Controlling Soft Robots via Adiabatic Spectral Submanifolds
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Soft robots offer flexibility and dexterity enabling their use in surgery or space exploration, where navigating delicate environments safely are routine. However, these same design features pose challenges for real-time model-based control. Specifically, modeling based on physical assumptions such as constant curvature or strain and linearity assumptions on the dynamics have struggled to control soft robots along complex spatially extended tracks that explore regions with significant nonlinear behavior. To address this, we develop a nonlinear model predictive control strategy based on recent theory of adiabatic spectral submanifolds (aSSMs). The applicability of this theory relies on a time-scale separation between the fast internal vibrations of the soft robot and the desired speed along its intended path. When this separation exists, low-dimensional attracting invariant manifolds (aSSMs) emanate from the path and capture the dominant dynamics of the robot. We identify five- or six-dimensional aSSMs for benchmark soft trunk simulators and a physical helicoid trunk-shaped soft robot purely from data. Notably, we demonstrate aSSM-reduced models outperform other data-driven modeling methods in closed-loop performance across a diverse set of target tracks.
