Title: Elastohydrodynamic instabilities of a soft robotic arm in a viscous fluid Show Chinese title

Title: 软体机械臂在粘性流体中的弹性水动力不稳定性

Abstract: The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here we show that this interplay leads to novel elastohydrodynamic instabilities in a clamped soft robotic arm driven terminally by a constant pressure in a viscous fluid. We model the arm as a Cosserat rod that can stretch, shear and bend. We obtain invariant, geometrically exact, non-linear equations of motion by using Cartan's method of moving frames. Stability to small perturbations of a straight rod is governed by a non-Hermitian linear operator. Eigenanalysis shows that stability is lost through a Hopf bifurcation with the increase of pressure above a first threshold. A surprising return to stability is obtained with further increase of pressure beyond a second threshold. Numerical solutions of the non-linear equations, using a geometrically exact spectral method, confirms stable limit-cycle oscillations between these two pressure thresholds. An asymptotic analysis in the beam limit rationalizes these results analytically. This counterintuitive sequence of bifurcations underscores the subtle nature of the elastohydrodynamic coupling in Cosserat rods and emphasizes their importance for the control of the viscous dynamics of soft robots. Show Chinese abstract

Abstract: 软体机器人在流体环境中操作的设计和控制需要仔细理解大弹性体变形与水动力之间的相互作用。 在这里，我们展示了这种相互作用导致了一种夹紧的软体机械臂中新型的弹性水动力不稳定性，该机械臂由粘性流体中的恒定压力驱动。 我们将手臂建模为一个可以拉伸、剪切和弯曲的柯西杆。 我们通过使用卡丹的移动框架方法，获得了不变的、几何精确的非线性运动方程。 直杆对小扰动的稳定性由一个非厄米特线性算子控制。 特征分析表明，当压力超过第一个阈值时，稳定性通过霍普夫分支而丧失。 在第二个阈值之后进一步增加压力，意外地恢复了稳定性。 使用几何精确谱方法求解非线性方程的数值解，证实了这两个压力阈值之间的稳定极限环振荡。 在梁极限下的渐近分析从理论上解释了这些结果。 这种反直觉的分叉序列突显了柯西杆中弹性水动力耦合的微妙性，并强调了它们在软体机器人粘性动力学控制中的重要性。