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 the effectiveness of our data-driven model in tracking dynamic trajectories across diverse tasks. We validate on high-fidelity, high-dimensional finite-element models of a soft trunk robot and Cosserat-rod-based elastic soft arms, with additional experiments confirming robust performance even in the presence of experimental noise. 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沿探索显著非线性行为区域的复杂空间扩展路径运动。为解决这些非线性问题，本文基于最新发展的绝热谱子流形理论，提出了一种模型预测控制策略。该理论的适用性源于：强过阻尼机器人的内部振动衰减速度远快于其沿预期路径运动的期望速度。在此条件下，从路径衍生出的低维吸引不变流形承载了机器人的主导动力学特性。借助这一前沿理论，我们仅基于数据设计了一种基于绝热谱子流形的模型预测控制方案。通过追踪不同任务的动力学轨迹，验证了数据驱动模型的有效性。我们在高保真高维有限元软体躯干机器人模型和基于Cosserat杆的弹性软臂模型上进行了验证，额外实验表明即使在存在实验噪声的情况下仍具有鲁棒性能。值得注意的是，五维或六维绝热谱子流形降阶模型在所有闭环控制任务中的轨迹追踪性能较其他数据驱动建模方法提升达10倍。