Add two new attributes to weld constraints:

- `anchor` determines the point of wrench application, in the frame of body2.
- `tfratio` scales applied torques relative to applied forces.
- Add visualisation of both anchor points to both weld and connect constraints.
- Add a test model showing how the new weld parameters behave.

PiperOrigin-RevId: 469228149
Change-Id: I836b0791f10fb624607a12ef3c687da991c21789

doc/APIreference.rst

@@ -3162,7 +3162,7 @@ Numeric constants
 +------------------+--------+----------------------------------------------------------------------------------------+
 | mjMAXVFSNAME     | 100    | The maximal number of characters in the name of each file in the virtual file system.  |
 +------------------+--------+----------------------------------------------------------------------------------------+
-| mjNEQDATA        | 11     | The maximal number of real-valued parameters used to define each equality constraint.  |
+| mjNEQDATA        | 7      | The maximal number of real-valued parameters used to define each equality constraint.  |
 |                  |        | Determines the size of mjModel.eq_data. This and the next five constants correspond to |
 |                  |        | array sizes which we have not fully settled. There may be reasons to increase them in  |
 |                  |        | the future, so as to accommodate extra parameters needed for more elaborate            |

doc/XMLreference.rst

@@ -812,9 +812,7 @@ in the second column of the table have the following meaning:
 |                          |    |    +-------------------------+-------------------------+-------------------------+ |
 |                          |    |    | :at:`body2`             | :at:`relpose`           | :at:`active`            | |
 |                          |    |    +-------------------------+-------------------------+-------------------------+ |
-|                          |    |    | :at:`solref`            | :at:`solimp`            | :at:`anchor`            | |
+|                          |    |    | :at:`solref`            | :at:`solimp`            |                         | |
-|                          |    |    +-------------------------+-------------------------+-------------------------+ |
-|                          |    |    | :at:`tfratio`           |                         |                         | |
 |                          |    |    +-------------------------+-------------------------+-------------------------+ |
 +--------------------------+----+------------------------------------------------------------------------------------+
 | |_2|:el:`joint`          | \* | .. table::                                                                         |
@@ -4022,16 +4020,6 @@ of the other body, without any joint elements in the child body.
    body1. If the quaternion part (i.e., last 4 components of the vector) are all zeros, as in the default setting, this
    attribute is ignored and the relative pose is the one corresponding to the model reference pose in qpos0. The unusual
    default is because all equality constraint types share the same default for their numeric parameters.
-:at:`anchor`: :at-val:`real(3), "0 0 0"`
-   Coordinates of the weld point relative to body2. If :at:`relpose` is not specified, the meaning of
-   this parameter is the same as for connect constraints, except that is relative to body2. If :at:`relpose` is
-   specified, body1 will use the pose to compute its anchor point.
-:at:`tfratio`: :at-val:`real, "1"`
-   Relative torque-to-force ratio. This ratio is used by the weld to scale how much it "cares" about rotational
-   displacements vs. translational displacements. Setting this value to 0 makes the :el:`weld` behave like a
-   :el:`connect` constraint. Note that this value has units of length and can therefore be interpreted as follows.
-   Imagining that the weld is implemented by a patch of glue sticking the two bodies together, :at:`tfratio` can be
-   interpreted as the diameter of this glue patch.
 
 .. _equality-joint:
 

doc/changelog.rst

@@ -15,13 +15,8 @@ General
 - Added :ref:`adhesion actuators<adhesion>` mimicking vacuum grippers and adhesive biomechanical appendages.
 - Added related `example model <https://github.com/deepmind/mujoco/tree/main/model/adhesion>`_ and video:
 - Added :ref:`mj_jacSubtreeCom` for computing the translational Jacobian of the center-of-mass of a subtree.
-- Added :at:`tfratio` and :at:`anchor` attributes to :el:`weld` constraints. :at:`tfratio` sets the torque-to-force
+- Added moment of inertia computation for concave meshes. This is currently activated by setting the compiler flag
-  ratio exerted by the constraint, :at:`anchor` sets the point at which the weld wrench is applied. See
+  :at:`exactmeshinertia` to ``true`` (defaults to ``false``). This default may change in the future.
-  :ref:`weld <equality-weld>` for more details.
-- Added visualisation of anchor points for both :el:`connect` and :el:`weld` constraints (activated by the 'N' key in
-  ``simulate``).
-- Added `example model <https://github.com/deepmind/mujoco/tree/main/test/engine/testdata/weld.xml>`_ showing different
-  uses of new weld attributes.
 - Joint and tendon ``limited`` attribute and actuator ``ctrllimited``, ``forcelimited`` and ``actlimited`` attributes
   now default to ``auto`` rather than ``false``. Limits are automatically set to ``true`` if the corresponding range *is
   defined* and ``false`` otherwise.
@@ -30,8 +25,6 @@ General
     This is a minor breaking change. In models where a range was defined but :at:`limited` was unspecified, the target
     element will now be limited. Explicitly set limited to ``false`` to revert to the previous behavior.
 
