A tolerance constrained robot path circular interpolation method for industrial SCARA robots

The linear robot path is tangential and curvature discontinuity, which will lead to vibration and unnecessary hesitation during execution. Local corner transition method and local spline interpolation method are used in state-of-art industrial robot controller to reduce vibration, while local corner transition method cannot interpolate target points and local spline interpolation method cannot constrain chord errors. This research proposes a robot path local interpolation method that eliminates deficiencies of each method. The smoothing method satisfies all of the following requirements: G1 continuity, target point interpolation and chord tolerance confined, shape-preserving (free of self-intersection), and unified parameterization. The generated smooth path consists of linear path and circular arc path with G1 continuity. A geometric iterative method cooperating with local corner transition method is used to generate local interpolation path. Simulations and actual experiments verify the generated smooth path is G1 continuous, tolerance constrained, shape-preserving, and have high computational efficiency.

Possibility of using local spline functions for estimating displacement values when observing deformations of buildings

This paper discusses the issue of determining the values of displacement points on the walls of buildings and structures during deformations using geodetic measurements of the values of displacements of adjacent points. It is proposed to use spline functions of one or two variables to calculate the offsets of points where no measurements were made, or where observations stopped starting from a certain stage. It is proposed to determine the spline coefficients either by interpolating the results from one observation cycle to arbitrary points, or by interpolating the observation results in previous cycles to points that were not observed in the new observation cycle. A specific example is used to evaluate the accuracy of the interpolation results and provide practical recommendations for using the methods in practical calculations. When considering the two-dimensional case, it is concluded that the approximation of the linear spline of two variables is not accurate enough, and it is proposed to use splines of a higher degree.

Interval estimation of trigonometrical splines

Quite often, it is necessary to quickly determine variation range of the function. If the function values are known at some points, then it is easy to construct the local spline approximation of this function and use the interval analysis rules. As a result, we get the area within which the approximation of this function changes. It is necessary to take into account the approximation error when studying the obtained area of change of function approximation. Thus, we get the range of changing the function with the approximation error. This paper discusses the features of using polynomial and trigonometrical splines of the third order approximation to determine the upper and lower boundaries of the area (domain) in which the values of the approximation are contained. Theorems of approximation by these local trigonometric and polynomial splines are formulated. The values of the constants in the estimates of the errors of approximation by the trigonometrical and polynomial splines are given. It is shown that these constants cannot be reduced. An algorithm for constructing the variation domain of the approximation of the function is described. The results of the numerical experiments are given.

Optimum regular local spline interpolation of signals

The study deals with an optimum approach to regular local signal interpolation by means of generalised splines. For the special case of local regular polynomial spline interpolation we derive quasi-optimal interpolation bases and provide corresponding recommendations dealing with selecting interpolation order and order of smoothness.