Single-Level Differentiable Contact Simulation

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.