It is challenging to perform identification on soft robots due to their underactuated, high dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory), that can be applied to systems with low-bandwidth actuation of the shape space. By exploiting temporal asymmetries in actuator dynamics, our approach enables the design of robots that can be driven by a single control input. We present a method for constructing a series connected model comprising actuator and locomotor dynamics based on data points from stochastically perturbed, repeated behaviors around the observed limit cycle. We demonstrate our methods on a real-world example of a soft crawler made by stimuli-responsive hydrogels that locomotes on merely one cycling control signal by utilizing its geometric and temporal asymmetry. For systems with first-order, low-pass actuator dynamics, such as swelling-driven actuators used in hydrogel crawlers, we show that first order Taylor approximations can well capture the dynamics of the system shape as well as its movements. Finally, we propose an approach of numerically optimizing control signals by iteratively refining models and optimizing the input waveform.

翻译：对软体机器人进行辨识具有挑战性，因为其欠驱动、高维度的动力学特性。在本工作中，我们提出了一种基于几何力学（也称为规范场论）的数据驱动建模框架，适用于形状空间具有低带宽驱动的系统。通过利用执行器动力学中的时间不对称性，我们的方法使得设计可由单一控制输入驱动的机器人成为可能。我们提出了一种方法，基于随机扰动下重复行为（围绕观测到的极限环）的数据点，构建由执行器动力学与游走动力学组成的串联连接模型。我们通过真实世界的软体爬行器实例验证了该方法，该爬行器由刺激响应型水凝胶制成，仅通过利用其几何与时间不对称性的循环控制信号即可实现运动。对于具有一阶低通执行器动力学的系统（如用于水凝胶爬行器的溶胀驱动执行器），我们证明一阶泰勒近似能够很好地捕捉系统形状及其运动的动力学特性。最后，我们提出了一种通过迭代优化模型和输入波形来数值优化控制信号的方法。