为软磁机器人壳体设计了一种精确的静态建模方法，可高效模拟大变形和旋转。
Geometrically Exact Hard Magneto-Elastic Cosserat Shells: Static Formulation for Shape Morphing
- 基于SE(3)李群构造无坐标几何模型，捕捉磁性粒子分布的六自由度行为
- 推导出强弱形式平衡方程，线性化后用于有限元计算，避免奇点与锁死问题
- 在严重旋转与位移下验证效果优越，适合磁驱动软体抓手和行走机器人
Cosserat杆理论是多数应用中建模磁性软体机器人（如生物医学领域）的主流1维细长结构方法。然而，近年来用于运动与操作的软体机器人常具有较大的宽长比，应归类为二维壳体。为分析与形状重构控制目的，本文提出一种适用于硬磁壳体（如软磁夹持器和行走机器人）的高效无坐标静态模型。该方法基于在特殊欧几里得群$ℝ(3)$上的新型Cosserat壳理论表述。壳体被视为材料点的二维流形，每个点具有六个自由度（位置与旋转），适用于描述均匀分布的球状硬磁颗粒嵌入在粘弹性聚合物中的行为。壳体构型流形为所有光滑映射$ℝ^2\rightarrowℝ(3)$的集合。根据基于$ℝ(3)$李群结构的新定义的局部变形梯度，我们推导了平衡方程的强形式与弱形式，遵循虚功原理。进一步提取弱形式的线性化版本以供数值实现。所提出的有限元方法可规避传统壳体建模中常见的奇点与锁死现象。通过一系列测试案例进行解析与实验验证，结果表明该模型在壳体经历强烈旋转与位移时表现优异。
原文摘要 · Abstract (English)
Cosserat rod theory is the popular approach to modeling ferromagnetic soft robots as 1-Dimensional (1D) slender structures in most applications, such as biomedical. However, recent soft robots designed for locomotion and manipulation often exhibit a large width-to-length ratio that categorizes them as 2D shells. For analysis and shape-morphing control purposes, we develop an efficient coordinate-free static model of hard-magnetic shells found in soft magnetic grippers and walking soft robots. The approach is based on a novel formulation of Cosserat shell theory on the Special Euclidean group ($\mathbf{SE}(3)$). The shell is assumed to be a 2D manifold of material points with six degrees of freedom (position & rotation) suitable for capturing the behavior of a uniformly distributed array of spheroidal hard magnetic particles embedded in the rheological elastomer. The shell's configuration manifold is the space of all smooth embeddings $\mathbb{R}^2\rightarrow\mathbf{SE}(3)$. According to a novel definition of local deformation gradient based on the Lie group structure of $\mathbf{SE}(3)$, we derive the strong and weak forms of equilibrium equations, following the principle of virtual work. We extract the linearized version of the weak form for numerical implementations. The resulting finite element approach can avoid well-known challenges such as singularity and locking phenomenon in modeling shell structures. The proposed model is analytically and experimentally validated through a series of test cases that demonstrate its superior efficacy, particularly when the shell undergoes severe rotations and displacements.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。