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Improve solver parameter documentation, in particular for frictional constraints.

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PiperOrigin-RevId: 873364458
Change-Id: Ie4da21abc2ee54d9eaaefc81b3d2624a520ad96e
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Yuval Tassa
2026-02-21 09:14:24 -08:00
committed by Copybara-Service
parent c428f675e7
commit 9d6d9089e5
3 changed files with 58 additions and 27 deletions
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doc/computation/index.rst
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@@ -1335,6 +1335,8 @@ It is a vector with dimensionality :math:`\nq` satisfying :math:`0<d<1` element-
the diagonal elements of the regularizer as
.. math::
:label: eq:impedance_R
R_{ii} = \frac{1-d_i}{d_i} \hat{A}_{ii}
Note that we are not using the diagonal of the actual :math:`A` matrix, but an approximation to it. This is because we
@@ -1354,17 +1356,22 @@ Next we explain how the reference acceleration is computed. As already mentioned
parameterized by *damping* and *stiffness* coefficients element-wise:
.. math::
:label: eq:aref
\ari = -b_i (J v)_i - k_i r_i
Recall that :math:`r` is the position residual (which is zero for friction loss and friction dimensions of elliptic
cones), while :math:`J v` is the joint velocity projected in constraint space; the indexing notation refers to one
component of the projected velocity vector.
Recall that :math:`r` is the position residual, while :math:`J v` is the joint velocity projected in constraint space;
the indexing notation refers to one component of the projected velocity vector. For friction loss and friction
dimensions of elliptic cones, :math:`r \equiv 0` and therefore :math:`k=0`, so the reference acceleration reduces to
pure damping: :math:`\ari = -b_i (J v)_i`. More detail is given in the :ref:`Friction<CSolverFriction>` section of the
Modeling chapter.
To summarize, the user specifies the vectors of impedance coefficients :math:`0<d<1`, damping coefficients :math:`b > 0`
and stiffness coefficients :math:`k > 0`. The quantities :math:`R, \ar` are then computed by MuJoCo as shown above, and
the selected optimization algorithm is applied to solve problem :eq:`eq:dual`. As explained in the :ref:`solver
parameters <CSolver>` section of the Modeling chapter, MuJoCo offers additional automation for setting :math:`d, b, k`
so as to achieve critical damping, or model a soft contact layer by varying :math:`d` with distance.
To summarize, the constraint behavior is determined by three per-constraint quantities: impedance :math:`0<d<1`, damping
:math:`b > 0` and stiffness :math:`k \geq 0`. These are computed from the :at:`solimp` and :at:`solref` attributes as
described in the :ref:`solver parameters <soRefScaling>` section of the Modeling chapter, which also offers additional
automation (e.g., achieving critical damping, or varying :math:`d` with distance to model a soft contact layer). The
quantities :math:`R, \ar` are then computed from :eq:`eq:impedance_R` and :eq:`eq:aref`, and the selected optimization
algorithm is applied to solve problem :eq:`eq:dual`.
.. _soCones: