# Highly-Efficient Differentiable Simulation for Robotics

arXiv: https://arxiv.org/abs/2409.07107 · HTML: https://mlsanity.com/paper/2409.07107/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2024.

## Built on by (most cited first, 6 of 6)

- [Learning Physics-Guided Residual Dynamics for Deformable Object Simulation](https://mlsanity.com/paper/2607.13451/) (2026)
- [Accelerating trajectory optimization with Sobolev-trained diffusion policies](https://mlsanity.com/paper/2604.19011/) (2026)
- [Tempered Sequential Monte Carlo for Trajectory and Policy Optimization with Differentiable Dynamics](https://mlsanity.com/paper/2604.21456/) (2026)
- [EUPHORIA: Efficient Universal Planning via Hybrid Optimization for Robust Industrial Robotic Assembly](https://mlsanity.com/paper/2605.18872/) (2026)
- [Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiation](https://mlsanity.com/paper/2607.24959/) (2026)
- [Shooting for Contact: Contact-Implicit Multiple Shooting for Dynamic Motion Retargeting](https://mlsanity.com/paper/2608.03116/) (2026)

## Abstract (arXiv)

Robotics simulators have improved significantly in computational speed and scalability, enabling them to generate years of simulated data for complex systems in minutes or hours. Despite these advances, efficiently and accurately computing simulation derivatives remains an open challenge. Addressing this would accelerate the convergence of reinforcement learning and trajectory optimization algorithms, particularly for contact-rich problems. This paper introduces a unifying framework for robotic simulation that accounts for all factors, including dynamics, collisions, and friction. The resulting algorithm computes analytical derivatives of the simulation by implicit differentiation, explicitly handling the intrinsic non-smoothness of the collision and frictional stages while exploiting the sparsity induced by the multi-body structure. Benchmark results demonstrate state-of-the-art performance, with timings ranging from 5,μs for a 7-dof manipulator to 95,μs for a 36-dof humanoid, an improvement of at least two orders of magnitude over alternative methods. Implemented in C++, the code will be open-sourced after the review process to support applications such as simulation-driven learning and real-time control.