Non-asymptotic fractional order differentiators via an algebraic parametric method

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations

Clustering for Different Scales of Measurement - the Gap-Ratio Weighted K-means Algorithm

This paper describes a method for clustering data that are spread out over large regions and which dimensions are on different scales of measurement. Such an algorithm was developed to implement a robotics application consisting in sorting and storing objects in an unsupervised way. The toy dataset used to validate such application consists of Lego bricks of different shapes and colors. The uncontrolled lighting conditions together with the use of RGB color features, respectively involve data with a large spread and different levels of measurement between data dimensions. To overcome the combination of these two characteristics in the data, we have developed a new weighted K-means algorithm, called gap-ratio K-means, which consists in weighting each dimension of the feature space before running the K-means algorithm. The weight associated with a feature is proportional to the ratio of the biggest gap between two consecutive data points, and the average of all the other gaps. This method is compared with two other variants of K-means on the Lego bricks clustering problem as well as two other common classification datasets.Comment: 13 pages, 6 figures, 2 tables. This paper is under the review process for AIAP 201

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.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

Improving the Accuracy of Industrial Robots by offline Compensation of Joints Errors

The use of industrial robots in many fields of industry like prototyping, pre-machining and end milling is limited because of their poor accuracy. Robot joints are mainly responsible for this poor accuracy. The flexibility of robots joints and the kinematic errors in the transmission systems produce a significant error of position in the level of the end-effector. This paper presents these two types of joint errors. Identification methods are presented with experimental validation on a 6 axes industrial robot, STAUBLI RX 170 BH. An offline correction method used to improve the accuracy of this robot is validated experimentally

Approximation spline L1C1 par fenêtres glissantes pour le signal et l'image

National audienceDans cet article, nous traitons le problème d'approximation de nuages de points par une courbe spline ou surface au sens de la norme L1. L'utilisation de cette norme permet de préserver la forme des données même en cas de changement brutal de celle-ci. Dans nos précédents travaux, nous avons introduit une méthode par fenêtre glissante de cinq points pour l'approximation courbe spline L1 et une méthode de croix glissante de neuf points pour l'approximation surface spline L1 de données type grille. Malgré leur complexité linéaire, ces méthodes peuvent demeurer lentes lorsqu'elles sont appliquées sur un large flot de données. Par conséquent, sur la base de nouveaux résultats algébriques sur l'approximation L1 sur un nombre restreint de données, nous proposons ici des méthodes reposant sur des fenêtres de taille inférieure et nous comparons les différentes méthodes. In this article, we adress the problem of approximating scattered data points by C1-smooth polynomial spline curves and surfaces using L1-norm optimization. The use of this norm helps us to preserve the shape of the data even near to abrupt changes. In our previous work, we introduced a five-point sliding window process for L1 spline curve approximation and a nine-point cross sliding window process for L1 spline surface approximation of grid datasets. Nethertheless, these methods can be still time consuming despite their linear complexity. Consequently, based on new algebraic results obtained for L1 approximation on restricted sets of points in both planar and spatial cases, we define in this article methods with smaller windows and we lead a comparison between the methods