Single-Level Differentiable Contact Simulation

TL;DR

This paper introduces a unified, differentiable contact simulation method for convex primitives that improves robustness and efficiency over previous bilevel approaches, enabling better optimization in robotic contact tasks.

Contribution

It presents a single-level optimization formulation for contact simulation that combines collision detection and contact dynamics, enhancing reliability and computational speed.

Findings

Improved simulation robustness compared to previous methods.

More than tenfold reduction in computational complexity.

Successful application to robotic manipulation tasks.

Abstract

We present a differentiable formulation of rigid-body contact dynamics for objects and robots represented as compositions of convex primitives. Existing optimization-based approaches simulating contact between convex primitives rely on a bilevel formulation that separates collision detection and contact simulation. These approaches are unreliable in realistic contact simulation scenarios because isolating the collision detection problem introduces contact location non-uniqueness. Our approach combines contact simulation and collision detection into a unified single-level optimization problem. This disambiguates the collision detection problem in a physics-informed manner. Compared to previous differentiable simulation approaches, our formulation features improved simulation robustness and a reduction in computational complexity by more than an order of magnitude. We illustrate the contact and collision differentiability on a robotic manipulation task requiring optimization-through-contact. We provide a numerically efficient implementation of our formulation in the Julia language called Silico.jl.