Математична модель та компютерна програма розв’язання оберненої задачі кінематики навчального роботаманіпулятора

Abstract

The article presents a mathematical description of a method for solving the inverse kinematics problem of an educational robot manipulator and proposes an algorithm for determining its generalized coordinates based on a given position and orientation of the end-effector. The developed approach also allows for calculating the spatial coordinates of objects relative to the base coordinate system, which ensures the correct positioning of the manipulator within the workspace. The proposed method can be used in the analysis, design, and programming of robotic systems for various purposes. The essence of the method lies in forming a system of kinematic equations and numerically solving the direct kinematics problem for each link of the robot manipulator with a pre-specified accuracy. Afterwards, the error is calculated as the sum of deviations between the given and calculated coordinates. The values of the robot’s generalized coordinates are determined by minimizing this error to achieve the closest approximation to the specified position of the end-effector. The proposed approach provides a unique solution to the inverse kinematics problem for manipulator designs where obtaining an exact analytical solution is either impossible or significantly complicated. It is shown that the use of numerical methods allows achieving the desired accuracy of results and adapting the algorithm to various kinematic schemes. Based on the proposed algorithm, a computer program has been developed that enables automated determination of coordinates for orienting the robot relative to an object or, conversely, determining the coordinates of an object given the known position of the robot. The article describes the operating principle of the software and provides fragments of the program code that implement the coordinate calculations.