A Convex Quasistatic Time-stepping Scheme for Rigid Multibody Systems with Contact and Friction

Motion planning for robotic manipulation makes heavy use of quasistatic models, but these same models have not yet proven useful for simulation. This is because in many multi-contact situations, the quasistatic models do not describe a unique next state for the system. A planner is able to use these models optimistically (checking only for feasibility of a motion), but simulation requires more. In this work, we enable quasistatic models to uniquely determine contact forces by modeling actuated robots as impedances instead of prescribed motions. Using this model with a well-known convex relaxation for Coulomb friction, time-stepping of quasistatic models can be formulated as a convex Quadratic Program (QP). This convex relaxation does admit mild non-physical behavior between relatively-sliding objects, but through simulations of various complexity, we show that the proposed quasistatic time-stepping scheme generates mostly physically-realistic behaviors, and scales well with the complexity of the simulated systems.