An improved algorithm for solving inverse problems of the dynamics of robotic devices at SCAS KIDYM

Abstract

The paper presents the results of studies of an analytical algorithm for constructing a resolving system of linear equations to determine the driving forces and moments in the links of robotic devices of arbitrary structure during movement. This algorithm is implemented as an analytical algorithm in a special computer algebra system (SCAS) KiDyM, on the basis of which numerical calculations of the specified forces and moments are generated in the process of performing work processes, positioning mechanisms in the required positions, parking movements, etc. The KiDyM software package is used to solve mechanics problems of a wide class of discrete mechanical systems of arbitrary structure and type of motion for engineering and scientific calculations. A theoretical justification for the developed new approach, analytical and numerical proof of its effectiveness from the point of view of the process of automatically obtaining resolving equations, computational efficiency and accuracy of results are presented. The proposed algorithm is the result of the development of an algorithm that was previously implemented in SCAS KiDyM and was similar in purpose. Unlike the previously implemented algorithm, which generates a resolving system of equations after constructing the dynamic equations, the new algorithm is built into the process of generating dynamic equations - it sorts the model elements - inertial, dissipative, elastic and force elements of known forces and moments form the right side, and force elements with unknown forces and moments, they form a matrix of the left side of equations that solve the inverse problem of dynamics. The article gives a comparative analytical conclusion of one and another algorithm and shows the coincidence of the resulting equations. Also, using examples of calculations of the inverse problem of the dynamics of a portal crane and two 6-degree manipulators, the advantages of the new approach are shown.