Add SO3 transmission and native orientation actuator.

https://youtu.be/17XpwnqyCXs

New transmission type mjTRN_SO3: a relative orientation, targeting a ball
joint or a site+refsite pair. It is the first transmission with more than
one force output: its length is the norm of the expmap vector of the
relative rotation and its moment axes are the 3 rows of the
relative rotational Jacobian, without projecting onto per-actuator gears.

New force law mjGAIN_SO3/mjBIAS_SO3: a geodesic PD servo, force =
kp * log(q_current^-1 * q_target) - kv * velocity, exact for arbitrary axis
combinations with a unique equilibrium at every commanded orientation.
Error, moment rows and velocity all live in the child frame (joint or
site): the right-difference error is the gradient of the geodesic
potential in that frame. The parent-frame (left) error is not: driving
child-frame torques with it pumps energy at large angles, settling into
steady-spinning limit cycles (the SO3LargeAngleConvergence test). The
integrator variant stores the 3D orientation setpoint in act (actnum = 3,
re-anchored to a bounded representative at integration time). Exposed in
MJCF as <orientation joint=|site=+refsite= kp kv|dampratio>, or via
<general gaintype="so3" biastype="so3">.

The setpoint input has two charts: an expmap target (3 controls, default)
or a quaternion target (4 controls) -- <orientation input="quat">, the
first actuator with different input and output widths. The signature is
recorded in a new per-actuator field actuator_ctrlspec (mjtCtrlChart),
whose meaning is scoped by the gain type the way gain/bias parameters are;
ctrlnum is derived from it at compile time and remains the layout
authority. An explicit field rather than width inference or a prm slot:
width-as-chart cannot express same-width signatures (upcoming servo input
subsets), and prm slots are the input_mode pattern this stack retires.
The force law normalizes the commanded quaternion, making it scale- and
antipodally-invariant. The all-zero ctrl still maps to the identity via
mju_normalize4, but it is a degenerate point (a nudge of any component
commands a half-turn), so quat inputs reset to the identity quaternion:
new mj_resetCtrl sets neutral ctrl values (zero, except qw = 1), called
by mj_resetData and the viewers' Clear All. The quat chart is
restricted to dyntype 'none': integrating a quaternion setpoint linearly
is not meaningful on the manifold. New mjsActuator.ctrlspec field carries
the signature through the spec and XML round-trip.

Actuator sensors (actuatorpos/vel/frc) now report one value per force
output; dim = 3 on an SO3 actuator.

As the first actuator with nu != nactuator, this commit also makes the
viewers multi-input aware: the control sliders in simulate and studio,
which indexed per-actuator arrays by control index (out of bounds on
this model class), are generated per control and labeled with the
actuator name plus an input suffix ("orient/qw"), via the new
introspection helper mj_actuatorInputName -- the single source of truth
for input names, extended by each new multi-input type (quaternion
components are w-first: qw, qx, qy, qz). Slider ranges now honor a
defined ctrlrange even when ctrllimited is false: range is the UI hint,
limited is the clamp -- wrapped and expmap setpoints are unbounded but
still want finite sliders, while quat components are truly bounded.

The rotational demo model is orientation.xml under
test/engine/testdata/actuation/, upgraded to a three-way contrast:
per-axis wrapped servos vs an expmap-commanded vs a quat-commanded
orientation actuator, on identical checker-textured boxes. It is loaded
by the mixed-axis contrast and input-name tests, and doubles as the
viewer test model (slider groups of 3 independent, 3 grouped, 4 grouped).

PiperOrigin-RevId: 951607063
Change-Id: If235dba8e2f2ca72672e7c62531a27e967c6a373

doc/changelog.rst

@@ -68,8 +68,11 @@ Engine
 .. admonition:: Breaking ABI changes
    :class: caution
 
+   - :ref:`mjModel` gained the ``actuator_ctrlspec`` field (input signature of each actuator), and :ref:`mjsActuator`
+     gained ``ctrlspec``, changing their size and layout. The :ref:`mjtGain` and :ref:`mjtBias` enums gained ``so3``
+     members, shifting the values of ``mjGAIN_USER`` and ``mjBIAS_USER``.
    - Added ``texid``, ``texuniform`` and ``texrepeat`` fields to :ref:`mjvGeom`.
-   - The :ref:`mjContact`` struct gained an ``adhesion`` member, changing its size and layout.
+   - The :ref:`mjContact` struct gained an ``adhesion`` member, changing its size and layout.
 
 .. admonition:: Bug fixes
    :class: admonition
@@ -93,6 +96,24 @@ Actuation
   :ref:`general<actuator-general>` actuators it defaults to "auto", so activation clamping is enabled by specifying
   ``actrange``. Unclamped integrated setpoints are well-behaved on rotational transmissions, where they wrap.
 
+.. youtube:: 17XpwnqyCXs
+   :align: right
+   :width: 35%
+
+- Added the :ref:`orientation<actuator-orientation>` actuator: a geodesic servo on a new SO(3) transmission (ball
+  joints, or a site with a :ref:`refsite<actuator-general-refsite>`), acting jointly on the full relative orientation
+  with an exact equilibrium at every commanded orientation. This is the first actuator with multiple force outputs
+  (3), and, with ``input="quat"``, the first with different input and output dimensions (4 controls, 3 outputs). The
+  input signature is recorded in the new ``mjModel.actuator_ctrlspec``, exposed as the
+  :ref:`input<actuator-general-input>` attribute.
+- Added :ref:`mj_actuatorInputName`, returning the name of an actuator input (e.g. "qw" for the first control of a
+  quaternion-commanded orientation actuator). The control sliders in :ref:`simulate<saSimulate>` and MuJoCo Studio are
+  now generated per control and labeled with the actuator name plus the input name suffix.
+- Viewer control sliders now use a defined :ref:`ctrlrange<actuator-general-ctrlrange>` even when
+  :ref:`ctrllimited<actuator-general-ctrllimited>` is "false": the range sets the slider span, while clamping remains
+  controlled by :at:`ctrllimited`.
+- Added :ref:`mj_resetCtrl`, setting controls to neutral values: zero, except quaternion inputs which reset to the
+  identity quaternion. Called by :ref:`mj_resetData` and the viewers' "Clear All".
 
 Solvers
 ^^^^^^^