The research status of industrial robot trajectory planning is discussed in detail, and the applicable occasions cubic polynomial interpolation, quintic B-spline curve, mixed interpolation other methods commonly used basic are comprehensively analyzed. At same time, various optimal for robots reviewed. advantages disadvantages compared important direction prospected.

Numerical solutions of the coupled Klein-Gordon-Schrödinger equations is obtained by using differential quadrature methods based on polynomials and quintic B-spline functions for space discretization and RungeKutta fourth order for time discretization. Stability of the schemes are studied using matrix stability analysis. The accuracy and efficiency of the methods are shown by conducting some nu...

In order to construct a C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme [5]. In this paper we introduce a nodal macroelement on the 12-split...

The construction of range restricted univariate and bivariate interpolants to gridded data is considered. We apply Gregory’s rational cubic C splines as well as related rational quintic C splines. Assume that the lower and upper obstacles are compatible with the data set. Then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range rest...