General inverse kinematics method for 7-DOF offset manipulators based on arm angle parameterization

Abstract

This paper proposes a general numerical methodology of inverse kinematics computation for 7-degree-of-freedom offset manipulators based on arm angle parameterization. First, analytical inverse kinematics solutions for two types of Spherical-Revolute-Spherical manipulators are derived based on arm angle parameterization. Then, the inverse kinematics of the offset manipulator is solved using a simplified manipulator. In each iteration of the algorithm, the inverse solution of the simplified manipulator is used to calculate the position and arm angle error between the actual manipulator and desired value. The error is utilized to compensate the position and arm angle of the simplified manipulator so that the inverse solution of the simplified manipulator gradually approaches the desired solution of the actual manipulator. Moreover, the problems of workspace reduction due to structure simplification and the placement of the iteration point outside of the workspace of the simplified manipulator are optimized. Additionally, the algorithm singularity problem of the offset manipulator is solved via the dual arm angle parameterization method. Finally, the method is validated by numerical simulation and physical experiments.