Nonlinear spectral modeling and control of soft-robotic muscles from data.

Artificial muscles are essential for compliant musculoskeletal robotics but complicate control due to nonlinear multiphysics dynamics. Electrohydraulic actuators, a class of soft artificial muscles, offer high performance but exhibit memory effects and hysteresis. Here we present a data-driven reduction and control strategy grounded in spectral submanifold theory. In the adiabatic regime, where inputs vary slowly relative to intrinsic transients, trajectories rapidly converge to a low-dimensional slow manifold. We learn an explicit input-to-output map on this manifold directly from forced-response trajectories, eliminating the need for decay experiments generated by large step inputs, which can induce pronounced hysteretic behavior and are often unrepresentative of normal operating conditions. We deploy the spectral-submanifold-based model for real-time control of an antagonistic electrohydraulic-clutch joint. This approach yields a substantial reduction in tracking error compared to feedback-only and feedforward-only baselines under identical settings. This record-and-control workflow enables rapid characterization and high-performance control of soft muscles and muscle-driven joints without detailed physics-based modeling.