  Untangling ropes, wires, and cables is a challenging task for robots due to
the high-dimensional configuration space, visual homogeneity, self-occlusions,
and complex dynamics. We consider dense (tight) knots that lack space between
self-intersections and present an iterative approach that uses learned
geometric structure in configurations. We instantiate this into an algorithm,
HULK: Hierarchical Untangling from Learned Keypoints, which combines
learning-based perception with a geometric planner into a policy that guides a
bilateral robot to untangle knots. To evaluate the policy, we perform
experiments both in a novel simulation environment modelling cables with varied
knot types and textures and in a physical system using the da Vinci surgical
robot. We find that HULK is able to untangle cables with dense figure-eight and
overhand knots and generalize to varied textures and appearances. We compare
two variants of HULK to three baselines and observe that HULK achieves 43.3%
higher success rates on a physical system compared to the next best baseline.
HULK successfully untangles a cable from a dense initial configuration
containing up to two overhand and figure-eight knots in 97.9% of 378 simulation
experiments with an average of 12.1 actions per trial. In physical experiments,
HULK achieves 61.7% untangling success, averaging 8.48 actions per trial.
Supplementary material, code, and videos can be found at
https://tinyurl.com/y3a88ycu.
