Hierarchical kinematic modeling and dual-phase geometric parameter identification of a hybrid robot for complex curved-surface fragment intelligent assembly

This article presents a Delta–RBR–2P hybrid robot architecture designed for complex curved-surface fragment intelligent assembly tasks. A general hierarchical kinematic modeling framework is established for this class of hybrid mechanisms, enabling decoupled motion representation and analytical formulation across three layers: the Delta stage, the 3R RBR wrist, and the parallel 2P microstage. A Dual-Phase Simplex–Sequential Quadratic Programming (DPSSQP) algorithm is proposed for geometric parameter optimization, integrating global exploration, constrained local refinement, intelligent result selection, and adaptive iteration control to improve optimization accuracy. Experimental validation using a laser tracker demonstrates that the DPSSQP algorithm reduces the mean end-effector positioning error from 14.7782 mm to 1.1195 mm (a 92.42% improvement), while also achieving higher optimization accuracy compared with conventional algorithms. These results confirm that the proposed kinematic modeling and geometric parameter calibration framework for the hybrid robot is both feasible and effective for complex curved-surface fragment intelligent assembly tasks.