Tying knot precisely

Simply pulling on the ends of string is sufficient to tighten simple knots such as the overhand knot, but many knots used for decoration or binding need to be tightened at particular locations along the string. For example, a shoelace knot should have equally-sized bows, as should a decorative cloverleaf knot. Knots tied in sounding lines (historically used to measure depth in the ocean) must be placed at precise distances apart. Precise control of tying also allows tangling to be avoided in complex knots. This paper explores an approach to tying knots precisely, so that friction locks occur at specified locations along the string. First, the knot is laid out on a fixture using an arm and a specialized gripper; then, the fixture contracts as string is pulled to tighten the knot. This is the first work we know of in robotic manipulation focused on precise knot tightening (rather than loose arrangement), and presents tying of a fairly complex decorative knot, the Ruyi knot, as a proof of concept. The fixtures are each specific to particular knots, but are designed automatically using the algorithm presented.