The mechanical complexity of soft robots creates significant challenges for their model-based control. Specifically, linear data-driven models have struggled to control soft robots on complex, spatially extended paths that explore regions with significant nonlinear behavior. To account for these nonlinearities, we develop here a model-predictive control strategy based on the recent theory of adiabatic spectral submanifolds (aSSMs). This theory is applicable because the internal vibrations of heavily overdamped robots decay at a speed that is much faster than the desired speed of the robot along its intended path. In that case, low-dimensional attracting invariant manifolds (aSSMs) emanate from the path and carry the dominant dynamics of the robot. Aided by this recent theory, we devise an aSSM-based model-predictive control scheme purely from data. We demonstrate our data-driven model's effectiveness in tracking dynamic trajectories across diverse tasks, validated on a high-fidelity, high-dimensional finite-element model of a soft trunk robot and a Cosserat rod-based elastic soft arm. Notably, we find that five- or six-dimensional aSSM-reduced models outperform the tracking performance of other data-driven modeling methods by a factor up to $10$ across all closed-loop control tasks.

翻译：软体机器人的机械复杂性为其基于模型的控制带来了重大挑战。具体而言，线性数据驱动模型难以控制软体机器人在复杂、空间扩展的路径上运动，这些路径会探索具有显著非线性行为的区域。为了考虑这些非线性因素，我们在此基于最近的绝热谱子流形理论，开发了一种模型预测控制策略。该理论之所以适用，是因为高度过阻尼机器人的内部振动衰减速度远快于机器人沿预期路径的期望运动速度。在这种情况下，低维吸引不变流形从路径中产生，并承载了机器人的主导动力学。借助这一最新理论，我们设计了一种纯粹基于数据的aSSM模型预测控制方案。我们在一个高保真、高维度的软体躯干机器人有限元模型和一个基于Cosserat杆的弹性软体臂上验证了我们的数据驱动模型在跟踪动态轨迹方面的有效性，涵盖了多种任务。值得注意的是，我们发现，在所有闭环控制任务中，五维或六维的aSSM降阶模型的跟踪性能比其他数据驱动建模方法高出多达$10$倍。