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A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method

Freus K., Freus S.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

67--76

The aim of this paper is to create an optimal shape of the 2D domain that is described by the Non-Uniform Rational B-Splines (NURBS) curves. This work presents a method based on the topological derivative for the Laplace equation that determines the sensitivity of a given cost function to the change of its topology. As a numerical approach, the boundary element method is considered. To check the effectiveness of the proposed approach, the example of computations was carried out.

Determination of temperature field in domain of complex shape using the NURBS curves and BEM

Freus K., Freus S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

43-48

Application of the rational B-spline curves for description of complex domain shape

Freus K., Freus S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

35-41

The comparison of elastic band and B-Spline polynomials methods in smoothing process of collision-free robot trajectory

Reclik D., Kost G.

Journal of Achievements in Materials and Manufacturing Engineering

2008

Vol. 29, nr 2

187-190

Purpose: The main reason of this paper was to prepare the system, which tests the use of elastic band for smoothing the collision-free trajectory. The aided robot off-line programming system is based on NURBS and B-Spline curves. Because there is a lot of information in references about using elastic band algorithm, authors decided to compare these two methods. The most important criterion in robotics is having the smoothest possible robot trajectory, so as a standard there the NURBS curves (C² smooth class) were used. Design/methodology/approach: Pascal language compiler was used for research. All algorithms were coded in this programming language and compiled. Results were set in Microsoft Excel worksheet. Findings: Results show that calculations, which were made with B-Spline method, have taken less time than calculations based on elastic band curves. Moreover, the elastic band method gave the smoothest curves but only in geometrical sense, which is less important (the first and second derivate are not continuous, which is the most important issue in presented case). That is why it was found that using the B-Spline algorithm is a better solution, because it takes less time and gives better quality results. Research limitations/implications: The MS Windows application was created, which generates smooth curves (in geometrical sense) by marking the interpolation base points which are calculated by the collision-free movement planner. This application generates curves by using both presented methods - B-Spline and elastic band. Both of these curves were compared in regard of standard deviation and variance of B-Spline and elastic band. Practical implications: Because the elastic band algorithm takes a lot of time (three times longer than B-Spline) it is not used in the final application. The authors used B-Spline method to make smoother and optimized trajectory in application for off-line collision-free robot programming. Originality/value: This is a new approach, which describes the comparison between elastic band and B-Spline polynomials methods in collision-free robot trajectory.