  From ancient times, humans have been using cables and ropes to tie, carry,
and manipulate objects by folding knots. However, automating knot folding is
challenging because it requires dexterity to move a cable over and under
itself. In this paper, we propose a method to fold knots in midair using a team
of aerial vehicles. We take advantage of the fact that vehicles are able to fly
in between cable segments without any re-grasping. So the team grasps the cable
from the floor, and releases it once the knot is folded. Based on a composition
of catenary curves, we simplify the complexity of dealing with an
infinite-dimensional configuration space of the cable, and formally propose a
new knot representation. Such representation allows us to design a trajectory
that can be used to fold knots using a leader-follower approach. We show that
our method works for different types of knots in simulations. Additionally, we
show that our solution is also computationally efficient and can be executed in
real-time.
