A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint

This paper presents a closed-form inverse kinematics solution for the 2n-degree of freedom (DOF) hyper-redundant serial manipulator with n identical universal joints (UJs). The proposed algorithm is based on a novel concept named as general spherical joint (GSJ). In this work, these universal joints are modeled as general spherical joints through introducing a virtual revolution between two adjacent universal joints. This virtual revolution acts as the third revolute DOF of the general spherical joint. Remarkably, the proposed general spherical joint can also realize the decoupling of position and orientation just as the spherical wrist. Further, based on this, the universal joint angles can be solved if all of the positions of the general spherical joints are known. The position of a general spherical joint can be determined by using three distances between this unknown general spherical joint and another three known ones. Finally, a closed-form solution for the whole manipulator is solved by applying the inverse kinematics of single general spherical joint section using these positions. Simulations are developed to verify the validity of the proposed closed-form inverse kinematics model.

Automated summary

This paper introduces a closed-form inverse kinematics solution for a 2n-degree of freedom hyper-redundant serial manipulator with n identical universal joints, based on a concept called general spherical joint (GSJ). The proposed algorithm allows for the decoupling of position and orientation, and solves the manipulator's problem by using distances between known and unknown general spherical joints. Simulation results validate the effectiveness of the proposed closed-form inverse kinematics model.