deploy: c05cd5e

Author: kevinzakka

.buildinfo

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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: e1b39df1e164151fde26803288e04875
+tags: 645f666f9bcd5a90fca523b33c5a78b7

.doctrees/configuration.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/configuration.rst
+
+.. _Configuration:
+
+Configuration
+=============
+
+.. automodule:: mink.configuration
+    :members:

.doctrees/derivations.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/derivation.rst
+
+.. _derivations:
+
+***********
+Derivations
+***********
+
+.. list-table::
+   :header-rows: 1
+
+   * - Variable Name
+     - Symbol
+   * - Configuration
+     - :math:`q`
+   * - Configuration displacement
+     - :math:`\Delta q`
+   * - Integration timestep
+     - :math:`dt`
+   * - Velocity in tangent space
+     - :math:`v = \frac{\Delta q}{dt}`
+   * - Configuration limits
+     - :math:`q_{\text{min}}, q_{\text{max}}`
+   * - Maximum joint velocity magnitude
+     - :math:`v_{\text{max}}`
+   * - Identity matrix
+     - :math:`I`
+
+------
+Limits
+------
+
+Configuration limit
+===================
+
+Using a first-order Taylor expansion on the configuration, we can write the limit as:
+
+.. math::
+    \begin{aligned}
+    q_{\text{min}} &\leq q \oplus v \cdot dt \leq q_{\text{max}} \\
+    q_{\text{min}} &\leq q \oplus \Delta q \leq q_{\text{max}} \\
+    q_{\text{min}} &\ominus q \leq \Delta q \leq q_{\text{max}} \ominus q
+    \end{aligned}
+
+Rewriting as :math:`G \Delta q \leq h`, we separate the inequalities:
+
+.. math::
+    \begin{aligned}
+    &+I \cdot \Delta q \leq q_{\text{max}} \ominus q \\
+    &-I \cdot \Delta q \leq q \ominus q_{\text{min}}
+    \end{aligned}
+
+Stacking these inequalities, we define:
+
+.. math::
+    \begin{aligned}
+    G &= \begin{bmatrix} +I \\ -I \end{bmatrix}, \\
+    h &= \begin{bmatrix} q_{\text{max}} \ominus q \\ q \ominus q_{\text{min}} \end{bmatrix}
+    \end{aligned}
+
+Velocity limit
+==============
+
+Given the maximum joint velocity magnitudes :math:`v_{\text{max}}`, the joint velocity limits can be expressed as:
+
+.. math::
+    \begin{aligned}
+    -v_{\text{max}} &\leq v \leq v_{\text{max}} \\
+    -v_{\text{max}} &\leq \frac{\Delta q}{dt} \leq v_{\text{max}} \\
+    -v_{\text{max}} \cdot dt &\leq \Delta q \leq v_{\text{max}} \cdot dt
+    \end{aligned}
+
+Rewriting as :math:`G \Delta q \leq h`, we separate the inequalities:
+
+.. math::
+    \begin{aligned}
+    &+I \cdot \Delta q \leq v_{\text{max}} \cdot dt \\
+    &-I \cdot \Delta q \leq v_{\text{max}} \cdot dt
+    \end{aligned}
+
+Stacking these inequalities, we define:
+
+.. math::
+    \begin{aligned}
+    G \Delta q &\leq h \\
+    \begin{bmatrix} +I \\ -I \end{bmatrix} \Delta q &\leq \begin{bmatrix} v_{\text{max}} \cdot dt \\ v_{\text{max}} \cdot dt \end{bmatrix}
+    \end{aligned}
+
+
+-----
+Tasks
+-----

.doctrees/environment.pickle

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/index.rst
+
+.. title:: Table of Contents
+
+####
+mink
+####
+
+mink is a library for differential inverse kinematics in Python, based on the `MuJoCo <https://github.com/google-deepmind/mujoco>`_ physics engine.
+
+.. image:: https://github.com/kevinzakka/mink/blob/assets/banner.png?raw=true
+   :alt: Banner for mink
+
+------------
+Installation
+------------
+
+You can install `mink` with `pip`:
+
+.. code:: bash
+
+   pip install mink
+
+To include example dependencies:
+
+.. code:: bash
+
+   pip install mink[examples]
+
+.. toctree::
+    :maxdepth: 1
+
+    configuration.rst
+    lie.rst
+    tasks.rst
+    limits.rst
+    inverse_kinematics.rst
+    utilities.rst
+    derivations.rst
+    references.rst

.doctrees/index.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/inverse_kinematics.rst
+
+******************
+Inverse kinematics
+******************
+
+.. autofunction:: mink.solve_ik.solve_ik
+
+.. autofunction:: mink.solve_ik.build_ik

.doctrees/inverse_kinematics.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/lie.rst
+
+***
+Lie
+***
+
+MuJoCo does not currently offer a native Lie group interface for rigid body transforms, though it
+does have a collection of functions for manipulating quaternions and rotation matrices. The goal
+of this library is to provide this unified interface. Whenever possible, the underlying
+lie operation leverages the corresponding MuJoCo function. For example,
+:py:meth:`~SO3.from_matrix` uses `mujoco.mju_mat2Quat` under the hood.
+
+This library is heavily ported from `jaxlie <https://github.com/brentyi/jaxlie>`__,
+swapping out JAX for Numpy and adding a few additional features.
+
+MatrixLieGroup
+==============
+
+.. autoclass:: mink.lie.base.MatrixLieGroup
+    :members:
+
+SO3
+===
+
+.. autoclass:: mink.lie.so3.SO3
+    :show-inheritance:
+    :inherited-members:
+    :members:
+
+SE3
+===
+
+.. autoclass:: mink.lie.se3.SE3
+    :show-inheritance:
+    :inherited-members:
+    :members:

.doctrees/lie.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/limits.rst
+
+.. _Limits:
+
+******
+Limits
+******
+
+Definition
+==========
+
+.. automodule:: mink.limits.limit
+    :members:
+
+Configuration limits
+====================
+
+.. automodule:: mink.limits.configuration_limit
+   :members:
+
+Velocity limits
+===============
+
+.. automodule:: mink.limits.velocity_limit
+   :members:
+
+
+Collision avoidance limits
+==========================
+
+.. automodule:: mink.limits.collision_avoidance_limit
+   :members:

.doctrees/limits.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/references.rst
+
+**********
+References
+**********
+
+.. [FrameTaskJacobian] `Jacobian of a kinematic task and derivatives on manifolds <https://scaron.info/robotics/jacobian-of-a-kinematic-task-and-derivatives-on-manifolds.html>`_. S. Caron. 2023.

.doctrees/references.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/tasks.rst
+
+.. _Tasks:
+
+*****
+Tasks
+*****
+
+.. automodule:: mink.tasks.task
+    :members:
+
+Frame task
+==========
+
+.. automodule:: mink.tasks.frame_task
+    :members:
+
+Relative frame task
+===================
+
+.. automodule:: mink.tasks.relative_frame_task
+    :members:
+
+Center of mass task
+===================
+
+.. automodule:: mink.tasks.com_task
+    :members:
+
+Posture task
+============
+
+.. automodule:: mink.tasks.posture_task
+    :members:
+
+Damping task
+============
+
+.. automodule:: mink.tasks.damping_task
+    :members:

.doctrees/tasks.doctree

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+:github_url: https://github.com/kevinzakka/mink/tree/main/doc/utilities.rst
+
+*********
+Utilities
+*********
+
+.. automodule:: mink.utils
+    :members: