# DiffCo: Auto-Differentiable Proxy Collision Detection with Multi-class Labels for Safety-Aware Trajectory Optimization

arXiv: https://arxiv.org/abs/2102.07413 · HTML: https://mlsanity.com/paper/2102.07413/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Perceive, Predict, and Plan: Safe Motion Planning Through Interpretable Semantic Representations](https://mlsanity.com/paper/2008.05930/) (2020)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Motion Planning Networks: Bridging the Gap Between Learning-based and Classical Motion Planners](https://mlsanity.com/paper/1907.06013/) (2019)
- [Neural Path Planning: Fixed Time, Near-Optimal Path Generation via Oracle Imitation](https://mlsanity.com/paper/1904.11102/) (2019)
- [Deeply Informed Neural Sampling for Robot Motion Planning](https://mlsanity.com/paper/1809.10252/) (2018)
- [Learning-Based Proxy Collision Detection for Robot Motion Planning Applications](https://mlsanity.com/paper/1902.08164/) (2019)
- [Constrained Motion Planning Networks X](https://mlsanity.com/paper/2010.08707/) (2020)
- [Forward Kinematics Kernel for Improved Proxy Collision Checking](https://mlsanity.com/paper/1910.06451/) (2019)
- [Neural Collision Clearance Estimator for Batched Motion Planning](https://mlsanity.com/paper/1910.05917/) (2019)
- [Stochastic Modeling of Distance to Collision for Robot Manipulators](https://mlsanity.com/paper/2005.14391/) (2020)

## Built on by (most cited first, 4 of 4)

- [PRESTO: Fast Motion Planning Using Diffusion Models Based on Key-Configuration Environment Representation](https://mlsanity.com/paper/2409.16012/) (2024)
- [RGB-Only Reconstruction of Tabletop Scenes for Collision-Free Manipulator Control](https://mlsanity.com/paper/2210.11668/) (2022)
- [Warm-Starting Optimization-Based Motion Planning for Robotic Manipulators via Point Cloud-Conditioned Flow Matching](https://mlsanity.com/paper/2510.03460/) (2025)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)

## Abstract (arXiv)

The objective of trajectory optimization algorithms is to achieve an optimal collision-free path between a start and goal state. In real-world scenarios where environments can be complex and non-homogeneous, a robot needs to be able to gauge whether a state will be in collision with various objects in order to meet some safety metrics. The collision detector should be computationally efficient and, ideally, analytically differentiable to facilitate stable and rapid gradient descent during optimization. However, methods today lack an elegant approach to detect collision differentiably, relying rather on numerical gradients that can be unstable. We present DiffCo, the first, fully auto-differentiable, non-parametric model for collision detection. Its non-parametric behavior allows one to compute collision boundaries on-the-fly and update them, requiring no pre-training and allowing it to update continuously in dynamic environments. It provides robust gradients for trajectory optimization via backpropagation and is often 10-100x faster to compute than its geometric counterparts. DiffCo also extends trivially to modeling different object collision classes for semantically informed trajectory optimization.