Adaptation de la loi de mouvement aux systemes de positionnement à dynamique élevée

L’augmentation des performances des machines de positionnement passe par l’augmentation des accélérations et donc des sollicitations transmises à la structure de la machine. Ces contraintes sont susceptibles d’engendrer des déformations et des vibrations dégradant le suivi de profil ainsi que le positionnement final. Les commandes numériques avancées disposent de différentes formes de loi de movement à jerk limité, polynomiale...) qui ont un effet notable sur le compromis entre la durée du mouvement effectif et la précision attendue. L’objectif de cet article vise à démystifier cet effet en proposant une analyse comparative de l’influence de différents types de lois de mouvement sur les vibrations, ainsi que sur la durée du mouvement d’un axe soumis à un mode de déformation prépondérant.National audienceL’augmentation des performances des machines de positionnement passe par l’augmentation des accélérations et donc des sollicitations transmises à la structure de la machine. Ces contraintes sont susceptibles d’engendrer des déformations et des vibrations dégradant le suivi de profil ainsi que le positionnement final. Les commandes numériques avancées disposent de différentes formes de loi de movement à jerk limité, polynomiale...) qui ont un effet notable sur le compromis entre la durée du mouvement effectif et la précision attendue. L’objectif de cet article vise à démystifier cet effet en proposant une analyse comparative de l’influence de différents types de lois de mouvement sur les vibrations, ainsi que sur la durée du mouvement d’un axe soumis à un mode de déformation prépondérant

Path planning with PH G2 splines in R2

International audienceIn this article, we justify the use of parametric planar Pythagorean Hodograph spline curves in path planning. The elegant properties of such splines enable us to design an efficient interpolator algorithm, more precise than the classical Taylor interpolators and faster than an interpolator based on arc length computations

Improving the Dynamic Accuracy of Elastic Industrial Robot Joint by Algebraic Identification Approach

International audienceIn this paper, an improvement of the dynamic accuracy of a flexible robot joint is addressed. Based on the observation of the measured axis deformation, a simplified elastic joint model is deduced. In the first step, the non-linear model component's is analyzed and identified in the cases of the gravity bias and the friction term. In the second step, a non asymptotically algebraic fast identification of the oscillatory behavior of the robot axis is introduced. Finally, the performances of the identification approach are exploited in order to improve the dynamic accuracy of a flexible robot axis. This is done experimentally by the combination of the adaptation of the jerk time profile to reduce the end-point vibration and the model-based precompensation of the end-point tracking error

Toward on-line robot vibratory modes estimation

International audienceThis paper is concerned with preliminary 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, \textit{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, Stäubli RX-170B

Feedrate planning for machining with industrial six-axis robots

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.International audienceNowadays, 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

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.International audienceThis 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

Numerical Aspects and Performances of Trajectory Planning Methods of Flexible Axes

Adequate Path Planning design is an important stage for controlling flexible axes because it may allow to cancel vibrations induced by oscillating modes. Among bang-bang profiles which are linked to optimal control, jerk assignment (acceleration derivative) and input shapers have been investigated. Theoretical results show the performance and robustness with respect to natural frequency mismatch. Practical validations on a real robot arm show the relevance of the jerk algorithm which is more robust with the same productivity performances as input shaping techniques

Improving the Dynamic Accuracy of Elastic Industrial Robot Joint by Algebraic Identification Approach

International audienceIn this paper, an improvement of the dynamic accuracy of a flexible robot joint is addressed. Based on the observation of the measured axis deformation, a simplified elastic joint model is deduced. In the first step, the non-linear model component's is analyzed and identified in the cases of the gravity bias and the friction term. In the second step, a non asymptotically algebraic fast identification of the oscillatory behavior of the robot axis is introduced. Finally, the performances of the identification approach are exploited in order to improve the dynamic accuracy of a flexible robot axis. This is done experimentally by the combination of the adaptation of the jerk time profile to reduce the end-point vibration and the model-based precompensation of the end-point tracking error

