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In this paper, we study the problem of zero-shot sim-to-real when the task requires both highly precise control with sub-millimetre error tolerance, and wide task space generalisation. Our framework involves a coarse-to-fine controller, where trajectories begin with classical motion planning using ICP-based pose estimation, and transition to a learned end-to-end controller which maps images to actions and is trained in simulation with domain randomisation. In this way, we achieve precise control whilst also generalising the controller across wide task spaces, and keeping the robustness of vision-based, end-to-end control. Real-world experiments on a range of different tasks show that, by exploiting the best of both worlds, our framework significantly outperforms purely motion planning methods, and purely learning-based methods. Furthermore, we answer a range of questions on best practices for precise sim-to-real …