# Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

arXiv: https://arxiv.org/abs/1709.03799 · HTML: https://mlsanity.com/paper/1709.03799/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2017.

## Built on by (most cited first, 11 of 11)

- [Contact Points Discovery for Soft-Body Manipulations with Differentiable Physics](https://mlsanity.com/paper/2205.02835/) (2022)
- [DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation](https://mlsanity.com/paper/2104.00837/) (2021)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?](https://mlsanity.com/paper/2207.05060/) (2022)
- [Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contact](https://mlsanity.com/paper/2309.04710/) (2023)
- [DiSECt: A Differentiable Simulator for Parameter Inference and Control in Robotic Cutting](https://mlsanity.com/paper/2203.10263/) (2022)
- [Differentiable model-based adaptive optics for two-photon microscopy](https://mlsanity.com/paper/2104.14308/) (2021)
- [Differentiable and Learnable Robot Models](https://mlsanity.com/paper/2202.11217/) (2022)
- [Optimizing Automatic Differentiation with Deep Reinforcement Learning](https://mlsanity.com/paper/2406.05027/) (2024)
- [Accelerating trajectory optimization with Sobolev-trained diffusion policies](https://mlsanity.com/paper/2604.19011/) (2026)
- [Rigid Body Adversarial Attacks](https://mlsanity.com/paper/2502.05669/) (2025)

## Abstract (arXiv)

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning.