# Improving Gradient Computation for Differentiable Physics Simulation with Contacts

arXiv: https://arxiv.org/abs/2305.00092 · HTML: https://mlsanity.com/paper/2305.00092/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 24 of 24)

- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [Do Differentiable Simulators Give Better Policy Gradients?](https://mlsanity.com/paper/2202.00817/) (2022)
- [NeuralSim: Augmenting Differentiable Simulators with Neural Networks](https://mlsanity.com/paper/2011.04217/) (2020)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting](https://mlsanity.com/paper/2105.12244/) (2021)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [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)
- [Grasp'D: Differentiable Contact-rich Grasp Synthesis for Multi-fingered Hands](https://mlsanity.com/paper/2208.12250/) (2022)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
- [Bundled Gradients through Contact via Randomized Smoothing](https://mlsanity.com/paper/2109.05143/) (2021)
- [Learning Physical Constraints with Neural Projections](https://mlsanity.com/paper/2006.12745/) (2020)
- [ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact](https://mlsanity.com/paper/2007.00987/) (2020)
- [DiffSDFSim: Differentiable Rigid-Body Dynamics With Implicit Shapes](https://mlsanity.com/paper/2111.15318/) (2021)
- [Learning to Slide Unknown Objects with Differentiable Physics Simulations](https://mlsanity.com/paper/2005.05456/) (2020)
- [Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?](https://mlsanity.com/paper/2207.05060/) (2022)
- [Solving Optimal Control Problems of Rigid-Body Dynamics with Collisions Using the Hybrid Minimum Principle](https://mlsanity.com/paper/2205.08622/) (2022)
- [Augmenting differentiable physics with randomized smoothing](https://mlsanity.com/paper/2206.11884/) (2022)

## Built on by (most cited first, 5 of 5)

- [Adaptive Horizon Actor-Critic for Policy Learning in Contact-Rich Differentiable Simulation](https://mlsanity.com/paper/2405.17784/) (2024)
- [Learning Physics-Guided Residual Dynamics for Deformable Object Simulation](https://mlsanity.com/paper/2607.13451/) (2026)
- [Reparameterization Proximal Policy Optimization](https://mlsanity.com/paper/2508.06214/) (2025)
- [Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiation](https://mlsanity.com/paper/2607.24959/) (2026)
- [On the Numerical Reliability of Differentiable Physics-Based Optimization for Robotic Material Manipulation](https://mlsanity.com/paper/2609.34666/) (2026)

## Abstract (arXiv)

Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradient-based optimization or embed the whole differentiable simulation as a layer in a deep learning model for downstream tasks, such as planning and control. However, differentiable simulation at its current stage is not perfect and might provide wrong gradients that deteriorate its performance in learning tasks. In this paper, we study differentiable rigid-body simulation with contacts. We find that existing differentiable simulation methods provide inaccurate gradients when the contact normal direction is not fixed - a general situation when the contacts are between two moving objects. We propose to improve gradient computation by continuous collision detection and leverage the time-of-impact (TOI) to calculate the post-collision velocities. We demonstrate our proposed method, referred to as TOI-Velocity, on two optimal control problems. We show that with TOI-Velocity, we are able to learn an optimal control sequence that matches the analytical solution, while without TOI-Velocity, existing differentiable simulation methods fail to do so.