types of sensors leads to method of weighted least squares. The first step is to calibrate the sensors and to estimate the effect on the calculated straightness.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/77462011-01-01T00:00:00ZBORIPATKOSOL, SiriwanLELEU, StéphaneCOOREVITS, ThierryGIBARU, OlivierIn this work, the straightness length 300 mm measurement under nanometer uncertainty. The proposed methodology represents a process known as propagation using the assumption of small displacement which leads to solving an overdetermined linear system. The experimental studies were carried out on the capacitive sensors and electronic levels. The least squares mathematic method is apply to calculate the optimal solution. This method requires taking into account the uncertainties of the two different types of sensors leads to method of weighted least squares. The first step is to calibrate the sensors and to estimate the effect on the calculated straightness.Reconstruction of freeform surfaces for metrology
http://hdl.handle.net/10985/8646
Reconstruction of freeform surfaces for metrology
EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier
The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/86462014-01-01T00:00:00ZEL HAYEK, NadimNOUIRA, HichemANWER, NabilDAMAK, MohamedGIBARU, OlivierThe application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.Fast B-Spline 2D Curve Fitting for unorganized Noisy Datasets
http://hdl.handle.net/10985/8635
Fast B-Spline 2D Curve Fitting for unorganized Noisy Datasets
EL HAYEK, Nadim; GIBARU, Olivier; DAMAK, Mohamed; NOUIRA, Hichem; ANWER, Nabil; NYIRI, Eric
In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98].
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/86352014-01-01T00:00:00ZEL HAYEK, NadimGIBARU, OlivierDAMAK, MohamedNOUIRA, HichemANWER, NabilNYIRI, EricIn the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98].A simple and generic CAD/CAM approach for AFM probe-based machining
http://hdl.handle.net/10985/10565
A simple and generic CAD/CAM approach for AFM probe-based machining
BROUSSEAU, Emmanuel; ARNAL, Benoît; THIERY, Stéphane; NYIRI, Eric; GIBARU, Olivier
Atomic Force Microscopy (AFM) probe-based machining allows surface structuring at the nano-scale via the mechanical modification of material. This results from the direct contact between the tip of an AFM probe and the surface of a sample. Given that AFM instruments are primarily developed for obtaining high-resolution topography information of inspected specimen, raster scanning typically defines the trajectory followed by the tip of an AFM probe. Although most AFM manufacturers provide software modules to perform user-defined tip displacement operations, such additional solutions can be limited with respect to 1) the range of tip motions that can be designed, 2) the level of automation when defining tip displacement strategies and 3) the portability for easily transferring trajectories data between different AFM instruments. In this context, this research presents a feasibility study, which aims to demonstrate the applicability of a simple and generic CAD/CAM approach when implementing AFM probe-based nano-machining for producing two-dimensional (2D) features with a commercial AFM instrument.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/105652015-01-01T00:00:00ZBROUSSEAU, EmmanuelARNAL, BenoîtTHIERY, StéphaneNYIRI, EricGIBARU, OlivierAtomic Force Microscopy (AFM) probe-based machining allows surface structuring at the nano-scale via the mechanical modification of material. This results from the direct contact between the tip of an AFM probe and the surface of a sample. Given that AFM instruments are primarily developed for obtaining high-resolution topography information of inspected specimen, raster scanning typically defines the trajectory followed by the tip of an AFM probe. Although most AFM manufacturers provide software modules to perform user-defined tip displacement operations, such additional solutions can be limited with respect to 1) the range of tip motions that can be designed, 2) the level of automation when defining tip displacement strategies and 3) the portability for easily transferring trajectories data between different AFM instruments. In this context, this research presents a feasibility study, which aims to demonstrate the applicability of a simple and generic CAD/CAM approach when implementing AFM probe-based nano-machining for producing two-dimensional (2D) features with a commercial AFM instrument.