Kinematic calibration of a 2PUPR-PRPU kinematically redundant parallel mechanism based on measurement pose optimization

Kinematically redundant parallel mechanisms (KR-PMs) exhibit complex error coupling and error amplification due to the existence of redundant branches, which poses enormous challenges to kinematic calibration. To address the key issue of insufficient excitation of error parameters caused by measurement noise and local convergence in traditional pose optimization algorithms, this study proposes a hybrid GOA-IOOPS measurement pose optimization algorithm for the kinematic calibration of the 2PUPR-PRPU KR-PM. First, based on the error mapping Jacobian matrix, a kinematic error model integrating error parameters of redundant branches is established using the closed-loop vector method and numerical differentiation. Innovatively, the grasshopper optimization algorithm (GOA) is fused with the iterative one-by-one pose search (IOOPS) algorithm: GOA undertakes global exploration to avoid local optima, while IOOPS performs local refinement to maximize the observability index O₃. For parameter identification, a regularized nonlinear least squares method based on the Levenberg-Marquardt (LM) algorithm is adopted to balance convergence speed and robustness. Numerical simulations confirm that the GOA-IOOPS algorithm outperforms the traditional IOOPS algorithm and random selection method. Prototype experiments verify that the proposed calibration method significantly improves the positioning accuracy of the 2PUPR-PRPU KR-PM.