A fixed time-step approach for multibody dynamics with contact and friction

We present a fixed time-step algorithm for the simulation of multi-rigid-body dynamics with joints, contact, collision, and friction. The method solves a linear complementarity problem (LCP) at each step. We show that the algorithm can be obtained as the stiff limit of fixed time-step schemes applied to regularized contact models. We do not perform collision detection. Instead, a noninterpenetration constraint is replaced by its linearization, which, together with a judicious choice of the active constraints, guarantees geometrical constraint stabilization without the need to perform a reduction of the time step to detect new collision or stick-slip transition events. Partially elastic collisions are accommodated by a suitable modification of the free term of the LCP.