-- Added moment of inertia computation for all well-formed meshes. This option is activated by setting the compiler
-  flag :at:`exactmeshinertia` to ``true`` (defaults to ``false``). This default may change in the future.
 - Added parameter :at:`shellinertia` to :at:`geom`, for locating the inferred inertia on the boundary (shell).
   Currently only meshes are supported.
 - For meshes from which volumetric inertia is inferred, raise error if the orientation of mesh faces is not consistent.

include/mujoco/mjmodel.h

@@ -30,7 +30,7 @@
 
 //---------------------------------- sizes ---------------------------------------------------------
 
-#define mjNEQDATA       11        // number of eq_data fields
+#define mjNEQDATA       7         // number of eq_data fields
 #define mjNDYN          10        // number of actuator dynamics parameters
 #define mjNGAIN         10        // number of actuator gain parameters
 #define mjNBIAS         10        // number of actuator bias parameters

src/engine/engine_core_constraint.c

@@ -398,16 +398,18 @@ void mj_instantiateEquality(const mjModel* m, mjData* d) {
         break;
 
       case mjEQ_WELD:                 // fix relative position and orientation
-        // find global points
+        // find global points and their Jacobians
         for (int j=0; j<2; j++) {
-          mjtNum* anchor = data + 3*(1-j);
+          // position offset for body1 only
-          mju_rotVecMat(pos[j], anchor, d->xmat + 9*id[j]);
+          if (j==0) {
+            mju_rotVecMat(pos[j], data, d->xmat + 9*id[j]);
+          } else {
+            mju_zero3(pos[j]);
+          }
+
           mju_addTo3(pos[j], d->xpos + 3*id[j]);
         }
 
-        // compute position error
-        mju_sub3(cpos, pos[0], pos[1]);
-
         // compute error Jacobian (opposite of contact: 0 - 1)
         NV = mj_jacDifPair(m, d, chain, id[1], id[0], pos[1], pos[0],
                            jac[1], jac[0], jacdif,
@@ -417,14 +419,19 @@ void mj_instantiateEquality(const mjModel* m, mjData* d) {
         mju_copy(jac[0], jacdif, 3*NV);
         mju_copy(jac[0]+3*NV, jacdif+3*nv, 3*NV);
 
-        // compute orientation error: neg(q1) * q0 * relpose (axis components only)
+        // get desired position offset in global frame
-        mjtNum* relpose = data+6;
+        mju_rotVecMat(cpos, data, d->xmat+9*id[0]);
-        mju_mulQuat(quat, d->xquat+4*id[0], relpose);   // quat = q0*relpose
+
+        // compute position error: p0 - p1 - data
+        mju_sub3(cpos, pos[0], pos[1]);
+
+        // compute orientation error: neg(q1) * q0 * data (axis components only)
+        mju_mulQuat(quat, d->xquat+4*id[0], data+3);    // quat = q0*data
         mju_negQuat(quat1, d->xquat+4*id[1]);           // quat1 = neg(q1)
-        mju_mulQuat(quat2, quat1, quat);                // quat2 = neg(q1)*q0*relpose
+        mju_mulQuat(quat2, quat1, quat);                // quat2 = neg(q1)*q0*data
         mju_copy3(cpos+3, quat2+1);                     // copy axis components
 
