Soft robots are commonly sought for safety-critical interactions in delicate environments, where accurate position and orientation control is imperative. Model predictive control (MPC) offers a solution, but it requires a model of the robot's infinite-dimensional nonlinear dynamics that is at once accurate and computationally cheap. Recent theory on adiabatic spectral submanifolds (aSSMs) and their applications to soft robots provide data-driven model-reduction methods to construct such models. Here, we extend these methods to identify aSSMs from enlarged observable datasets and upgrade the currently available aSSM-MPC schemes. Evaluated on a high-fidelity finite-element simulation of a pressure-actuated soft arm, our controller reduces position and orientation tracking error by more than 60% compared to existing data-driven baselines.

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