Fix bugs related to saving of <statistics> values.

Before this change:
- User-modified values of `mjModel.stat.{meanmass, meaninertia}` would not be saved to XML.
- Non-user-modified values of `mjModel.stat.{meansize, extent, center}` would always get saved to XML.

After this change values are saved to XML only if provided by the user, either in the XML or by changing values in `mjModel` before saving.

PiperOrigin-RevId: 589473351
Change-Id: I4dcf4892ef61c35edf424226e731232d861bad8d

src/user/user_model.cc

@@ -114,6 +114,16 @@ mjCModel::mjCModel() {
   center[0] = mjNAN;
   center[1] = center[2] = 0;
 
+  //------------------------ auto-computed statistics
+#ifndef MEMORY_SANITIZER
+  // initializing as best practice, but want MSAN to catch unintialized use
+  meaninertia_auto = 0;
+  meanmass_auto = 0;
+  meansize_auto = 0;
+  extent_auto = 0;
+  center_auto[0] = center_auto[1] = center_auto[2] = 0;
+#endif
+
   //------------------------ engine data
   modelname = "MuJoCo Model";
   mj_defaultOption(&option);
@@ -3157,6 +3167,13 @@ void mjCModel::TryCompile(mjModel*& m, mjData*& d, const mjVFS* vfs) {
   // actuator lengthrange computation
   LengthRange(m, d);
 
+  // save automatically-computed statistics, to disambiguate when saving
+  extent_auto = m->stat.extent;
+  meaninertia_auto = m->stat.meaninertia;
+  meanmass_auto = m->stat.meanmass;
+  meansize_auto = m->stat.meansize;
+  copyvec(center_auto, m->stat.center, 3);
+
   // override model statistics if defined by user
   if (mjuu_defined(extent)) m->stat.extent = (mjtNum)extent;
   if (mjuu_defined(meaninertia)) m->stat.meaninertia = (mjtNum)meaninertia;
@@ -3233,10 +3250,16 @@ bool mjCModel::CopyBack(const mjModel* m) {
   option = m->opt;
   visual = m->vis;
 
-  // runtime-modifiable members of mjStatistic
-  meansize = m->stat.meansize;
-  extent = m->stat.extent;
-  mju_copy3(center, m->stat.center);
+  // runtime-modifiable members of mjStatistic, if different from computed values
+  if (m->stat.meaninertia != meaninertia_auto) meaninertia = m->stat.meaninertia;
+  if (m->stat.meanmass != meanmass_auto) meanmass = m->stat.meanmass;
+  if (m->stat.meansize != meansize_auto) meansize = m->stat.meansize;
+  if (m->stat.extent != extent_auto) extent = m->stat.extent;
+  if (m->stat.center[0] != center_auto[0] ||
+      m->stat.center[1] != center_auto[1] ||
+      m->stat.center[2] != center_auto[2]) {
+    mju_copy3(center, m->stat.center);
+  }
 
   // qpos0, qpos_spring
   for (int i=0; i<njnt; i++) {

src/user/user_model.h

@@ -292,10 +292,18 @@ class mjCModel {
   std::vector<mjCCamera*> cameras;  // list of cameras
   std::vector<mjCLight*>  lights;   // list of lights
 
+  //------------------------ internal variables
+
+  // statistics, as computed by mj_setConst
+  double meaninertia_auto;        // mean diagonal inertia, as computed by mj_setConst
+  double meanmass_auto;           // mean body mass, as computed by mj_setConst
+  double meansize_auto;           // mean body size, as computed by mj_setConst
+  double extent_auto;             // spatial extent, as computed by mj_setConst
+  double center_auto[3];          // center of model, as computed by mj_setConst
+
   // map from object names to ids
   mjListKeyMap ids;
 
-  //------------------------ internal variables
   bool hasImplicitPluginElem;     // already encountered an implicit plugin sensor/actuator
   bool compiled;                  // already compiled flag (cannot be compiled again)
   mjCError errInfo;               // last error info