Physics-Informed Neural Networks for Estimating the Cable Dynamics via Cartesian Measurements

Aerial robots equipped with cables used as soft endeffectors represent a new, versatile robotic paradigm to solve multiple tasks. However, to fully exploit the versatility of soft robots, the modeling problem must be addressed. The main challenges depend on the hard-to-model continuum dynamics. To solve this challenge, this work proposes multiple physics-informed neural network architectures to model a cable's dynamics using Cartesian measurements. We apply a classic Lagrangian Neural Network architecture and propose a new Lagrangian-informed Transformer-based architecture, and establish local contraction bounds for their training dynamics. underactuation of the system, highlight its mechanical nature, and return the cable positions, velocities, and accelerations in Cartesian space, enforcing energy conservation by exploiting the Lagrangian structure. Finally, we test the modeling performance via experiments with varying trajectories and models, comparing the proposed architectures with state-of-the-art networks and reduced-order model baselines.