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Improve documentation w.r.t smoothness, differentiability and finite-differencing.

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PiperOrigin-RevId: 662848709
Change-Id: Icb7dc03a2c53d43d0d3a9e4ac95d963e5bc6853c
This commit is contained in:
Yuval Tassa
2024-08-14 03:10:28 -07:00
committed by Copybara-Service
parent 7efd690471
commit 2cb601c98d
4 changed files with 66 additions and 24 deletions
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doc/APIreference/functions.rst
+20 -6
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@@ -2589,7 +2589,7 @@ mjd_transitionFD
.. mujoco-include:: mjd_transitionFD
Finite-differenced discrete-time transition matrices.
Compute finite-differenced discrete-time transition matrices.
Letting :math:`x, u` denote the current :ref:`state<gePhysicsState>` and :ref:`control<geInput>`
vector in an mjData instance, and letting :math:`y, s` denote the next state and sensor
@@ -2610,12 +2610,26 @@ These matrices and their dimensions are:
- All outputs are optional (can be NULL).
- ``eps`` is the finite-differencing epsilon.
- ``flg_centered`` denotes whether to use forward (0) or centered (1) differences.
- Accuracy can be somewhat improved if solver :ref:`iterations<option-iterations>` are set to a
fixed (small) value and solver :ref:`tolerance<option-tolerance>` is set to 0. This insures that
all calls to the solver will perform exactly the same number of iterations.
- The Runge-Kutta integrator (:ref:`mjINT_RK4<mjtIntegrator>`) is not supported.
.. attention::
- The Runge-Kutta 4th-order integrator (``mjINT_RK4``) is not supported.
.. admonition:: Improving speed and accuracy
:class: tip
warmstart
If warm-starts are not :ref:`disabled<option-flag-warmstart>`, the warm-start accelerations
``mjData.qacc_warmstart`` which are present at call-time are loaded at the start of every relevant pipeline call,
to preserve determinism. If solver computations are an expensive part of the simulation, the following trick can
lead to significant speed-ups: First call :ref:`mj_forward` to let the solver converge, then reduce :ref:`solver
iterations<option-iterations>` significantly, then call :ref:`mjd_transitionFD`, finally, restore the original
value of :ref:`iterations<option-iterations>`. Because we are already near the solution, few iteration are required
to find the new minimum. This is especially true for the :ref:`Newton<option-solver>` solver, where the required
number of iteration for convergence near the minimum can be as low as 1.
tolerance
Accuracy can be improved if solver :ref:`tolerance<option-tolerance>` is set to 0. This means that all calls to
the solver will perform exactly the same number of iterations, preventing numerical errors due to early
termination. Of course, this means that :ref:`solver iterations<option-iterations>` should be small, to not tread
water at the minimum. This method and the one described above can and should be combined.
.. _mjd_inverseFD:
doc/APIreference/functions_override.rst
+21 -6
View File
@@ -567,7 +567,7 @@ outputs of derivative functions are the trailing rather than leading arguments.
.. _mjd_transitionFD:
Finite-differenced discrete-time transition matrices.
Compute finite-differenced discrete-time transition matrices.
Letting :math:`x, u` denote the current :ref:`state<gePhysicsState>` and :ref:`control<geInput>`
vector in an mjData instance, and letting :math:`y, s` denote the next state and sensor
@@ -588,12 +588,27 @@ These matrices and their dimensions are:
- All outputs are optional (can be NULL).
- ``eps`` is the finite-differencing epsilon.
- ``flg_centered`` denotes whether to use forward (0) or centered (1) differences.
- Accuracy can be somewhat improved if solver :ref:`iterations<option-iterations>` are set to a
fixed (small) value and solver :ref:`tolerance<option-tolerance>` is set to 0. This insures that
all calls to the solver will perform exactly the same number of iterations.
- The Runge-Kutta integrator (:ref:`mjINT_RK4<mjtIntegrator>`) is not supported.
.. admonition:: Improving speed and accuracy
:class: tip
warmstart
If warm-starts are not :ref:`disabled<option-flag-warmstart>`, the warm-start accelerations
``mjData.qacc_warmstart`` which are present at call-time are loaded at the start of every relevant pipeline call,
to preserve determinism. If solver computations are an expensive part of the simulation, the following trick can
lead to significant speed-ups: First call :ref:`mj_forward` to let the solver converge, then reduce :ref:`solver
iterations<option-iterations>` significantly, then call :ref:`mjd_transitionFD`, finally, restore the original
value of :ref:`iterations<option-iterations>`. Because we are already near the solution, few iteration are required
to find the new minimum. This is especially true for the :ref:`Newton<option-solver>` solver, where the required
number of iteration for convergence near the minimum can be as low as 1.
tolerance
Accuracy can be improved if solver :ref:`tolerance<option-tolerance>` is set to 0. This means that all calls to
the solver will perform exactly the same number of iterations, preventing numerical errors due to early
termination. Of course, this means that :ref:`solver iterations<option-iterations>` should be small, to not tread
water at the minimum. This method and the one described above can and should be combined.
.. attention::
- The Runge-Kutta 4th-order integrator (``mjINT_RK4``) is not supported.
.. _mjd_inverseFD: