Eric Nyiri

Enhanced trajectory planning for machining with industrial six-axis robots

This paper presents a practical approach to adapt the trajectory planning stage for industrial robots to realize continuous machining operations. Firstly, L1 interpolation is introduced to generate efficiently the tool-paths in the form of shape-preserving quintic splines. Then, the tool-tip feedrate planning in Cartesian space is done using a smooth jerk limited pattern and taking into account the joints kinematics constraints. Experimental validations conducted on a 6-axis industrial robot demonstrate the effectiveness of the proposed methodology of trajectory planning in the context of machining.

L1C1 polynomial spline approximation algorithms for large data sets

In this article, we address the problem of approximating data points by C1-smooth polynomial spline curves or surfaces using L1-norm. The use of this norm helps to preserve the data shape and it reduces extraneous oscillations. In our approach, we introduce a new functional which enables to control directly the distance between the data points and the resulting spline solution. The computational complexity of the minimization algorithm is nonlinear. A local minimization method using sliding windows allows to compute approximation splines within a linear complexity. This strategy seems to be more robust than a global method when applied on large data sets. When the data are noisy, we iteratively apply this method to globally smooth the solution while preserving the data shape. This method is applied to image denoising.

Nonlinear L 1 C 1 interpolation: application to Images

In this article, we address the problem of interpolating data points lying on a regular grid by C1-continuous L1-bicubic spline surfaces. Our algorithm is based on a local univariate L1 minimization method which enable us to calculate first derivative values for C1-cubic spline curves. In order to construct the interpolation surface, we calculate four derivative values at each data point using this local method. At is was shown in [17], our local interpolation L1 cubic spline curve algorithm preserves well the shape of the data even for abrupt changes.The sequential computational complexity of this local method is linear and the parallel computational complexity is O(1). Consequently, we can address in this manner data on large grids. In order to keep this linear complexity for spline surface interpolation, we define an interpolation scheme based on four linear directions so as to construct our L1-bicubic surface. Some image interpolation examples show the efficiency of this non linear interpolation scheme.

Best L 1 approximation of Heaviside-type functions from Chebyshev and weak-Chebyshev spaces

In this article, we study the problem of best L1 approximation of Heaviside-type functions from Chebyshev and weak-Chebyshev spaces. We extend the Hobby-Rice theorem (Proc. Am. Math. Soc., 16, 665–670, 1965) into an appropriate framework and prove the unicity of best L1 approximation of Heaviside-type functions from an even-dimensional Chebyshev space under some assumptions on the dimension of the subspaces composed of the odd and even functions. We also apply the results to compute best L1 approximations of Heaviside-type functions by polynomials and Hermite polynomial splines with fixed knots.

Locally optimal control under unknown dynamics with learnt cost function: application to industrial robot positioning

Recent methods of Reinforcement Learning have enabled to solve difficult, high dimensional, robotic tasks under unknown dynamics using iterative Linear Quadratic Gaussian control theory. These algorithms are based on building a local time-varying linear model of the dynamics from data gathered through interaction with the environment. In such tasks, the cost function is often expressed directly in terms of the state and control variables so that it can be locally quadratized to run the algorithm. If the cost is expressed in terms of other variables, a model is required to compute the cost function from the variables manipulated. We propose a method to learn the cost function directly from the data, in the same way as for the dynamics. This way, the cost function can be defined in terms of any measurable quantity and thus can be chosen more appropriately for the task to be carried out. With our method, any sensor information can be used to design the cost function. We demonstrate the efficiency of this method through simulating, with the V-REP software, the learning of a Cartesian positioning task on several industrial robots with different characteristics. The robots are controlled in joint space and no model is provided a priori. Our results are compared with another model free technique, consisting in writing the cost function as a state variable.

Fast Polynomial Spline Approximation for Large Scattered Data Sets via L1 Minimization

In this article, we adress the problem of approximating scattered data points by C 1-smooth polynomial spline curves using L 1-norm optimization. The use of this norm helps us to preserve the shape of the data even near to abrupt changes. We introduced a five-point sliding window process for L 1 spline approximation but this method can be still time consuming despite its linear complexity. Consequently, based on new algebraic results obtained for L 1 approximation on any three points, we define in this article a more efficient method.

L 1 spline fits via sliding window process: continuous and discrete cases

The best L1 approximation of the Heaviside function and the best ℓ1 approximation of multiscale univariate datasets by a cubic spline have a Gibbs phenomenon near the discontinuity. We show by numerical experiments that the Gibbs phenomenon can be reduced by using L1 spline fits which are the best L1 approximations in an appropriate spline space obtained by the union of L1 interpolation splines. We prove here the existence of L1 spline fits for function approximation which has never previously been done to the best of our knowledge. A major disadvantage of this technique is an increased computation time. Thus, we propose a sliding window algorithm on seven nodes which is as efficient as the global method both for functions and datasets with abrupt changes of magnitude, but within a linear complexity on the number of spline nodes.

Unsupervised Robotic Sorting : Towards Autonomous Decision Making Robots

Autonomous sorting is a crucial task in industrial robotics which can be very challenging depending on the expected amount of automation. Usually, to decide where to sort an object, the system needs to solve either an instance retrieval (known object) or a supervised classification (predefined set of classes) problem. In this paper, we introduce a new decision making module, where the robotic system chooses how to sort the objects in an unsupervised way. We call this problem Unsupervised Robotic Sorting (URS) and propose an implementation on an industrial robotic system, using deep CNN feature extraction and standard clustering algorithms. We carry out extensive experiments on various standard datasets to demonstrate the efficiency of the proposed image clustering pipeline. To evaluate the robustness of our URS implementation, we also introduce a complex real world dataset containing images of objects under various background and lighting conditions. This dataset is used to fine tune the design choices (CNN and clustering algorithm) for URS. Finally, we propose a method combining our pipeline with ensemble clustering to use multiple images of each object. This redundancy of information about the objects is shown to increase the clustering results.

A Computer-Aided Design and Manufacturing Implementation of the Atomic Force Microscope Tip-Based Nanomachining Process for Two-Dimensional Patterning

This paper reports a feasibility study that demonstrates the implementation of a computer-aided design and manufacturing (CAD/CAM) approach for producing two-dimensional (2D) patterns on the nanoscale using the atomic force microscope (AFM) tip-based nanomachining process. To achieve this, simple software tools and neutral file formats were used. A G-code postprocessor was also developed to ensure that the controller of the AFM equipment utilized could interpret the G-code representation of tip path trajectories generated using the computer-aided manufacturing (CAM) software. In addition, the error between a machined pattern and its theoretical geometry was also evaluated. The analyzed pattern covered an area of 20 μm × 20 μm. The average machined error in this case was estimated to be 66 nm. This value corresponds to 15% of the average width of machined grooves. Such machining errors are most likely due to the flexible nature of AFM probe cantilevers. Overall, it is anticipated that such a CAD/CAM approach could contribute to the development of a more flexible and portable solution for a range of tip-based nanofabrication tasks, which would not be restricted to particular customised software or AFM instruments. In the case of nanomachining operations, however, further work is required first to generate trajectories, which can compensate for the observed machining errors.