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Due to the friction, serial robots with harmonic drives may appear rough running and control precision deterioration at low speed. To deal with this problem, a desired compensation robust controller (DCRC) with friction compensation was constructed. First, based on the frequency domain analysis of the friction data, a new friction model, which is the combination of Stribeck model and sine/cosine functions, was involved to model the friction of harmonic-drive-based joint. Second, DCRC was designed to handle the effect of joint friction and model uncertainties. In this control scheme, a feed-forward term calculated off-line using desired motion data was designed to avoid introducing measurement noise and improve the real-time performance. In this term, the joint friction compensation was also included. A robust term was designed utilizing the bounds of the uncertainty to guarantee the robustness. In addition, the globally uniformly ultimately bounded stability of the resulting closed-loop system was proved by using Lyapunov theory. Finally, experimental results illustrate that adopting the proposed friction model and controller, stable trajectory tracking at low speed can be achieved, and the average tracking error in joint space is less than 0.005°.