Neural Linear Oscillator Networks and their Application to Soft Robots Model Learning and Control

Recent advances in machine learning have begun to embed oscillatory network principles within neural architectures, aiming to enhance computational efficiency and robustness in time-series regression. Building on these developments, we take a step toward applying such principles to the learning of physical dynamics. We introduce Neural Linear Oscillator Networks (nLON): a vision-based framework that extracts compact latent representations of complex motion directly from image sequences. A convolutional autoencoder encodes position and velocity into a low-dimensional manifold, whose temporal evolution is governed by coupled linear mechanical oscillators driven by a linear combination of the inputs. This strong structural prior not only promotes sample efficiency and interpretability but also guarantees that the learned model remains a mechanical, Wiener-type system. From this formulation, we derive closed-loop controllers that ensure stable regulation. We focus on soft robots-systems whose nonlinear, continuous, and high-dimensional dynamics make them both a challenging and ideal testbed for our approach. Using tentacle robots in high-fidelity simulations and real-world experiments, we validate that our framework delivers accurate long-horizon predictions and consistently surpasses state-of-the-art baselines, achieving superior structural fidelity and final-step accuracy. Finally, we leverage the learned dynamics for model-based control, demonstrating in simulation that the resulting scheme achieves robust and reliable tracking.