Discrete Approximation of Pressure Field Contact Patches

Rich interaction with the world requires extensive contact between robots and the objects in their environment. Most such contacts involve significant compliance between the contacting surfaces due to rubber pads or inflated grippers, soft objects to be manipulated, and soft surfaces for safe human-robot interaction. Accurate simulation of these contacts is critical for meaningful sim-to-real transfer. Compliant contact interactions generate contact surfaces of considerable extent, over which contact forces are distributed with varying pressure. Finite element methods can capture these effects but are too slow for most robotics applications. Consequently, in order to enable real-time simulation rates, most current simulation tools model contact as occurring between rigid bodies at a point or set of points using ad hoc methods to incorporate localized compliance. However, point contact is non-smooth, hard to extend to arbitrary geometry, and often introduces non-physical artifacts. Moreover, point contact misses important area-dependent phenomena critical for robust manipulation, such as net contact moment and slip control. Pressure Field Contact (PFC) was recently introduced as a method for detailed modeling of contact interface regions at rates much faster than elasticity-theory models, while at the same time predicting essential trends and capturing rich contact behavior. PFC was designed to work with coarsely-meshed objects while preserving continuity to permit use with error-controlled integrators. Here we introduce a discrete approximation of PFC suitable for use with velocity-level time steppers that enables execution at real-time rates. We evaluate the accuracy and performance gains of our approach and demonstrate its effectiveness in simulation of relevant manipulation tasks. The method is available in open source as part of Drake's Hydroelastic Contact model.