Application of the symbolic regression method for solving the inverse problem of control of the 3-RPR platform

Abstract

The paper is devoted to finding the functional dependence of the position of the 3-RPR platform on the control. In this construction, the controls are the lengths of the brackets attached to the corners of the platform. To solve the problem, one of the methods of symbolic regression the network operator method is used. Initially we got a training sample. The coordinates of the corners of the platform are found for the set of control by a numerical evolutionary PSO algorithm. Then, at the second stage, approximation of the obtained data was the network operator method. As a result, we obtain six functional equations that describe depending on the coordinates of the platform angles on the plane, on the values of the lengths of the control leashes. The solution of the inverse problem was performed for each coordinate of the platform angle separately. The feature of this task is that for the same value of control the platform has several provisions. To account for this property, an additional parameter is introduced into the 3-RPR platform control model, which takes an integer value. Each value of the additional parameter corresponds to one position.