  In the realm of robotic cloth manipulation, accurately estimating the cloth
state during or post-execution is imperative. However, the inherent
complexities in a cloth's dynamic behavior and its near-infinite degrees of
freedom (DoF) pose significant challenges. Traditional methods have been
restricted to using keypoints or boundaries as cues for cloth state, which do
not holistically capture the cloth's structure, especially during intricate
tasks like folding. Additionally, the critical influence of cloth physics has
often been overlooked in past research. Addressing these concerns, we introduce
DiffCP, a novel differentiable pipeline that leverages the Anisotropic
Elasto-Plastic (A-EP) constitutive model, tailored for differentiable
computation and robotic tasks. DiffCP adopts a ``real-to-sim-to-real''
methodology. By observing real-world cloth states through an RGB-D camera and
projecting this data into a differentiable simulator, the system identifies
physics parameters by minimizing the geometric variance between observed and
target states. Extensive experiments demonstrate DiffCP's ability and stability
to determine physics parameters under varying manipulations, grasping points,
and speeds. Additionally, its applications extend to cloth material
identification, manipulation trajectory generation, and more notably, enhancing
cloth pose estimation accuracy. More experiments and videos can be found in the
supplementary materials and on the website:
https://sites.google.com/view/diffcp.
