# Differentiable Collision Detection: a Randomized Smoothing Approach

arXiv: https://arxiv.org/abs/2209.09012 · HTML: https://mlsanity.com/paper/2209.09012/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2022.

## Built on by (most cited first, 6 of 6)

- [Multi-Agent Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2408.09675/) (2024)
- [Uncertainty Quantification via Stable Distribution Propagation](https://mlsanity.com/paper/2402.08324/) (2024)
- [DeepSimHO: Stable Pose Estimation for Hand-Object Interaction via Physics Simulation](https://mlsanity.com/paper/2310.07206/) (2023)
- [Zero Grads: Learning Local Surrogate Losses for Non-Differentiable Graphics](https://mlsanity.com/paper/2308.05739/) (2023)
- [PhysPose: Refining 6D Object Poses with Physical Constraints](https://mlsanity.com/paper/2503.23587/) (2025)
- [EUPHORIA: Efficient Universal Planning via Hybrid Optimization for Robust Industrial Robotic Assembly](https://mlsanity.com/paper/2605.18872/) (2026)

## Abstract (arXiv)

Collision detection appears as a canonical operation in a large range of robotics applications from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only recently that the question of properly differentiating collision detection has emerged as a central issue, thanks notably to the ongoing and various efforts made by the scientific community around the topic of differentiable physics. Yet, very few solutions have been suggested so far, and only with a strong assumption on the nature of the shapes involved. In this work, we introduce a generic and efficient approach to compute the derivatives of collision detection for any pair of convex shapes, by notably leveraging randomized smoothing techniques which have shown to be particularly adapted to capture the derivatives of non-smooth problems. This approach is implemented in the HPP-FCL and Pinocchio ecosystems, and evaluated on classic datasets and problems of the robotics literature, demonstrating few micro-second timings to compute informative derivatives directly exploitable by many real robotic applications including differentiable simulation.