mlsanityData to 7 Oct 2026

Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact

arXiv 2103.16021 ↗First posted 30 Mar 2021cs.RO cs.AI cs.LGcited by 50

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Abstract (arXiv)

We present a fast and feature-complete differentiable physics engine, Nimble (nimblephysics.org), that supports Lagrangian dynamics and hard contact constraints for articulated rigid body simulation. Our differentiable physics engine offers a complete set of features that are typically only available in non-differentiable physics simulators commonly used by robotics applications. We solve contact constraints precisely using linear complementarity problems (LCPs). We present efficient and novel analytical gradients through the LCP formulation of inelastic contact that exploit the sparsity of the LCP solution. We support complex contact geometry, and gradients approximating continuous-time elastic collision. We also introduce a novel method to compute complementarity-aware gradients that help downstream optimization tasks avoid stalling in saddle points. We show that an implementation of this combination in an existing physics engine (DART) is capable of a 87x single-core speedup over finite-differencing in computing analytical Jacobians for a single timestep, while preserving all the expressiveness of original DART.

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). Builds on 16 of its 43 references that are in the map. First posted on arXiv 30 Mar 2021.

Builds on

16 of 43 references.

References · 16

  1. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  2. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  3. 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 248
  4. 2020Learning to Control PDEs with Differentiable Physicscited by 131
  5. 2016A Compositional Object-Based Approach to Learning Physical Dynamicscited by 119
  6. 2016A Differentiable Physics Engine for Deep Learning in Roboticscited by 107
  7. 2018ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Roboticscited by 98
  8. 2018Flexible Neural Representation for Physics Predictioncited by 91
  9. 2020Scalable Differentiable Physics for Learning and Controlcited by 72
  10. 2016Theano: A Python framework for fast computation of mathematical expressionscited by 64
  11. 2018SPNets: Differentiable Fluid Dynamics for Deep Neural Networkscited by 62
  12. 2019Interactive Differentiable Simulationcited by 17
4 more
  1. 2020Learning to Slide Unknown Objects with Differentiable Physics Simulationscited by 12
  2. 2020Augmenting Differentiable Simulators with Neural Networks to Close the Sim2Real Gapcited by 9
  3. 2020Automatic Differentiation and Continuous Sensitivity Analysis of Rigid Body Dynamicscited by 4
  4. 2019Constrained Sampling-based Trajectory Optimization using Stochastic Approximationcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 17; 2023: 10; 2024: 7; 2025: 6; 2026: 6.

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  1. 2021Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulationcited by 375
  2. 2022Do Differentiable Simulators Give Better Policy Gradients?cited by 83
  3. 2021Gradients are Not All You Needcited by 82
  4. 2022Human Trajectory Prediction via Neural Social Physicscited by 66
  5. 2022NeuPhysics: Editable Neural Geometry and Physics from Monocular Videoscited by 50
  6. 2022Differentiable Physics Simulation of Dynamics-Augmented Neural Objectscited by 45
  7. 2022DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Toolscited by 44
  8. 2022Differentiable Simulation of Soft Multi-body Systemscited by 39
  9. 2022Differentiable Dynamics for Articulated 3d Human Motion Reconstructioncited by 38
  10. 2023DexDeform: Dexterous Deformable Object Manipulation with Human Demonstrations and Differentiable Physicscited by 23
  11. 2022SAM-RL: Sensing-Aware Model-Based Reinforcement Learning via Differentiable Physics-Based Simulation and Renderingcited by 22
  12. 2023A Survey on Physics Informed Reinforcement Learning: Review and Open Problemscited by 22
38 more
  1. 2024Learning Quadruped Locomotion Using Differentiable Simulationcited by 22
  2. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  3. 2021SAGCI-System: Towards Sample-Efficient, Generalizable, Compositional, and Incremental Robot Learningcited by 16
  4. 2022Contact Points Discovery for Soft-Body Manipulations with Differentiable Physicscited by 14
  5. 2022A Survey on Reinforcement Learning Methods in Character Animationcited by 12
  6. 2022Learning Tool Morphology for Contact-Rich Manipulation Tasks with Differentiable Simulationcited by 9
  7. 2023SoftMAC: Differentiable Soft Body Simulation with Forecast-based Contact Model and Two-way Coupling with Articulated Rigid Bodies and Clothescited by 9
  8. 2023DeepSimHO: Stable Pose Estimation for Hand-Object Interaction via Physics Simulationcited by 8
  9. 2023Jade: A Differentiable Physics Engine for Articulated Rigid Bodies with Intersection-Free Frictional Contactcited by 7
  10. 2023Differentiable Visual Computing for Inverse Problems and Machine Learningcited by 7
  11. 2022Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?cited by 6
  12. 2023DiffVL: Scaling Up Soft Body Manipulation using Vision-Language Driven Differentiable Physicscited by 6
  13. 2023Improving Gradient Computation for Differentiable Physics Simulation with Contactscited by 5
  14. 2024Human Motion Prediction under Unexpected Perturbationcited by 5
  15. 2022Differentiable Analog Quantum Computing for Optimization and Controlcited by 4
  16. 2025From 2D to 3D Cognition: A Brief Survey of General World Modelscited by 4
  17. 2025Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challengescited by 4
  18. 2024Learning Object Properties Using Robot Proprioception via Differentiable Robot-Object Interactioncited by 3
  19. 2025PhysPose: Refining 6D Object Poses with Physical Constraintscited by 3
  20. 2026IRIS: A Real-World Benchmark for Inverse Recovery and Identification of Physical Dynamic Systems from Monocular Videocited by 3
  21. 2022Predicting Physical Object Properties from Videocited by 2
  22. 2024DiffGen: Robot Demonstration Generation via Differentiable Physics Simulation, Differentiable Rendering, and Vision-Language Modelcited by 2
  23. 2024DiffSim2Real: Deploying Quadrupedal Locomotion Policies Purely Trained in Differentiable Simulationcited by 2
  24. 2025Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisionscited by 2
  25. 2026Learning Physics-Guided Residual Dynamics for Deformable Object Simulationcited by 2
  26. 2022Differentiable and Learnable Robot Modelscited by 1
  27. 2023Diff-Transfer: Model-based Robotic Manipulation Skill Transfer via Differentiable Physics Simulationcited by 1
  28. 2025Learning Extremely High Density Crowds as Active Matterscited by 1
  29. 2025Accelerated Learning with Linear Temporal Logic using Differentiable Simulationcited by 1
  30. 2026Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulationcited by 1
  31. 2022Unified Simulation, Perception, and Generation of Human Behaviorcited by 0
  32. 2022Relative Policy-Transition Optimization for Fast Policy Transfercited by 0
  33. 2023The Impact of Time Step Frequency on the Realism of Robotic Manipulation Simulation for Objects of Different Scalescited by 0
  34. 2024Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfercited by 0
  35. 2024Physics Augmented Tuple Transformer for Autism Severity Level Detectioncited by 0
  36. 2026Does "Do Differentiable Simulators Give Better Policy Gradients?'' Give Better Policy Gradients?cited by 0
  37. 2026URDF Synthesis from RGB-D Sequences via Differentiable Joint Inference and Energy-Consistent Verificationcited by 0
  38. 2026Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiationcited by 0