mlsanityData to 14 Oct 2026

Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Control

arXiv 2506.14186 ↗First posted 17 Jun 2025cs.RO cs.LG cs.SYcited by 5

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Abstract (arXiv)

Contact forces introduce discontinuities into robot dynamics that severely limit the use of simulators for gradient-based optimization. Penalty-based simulators such as MuJoCo, soften contact resolution to enable gradient computation. However, realistically simulating hard contacts requires stiff solver settings, which leads to incorrect simulator gradients when using automatic differentiation. Contrarily, using non-stiff settings strongly increases the sim-to-real gap. We analyze penalty-based simulators to pinpoint why gradients degrade under hard contacts. Building on these insights, we propose DiffMJX, which couples adaptive time integration with penalty-based simulation to substantially improve gradient accuracy. A second challenge is that contact gradients vanish when bodies separate. To address this, we introduce contacts from distance (CFD) which combines penalty-based simulation with straight-through estimation. By applying CFD exclusively in the backward pass, we obtain informative pre-contact gradients while retaining physical realism.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 38 of its 78 references that are in the map. First posted on arXiv 17 Jun 2025.

Builds on

38 of 78 references.

References · 38

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2013Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computationcited by 2,079
  3. 2018Learning Dexterous In-Hand Manipulationcited by 687
  4. 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 604
  5. 2021Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulationcited by 407
  6. 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 319
  7. 2022On Neural Differential Equationscited by 268
  8. 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 258
  9. 2023Real-World Humanoid Locomotion with Reinforcement Learningcited by 187
  10. 2021Equinox: neural networks in JAX via callable PyTrees and filtered transformationscited by 148
  11. 2022Accelerated Policy Learning with Parallel Differentiable Simulationcited by 104
  12. 2018ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Roboticscited by 98
26 more
  1. 2020Sample-efficient Cross-Entropy Method for Real-time Planningcited by 95
  2. 2018GPU-Accelerated Robotic Simulation for Distributed Reinforcement Learningcited by 90
  3. 2020NeuralSim: Augmenting Differentiable Simulators with Neural Networkscited by 82
  4. 2022MyoSuite -- A contact-rich simulation suite for musculoskeletal motor controlcited by 80
  5. 2021Deep Regression on Manifolds: A 3D Rotation Case Studycited by 67
  6. 2022Global Planning for Contact-Rich Manipulation via Local Smoothing of Quasi-dynamic Contact Modelscited by 49
  7. 2022Predictive Sampling: Real-time Behaviour Synthesis with MuJoCocited by 47
  8. 2022Learning Agile Skills via Adversarial Imitation of Rough Partial Demonstrationscited by 45
  9. 2024Learning with 3D rotations, a hitchhiker's guide to SO(3)cited by 42
  10. 2020ContactNets: Learning Discontinuous Contact Dynamics with Smooth, Implicit Representationscited by 38
  11. 2023Simulation and Retargeting of Complex Multi-Character Interactionscited by 34
  12. 2024Learning Quadruped Locomotion Using Differentiable Simulationcited by 32
  13. 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
  14. 2022DEP-RL: Embodied Exploration for Reinforcement Learning in Overactuated and Musculoskeletal Systemscited by 29
  15. 2024A Review of Differentiable Simulatorscited by 28
  16. 2021Bundled Gradients through Contact via Randomized Smoothingcited by 24
  17. 2024Adaptive Horizon Actor-Critic for Policy Learning in Contact-Rich Differentiable Simulationcited by 20
  18. 2021Sparsely Changing Latent States for Prediction and Planning in Partially Observable Domainscited by 18
  19. 2021Validating Robotics Simulators on Real-World Impactscited by 11
  20. 2021Fundamental Challenges in Deep Learning for Stiff Contact Dynamicscited by 9
  21. 2023SoftMAC: Differentiable Soft Body Simulation with Forecast-based Contact Model and Two-way Coupling with Articulated Rigid Bodies and Clothescited by 9
  22. 2019A pressure field model for fast, robust approximation of net contact force and moment between nominally rigid objectscited by 8
  23. 2023Simultaneous Learning of Contact and Continuous Dynamicscited by 8
  24. 2023Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contactcited by 7
  25. 2025The Resurrection of the ReLUcited by 6
  26. 2025A Smooth Analytical Formulation of Collision Detection and Rigid Body Dynamics With Contactcited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026SoftJAX & SoftTorch: Empowering Automatic Differentiation Libraries with Informative Gradientscited by 2
  2. 2026NDPP-Grasp: Non-Differentiable Physical Plausibility Constraint-Guided Task-Oriented Dexterous Grasp Generationcited by 0
  3. 2026Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiationcited by 0
  4. 2026Ostrich: Taking Large Strides Through Stiff Contact in Differentiable Dynamicscited by 0
  5. 2026WorldAgent: Verification-Guided Agentic Physical World Constructioncited by 0