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There is a growing tendency to use the Internet as the transmission medium of the telerobotic system since the Internet is inexpensive and available all over the world. However, the bilateral real-time teleoperation can be unstable due to the random time delays of the Internet. The event-based teleoperation is one of the fine approaches to overcome the ransom time delays. Since the event based control uses a non-time action reference, the stability and response performance of the system are affected by the time, which an event is held for. This study introduces the variable holding time to secure stability and response performance at once. The proper holding time for each event is obtained depending on the characteristics of the task through the fuzzy logic. The proposed control scheme was implemented on a robot arm over the Internet to show its effectiveness.