-        // correct rotation Jacobian: 0.5 * neg(q1) * (jac0-jac1) * q0 * relpose
+        // correct rotation Jacobian: 0.5 * neg(q1) * (jac0-jac1) * q0 * data
         for (int j=0; j<NV; j++) {
           // axis = [jac0-jac1]_col(j)
           axis[0] = jac[0][3*NV+j];
@@ -433,7 +440,7 @@ void mj_instantiateEquality(const mjModel* m, mjData* d) {
 
           // apply formula
           mju_mulQuatAxis(quat2, quat1, axis);    // quat2 = neg(q1)*(jac0-jac1)
-          mju_mulQuat(quat3, quat2, quat);        // quat3 = neg(q1)*(jac0-jac1)*q0*relpose
+          mju_mulQuat(quat3, quat2, quat);        // quat3 = neg(q1)*(jac0-jac1)*q0*data
 
           // correct Jacobian
           jac[0][3*NV+j] = 0.5*quat3[1];
@@ -441,10 +448,6 @@ void mj_instantiateEquality(const mjModel* m, mjData* d) {
           jac[0][5*NV+j] = 0.5*quat3[3];
         }
 
-        // scale rotational jacobian by tfratio factor
-        mjtNum tfratio = data[10];
-        mju_scl(jac[0]+3*NV, jac[0]+3*NV, tfratio, 3*NV);
-
         size = 6;
         break;
 
@@ -1051,16 +1054,8 @@ static void getposdim(const mjModel* m, const mjData* d, int i, mjtNum* pos, int
 
   case mjCNSTR_EQUALITY:
     if (m->eq_type[id]==mjEQ_WELD) {
-      mjtNum rotlinratio = m->eq_data[mjNEQDATA*id+10];
-      mjtNum efc_pos[6];
-
-      // copy translational residual
-      mju_copy3(efc_pos, d->efc_pos+i);
-
-      // multiply orientations by tfratio
-      mju_scl3(efc_pos+3, d->efc_pos+i+3, rotlinratio);
       *dim = 6;
-      *pos = mju_norm(efc_pos, 6);
+      *pos = mju_norm(d->efc_pos+i, 6);  // mixes translation and rotation!
     } else if (m->eq_type[id]==mjEQ_CONNECT) {
       *dim = 3;
       *pos = mju_norm(d->efc_pos+i, 3);

src/engine/engine_core_smooth.c

@@ -1814,7 +1814,7 @@ void mj_rne(const mjModel* m, mjData* d, int flg_acc, mjtNum* result) {
 // RNE with complete data: compute cacc, cfrc_ext, cfrc_int
 void mj_rnePostConstraint(const mjModel* m, mjData* d) {
   int nbody=m->nbody;
-  mjtNum cfrc_com[6], cfrc[6], lfrc[6];
+  mjtNum cfrc_body[6], tmp[6], tmp1[6];
   mjContact* con;
 
   // clear cacc, set world acceleration to -gravity
@@ -1828,14 +1828,14 @@ void mj_rnePostConstraint(const mjModel* m, mjData* d) {
   for (int i=1; i<nbody; i++)
     if (!mju_isZero(d->xfrc_applied+6*i, 6)) {
       // rearrange as torque:force
-      mju_copy3(cfrc, d->xfrc_applied+6*i+3);
+      mju_copy3(tmp1, d->xfrc_applied+6*i+3);
-      mju_copy3(cfrc+3, d->xfrc_applied+6*i);
+      mju_copy3(tmp1+3, d->xfrc_applied+6*i);
 
       // map force from application point to com; both world-oriented
-      mju_transformSpatial(cfrc_com, cfrc, 1, d->subtree_com+3*m->body_rootid[i], d->xipos+3*i, 0);
+      mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[i], d->xipos+3*i, 0);
 
       // accumulate
-      mju_addTo(d->cfrc_ext+6*i, cfrc_com, 6);
+      mju_addTo(d->cfrc_ext+6*i, tmp, 6);
     }
 
   // cfrc_ext += contacts
@@ -1845,29 +1845,29 @@ void mj_rnePostConstraint(const mjModel* m, mjData* d) {
       con = d->contact+i;
 
       // tmp = contact-local force:torque vector
-      mj_contactForce(m, d, i, lfrc);
+      mj_contactForce(m, d, i, tmp);
 
