Large-Dimensional Multibody Dynamics Simulation Using Contact Nodalization and Diagonalization

In this article, we propose a novel multibody dynamics simulation framework that can efficiently deal with large-dimensionality and complementarity multicontact conditions. Typical contact simulation approaches require performing contact impulse fixed-point iteration, which has high time-complexity from large-size matrix factorization and multiplication, as well as susceptibility to ill-conditioned contact situations. To circumvent this, we propose a novel framework based on velocity fixed-point iteration (V-FPI), which, by utilizing a certain surrogate dynamics and contact nodalization (with virtual nodes), we achieve not only intercontact decoupling but also their interaxes decoupling (i.e., contact diagonalization) at each iteration step. This then enables us to one-shot/parallel-solve the contact problem during each V-FPI iteration-loop, while avoiding large-size/dense matrix inversion/multiplication, thereby, significantly speeding up the simulation time with improved convergence property. We theoretically show that the solution of our framework is consistent with that of the original problem and, further, elucidate mathematical conditions for the convergence of our proposed solver. Performance and properties of our proposed simulation framework are also demonstrated and experimentally validated for various large-dimensional/multicontact scenarios including deformable objects.