  This paper addresses the task of modeling Deformable Linear Objects (DLOs),
such as ropes and cables, during dynamic motion over long time horizons. This
task presents significant challenges due to the complex dynamics of DLOs. To
address these challenges, this paper proposes differentiable Discrete Elastic
Rods For deformable linear Objects with Real-time Modeling (DEFORM), a novel
framework that combines a differentiable physics-based model with a learning
framework to model DLOs accurately and in real-time. The performance of DEFORM
is evaluated in an experimental setup involving two industrial robots and a
variety of sensors. A comprehensive series of experiments demonstrate the
efficacy of DEFORM in terms of accuracy, computational speed, and
generalizability when compared to state-of-the-art alternatives. To further
demonstrate the utility of DEFORM, this paper integrates it into a perception
pipeline and illustrates its superior performance when compared to the
state-of-the-art methods while tracking a DLO even in the presence of
occlusions. Finally, this paper illustrates the superior performance of DEFORM
when compared to state-of-the-art methods when it is applied to perform
autonomous planning and control of DLOs. Project page:
https://roahmlab.github.io/DEFORM/.
