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

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.