Uncertain disturbance factors such as clock drift, dynamic obstacles, and AGV failures lead to spatio-temporal deviations between the actual execution and planned paths of multi-AGV systems, resulting in frequent path conflicts. To address this, a two-stage robust optimization model is proposed, designed to maintain performance close to that of a deterministic model under uncertain disturbances. In the first stage, a dimension-sensitive k-robust safe interval planning algorithm is introduced. It determines the k-robust factor using a deep surrogate model and a three-dimensional mapping table, generating a global robust path plan under explicit disturbances and significantly reducing redundant waiting time for Multi-AGV. In the second stage, an any-angle geometric nearest neighbor search algorithm is proposed. It performs online repair of paths invalidated by disturbances through geometric nearest neighbor search and collision time interval estimation, further enhancing system robustness. A multi-dimensional robustness performance evaluation index system is designed to calculate the closeness between various path plans under uncertain disturbances and the optimal solution of the deterministic model, enabling an objective and quantitative assessment of robustness. Simulation experiments were conducted on four datasets of varying scales, involving three types of disturbance scenarios and comparisons with four categories of benchmark algorithms. The results demonstrate that the proposed method improves closeness by an average of 8% compared to the benchmark algorithms, exhibited the highest closeness to the deterministic model under uncertain disturbances, effectively balanced temporal and spatial costs, and demonstrated the strongest robustness.