ContactSDF: Signed Distance Functions as Multi-Contact Models for Dexterous Manipulation

In this paper, we propose ContactSDF, a method that uses signed distance functions (SDFs) to approximate multi-contact models, including both collision detection and time-stepping routines. ContactSDF first establishes an SDF using the supporting plane representation of an object for collision detection, and then use the generated contact dual cones to build a second SDF for time stepping prediction of the next state. Those two SDFs create a differentiable and closed-form multi-contact dynamic model for state prediction, enabling efficient model learning and optimization for contact-rich manipulation. We perform extensive simulation experiments to show the effectiveness of ContactSDF for model learning and real-time control of dexterous manipulation. We further evaluate the ContactSDF on a hardware Allegro hand for on-palm reorientation tasks. Results show with around 2 minutes of learning on hardware, the ContactSDF achieves high-quality dexterous manipulation at a frequency of 30-60Hz.