This paper presents a fast tight-tolerance threading technique for string and rope. Instead of relying on simulations of these deformable objects to plan a path or compute control actions, we control the movement of the string with a virtual magnetic vector field emanating from the narrow openings we wish to thread through. We compute an approximate Jacobian to move the tip of the string through the vector field and propose a method to promote alignment of the head of the string to the opening. We also propose a method for re-grasping the string based on the relationship between the string's configuration, the orientation of the opening, and direction of gravity. This re-grasping method in conjunction with our controller can be used to thread the string through a sequence of openings. We evaluated our method in simulation (with simulated sensor noise) and on the Da Vinci surgical robot. Our results suggest that our method is quite robust to errors in sensing, and is capable of real-world threading tasks with the da Vinci robot, where the diameter of the string (3.5mm) and opening (4.9mm) differ by only 1.4 mm.
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