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/user/user_objects.cc

@@ -6931,8 +6931,10 @@ mjCActuator::mjCActuator(mjCModel* _model, mjCDef* _def) {
   // input and output blocks, set by mjCModel; all actuator types are currently 1x1
   ctrladr_ = -1;
   ctrlnum_ = 1;
+  ctrlspec_ = 0;
   outadr_ = -1;
   outnum_ = 1;
+  so3_ = false;
 }
 
 
@@ -7123,6 +7125,12 @@ void mjCActuator::ResolveReferences(const mjCModel* m) {
 void mjCActuator::Compile(void) {
   CopyFromSpec();
 
+  // reset input/output block widths, resolved below
+  ctrlnum_ = 1;
+  ctrlspec_ = 0;
+  outnum_ = 1;
+  so3_ = false;
+
   // resize userdata
   if (userdata_.size() > model->nuser_actuator) {
     throw mjCError(this, "user has more values than nuser_actuator in actuator '%s' (id = %d)",
@@ -7139,6 +7147,79 @@ void mjCActuator::Compile(void) {
   // find transmission target in object arrays
   ResolveReferences(model);
 
+  // SO3 geodesic servo: validate and resolve the SO3 transmission
+  if (gaintype == mjGAIN_SO3 || biastype == mjBIAS_SO3) {
+    if (gaintype != mjGAIN_SO3 || biastype != mjBIAS_SO3) {
+      throw mjCError(this, "gaintype and biastype must both be 'so3' in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+    if (dyntype != mjDYN_NONE && dyntype != mjDYN_INTEGRATOR) {
+      throw mjCError(this, "so3 requires dyntype 'none' or 'integrator' in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+    if (gainprm[0] != -biasprm[1]) {
+      throw mjCError(this, "so3 requires gainprm[0] == -biasprm[1] in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+    if (trntype == mjTRN_SITE) {
+      if (refsite_.empty()) {
+        throw mjCError(this, "so3 site transmission requires refsite in actuator '%s' (id = %d)",
+                       name.c_str(), id);
+      }
+    } else if (trntype == mjTRN_JOINT) {
+      if (((mjCJoint*)ptarget)->spec.type != mjJNT_BALL) {
+        throw mjCError(this, "so3 joint transmission requires a ball joint in actuator '%s' "
+                       "(id = %d)", name.c_str(), id);
+      }
+    } else {
+      throw mjCError(this, "so3 requires site or ball joint transmission in actuator '%s' "
+                     "(id = %d)", name.c_str(), id);
+    }
+
+    // integrator variant: activation is the 3D orientation setpoint
+    if (dyntype == mjDYN_INTEGRATOR) {
+      if (actdim > 0 && actdim != 3) {
+        throw mjCError(this, "so3 integrator requires actdim 3 in actuator '%s' (id = %d)",
+                       name.c_str(), id);
+      }
+      actdim = 3;
+
+      // the act setpoint is re-anchored to a bounded representative at integration time
+      if (actlimited == mjLIMITED_TRUE && actrange[0] == 0 && actrange[1] == 0) {
+        actlimited = mjLIMITED_FALSE;
+      }
+    }
+
+    // input chart: expmap (3 controls, default) or quat (4 controls)
+    ctrlspec_ = ctrlspec ? ctrlspec : mjCHART_EXPMAP;
+    if (ctrlspec_ == mjCHART_QUAT) {
+      if (dyntype != mjDYN_NONE) {
+        throw mjCError(this, "so3 quat input requires dyntype 'none' in actuator '%s' (id = %d)",
+                       name.c_str(), id);
+      }
+    } else if (ctrlspec_ != mjCHART_EXPMAP) {
+      throw mjCError(this, "so3 input must be expmap or quat in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+
+    // force is clamped on the norm of the output torque: lower bound must be 0
+    if (is_forcelimited() && forcerange[0] != 0) {
+      throw mjCError(this, "so3 forcerange bounds the force norm, lower bound must be 0 in "
+                     "actuator '%s' (id = %d)", name.c_str(), id);
+    }
+
+    // input and output blocks
+    ctrlnum_ = ctrlspec_ == mjCHART_QUAT ? 4 : 3;
+    outnum_ = 3;
+    so3_ = true;
+  }
+
+  // input signature selection is so3-only
+  if (ctrlspec && gaintype != mjGAIN_SO3) {
+    throw mjCError(this, "input is only available for so3 actuators, actuator '%s' (id = %d)",
+                   name.c_str(), id);
+  }
+
   // check damping/armature only valid for joint and tendon transmission
   bool has_damping = false;
   for (int i = 0; i < mjNPOLY+1; i++) {
@@ -7234,7 +7315,7 @@ void mjCActuator::Compile(void) {
 
   // check and set actdim
   if (!plugin.active) {
-    if (actdim > 1 && dyntype != mjDYN_USER && dyntype != mjDYN_DCMOTOR) {
+    if (actdim > 1 && dyntype != mjDYN_USER && dyntype != mjDYN_DCMOTOR && !so3_) {
       throw mjCError(this, "actdim > 1 is only allowed for dyntype 'user' and 'dcmotor'");
     }
     if (actdim == 1 && dyntype == mjDYN_NONE) {
@@ -7970,6 +8051,11 @@ void mjCSensor::Compile(void) {
 
   dim = mjs_sensorDim(this);
 
+  // actuator sensors report one value per force output
+  if (type == mjSENS_ACTUATORPOS || type == mjSENS_ACTUATORVEL || type == mjSENS_ACTUATORFRC) {
+    dim = ((mjCActuator*)obj)->outnum_;
+  }
+
   // check cutoff for incompatible data types
   if (cutoff > 0 && (datatype == mjDATATYPE_QUATERNION ||
                      (datatype == mjDATATYPE_AXIS && type != mjSENS_GEOMNORMAL))) {