Inverse Kinematic Problem of Movement of Six Degrees of Freedom Robotic Arm (Solved by a Numerical Method)

Abstract

Robot manipulators are widely used in engineering for solving various tasks in accordance with their purpose. Manipulators usually consist of sequentially connected rigid links and connections between them – joints. One of the most complex types of robot manipulators is the articulated robot, also called the Robotic Arm. It has a structure similar to a human arm with three rigid links and only rotational joints. Such a structure provides greater flexibility, manageability and versatility. At the same time, the accuracy is reduced and the kinematic calculation is complicated. The direct kinematic problem is fairly well known and is uniquely solved using Euler angles or quaternion matrices. At the same time, the inverse kinematic problem has a multivariate solution and, therefore, it must be an optimization. The article proposes a new approach to solving the inverse kinematic problem based on numerical methods and parametric optimization. Formulas of transformations of Cartesian coordinates for a direct kinematic problem act as a mathematical model. However, in the formulas, the angles of rotation of the joints are unknown. Their values are determined during the minimization of the objective function in the form of a sum of squares of the difference between the specified and obtained Cartesian coordinates of the end-effector. The article describes a robot with 6 Degrees of Freedom. Based on the above approach, modeling was performed in the MATLAB software environment. It is proposed to use the sum of the angles of the links of the robot as an optimization criterion. Analysis of the results showed that the optimal solution allows reducing the rotation angles of all links of the robot approximately two times.