This paper studies the high telepresence control for the relay communication based space teleoperation. High telepresence requires real-time, accurate force perception and good position tracking, but all of them are destroyed or affected by time delay. To eliminate the influence of time delay, direct recursive generalized predictive control (DR-GPC) is quoted into this paper to realize position tracking. As for the other two properties, the pseudo position-force (Pseudo-PF) feedback strategy (composed of parameter identification and force reconstruction) is a good way as it can provide real-ti...