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XPBD算法的Cosserat杆约束函数设计与分组求解方法

DESIGN OF COSSERAT ROD CONSTRAINT FUNCTIONS AND GROUP SOLVING TECHNIQUES FOR XPBD ALGORITHM

  • 摘要: 柔性绳索结构因质量轻、高柔性和可设计性强等特点, 在航空航天及机器人等工程领域得到广泛应用. 由于几何大变形与材料非线性等因素影响, 利用非线性有限元等高精度方法分析这类柔性结构的动力学特性时, 存在模型复杂、计算量大和难以高效仿真等问题. 文章改进了起源于计算机图形学的XPBD (extended position based dynamics)算法, 设计了新的约束函数与迭代方法, 使其适用于柔性绳索结构的动力学仿真. 主要贡献包括: 引入旋转向量以更准确描述结构姿态, 基于Cosserat弹性杆理论设计了更精确的约束函数, 采用约束能量作为迭代收敛判据以提高仿真精度, 提出分组求解约束的方法提高迭代计算效率. 还以索-杆复合结构为例验证了改进算法的有效性: 与ADAMS软件相比, 改进算法具有更好的稳定性, 且计算效率大致相当; 与原XPBD算法相比, 改进算法显著提高了求解精度. 改进算法引入了旋转向量, 使约束函数的设计更灵活, 计算框架也更利于并行化, 具有在复杂柔性结构动力学仿真中进一步应用的优势和潜力.

     

    Abstract: Flexible cable structures are extensively utilized in engineering domains such as aerospace and robotics owing to their lightweight nature, high flexibility, and design versatility. Nevertheless, due to geometrically large deformations and material nonlinearity, traditional high-precision approaches (e.g., the nonlinear finite element method) encounter challenges in analyzing the dynamic characteristics of such flexible cable structures. These challenges encompass model complexity, high computational cost, and difficulties in achieving high-speed simulation. To tackle these issues, this paper enhances the extended position based dynamics (XPBD) algorithm, which has its origin in computer graphics. This is accomplished by devising novel constraint functions and iterative methods specifically tailored for the dynamic simulation of flexible cables. The key contributions of this paper are as follows: the introduction of rotation vectors for a more precise description of structural orientation; the design of higher-fidelity constraint functions based on the Cosserat rod theory; the proposal of constraint energy as the convergence criterion to enhance simulation accuracy; and the development of a group-based constraint solving approach to improve computational efficiency. This paper also uses a cable-rod composite structure as an example to verify the effectiveness of the proposed algorithm. In comparison with the ADAMS software, the improved algorithm exhibits superior stability while maintaining comparable computational efficiency. When contrasted with the original XPBD algorithm, it achieves a remarkable improvement in solution accuracy. Moreover, by incorporating rotation vectors, the enhanced algorithm allows for more flexible constraint function design and provides a computational framework conducive to parallelization, thus showing considerable potential for further applications in the dynamic simulation of complex flexible structures.

     

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