Rope through Loop Insertion for Robotic Knotting: A Virtual Magnetic   Field Formulation
  Inserting an end of a rope through a loop is a common and important action that is required for creating most types of knots. To perform this action, we need to pass the end of the rope through an area that is enclosed by another segment of rope. As for all knotting actions, the robot must for this exercise control over a semi-compliant and flexible body whose complex 3d shape is difficult to perceive and follow. Additionally, the target loop often deforms during the insertion. We address this problem by defining a virtual magnetic field through the loop's interior and use the Biot Savart law to guide the robotic manipulator that holds the end of the rope. This approach directly defines, for any manipulator position, a motion vector that results in a path that passes through the loop. The motion vector is directly derived from the position of the loop and changes as soon as it moves or deforms. In simulation, we test the insertion action against dynamic loop deformation of different intensity. We also combine insertion with grasp and release actions, coordinated by a hybrid control system, to tie knots in simulation and with a NAO robot. 
Alejandro Marzinotto and Johannes A. Stork
cs.RO