A Fast and Robust Multistage Hybrid Algorithm for Inverse Kinematics of Redundant Mill Relining Manipulator

This paper proposed a new multistage hybrid algorithm MH‐IK to solve the inverse kinematics (IK) problem of redundant manipulators in terms of position, orientation, and collision errors. An improved cyclic coordinate descent method is proposed to satisfy the iteration of prismatic joints and avoid singularities. Halley's method is integrated to achieve fast convergence. On the basis of geometric analysis and the Beta distribution, a global search method is developed to overcome the local minimum problem. Four strategies are designed to further improve the adaptability during iterative loops. The proposed algorithm is applied to a seven‐degrees‐of‐freedom mill relining manipulator. Unlike conventional arms, the IK solution of this special manipulator has more requirements to be satisfied, including solvability, stability, real‐time, joint limits, and collision avoidance in a confined inner workspace. The superiority of MH‐IK is demonstrated through convergence analysis, ablation and comparison experiments against nine nonlinear algorithms and three millisecond‐level solvers. Furthermore, the hardware experiments are carried out in an established digital twin system to further verify the effectiveness of the proposed method. Although MH‐IK lacks solution diversity, it significantly outperforms other algorithms in almost all metrics, such as 5.27 ms solving time, 99.5% success rate, and 0.51% collision rate.