  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.
