This paper investigates the problem of cooperative path following and obstacle avoidance of multiple UAV systems in three-dimensional space. Aiming at the limitations faced by existing studies in practical applications, such as actuator faults and wind disturbances, this paper proposes a new robust control strategy. The unmodeled uncertainties are more accurately estimated and compensated by introducing a predefined-time disturbance observer and a Gaussian radial basis neural network. A control barrier function-based algorithm is constructed to realize obstacle avoidance with bounded disturbance estimation error. In addition, a communication method based on a dynamic event-triggered mechanism is proposed to reduce the communication burden while maintain the system’s cooperative performance.