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Flexible endoscopy requires high skills to manipulate both the endoscope and associated instruments. In most robotic flexible endoscopic systems, the endoscope and instruments are controlled separately by two operators, which may result in communication errors and inefficient operation. We present a novel teleoperation robotic endoscopic system that can be commanded by a surgeon alone. This 13 degrees-of-freedom (DoF) system integrates a foot-controlled robotic flexible endoscope and two hand-controlled robotic endoscopic instruments (a robotic grasper and a robotic cauterizing hook). A foot-controlled human-machine interface maps the natural foot gestures to the 4-DoF movements of the endoscope, and two hand-controlled interfaces map the movements of the two hands to the two instruments individually. The proposed robotic system was validated in an ex-vivo experiment carried out by six subjects, where foot control was also compared with a sequential clutch-based hand control scheme. The participants could successfully teleoperate the endoscope and the two instruments to cut the tissues at scattered target areas in a porcine stomach. Foot control yielded 43.7% faster task completion and required less mental effort as compared to the clutch-based hand control scheme. The system introduced in this paper is intuitive for three-limb manipulation even for operators without experience of handling the endoscope and robotic instruments. This three-limb teleoperated robotic system enables one surgeon to intuitively control three endoscopic tools which normally require two operators, leading to reduced manpower, less communication errors, and improved efficiency.