The characteristic ``in-plane" bending associated with soft robots' deformation make them preferred over rigid robots in sophisticated manipulation and movement tasks. Executing such motion strategies to precision in soft deformable robots and structures is however fraught with modeling and control challenges given their infinite degrees-of-freedom. Imposing \textit{piecewise constant strains} (PCS) across (discretized) Cosserat microsolids on the continuum material however, their dynamics become amenable to tractable mathematical analysis. While this PCS model handles the characteristic difficult-to-model ``in-plane" bending well, its Lagrangian properties are not exploited for control in literature neither is there a rigorous study on the dynamic performance of multisection deformable materials for ``in-plane" bending that guarantees steady-state convergence. In this sentiment, we first establish the PCS model's structural Lagrangian properties. Second, we exploit these for control on various strain goal states. Third, we benchmark our hypotheses against an Octopus-inspired robot arm under different constant tip loads. These induce non-constant ``in-plane" deformation and we regulate strain states throughout the continuum in these configurations. Our numerical results establish convergence to desired equilibrium throughout the continuum in all of our tests. Within the bounds here set, we conjecture that our methods can find wide adoption in the control of cable- and fluid-driven multisection soft robotic arms; and may be extensible to the (learning-based) control of deformable agents employed in simulated, mixed, or augmented reality.

翻译：软体机器人变形过程中特有的“平面内”弯曲特性，使其在执行复杂操作与运动任务时相较于刚性机器人更具优势。然而，这类软体可变形机器人与结构由于具有无限自由度，其高精度运动策略的执行面临建模与控制的巨大挑战。通过将连续材料离散化为服从\textit{分段常应变}（PCS）的Cosserat微元体，其动力学特性可转化为易于处理的数学分析框架。尽管PCS模型能够有效处理传统难以建模的“平面内”弯曲特性，但现有文献尚未利用其拉格朗日性质进行控制设计，也未对多段可变形材料在“平面内”弯曲中保证稳态收敛的动态性能开展严格研究。基于此，我们首先建立了PCS模型的结构化拉格朗日特性；其次，利用这些特性针对多种应变目标状态设计控制策略；最后，以章鱼仿生机械臂为实验对象，在不同恒定末端载荷条件下验证了所提假设。这些载荷会诱发非恒定“平面内”变形，我们在该构型下对连续体各应变状态进行调控。数值结果表明，在所有测试中连续体均收敛至期望平衡态。基于本文设定的边界条件，我们推测该方法可广泛应用于缆索驱动与流体驱动的多段软体机械臂控制，并可扩展至模拟现实、混合现实或增强现实中可变形体代理的（基于学习的）控制。