Learning deformable linear object dynamics from a single trajectory

TL;DR

This work tackles the challenge of modeling deformable linear object dynamics for model-based control under limited data. It introduces Neural PRBA (NPRBA), a physics-informed neural ODE that represents a DLO as a chain of pseudo-rigid bodies and learns nonlinear interaction torques via neural networks, while leveraging forward kinematics as a decoder. Trained on a single ~30-second trajectory, NPRBA achieves accurate end-effector predictions for both an aluminum rod and a foam cylinder and generalizes to longer horizons, outperforming traditional PRBA and black-box baselines in the small-data regime. The approach enables efficient, real-time DLO manipulation and highlights the importance of nonlinear interaction torques and discretization optimization for capturing both elastic and plastic deformations.

Abstract

The manipulation of deformable linear objects (DLOs) via model-based control requires an accurate and computationally efficient dynamics model. Yet, data-driven DLO dynamics models require large training data sets while their predictions often do not generalize, whereas physics-based models rely on good approximations of physical phenomena and often lack accuracy. To address these challenges, we propose a physics-informed neural ODE capable of predicting agile movements with significantly less data and hyper-parameter tuning. In particular, we model DLOs as serial chains of rigid bodies interconnected by passive elastic joints in which interaction forces are predicted by neural networks. The proposed model accurately predicts the motion of an robotically-actuated aluminium rod and an elastic foam cylinder after being trained on only thirty seconds of data. The project code and data are available at: \url{https://tinyurl.com/neuralprba}

Figures (11)

• Figure 1: Overview on the proposed physics-informed neural ODE for modeling DLO dynamics. We discretize a DLO as a chain of pseudo-rigid bodies whose hybrid dynamics are derived via the articulated body algorithm. The interaction forces acting between the pseudo-bodies are learned by neural networks.
• Figure 1: The one-second-ahead prediction accuracy on the test data for the the different DLO dynamics models.
• Figure 2: The notation used throughout the paper. $\{\mathrm{B}\}$ is the inertial frame attached to the base of Panda, $\{\mathrm{b}\}$ and $\{\mathrm{e}\}$ are frames attached to the start and end of a DLO, respectively.
• Figure 3: The DLO end positions along the $Z-$axis at rest for different trajectories with the order of recording $n_{\text{traj}}$. During the last trajectories, the metal rod got permanently deformed.
• Figure 4: Left: Prediction error over varying prediction horizons. Center: Computation times of the continuous-time models for decoder evaluation $t_h$ (common for all models), continuous-time dynamics evaluation $t_f$, and the one-step integration $t_F$. Right: Influence of discretization (number of pseudo-rigid bodies) on NPRBA's RMSE between measured and predicted DLO's end state.