Prise en compte des phénomènes vibratoires dans la génération de commande des machines-outils à dynamique élevée

The increasing demands in terms of productivity lead the high-dynamics systems to the maximum of their technological and structural capacities, invalidating the classical assumption of a rigid body dynamics. Consequently, the system control cannot neglect the influence of the vibratory phenomena on the accuracy of the contour tracking, but it has to modulate the command efforts in order to realize the adequacy between the intrinsic system characteristics and the speed and accuracy criteria. This study aims at improving the dynamic behavior of these machines by a direct action on the command generation. The command generation is divided into two main functions: (1) the elaboration of a movement law for the system states to control, which is used as reference for controls (indirect control) (2) the definition of a prefilter transforming the movement law into a reference signal for the input of the physical system (direct control). If correctly managed, these two functions make it possible to dissociate the regulation and the contour tracking problems. Initially, they are specifically study in the case of one axis movement. Thus, the influence of various movement laws (harmonic, polynomial, piecewise polynomial or multi-switch bang-bang law) on the vibrations and on the movement time is formalized. A design methodology for the prefilter adapted to the flexibilities of an axis is presented it puts forward the required degree of continuity, which the law of movement must satisfy. Then, after experimental validations on several high-dynamics test-setups, the results and methodologies are adapted to the contour-tracking problem for two Cartesian axes.La recherche de performances toujours plus élevées conduit les systèmes de positionnement à dynamique élevée à la limite de leurs possibilités technologiques et structurelles, invalidant de ce fait l'hypothèse classiquement retenue d'une dynamique d'ensemble assimilable à celle d'un corps rigide. Il s'ensuit que la commande du système ne peut plus sous-estimer l'influence des phénomènes vibratoires sur la qualité du suivi de profil, mais doit moduler les efforts moteurs afin de réaliser l'adéquation entre les caractéristiques intrinsèques au système et les critères de rapidité et de précision escomptés. Les travaux développés dans cette étude visent une amélioration du comportement dynamique du système par une action sur la génération de commande. La génération de commande s'articule autour de deux principales fonctions: (1) l'élaboration d'une loi de mouvement pour la ou les variables du système à contrôler servant de référence pour les asservissements (commande indirecte) (2) la définition d'une précommande transformant la loi de mouvement en un signal de référence pour l'entrée du système physique (commande directe). Ces deux fonctions, correctement gérées, permettent de découpler les problèmes de régulation et de suivi de profil. Dans un premier temps, elles sont traitées spécifiquement pour le cas du mouvement d'un système monoaxe. Ainsi, l'influence de différentes classes de lois de mouvement (harmoniques, polynomiales, polynomiales par morceaux ou bang-bang) sur les vibrations et la durée du mouvement est formalisée. Une méthodologie d'élaboration d'une précommande adaptée aux souplesses d'un axe est présentée elle permet de mettre en exergue les contrainte

Etat de l’art de la compensation de vibration par la generation de trajectoire – application a la robotique industrielle

National audienceDans un contexte d’amélioration constante de la productivité et de la flexibilité desmachines de production, les vibrations mécaniques demeurent un phénomène limitant les performances dynamiques. Le problème de réduction des vibrations induites par lesperturbations extérieures (environnement dynamique, procédés de coupe) est généralement abordé par le biais de la mise en oeuvre de systèmes de dissipation passifs ou actifs. Quant aux vibrations induites par le mouvement des axes de la machine, elles peuvent être efficacement prises en compte lors de la synthèse de la trajectoire du système. Ce papier dresse un état de l’art des méthodes de réduction de vibration s’appuyant sur une adaptation de la trajectoire du système. Une analyse unifiée des méthodes applicables au domaine de la machine de production est réalisée. Des essais menés sur un robot industriel 6 axes viennent illustrer cette analyse