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

src/engine/engine_derivative.c

@@ -2016,10 +2016,18 @@ void mjd_actuator_vel(const mjModel* m, mjData* d) {
 
     // skip if force is clamped by forcerange
     if (m->actuator_forcelimited[i]) {
-      mjtNum force = d->actuator_force[oadr];
-      mjtNum* range = m->actuator_forcerange + 2*oadr;
-      if (force <= range[0] || force >= range[1]) {
-        continue;
+      const mjtNum* range = m->actuator_forcerange + 2*i;
+
+      // SO3: force is norm-clamped (approximation: saturated force still varies tangentially)
+      if (m->actuator_gaintype[i] == mjGAIN_SO3) {
+        if (mju_norm3(d->actuator_force + oadr) >= range[1]) {
+          continue;
+        }
+      } else {
+        mjtNum force = d->actuator_force[oadr];
+        if (force <= range[0] || force >= range[1]) {
+          continue;
+        }
       }
     }
 
@@ -2031,6 +2039,11 @@ void mjd_actuator_vel(const mjModel* m, mjData* d) {
       bias_vel = (m->actuator_biasprm + mjNBIAS*i)[2];
     }
 
+    // SO3 geodesic servo: kv term, applied to each output row below
+    else if (m->actuator_biastype[i] == mjBIAS_SO3) {
+      bias_vel = (m->actuator_biasprm + mjNBIAS*i)[2];
+    }
+
     // DC motor bias (back-EMF)
     else if (m->actuator_biastype[i] == mjBIAS_DCMOTOR) {
       const mjtNum* dynprm = m->actuator_dynprm + mjNDYN*i;
@@ -2108,10 +2121,12 @@ void mjd_actuator_vel(const mjModel* m, mjData* d) {
       }
     }
 
-    // add
+    // add, once per output row
     if (bias_vel != 0) {
-      addJTBJSparse(m, d, d->actuator_moment, &bias_vel, 1, oadr,
-                    d->moment_rownnz, d->moment_rowadr, d->moment_colind);
+      for (int k=0; k < m->actuator_outnum[i]; k++) {
+        addJTBJSparse(m, d, d->actuator_moment, &bias_vel, 1, oadr+k,
+                      d->moment_rownnz, d->moment_rowadr, d->moment_colind);
+      }
     }
   }
 }