Numerical method of working area approximation of the tripod robot taking into account the singularity zones

Abstract

The article describes the use of optimization algorithms for solving the problem of determining the working area of a tripod robot. The method of approximation of the set of solutions of a system of nonlinear inequalities describing constraints on the geometric parameters of the robot, based on the concept of non-uniform covering, is considered. Based on the method, internal approximations are obtained, defined as a set of boxes. The zones of singularity arising at some positions of the robot are investigated. The conditions for the emergence of singularity zones corresponding to its singularity zones are revealed. The influence of various geometric parameters on the volume of the working area of the robot is analyzed. For the approximation of the working area, the developed algorithm and its modifications with different dimensions of boxes and approaches to the transfer of constraints from the space of input coordinates to the output coordinates are used in connection with the complexity of the computational problem. To implement the algorithms, a software package in the C ++ language has been developed. The results of mathematical modeling are presented. Experimentally verified various dimensions of the grid to calculate the functions, as well as the accuracy of approximation. The obtained results can be used when choosing the geometrical parameters of a tripod robot, providing the boundaries of the working area specified by the technological process, as well as when planning the trajectory, taking into account the circumvention of singularity zones in which the mechanism theoretically controls.