Multibody simulation with frictional contact has been a challenging subject of research for the past thirty years. Rigid-body assumptions are commonly used to approximate the physics of contact, and together with Coulomb friction, lead to challenging-to-solve nonlinear complementarity problems (NCP). On the other hand, robot grippers often introduce significant compliance. Compliant contact, combined with regularized friction, can be modeled entirely with ODEs, avoiding NCP solves. Unfortunately, regularized friction introduces high-frequency stiff dynamics and even implicit methods struggle with these systems, especially during slip-stick transitions. To improve the performance of implicit integration for these systems we introduce a Transition-Aware Line Search (TALS), which greatly improves the convergence of the Newton-Raphson iterations performed by implicit integrators. We find that TALS works best with semi-implicit integration, but that the explicit treatment of normal compliance can be problematic. To address this, we develop a Transition-Aware Modified Semi-Implicit (TAMSI) integrator that has similar computational cost to semi-implicit methods but implicitly couples compliant contact forces, leading to a more robust method. We evaluate the robustness, accuracy and performance of TAMSI and demonstrate our approach alongside a sim-to-real manipulation task.
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