-      // cfrc = world-oriented torque:force vector (swap in the process)
+      // tmp1 = world-oriented torque:force vector (swap in the process)
-      mju_rotVecMatT(cfrc, lfrc+3, con->frame);
+      mju_rotVecMatT(tmp1, tmp+3, con->frame);
-      mju_rotVecMatT(cfrc+3, lfrc, con->frame);
+      mju_rotVecMatT(tmp1+3, tmp, con->frame);
 
       // body 1
       int k;
       if ((k = m->geom_bodyid[con->geom1])) {
         // tmp = subtree CoM-based torque_force vector
-        mju_transformSpatial(cfrc_com, cfrc, 1, d->subtree_com+3*m->body_rootid[k], con->pos, 0);
+        mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[k], con->pos, 0);
 
         // apply (opposite for body 1)
-        mju_subFrom(d->cfrc_ext+6*k, cfrc_com, 6);
+        mju_subFrom(d->cfrc_ext+6*k, tmp, 6);
       }
 
       // body 2
       if ((k = m->geom_bodyid[con->geom2])) {
         // tmp = subtree CoM-based torque_force vector
-        mju_transformSpatial(cfrc_com, cfrc, 1, d->subtree_com+3*m->body_rootid[k], con->pos, 0);
+        mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[k], con->pos, 0);
 
         // apply
-        mju_addTo(d->cfrc_ext+6*k, cfrc_com, 6);
+        mju_addTo(d->cfrc_ext+6*k, tmp, 6);
       }
     }
 
@@ -1883,41 +1883,73 @@ void mj_rnePostConstraint(const mjModel* m, mjData* d) {
     int k;
     switch (m->eq_type[id]) {
     case mjEQ_CONNECT:
-    case mjEQ_WELD:
+      // tmp1 = world-oriented torque:force vector
-      // cfrc = world-oriented torque:force vector
+      mju_zero3(tmp1);  // no torque from connect
-      mju_copy3(cfrc + 3, d->efc_force + i);
+      mju_copy3(tmp1 + 3, d->efc_force + i);
-      if (m->eq_type[id]==mjEQ_WELD) {
-        mju_copy3(cfrc, d->efc_force + i + 3);
-      } else {
-        mju_zero3(cfrc);  // no torque from connect
-      }
 
       // body 1
       if ((k = m->eq_obj1id[id])) {
-        // transform point on body1: local -> global
+        // transform connect point on body1: local -> global
-        mj_local2Global(d, pos, 0, eq_data + 3*(m->eq_type[id]==mjEQ_WELD), 0, k, 0);
+        mju_rotVecMat(pos, eq_data, d->xmat+9*k);
+        mju_addTo3(pos, d->xpos+3*k);
 
         // tmp = subtree CoM-based torque_force vector
-        mju_transformSpatial(cfrc_com, cfrc, 1, d->subtree_com+3*m->body_rootid[k], pos, 0);
+        mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[k], pos, 0);
 
         // apply (opposite for body 1)
-        mju_addTo(d->cfrc_ext+6*k, cfrc_com, 6);
+        mju_addTo(d->cfrc_ext+6*k, tmp, 6);
       }
 
       // body 2
       if ((k = m->eq_obj2id[id])) {
-        // transform point on body2: local -> global
+        // transform connect point on body2: local -> global
-        mj_local2Global(d, pos, 0, eq_data + 3*(m->eq_type[id]==mjEQ_CONNECT), 0, k, 0);
+        mju_rotVecMat(pos, eq_data + 3, d->xmat+9*k);
+        mju_addTo3(pos, d->xpos+3*k);
 
         // tmp = subtree CoM-based torque_force vector
-        mju_transformSpatial(cfrc_com, cfrc, 1, d->subtree_com+3*m->body_rootid[k], pos, 0);
+        mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[k], pos, 0);
 
         // apply
-        mju_subFrom(d->cfrc_ext+6*k, cfrc_com, 6);
+        mju_subFrom(d->cfrc_ext+6*k, tmp, 6);
       }
 
