# ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

arXiv: https://arxiv.org/abs/1810.01054 · HTML: https://mlsanity.com/paper/1810.01054/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2018.

## Built on by (most cited first, 30 of 98)

- [UniSim: A Neural Closed-Loop Sensor Simulator](https://mlsanity.com/paper/2308.01898/) (2023)
- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [Robot Learning from Randomized Simulations: A Review](https://mlsanity.com/paper/2111.00956/) (2021)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [An End-to-End Differentiable Framework for Contact-Aware Robot Design](https://mlsanity.com/paper/2107.07501/) (2021)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [NeuPhysics: Editable Neural Geometry and Physics from Monocular Videos](https://mlsanity.com/paper/2210.12352/) (2022)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)
- [Virtual Elastic Objects](https://mlsanity.com/paper/2201.04623/) (2022)
- [DiffCloud: Real-to-Sim from Point Clouds with Differentiable Simulation and Rendering of Deformable Objects](https://mlsanity.com/paper/2204.03139/) (2022)
- [DiffuseBot: Breeding Soft Robots With Physics-Augmented Generative Diffusion Models](https://mlsanity.com/paper/2311.17053/) (2023)
- [RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimation](https://mlsanity.com/paper/2205.05678/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [ACID: Action-Conditional Implicit Visual Dynamics for Deformable Object Manipulation](https://mlsanity.com/paper/2203.06856/) (2022)
- [Rethinking Optimization with Differentiable Simulation from a Global Perspective](https://mlsanity.com/paper/2207.00167/) (2022)
- [Deep Inventory Management](https://mlsanity.com/paper/2210.03137/) (2022)
- [DexDeform: Dexterous Deformable Object Manipulation with Human Demonstrations and Differentiable Physics](https://mlsanity.com/paper/2304.03223/) (2023)
- [SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments](https://mlsanity.com/paper/2303.09555/) (2023)
- [Adaptive Horizon Actor-Critic for Policy Learning in Contact-Rich Differentiable Simulation](https://mlsanity.com/paper/2405.17784/) (2024)
- [Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulation](https://mlsanity.com/paper/2412.12089/) (2024)
- [Dress-1-to-3: Single Image to Simulation-Ready 3D Outfit with Diffusion Prior and Differentiable Physics](https://mlsanity.com/paper/2502.03449/) (2025)
- [DiffMimic: Efficient Motion Mimicking with Differentiable Physics](https://mlsanity.com/paper/2304.03274/) (2023)

## Abstract (arXiv)

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.