# Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contact

arXiv: https://arxiv.org/abs/2309.04710 · HTML: https://mlsanity.com/paper/2309.04710/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 9 Sep 2023.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [NeuralSim: Augmenting Differentiable Simulators with Neural Networks](https://mlsanity.com/paper/2011.04217/) (2020)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [SAM-RL: Sensing-Aware Model-Based Reinforcement Learning via Differentiable Physics-Based Simulation and Rendering](https://mlsanity.com/paper/2210.15185/) (2022)
- [SAGCI-System: Towards Sample-Efficient, Generalizable, Compositional, and Incremental Robot Learning](https://mlsanity.com/paper/2111.14693/) (2021)
- [Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation](https://mlsanity.com/paper/1709.03799/) (2017)
- [A Large Scale Benchmark and an Inclusion-Based Algorithm for Continuous Collision Detection](https://mlsanity.com/paper/2009.13349/) (2020)
- [Midas: A Multi-Joint Robotics Simulator with Intersection-Free Frictional Contact](https://mlsanity.com/paper/2210.00130/) (2022)

## Built on by (most cited first, 7 of 7)

- [Dexonomy: Synthesizing All Dexterous Grasp Types in a Grasp Taxonomy](https://mlsanity.com/paper/2504.18829/) (2025)
- [ManiFoundation Model for General-Purpose Robotic Manipulation of Contact Synthesis with Arbitrary Objects and Robots](https://mlsanity.com/paper/2405.06964/) (2024)
- [SoftMAC: Differentiable Soft Body Simulation with Forecast-based Contact Model and Two-way Coupling with Articulated Rigid Bodies and Clothes](https://mlsanity.com/paper/2312.03297/) (2023)
- [Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Control](https://mlsanity.com/paper/2506.14186/) (2025)
- [DiffGen: Robot Demonstration Generation via Differentiable Physics Simulation, Differentiable Rendering, and Vision-Language Model](https://mlsanity.com/paper/2405.07309/) (2024)
- [Diff-Transfer: Model-based Robotic Manipulation Skill Transfer via Differentiable Physics Simulation](https://mlsanity.com/paper/2310.04930/) (2023)
- [Rigid Body Adversarial Attacks](https://mlsanity.com/paper/2502.05669/) (2025)

## Abstract (arXiv)

We present Jade, a differentiable physics engine for articulated rigid bodies. Jade models contacts as the Linear Complementarity Problem (LCP). Compared to existing differentiable simulations, Jade offers features including intersection-free collision simulation and stable LCP solutions for multiple frictional contacts. We use continuous collision detection to detect the time of impact and adopt the backtracking strategy to prevent intersection between bodies with complex geometry shapes. We derive the gradient calculation to ensure the whole simulation process is differentiable under the backtracking mechanism. We modify the popular Dantzig algorithm to get valid solutions under multiple frictional contacts. We conduct extensive experiments to demonstrate the effectiveness of our differentiable physics simulation over a variety of contact-rich tasks.