通过约束鞍点搜索，发现新型奇异可变形杆框架结构。
A Constrained Saddle Search Approach for Constructing Singular and Flexible Bar Frameworks
- 将杆框架奇异点建模为约束流形上的鞍点
- 找到多个此前未知的奇异可变形结构实例
- 适用于机器人运动学奇异分析与设计
奇异性分析在机器人运动学中至关重要，因奇异构型会导致控制失效和运动不确定性。本文将杆框架的奇异性建模为约束流形上的鞍点。给定一个欠约束且非奇异的杆框架，允许其中一个杆件长度变化而固定其余杆长，将自由杆的平方长度定义为能量泛函，证明其局部鞍点对应奇异且可变形的框架。通过所提出的约束鞍点搜索方法，识别出此前未知的奇异可变形杆框架，为奇异机器人设计与分析提供了新见解。
原文摘要 · Abstract (English)
Singularity analysis is essential in robot kinematics, as singular configurations cause loss of control and kinematic indeterminacy. This paper models singularities in bar frameworks as saddle points on constrained manifolds. Given an under-constrained, non-singular bar framework, by allowing one edge to vary its length while fixing lengths of others, we define the squared length of the free edge as an energy functional and show that its local saddle points correspond to singular and flexible frameworks. Using our constrained saddle search approach, we identify previously unknown singular and flexible bar frameworks, providing new insights into singular robotics design and analysis.
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