For large-scale fabrication and manufacturing of products with curved surfaces, three-dimensional additive manufacturing using vertical articulated robots is desirable because of a wide working range and high kinematic flexibility. In particular, extrusion-based additive manufacturing employing multi-axis vertically articulated robots has attracted increasing attention due to its potential for complex and flexible tool path motions in material deposition. Our laboratory has proposed and studied a method of curved surface deposition using vertical articulated robots. However, conventional systems often struggle to maintain a constant tool speed and to achieve precise synchronization between the robot motion and the extrusion rate, resulting in diminished fabrication accuracy. To address this issue, in this paper, a fabrication method that utilizes ROS2 to dynamically control the extrusion rate in response to the tool speed, which is calculated by a robot motion planning system and can be predicted through simulation. Experimental evaluation was conducted to investigate whether the proposed method can effectively reduce variations in material deposition amount and shape errors. The results showed that the method improved quality of fabricated products in extrusion-based additive manufacturing. Additionally, in order to control the amount of extrusion rate appropriately even if the tool speed changes dynamically, an extended to a cyber-physical system is proposed, where real motion data in distributed robots are monitored and collected into a database for extracting a sophisticated processing method.