Unified Geometric Error Modeling and Cooperative Calibration Method for High Precision Dual-Robot Machining Systems

In advanced manufacturing fields such as aerospace, achieving high-precision cooperative positioning for dual-robot systems remains a critical challenge. Traditional calibration methods, which address multi-source geometric errors in a decoupled, stepwise manner, suffer from error propagation and accumulation, failing to effectively compensate for the highly coupled nature of the system. This paper proposes a unified calibration framework that overcomes these limitations. The core innovation is to model the entire dual-robot system—encompassing the master robot, the slave robot, and their base-to-base relationship—as a single, continuous kinematic chain. Based on this unified model, a complete cooperative error Jacobian matrix, incorporating a total of 78 geometric error parameters, is systematically derived. The Levenberg-Marquardt algorithm is then employed for parameter identification. Experimental results show that the mean absolute positioning errors in the x, y, and z directions decreased from 1.386 mm, 1.361 mm, and 0.341 mm to 0.391 mm, 0.387 mm, and 0.245 mm, respectively, achieving accuracy improvements of 71.8%, 71.6%, and 34.5%. Crucially, after calibration the cooperative positioning error of the dual-robot system was contained within 0.8 mm. This breakthrough provides a robust accuracy foundation for complex industrial applications, including high-precision assembly, riveting, and collaborative manufacturing, thereby enhancing the capabilities of computer-integrated manufacturing systems.