DEFT: Differentiable Branched Discrete Elastic Rods for Modeling Furcated DLOs in Real-Time

TL;DR

This work tackles real-time planning for manipulating Branched Deformable Linear Objects (BDLOs) by introducing DEFT, a differentiable BDLO simulator that blends physics-based BDLO modeling with residual learning. DEFT partitions BDLOs into a parent and multiple branches, computes dynamics in parallel, and corrects integration errors through momentum-preserving constraints and a graph neural network for residuals, enabling accurate long-horizon predictions. The approach achieves higher accuracy, real-time inference (>100 Hz), and improved planning performance on 3-D shape matching and thread-insertion tasks, outperforming state-of-the-art baselines and ablations. The framework holds practical impact for autonomous BDLO manipulation in manufacturing, with demonstrated integration into planning/control pipelines like ARMOUR for real-world wire-harness assembly tasks.

Abstract

Autonomous wire harness assembly requires robots to manipulate complex branched cables with high precision and reliability. A key challenge in automating this process is predicting how these flexible and branched structures behave under manipulation. Without accurate predictions, it is difficult for robots to reliably plan or execute assembly operations. While existing research has made progress in modeling single-threaded Deformable Linear Objects (DLOs), extending these approaches to Branched Deformable Linear Objects (BDLOs) presents fundamental challenges. The junction points in BDLOs create complex force interactions and strain propagation patterns that cannot be adequately captured by simply connecting multiple single-DLO models. To address these challenges, this paper presents Differentiable discrete branched Elastic rods for modeling Furcated DLOs in real-Time (DEFT), a novel framework that combines a differentiable physics-based model with a learning framework to: 1) accurately model BDLO dynamics, including dynamic propagation at junction points and grasping in the middle of a BDLO, 2) achieve efficient computation for real-time inference, and 3) enable planning to demonstrate dexterous BDLO manipulation. A comprehensive series of real-world experiments demonstrates DEFT's efficacy in terms of accuracy, computational speed, and generalizability compared to state-of-the-art alternatives. Project page:https://roahmlab.github.io/DEFT/.

Figures (13)

• Figure 1: As this paper illustrates, DEFT can be used in concert with a motion planning algorithm to autonomously manipulate BDLOs. The figures above illustrate how DEFT can be used to autonomously complete a wire insertion task. Left: The system first plans a shape-matching motion, transitioning the BDLO from its initial configuration to the target shape (contoured with yellow), which serves as an intermediate waypoint. Right: Starting from the intermediate configuration, the system performs thread insertion, guiding the BDLO into the target hole while also matching the target shape. Notably, DEFT predicts the state of the wire recursively without relying on ground truth or perception data at any point in the process.
• Figure 2: Left: An example configuration of BDLO manipulation, relevant notation and structure at a junction. Right: The adjacency matrix $\mathbf{A}$ for the junction in left captures both self-loops (diagonal entries) and inter-node connections (off-diagonal entries). By embedding each node’s local dynamics alongside its coupling to neighboring nodes, $\mathbf{A}$ enables an graph representation of the BDLO’s behavior.
• Figure 3: Visualization of predicted trajectories for BDLO 1 under scenarios where one robot grasps an end and the other grasps the midpoint, comparing DEFT, a DEFT ablation without enforcing junction near-rigidity (§\ref{['section:constratins']}), and Tree-LSTM. Ground-truth vertex positions transition from blue (initial) to pink (final) via gradients indicating intermediate positions. Predictions similarly use gradients from dark to light. Ground truth is provided only at $t=0$ s, with recursive predictions performed until $t=8$ s without additional perception inputs.
• Figure 4: Visualization of planning for BDLO 1 for thread insertion, using DEFT, DEFT ablation without enforcing junction near-rigidity (§\ref{['section:constratins']}), and Tree-LSTM. The BDLO’s goal configuration is highlighted in yellow, while the target hole is shown in red. The DEFT model enables the planning algorithm to successfully complete the task, whereas the ablation approach of DEFT and the Tree-LSTM model both fail to finish tasks.
• Figure 5: An illustration of DER coordinate frames.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2
• Theorem 3: Computing the Corrections to Enforce Inextensibility
• Theorem 4
• Theorem 5