Differentiable Discrete Elastic Rods for Real-Time Modeling of Deformable Linear Objects

TL;DR

The paper tackles the challenge of real-time, long-horizon modeling of deformable linear objects (DLOs) during dynamic robotic manipulation. It presents DEFORM, a framework that fuses a differentiable Discrete Elastic Rod (DDER) model with residual learning and a momentum-preserving inextensibility enforcement to achieve accurate, stable predictions over extended time horizons. The key contributions include the differentiable reformulation of DER (DDER), a residual integration scheme grounded in physics, and a PBD-based, momentum-conserving inextensibility mechanism, validated against multiple baselines and demonstrated in perception and planning tasks. The work enables robust tracking under occlusion and improves 3D shape-matching manipulation, offering practical impact for real-time control and perception in cable/wire manipulation tasks.

Abstract

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/.

Figures (10)

• Figure 1: This paper introduces DEFORM, a novel framework that combines a differentiable physics-based model with a learning framework to model and predict dynamic DLO behavior accurately in real-time. The figure shows DEFORM's predicted states (yellow) and the actual states (red) for a DLO over 4.5 seconds at 100 Hz. Note that the prediction is performed recursively, without requiring access to ground truth or perception during the process. A video of related experiments can be found in the supplementary material.
• Figure 2: Overview of DEFORM contributions (green). a) DER models discretize DLOs into vertices, segment them into elastic rods, and model their dynamic propagation. DEFORM reformulates DER into Differentiable DER (DDER) which describes how to compute gradients from the prediction loss, enabling efficient system identification and incorporation into deep learning pipelines. b) To compensate for the error from DER's numerical integration, DEFORM introduces residual learning via DNNs. c) $1 \rightarrow 2$: DER enforces inextensibility, but this does not satisfy classical conservation principles. $1 \rightarrow 3$: DEFORM enforces inextensibility with momentum conservation, which allows dynamic modeling while maintaining simulation stability.
• Figure 3: Visualization of the performance of DEFORM and Bi-LSTM in predicting trajectories for DLOs 1 and 2. The ground truth vertices of the DLOs are marked with red hollow circles. The predicted vertices are marked with orange solid circles for DEFORM and blue solid circles for the Bi-LSTM model, respectively.
• Figure 4: The average L1 loss (m) while performing state estimation.
• Figure 5: A time lapse comparison of the DEFORM model and the Bi-LSTM model when each is used to perform a shape matching task. The goal configuration is green whereas the start configuration is pink. The DEFORM model enables the planning algorithm to successfully complete the task whereas the planning algorithm using the Bi-LSTM model fails to complete the task.