Robust Predictive Control for Soft Robots via Physics-Data Fused Spectral Submanifold Reduction With EKF

Abstract

Soft robots pose significant challenges for model-based control due to their inherent high dimensionality and nonlinearity. To tackle these challenges, this letter develops a robust model predictive control (MPC) framework for soft robots, referred to as SSMR-PF-EKF, by adopting physics-data fused spectral submanifold reduction together with an extended Kalman filter. Specifically, a SSMR-PF modeling method is proposed, which embeds physical priors into spectral submanifold reduced-order models by constructing a physics-data fused control matrix. A tailored sim-to-real transfer strategy is developed to match this method: autonomous dynamics are learned from simulation-derived full-state decay trajectories, whereas real-robot input-output data are leveraged to fit a data-driven correction term upon a physics-based control matrix for compensating unmodeled dynamics. Using this refined low-order SSMR-PF model, an integrated EKF-MPC closed-loop control architecture is formulated to suppress measurement noise and achieve high-precision trajectory tracking. Rigorous local practical stability analysis is conducted for the closed-loop system. Experiments on a pneumatic soft robotic manipulator (PSRM) validate the SSMR-PF-EKF framework and demonstrate its improved tracking accuracy and noise robustness against baseline controllers.