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A novel motion prediction approach is proposed based on a state observer with a cascade structure. The actual positions of master robot are estimated on the slave side by using delayed information of measurements. The prediction errors remain bounded under an appropriate set of assumptions for the system uncertainties. Moreover, an essential theorem for slave controller design is proposed to demonstrate performance recovery of the closed-loop system with cascade observer. By using the predictions, the forward time delay is effectively compensated when we design the controller of slave robot. Simulations are performed to verify the effectiveness of proposed method. 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