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

Autonomous wire-harness assembly requires precise, reliable manipulation of branched cables, whose deformation is difficult to predict. Models for single Deformable Linear Objects (DLOs) do not extend directly to Branched DLOs (BDLOs), whose junctions couple bending, twisting, and stretching across branches. We introduce Differentiable discrete branched Elastic rods for modeling Furcated DLOs in real-Time (DEFT), a framework combining differentiable physics and learning for accurate BDLO dynamics, real-time inference, and dexterous manipulation planning. DEFT introduces momentum-conserving junction constraints to capture cross-branch coupling, supports mid-structure grasping, uses analytical gradients and branch-parallel computation for efficient parameter learning and inference, and incorporates a residual Graph Neural Network (GNN) to reduce long-horizon prediction errors. Experiments on six physical BDLOs with different topologies and materials demonstrate formulation-level generalization: the same formulation and residual-GNN architecture apply without redesign, with physical and learned parameters fitted separately for each BDLO. DEFT outperforms state-of-the-art physics-based and learning-based methods, achieving RMSEs of 0.93-2.14 cm over five-second recursive open-loop predictions and inference above 100 Hz. In real-world planning, DEFT achieves success rates of 36/40 for shape matching, 40/40 for parent-branch insertion, and 16/20 for child-branch insertion. These results demonstrate accurate, efficient, planning-compatible BDLO prediction for autonomous wire-harness manipulation. Project website: https://roahmlab.github.io/DEFT/.