# ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

arXiv: https://arxiv.org/abs/2007.00987 · HTML: https://mlsanity.com/paper/2007.00987/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 17 of 17)

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- [Improving Gradient Computation for Differentiable Physics Simulation with Contacts](https://mlsanity.com/paper/2305.00092/) (2023)
- [Learning Linear Complementarity Systems](https://mlsanity.com/paper/2112.13284/) (2021)
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- [Learning Solution Manifolds for Control Problems via Energy Minimization](https://mlsanity.com/paper/2203.03432/) (2022)
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## Abstract (arXiv)

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.