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- Provides all the quantities included in the Euler-Poincarè formulation of the equations of motion.
- Supports body-fixed, inertial-fixed, and mixed [velocity representations][notation].
- Exposes all the necessary quantities to develop controllers in centroidal coordinates.
- Supports running open-loop and full closed-loop control architectures on hardware accelerators.

### JaxSim for robot learning

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pip install jaxsim
```

Check [`setup.cfg`](setup.cfg) for the complete list of optional dependencies.
Check [`pyproject.toml`](pyproject.toml) for the complete list of optional dependencies.
You can obtain a full installation using `jaxsim[all]`.

If you need GPU support, follow the official [installation instructions][jax_gpu] of JAX.
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[venv]: https://docs.python.org/3/tutorial/venv.html
[jax_gpu]: https://github.com/google/jax/#installation

## Overview

```
# tree -L 2 -I "__pycache__" -I "__init__*" -I "__main__*" src/jaxsim
src/jaxsim
|-- api..........................# Package containing the main functional APIs.
| |-- com.py...................# |-- APIs for computing quantities related to the center of mass.
| |-- common.py................# |-- Common utilities used in the current package.
| |-- contact.py...............# |-- APIs for computing quantities related to the collidable points.
| |-- data.py..................# |-- Class storing the data of a simulated model.
| |-- frame.py.................# |-- APIs for computing quantities related to additional frames.
| |-- joint.py.................# |-- APIs for computing quantities related to the joints.
| |-- kin_dyn_parameters.py....# |-- Class storing kinematic and dynamic parameters of a model.
| |-- link.py..................# |-- APIs for computing quantities related to the links.
| |-- model.py.................# |-- Class defining a simulated model and APIs for computing related quantities.
| |-- ode.py...................# |-- APIs for computing quantities related to the system dynamics.
| |-- ode_data.py..............# |-- Set of classes to store the data of the system dynamics.
| `-- references.py............# `-- Helper class to create references (link forces and joint torques).
|-- exceptions.py................# Module containing functions to raise exceptions from JIT-compiled functions.
|-- integrators..................# Package containing the integrators used to simulate the system dynamics.
| |-- common.py................# |-- Common utilities used in the current package.
| |-- fixed_step.py............# |-- Fixed-step integrators (explicit Runge-Kutta schemes).
| `-- variable_step.py.........# `-- Variable-step integrators (embedded Runge-Kutta schemes).
|-- logging.py...................# Module containing logging utilities.
|-- math.........................# Package containing mathematical utilities.
| |-- adjoint.py...............# |-- APIs for creating and manipulating 6D transformations.
| |-- cross.py.................# |-- APIs for computing cross products of 6D quantities.
| |-- inertia.py...............# |-- APIs for creating and manipulating 6D inertia matrices.
| |-- joint_model.py...........# |-- APIs defining the supported joint model and the corresponding transformations.
| |-- quaternion.py............# |-- APIs for creating and manipulating quaternions.
| |-- rotation.py..............# |-- APIs for creating and manipulating rotation matrices.
| |-- skew.py..................# |-- APIs for creating and manipulating skew-symmetric matrices.
| `-- transform.py.............# `-- APIs for creating and manipulating homogeneous transformations.
|-- mujoco.......................# Package containing utilities to interact with the Mujoco passive viewer.
| |-- loaders.py...............# |-- Utilities for converting JaxSim models to Mujoco models.
| |-- model.py.................# |-- Class providing high-level methods to compute quantities using Mujoco.
| `-- visualizer.py............# `-- Class that simplifies opening the passive viewer and record videos.
|-- parsers......................# Package containing utilities to parse model descriptions (SDF and URDF models).
| |-- descriptions/............# |-- Package containing the intermediate representation of a model description.
| |-- kinematic_graph.py.......# |-- Definition of the kinematic graph associated to a parsed model description.
| `-- rod/.....................# `-- Package to create the intermediate representation from model descriptions using ROD.
|-- rbda.........................# Package containing the low-level rigid body dynamics algorithms.
| |-- aba.py...................# |-- The Articulated Body Algorithm.
| |-- collidable_points.py.....# |-- Kinematics of collidable points.
| |-- contacts/................# |-- Package containing the supported contact models.
| |-- crba.py..................# |-- The Composite Rigid Body Algorithm.
| |-- forward_kinematics.py....# |-- Forward kinematics of the model.
| |-- jacobian.py..............# |-- Full Jacobian and full Jacobian derivative.
| |-- rnea.py..................# |-- The Recursive Newton-Euler Algorithm.
| `-- utils.py.................# `-- Common utilities used in the current package.
|-- terrain......................# Package containing resources to specify the terrain.
| `-- terrain.py...............# |-- Classes defining the supported terrains.
|-- typing.py....................# Module containing type hints.
`-- utils........................# Package of common utilities.
|-- jaxsim_dataclass.py......# |-- Utilities to operate on pytree dataclasses.
|-- tracing.py...............# |-- Utilities to use when JAX is tracing functions.
`-- wrappers.py..............# `-- Utilities to wrap objects for specific use-cases on pytree dataclass attributes.
```

## Credits

The RBDAs are based on the theory of the [Rigid Body Dynamics Algorithms][RBDA]
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}
```

Theoretical aspects of JaxSim are based on Chapters 7 and 8 of the following Ph.D. thesis:

```bibtex
@phdthesis{ferigo_phd_thesis_2022,
title = {Simulation Architectures for Reinforcement Learning applied to Robotics},
author = {Diego Ferigo},
school = {University of Manchester},
type = {PhD Thesis},
month = {July},
year = {2022},
}
```

## People

| Author | Maintainers |
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