  Robot manipulation of rope-like objects is an interesting problem that has
some critical applications, such as autonomous robotic suturing. Solving for
and controlling rope is difficult due to the complexity of rope physics and the
challenge of building fast and accurate models of deformable materials. While
more data-driven approaches have become more popular for finding controllers
that learn to do a single task, there is still a strong motivation for a
model-based method that could be used to solve a large variety of optimization
problems. Towards this end, we introduced compliant, position-based dynamics
(XPBD) to model rope-like objects. Using geometric constraints, the model can
represent the coupling of shear/stretch and bend/twist effects. Of crucial
importance is that our formulation is differentiable, which can solve parameter
estimation problems and improve the matching of rope physics to real-life
scenarios (i.e., the real-to-sim problem). For the generality of rope-like
objects, two different solvers are proposed to handle the inextensible and
extensible effects of varied material stiffness for the rope. We demonstrate
our framework's robustness and accuracy on real-to-sim experimental setups
using the Baxter robot and the da Vinci research kit (DVRK). Our work leads to
a new path for robotic manipulation of the deformable rope-like object taking
advantage of the ready-to-use gradients.
