Combining closed-form and numerical solutions for the inverse kinematics of six-degrees-of-freedom collaborative handling robot

Abstract

In the process of solving the inverse kinematics of six-degrees-of-freedom collaborative robots, the numerical solution has problems such as low accuracy and singular configurations. Moreover, due to the high coupling of its position and attitude, the direct closed-form solution fails. To address these problems, an inverse kinematics algorithm that combines closed-form and numerical solutions was proposed. The Jacobian matrix was established based on the forward kinematics equation of the six-degrees-of-freedom collaborative robot. Its inverse matrix was obtained by a singular value decomposition of the matrix using the Manocha elimination method to avoid the singularities of the Jacobian matrix. The optimal inverse kinematics solution was obtained using the Newton–Raphson iterative method. A computer simulation implemented in MATLAB and Visual C++ was used to evaluate the accuracy and speed of the proposed algorithm. The results of the trajectory planning experiments demonstrate that the algorithm satisfies the requirements for real-time smooth motion. This study of inverse kinematics lays the theoretical foundation for solutions to the inverse problem and real-time control of collaborative robots.