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This paper introduces new planning and control methods for supermedia-enhanced real-time telerobotic operations via the Internet. Supermedia is the collection of video, audio, haptic information, temperature, and other sensory feedback. However, when the communication medium used, such as the Internet, introduces random communication time delay, several challenges and difficulties arise. Most importantly, random communication delay causes instability, loss of transparency, and desynchronization in real-time closed-loop telerobotic systems. Due to the complexity and diversity of such systems, the first challenge is to develop a general and efficient modeling and analysis tool. This paper proposes the use of Petri net modeling to capture the concurrency and complexity of Internet-based teleoperation. Combined with the event-based planning and control method, it also provides an efficient analysis and design tool to study the stability, transparency, and synchronization of such systems. In addition, the concepts of event transparency and event synchronization are introduced and analyzed. This modeling and control method has been applied to the design of several supermedia-enhanced Internet-based telerobotic systems, including the bilateral control of mobile robots and mobile manipulators. These systems have been experimentally implemented in three sites test bed consisting of robotic laboratories in the USA, Hong Kong, and Japan. The experimental results have verified the theoretical development and further demonstrated the stability, event transparency, and event synchronization of the systems.