Iterative refinement algorithm for efficient velocities and accelerations solutions in closed-loop multibody dynamics

Abstract

To simulate closed-loop multibody systems in effective and accurate way, the semi-recursive formulations can be used together with optimal numerical integrators. Although numerous contributions have been reported in this field, there still exists a demand to improve the computation efficiency for the faster-than-real-time simulation and hardware-in-the-loop control applications. This paper presents an iterative refinement algorithm to accelerate the numerical integration process of a semi-recursive multibody formulation. By reusing the constraint Jacobian matrix factorization and generalized mass matrix factorization, respectively, the presented algorithm is introduced to enhance the solution of dependent relative velocities and independent relative accelerations. The introduced procedure consists of three steps; initial guess determination, iterative refinement process and termination criteria. The iterative refinement process is designed to find an accurate numerical solution, which contains residual computing, solution increment computing and solution updating. For higher efficiency, the initial guess can be re-determined to repeat the iterative refinement process. Three closed-loop multibody systems with increasing complexity are taken as numerical examples to verify the accuracy and efficiency of the presented iterative refinement algorithm. The results highlight more than 15% efficiency gain. The algorithm also can be implemented in other numerical integrators and multibody formulations.