Research on Internet-based teleoperation has received increased attention in the past few years. In this paper, an Internet-based teleoperation system was implemented. In order to robustly transmit the surroundings and control information of the robot, packet-type data were used. The central problem in Internet-based teleoperation is data transmission latency or data loss. For this specific problem, an autonomous mobile robot with optimal two-layer fuzzy controller (2LFC) was introduced. When data transmission is failed, the robot automatically moves and protects itself. In addition, a color detection system was implemented so that the robot can perceive an object and move to another object. The fuzzy controller was optimized by using the schema coevolutionary algorithm (SCEA), which finds an optimal solution. Using these technologies, the efficacies of the 2LFC, the SCEA, and the teleoperation system were verified