Analytical inverse kinematic solution for the redundant 7-DoF manipulator

This paper proposes a novel parameterization analytical method to solve the inverse kinematics of a redundant 7-DoF manipulator. The current arm-angle parameterization methods cannot describe the self-motion of the elbow joint well. To address this issue, a novel arm length parameter that describes the manipulator's redundancy is defined to represent the self-motion manifold of the elbow motion. Then the analytical inverse kinematics solutions can be obtained by utilizing arm length parameter and global configuration parameters. The joint angle constraints and singularity constraints are mapped to the arm length parameter space, and the feasible arm length intervals are derived. Furthermore, a redundant parameter optimization method is proposed based on the hierarchical motion control strategy, which applies the feasible arm length interval into the redundancy resolution problem. Numerical simulations are conducted to verify the proposed inverse kinematics method can reduce motion amplitude of joint angles during trajectory tracking and thus improve the motion accuracy of the manipulator compared with the traditional methods.