标题： 多磁铁嵌入式软连续机器人的统一建模与结构优化以增强运动学性能 显示英文标题

标题： Unified Modeling and Structural Optimization of Multi-magnet Embedded Soft Continuum Robots for Enhanced Kinematic Performances

摘要： 本文提出了一种统一的建模和优化框架，以提高多磁体嵌入软连续机器人（MeSCRs）的运动性能。为此，我们建立了一个基于扩展伪刚体模型的可微系统公式。该公式能够分析在磁驱动下的平衡适定性和所诱导配置的几何特性。特别是，我们证明了MeSCR的最大可控自由度等于嵌入磁体数量的两倍。随后，我们开发了一个基于微分几何的结构优化框架，将经典的运动学度量（例如操作性和灵活性）与嵌入磁体的配置联系起来。所得的优化条件表明，提高局部性能需要结构性地调节配置空间度量的谱以抵消其畸变。在代表性条件下推导了最优磁体配置的显式解，并提出了一种基于梯度的数值方法用于一般设计场景。仿真研究验证了所提出框架的有效性。 显示英文摘要

摘要： This paper presents a unified modeling and optimization framework to enhance the kinematic performance of multi-magnet embedded soft continuum robots (MeSCRs). To this end, we establish a differentiable system formulation based on an extended pseudo-rigid-body model. This formulation enables analysis of the equilibrium well-posedness and the geometry of the induced configuration under magnetic actuation. In particular, we show that the maximum controllable degrees of freedom of a MeSCR equal twice the number of embedded magnets. We subsequently develop a structural optimization framework based on differential geometry that links classical kinematic measures (e.g., manipulability and dexterity) to the configuration of embedded magnets. The resulting optimization condition reveals that improving local performance requires structurally modulating the spectrum of the configuration space metric to counteract its distortion. Closed-form solutions for optimal magnet configurations are derived under representative conditions, and a gradient-based numerical method is proposed for general design scenarios. Simulation studies validate the effectiveness of the proposed framework.