# Single-Level Differentiable Contact Simulation

arXiv: https://arxiv.org/abs/2212.06764 · HTML: https://mlsanity.com/paper/2212.06764/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2022.

## Built on by (most cited first, 1 of 1)

- [Shooting for Contact: Contact-Implicit Multiple Shooting for Dynamic Motion Retargeting](https://mlsanity.com/paper/2608.03116/) (2026)

## Abstract (arXiv)

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.