A closed-form solution for inverse kinematics of redundant space manipulator with multiple joint offsets

This paper proposes a novel parameterization analytical method to solve the inverse kinematics of a redundant space manipulator, which has link offsets at the shoulder, elbow, and wrist parts. Due to the manipulator's particular configuration, current arm angle concepts cannot provide the analytical solution directly. Hence, this paper defines a new arm angle parameter that describes the manipulator's redundancy and obtains the closed-form solutions directly. This is because, unlike manipulators without offset links, existing approaches involve parameters that may cause the inverse kinematic solution to fail when applied to the manipulator type considered in this work. Specifically, we analyze the parameter interplay on the inverse kinematic computation and then investigate the relations between the singularity and arm angle based on the singularity conditions of the Jacobian matrix. Besides, a semi-analytical method is proposed to determine the feasible arm angle intervals, while avoiding the singularity and inverse kinematic computation. Finally, a simple approach is proposed to compute the arm angle according to the feasible intervals. The proposed method has obvious geometric significance, is suitable for configuration control, and can be implemented in real-time control systems.