chenlin/Mujoco_WASM
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Update mjd_transitionFD documentation.

Browse Source 
Fixes #713

PiperOrigin-RevId: 506248062
Change-Id: I1fbf8b378f500a6463a07eb5da5349c4f01ccb88
This commit is contained in:
Yuval Tassa
2023-02-01 01:52:20 -08:00
committed by Copybara-Service
parent a7888d473c
commit e2691f58a5
3 changed files with 47 additions and 12 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/computation.rst
+10 -8
View File
@@ -1556,20 +1556,22 @@ MuJoCo's entire computational pipline and uniquely -- its constraint solver -- a
efficient implementations of these derivatives is a long term goal of the development team. Analytic derivatives of the
smooth dynamics with respect to velocity are already in place and power the :ref:`implicit integrator<geIntegration>`.
The function ``mjd_transitionFD`` computes state-transition and control-transition Jacobians. Given any valid MuJoCo
The function :ref:`mjd_transitionFD` computes state-transition and control-transition Jacobians. Given any valid MuJoCo
model ``mjModel* m`` with an initial :ref:`simulation state<geState>` in ``mjData* d``,
- Let :math:`x` denote the *physics state* of the simulation at time :math:`t` -- the concatenation of positions,
velocities and actuator states ``[d->qpos; d->qvel; d->act]``.
- Let :math:`x` denote the :ref:`physics state<gePhysicsState>` of the simulation at time :math:`t` -- the concatenation
of positions, velocities and actuator states ``[d->qpos; d->qvel; d->act]``.
- Let :math:`u` denote the vector of controls at time :math:`t`, corresponding to ``d->ctrl``.
- Let :math:`y` denote the physical state of the simulation at time :math:`t+h`, where :math:`h` corresponds to
``m->opt.timstep``.
- The high level function ``mj_step(m, d)`` computes :math:`y(x, u)` -- the next state as a function of
the current state and control.
- ``mjd_transitionFD`` computes the Jacobians :math:`A = \frac{\partial y}{\partial x}` and
:math:`B = \frac{\partial y}{\partial u}` using efficient finite-differencing of ``mj_step``.
- Let :math:`s` denote the values of the sensors defined in the model.
- The high level function :ref:`mj_step` computes :math:`(x,u) \rightarrow (y,s)`: the next state and
sensor values as a function of the current state and control.
- ``mjd_transitionFD`` computes the Jacobians :math:`A = \frac{\partial y}{\partial x}`,
:math:`B = \frac{\partial y}{\partial u}`, :math:`C = \frac{\partial s}{\partial x}` and
:math:`D = \frac{\partial s}{\partial u}` using efficient finite-differencing of :ref:`mj_step`.
These derivatives are efficient by exploiting MuJoCo's configurable computation pipeline so that quantities are not
These derivatives are made efficient by exploiting MuJoCo's configurable computation pipeline so that quantities are not
recomputed when not required. For example when differencing with respect to controls, quantities which depend only on
position and velocity are not recomputed. Additionally, solver warmstarts, quaternions and control clamping are handled
correctly. Both forward and centered differences are supported.