Error modeling and flexure-based calibration of large-aperture optical adjustment mechanisms using an improved particle swarm optimization algorithm

Abstract Meter-scale large-aperture gratings are essential in petawatt-class picosecond laser systems. Their grating mounts must support heavy-load arrays and high alignment accuracy due to high energy density and long beam paths. However, nonlinear errors from parasitic motions and transmission gaps can significantly degrade precision. This study presents a kinetostatic modeling and error calibration framework for the grating mount, incorporating an improved particle swarm optimization (PSO) algorithm. The nonlinear error model combines energy-based and pseudo-rigid-body methods, with equivalent representations of structural gaps and parasitic motions. To capture multi-source nonlinear interactions, a global–dynamic multi-subgroup PSO enhances calibration via coordinated global exploration and local refinement. Experiments indicate that, compared with conventional models, first-round compensation reduces average errors by over 65.4%, 79.8% and 74.8% in rotation, tip and tilt, respectively. The method integrates nonlinear pose modeling, unified gap representation and an enhanced PSO strategy, offering an effective solution for error compensation in meter-scale, heavy-load compliant mechanisms.