Addressing the trajectory planning problem for multiple autonomous underwater vehicle formations under the conditions of random communication delays and time-varying communication topology, this paper introduces the stochastic gradient ascent algorithm into the distributed model predictive control method and proposes an online distributed trajectory planning approach. By sampling Bézier curves, the trajectory planning problem is transformed into a series of optimization problems, which are then solved distributively through the Lagrange dual function method, maintaining communication links between members while completing point-to-point trajectory planning tasks. Finally, based on the Lagrange duality theory framework, this paper derives the quantitative relationship between the convergence rate of the proposed algorithm and the maximum communication delay, and verifies the feasibility and effectiveness of the proposed method through comparative experiments with existing methods in simulation scenarios.