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Algorithm for the automated construction of the movement curve of the working tool with the possibility of interpolation of the step function of the displacement used to control gantry machines

The paper proposes a solution to the problem of interpolation of the step function of displacement, obtained from the movement's formation by simple systems of object analysis. The analysis of the motion curve is carried out, taking into account the transformation of data into Cartesian coordinate systems and the processing of 2D signals. A multicriteria objective function is used as an interpolation method. This approach is based on solving the problem of minimizing the functional simultaneously according to three criteria. The first criterion is the mean square of the measure of the discrepancy between the input values and those obtained due to minimization. This criterion is to set the degree of approximation to the input data. As the second criterion, the function of the root-mean-square spread of the neighboring elements of the obtained values is used. This criterion allows you to minimize the scatter of data and set the smoothness of the function. As the third criterion, the root-mean-square functional between adjacent elements of the second group is used. This criterion allows one to increase the degree of smoothness of the function and the rate of convergence. The weighting function is adjusted using weighting factors. The paper provides recommendations on choosing these values, and the diagrams show the rationale for this choice. The graphs showing the effect of the rate of convergence of the results on the degree of smoothness of the function and the selected parameters of the method are presented. The graphs of the tool exit speed to the working point and the calculation of the path lengths are given. Examples of plotting the curves of functions obtained by machine vision systems located on robotic portal complexes are presented on test data sets. Data obtained in the visible range, with a resolution of 1280x1024 pixels, are presented in grayscale.