JPSP-IK: A Fast Reduced-Space Inverse Kinematics Framework for Industrial Redundant Manipulators

Redundant manipulators offer greater flexibility in executing complex trajectory-tracking tasks in industrial applications, owing to their additional degrees of freedom (DOFs). However, their inverse kinematics (IK) remains computationally expensive, limiting their practical application. By combining the joint parameterization method (JPM) and the stationary point solver (SPS), the JPSP-IK framework is proposed to provide closed-form joint solutions while significantly reducing the computational burden. JPM treats the redundant variables as free parameters and analytically reconstructs the remaining joints in closed form from these variables and the target end-effector pose, thereby reducing the original full-space IK problem to a low-dimensional redundancy-resolution problem. On this basis, the SPS is developed to efficiently determine the redundant variables with respect to the secondary objective, considering joint-limit avoidance and motion smoothness, and the complete joint solution is analytically reconstructed through the analytical mapping derived by the JPM. Validation and comparative experiments demonstrate that JPSP-IK achieves substantially lower computation times than representative full-space and JPM-based IK methods.