Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?
Yaofeng Desmond Zhong, Jiequn Han, Georgia Olympia Brikis | 2022
This repository contains scripts to reproduce results in our paper.
All experiments do not require GPUs.
To install all dependencies:
pip install -r requirements.txt
# or to install the exact versions of packages as done in this work.
pip install -r requirements_freeze.txtPlease check out the README files in the task folders for how to reproduce the results shown in the paper.
In this work, we compare the gradients calculated by different differentiable contact models as shown in the following table.
| Differentiable contact models | Implementations |
|---|---|
| Linear complementarity problems (LCPs) | NimblePhysics |
| Convex optimization | DiffCoSim |
| Compliant models | Warp and Brax |
| Position-based dynamics (PBD) | Warp and Brax |
| Direct Velocity Impulse | DiffTaichi |
We apply these implementations to three tasks.
| Task 1. Gradients with a Simple Collision | Task 2. Optimize the Initial Velocity of a Bouncing Ball to Hit a Target | Task 3. Learning Optimal Control with a Two-ball Collision |
|---|---|---|
 |
 |
 |
Our results show that gradients calculated by different implementation do not agree. Some implementations fail to achieve the optimization tasks. Please check out our paper for more details.
In this tasks, we are able to derive the analytical gradients and the analytical optimal control. Here we plot the analytical optimal loss along with the learning curves as well as the analytical optimal control and learned optimal controls. We observe that some differentiable simulators learn zero control sequences and fail to achieve the optimization task.
If you find this work helpful, please consider citing our paper using the following Bibtex.
@article{zhong2022differentiable,
title={Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?},
author={Zhong, Yaofeng Desmond and Han, Jiequn and Brikis, Georgia Olympia},
journal={arXiv preprint arXiv:2207.05060},
year={2022}
}