Design of Cosserat Rod Constraint Functions and Group Solving Techniques for XPBD Algorithm

This paper introduces significant improvements to the eXtended Position Based Dynamics (XPBD) algorithm, making it well-suited for dynamic simulations of flexible ropes. The improvements include: incorporating rotational vectors for a more precise representation of structural attitude, developing more accurate constraint functions based on Cosserat elastic rod theory, employing constraint energy as the convergence criterion for iterations to enhance simulation accuracy, and introducing a grouping method for constraints to improve the efficiency of iterative calculations. The validity of the upgraded algorithm is confirmed through comparisons with results of ADAMS software. Compared with the original XPBD algorithm, the improved algorithm significantly enhances the solution accuracy, and its computational efficiency is roughly equivalent to that the ADAMS software, highlighting its potential for simulating more complex structures.