As the adoption of large-scale model-based AI grows, the field of robotics is undergoing significant changes. The emergence of cloud robotics, where advanced tasks are offloaded to fog or cloud servers, is gaining attention. However, the widely used Robot Operating System (ROS) does not support communication between robot software across different networks. This paper introduces ROS Gateway, a middleware designed to improve the usability and extend the communication range of ROS in multi-network environments, which is important for processing sensor data in cloud robotics. We detail its structure, protocols, and algorithms, highlighting improvements over traditional ROS configurations. The ROS Gateway efficiently handles high-volume data from advanced sensors such as depth cameras and LiDAR, ensuring reliable transmission. Based on the rosbridge protocol and implemented in Python 3, ROS Gateway is compatible with rosbridge-based tools and runs on both x86 and ARM-based Linux environments. Our experiments show that the ROS Gateway significantly improves performance metrics such as topic rate and delay compared to standard ROS setups. We also provide predictive formulas for topic receive rates to guide the design and deployment of robotic applications using ROS Gateway, supporting performance estimation and system optimization. These enhancements are essential for developing responsive and intelligent robotic systems in dynamic environments.