Yuval Tassa f0fa3d8260 Remove midpoint integration, superseded by free-body gyroscopic derivatives.
The gyroscopic (bias) derivatives applied to standalone free bodies by the
implicitfast integrator provide comparable stability for spinning bodies,
with none of midpoint's restrictions: they apply under contacts, fluid
forces and constraints, and preserve the linear force-velocity relation
required by discrete-time inverse dynamics. The invdiscrete flag reverts to
its original single meaning and no longer affects forward dynamics.

Restore implicitfast coverage in the DiscreteInverseMatch test, removed
when midpoint made discrete inverse dynamics untestable.

Add implicit gyroscopic (bias) derivatives for free bodies in implicitfast.

The implicitfast integrator drops the RNE (bias) derivative to stay on the
symmetric Cholesky path, so fast-spinning free bodies integrate gyroscopic
forces explicitly and can gain energy. Symmetrizing the gyroscopic Jacobian
is not an option: its stabilizing content is the antisymmetric part, and
adding only the symmetric part is destabilizing.

Instead, exploit the fact that for a standalone free body the 6x6 block of
M - h*D is decoupled from the rest of the system (qDeriv sparsity is
tree-local): after the global solve, rebuild the block with the exact bias
derivative in closed form (mjd_freeBias_vel) and re-solve it with dense
unsymmetric LU, overwriting the block's rows of qacc. For lone spinning
bodies this makes implicitfast match implicit to rounding, at ~150ns per
eligible body: cheaper than the midpoint machinery it will replace.
Eligibility is structural only; contacts, fluid and constraints need no
gating. The same block is mirrored in discrete inverse dynamics
(mj_discreteAcc), making invdiscrete exact for spinning free bodies.

PiperOrigin-RevId: 948472495
Change-Id: I813ef3d98c7b399881bc8603b9f9208cfb02eb58
2026-07-15 12:07:44 -07:00
2026-07-04 11:27:27 -07:00
2026-02-18 12:43:31 +00:00
2026-05-08 20:23:30 +01:00
2022-01-31 23:00:20 +00:00
2025-11-07 03:33:07 -08:00
2026-02-12 02:11:20 -08:00

MuJoCo

MuJoCo stands for Multi-Joint dynamics with Contact. It is a general purpose physics engine that aims to facilitate research and development in robotics, biomechanics, graphics and animation, machine learning, and other areas which demand fast and accurate simulation of articulated structures interacting with their environment.

This repository is maintained by Google DeepMind.

MuJoCo has a C API and is intended for researchers and developers. The runtime simulation module is tuned to maximize performance and operates on low-level data structures that are preallocated by the built-in XML compiler. The library includes interactive visualization with a native GUI, rendered in OpenGL. MuJoCo further exposes a large number of utility functions for computing physics-related quantities.

We also provide Python bindings and a plug-in for the Unity game engine.

Documentation

MuJoCo's documentation can be found at mujoco.readthedocs.io. Upcoming features due for the next release can be found in the changelog in the "latest" branch.

Getting Started

There are two easy ways to get started with MuJoCo:

  1. Run simulate on your machine. This video shows a screen capture of simulate, MuJoCo's native interactive viewer. Follow the steps described in the Getting Started section of the documentation to get simulate running on your machine.

  2. Explore our online IPython notebooks. If you are a Python user, you might want to start with our tutorial notebooks running on Google Colab:

  • The introductory tutorial teaches MuJoCo basics: Open In Colab
  • The Model Editing tutorial shows how to create and edit models procedurally: Open In Colab
  • The rollout tutorial shows how to use the multithreaded rollout module: Open In Colab
  • The LQR tutorial synthesizes a linear-quadratic controller, balancing a humanoid on one leg: Open In Colab
  • The least-squares tutorial explains how to use the Python-based nonlinear least-squares solver: Open In Colab
  • The MJX tutorial provides usage examples of MuJoCo XLA, a branch of MuJoCo written in JAX: Open In Colab
  • The differentiable physics tutorial trains locomotion policies with analytical gradients automatically derived from MuJoCo's physics step: Open In Colab

Installation

Prebuilt binaries

Versioned releases are available as precompiled binaries from the GitHub releases page, built for Linux (x86-64 and AArch64), Windows (x86-64 only), and macOS (universal). This is the recommended way to use the software.

Building from source

Users who wish to build MuJoCo from source should consult the build from source section of the documentation. However, note that the commit at the tip of the main branch may be unstable.

Python (>= 3.10)

The native Python bindings, which come pre-packaged with a copy of MuJoCo, can be installed from PyPI via:

pip install mujoco

Note that Pre-built Linux wheels target manylinux2014, see here for compatible distributions. For more information such as building the bindings from source, see the Python bindings section of the documentation.

Versioning

We aim to release MuJoCo in the first week of each month. Our versioning standards changed to modified Semantic Versioning in 3.5.0, see versioning for details.

Contributing

We welcome community engagement: questions, requests for help, bug reports and feature requests. To read more about bug reports, feature requests and more ambitious contributions, please see our contributors guide and style guide.

Asking Questions

Questions and requests for help are welcome as a GitHub "Asking for Help" Discussion and should focus on a specific problem or question.

Bug reports and feature requests

GitHub Issues are reserved for bug reports, feature requests and other development-related subjects.

MuJoCo is the backbone for numerous environment packages. Below we list several bindings and converters.

Bindings

These packages give users of various languages access to MuJoCo functionality:

First-party bindings:

Third-party bindings:

Converters

  • OpenSim: MyoConverter converts OpenSim models to MJCF.
  • SDFormat: gz-mujoco is a two-way SDFormat <-> MJCF conversion tool.
  • OBJ: obj2mjcf a script for converting composite OBJ files into a loadable MJCF model.
  • onshape: Onshape to Robot Converts onshape CAD assemblies to MJCF.

Citation

If you use MuJoCo for published research, please cite:

@inproceedings{todorov2012mujoco,
  title={MuJoCo: A physics engine for model-based control},
  author={Todorov, Emanuel and Erez, Tom and Tassa, Yuval},
  booktitle={2012 IEEE/RSJ International Conference on Intelligent Robots and Systems},
  pages={5026--5033},
  year={2012},
  organization={IEEE},
  doi={10.1109/IROS.2012.6386109}
}

License and Disclaimer

Copyright 2021 DeepMind Technologies Limited.

Box collision code (engine_collision_box.c) is Copyright 2016 Svetoslav Kolev.

ReStructuredText documents, images, and videos in the doc directory are made available under the terms of the Creative Commons Attribution 4.0 (CC BY 4.0) license. You may obtain a copy of the License at https://creativecommons.org/licenses/by/4.0/legalcode.

Source code is licensed under the Apache License, Version 2.0. You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0.

This is not an officially supported Google product.

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