Reliability analysis of positioning accuracy for industrial robots incorporating kinematic and flexible parameter uncertainties

The motion accuracy of industrial robots serves as a critical factor in ensuring the quality of welding, cutting, and assembly processes during the manufacturing of maritime equipment, directly determining the operational reliability and long-term operational safety of the overall structures. To evaluate the impact of uncertainties in kinematic and flexible parameters on the motion accuracy of industrial robots, this paper proposes a reliability analysis method for positioning accuracy based on a mixed Gamma function approximation. Given that numerous factors influence robotic manipulator positioning errors, the kinematic error model is insufficient to capture real-world working conditions. Therefore, a comprehensive positioning error reliability model is established, incorporating both kinematic and flexibility-induced errors. Based on this model, a mixed Gamma function approach is introduced to approximate the complex nonlinear performance function. The parameters of the mixed Gamma function are determined by matching the first few cumulants of the positioning accuracy function, thereby enabling the computation of positioning accuracy reliability using numerical integration. Ultimately, a case study on the six degrees of freedom industrial robot compares the proposed method with existing approaches, demonstrating its effectiveness. The results indicate that the proposed method outperforms existing approaches in terms of accuracy, efficiency, and applicability in positioning accuracy reliability analysis.