Large-Dimensional Multibody Dynamics Simulation Using Contact Nodalization and Diagonalization

TL;DR

This paper introduces a new multibody dynamics simulation method that efficiently handles large-dimensional contact problems by decoupling contacts and axes, enabling faster and more stable simulations, especially for complex multi-contact scenarios.

Contribution

The paper presents a velocity-level fixed-point iteration framework with contact nodalization and diagonalization, reducing computational complexity and improving convergence in large-scale multibody contact simulations.

Findings

Significantly faster simulation times compared to traditional methods.

Effective decoupling of inter-contact and inter-axis interactions.

Validated performance on large-dimensional and deformable object scenarios.

Abstract

We propose a novel multibody dynamics simulation framework that can efficiently deal with large-dimensionality and complementarity multi-contact conditions. Typical contact simulation approaches perform contact impulse-level fixed-point iteration (IL-FPI), which has high time-complexity from large-size matrix inversion and multiplication, as well as susceptibility to ill-conditioned contact situations. To circumvent this, we propose a novel framework based on velocity-level fixed-point iteration (VL-FPI), which, by utilizing a certain surrogate dynamics and contact nodalization (with virtual nodes), can achieve not only inter-contact decoupling but also their inter-axes decoupling (i.e., contact diagonalization). This then enables us to one-shot/parallel-solve the contact problem during each VL-FPI iteration-loop, while the surrogate dynamics structure allows us to circumvent 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/multi-contact scenarios including deformable objects.