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

test/engine/engine_derivative_test.cc

@@ -1226,6 +1226,59 @@ TEST_F(DerivativeTest, ForcerangeClampedDerivative) {
       << "when forcerange derivatives are correctly handled";
 }
 
+// forcelimited actuator following a multi-output SO3 actuator: the derivative
+// skip for saturated actuators must index forcerange per actuator, not per
+// output.
+TEST_F(DerivativeTest, ForcerangeClampedAfterSO3) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <option>
+      <flag contact="disable" gravity="disable"/>
+    </option>
+    <worldbody>
+      <body>
+        <joint name="ball" type="ball"/>
+        <geom type="box" size=".05 .07 .03"/>
+      </body>
+      <body pos="0 0 .3">
+        <joint name="hinge"/>
+        <geom size=".05"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <orientation joint="ball" kp="1" kv="1"/>
+      <velocity joint="hinge" kv="10" forcerange="-1 1"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  MjDataPtr data = MakeData(model);
+  mjModel* m = model.get();
+  mjData* d = data.get();
+
+  // spin the hinge so the velocity actuator saturates: force -50, clamped -1
+  mjtNum qvel[4] = {0.1, 0.2, 0.3, 5};
+  mju_copy(d->qvel, qvel, 4);
+  mj_forward(m, d);
+  ASSERT_EQ(d->actuator_force[3], -1);
+
+  // analytic qDeriv
+  mju_zero(d->qDeriv, m->nD);
+  mjd_smooth_vel(m, d, /*flg_bias=*/1);
+  vector<mjtNum> qDerivAnalytic = AsVector(d->qDeriv, m->nD);
+  EXPECT_GT(mju_norm(qDerivAnalytic.data(), m->nD), 0);
+
+  // expect match with finite differences: the saturated actuator contributes
+  // nothing, the SO3 actuator's damping is unaffected by its neighbor
+  mjtNum eps = MjTol(1e-7, 1e-3);
+  mju_zero(d->qDeriv, m->nD);
+  mjd_smooth_velFD(m, d, eps);
+  EXPECT_THAT(AsVector(d->qDeriv, m->nD),
+              Pointwise(MjNear(1e-7, 3e-3), qDerivAnalytic));
+}
+
 TEST_F(DerivativeTest, NonlinearDampingDerivative) {
   static constexpr char xml[] = R"(
   <mujoco>