Inverse Kinematics Optimization for Redundant Manipulators Using Motion-Level Factor

Redundant manipulators (RMs) are widely used in various fields due to their flexibility and versatility, but challenges remain in adjusting their inverse kinematics (IK) solutions. Adjustable IK solutions are crucial as they not only avoid joint limits but also enable the manipulability of the manipulator to be regulated. To address this issue, this paper proposes an IK optimization method. First, a performance metric for adjustable IK solutions is developed by introducing the motion-level factor. By setting the desired joint motion level, the IK solutions can be adjusted accordingly. Furthermore, a two-stage optimization algorithm is proposed to obtain the adjustable IK solutions. In the first stage, a modified gradient projection method is used to optimize the performance metric, generating a set of initial optimal solutions. However, cumulative errors may arise during this stage. To counteract this, the forward and backward reaching inverse kinematics algorithm is employed in the second stage to enhance the accuracy of the initial solutions. Finally, the effectiveness of the proposed method is validated through simulations and experiments using a planar cable-driven redundant manipulator. The results demonstrate that the IK solutions can be adjusted by modifying the motion-level factors. The proposed two-stage optimization algorithm integrates the advantages of the gradient projection method and the forward and backward reaching inverse kinematics algorithm, yielding a set of accurate and optimal IK solutions. Furthermore, the adjustable IK solutions facilitate the regulation of the RM’s manipulability, enhancing its adaptability and flexibility.