-      // increment rows
+      // increment 3 rows of connect
-      i += m->eq_type[id]==mjEQ_WELD ? 6 : 3;
+      i += 3;
+
+      break;
+
+    case mjEQ_WELD:
+      // tmp1 = world-oriented torque:force vector (efc is f:t, so swap)
+      mju_copy3(tmp1, d->efc_force + i + 3);
+      mju_copy3(tmp1 + 3, d->efc_force + i);
+
+      // body 1
+      if ((k = m->eq_obj1id[id])) {
+        // transform weld point on body1: local -> global
+        mju_rotVecMat(pos, eq_data, d->xmat+9*k);
+        mju_addTo3(pos, d->xpos+3*k);
+
+        // tmp = subtree CoM-based torque_force vector
+        mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[k], pos, 0);
+
+        // apply (opposite for body 1)
+        mju_addTo(d->cfrc_ext+6*k, tmp, 6);
+      }
+
+      // body 2
+      if ((k = m->eq_obj2id[id])) {
+        // weld force on body2 is always applied at body root
+        mju_copy3(pos, d->xpos+3*k);
+
+        // tmp = subtree CoM-based torque_force vector
+        mju_transformSpatial(tmp, tmp1, 1, d->subtree_com+3*m->body_rootid[k], pos, 0);
+
+        // apply
+        mju_subFrom(d->cfrc_ext+6*k, tmp, 6);
+      }
+
+      // increment 6 rows of weld
+      i += 6;
       break;
 
     case mjEQ_JOINT:
@@ -1935,23 +1967,22 @@ void mj_rnePostConstraint(const mjModel* m, mjData* d) {
   }
 
   // forward pass over bodies: compute cacc, cfrc_int
-  mjtNum cacc[6], cfrc_body[6], cfrc_corr[6];
   mju_zero(d->cfrc_int, 6);
   for (int i=1; i<m->nbody; i++) {
     // get body's first dof address
     int bda = m->body_dofadr[i];
 
     // cacc = cacc_parent + cdofdot * qvel + cdof * qacc
-    mju_mulDofVec(cacc, d->cdof_dot+6*bda, d->qvel+bda, m->body_dofnum[i]);
+    mju_mulDofVec(tmp, d->cdof_dot+6*bda, d->qvel+bda, m->body_dofnum[i]);
-    mju_add(d->cacc+6*i, d->cacc+6*m->body_parentid[i], cacc, 6);
+    mju_add(d->cacc+6*i, d->cacc+6*m->body_parentid[i], tmp, 6);
-    mju_mulDofVec(cacc, d->cdof+6*bda, d->qacc+bda, m->body_dofnum[i]);
+    mju_mulDofVec(tmp, d->cdof+6*bda, d->qacc+bda, m->body_dofnum[i]);
-    mju_addTo(d->cacc+6*i, cacc, 6);
+    mju_addTo(d->cacc+6*i, tmp, 6);
 
     // cfrc_body = cinert * cacc + cvel x (cinert * cvel)
     mju_mulInertVec(cfrc_body, d->cinert+10*i, d->cacc+6*i);
-    mju_mulInertVec(cfrc_corr, d->cinert+10*i, d->cvel+6*i);
+    mju_mulInertVec(tmp, d->cinert+10*i, d->cvel+6*i);
-    mju_crossForce(cfrc, d->cvel+6*i, cfrc_corr);
+    mju_crossForce(tmp1, d->cvel+6*i, tmp);
-    mju_addTo(cfrc_body, cfrc, 6);
+    mju_addTo(cfrc_body, tmp1, 6);
 
     // set cfrc_int = cfrc_body - cfrc_ext
     mju_sub(d->cfrc_int+6*i, cfrc_body, d->cfrc_ext+6*i, 6);

src/engine/engine_setconst.c

@@ -185,25 +185,22 @@ static void set0(mjModel* m, mjData* d) {
     // weld constraint
     else if (m->eq_type[i]==mjEQ_WELD) {
       // skip if user has set any quaternion data
-      if (m->eq_data[mjNEQDATA*i+6] ||
+      if (m->eq_data[mjNEQDATA*i+3] ||
-          m->eq_data[mjNEQDATA*i+7] ||
+          m->eq_data[mjNEQDATA*i+4] ||
-          m->eq_data[mjNEQDATA*i+8] ||
+          m->eq_data[mjNEQDATA*i+5] ||
-          m->eq_data[mjNEQDATA*i+9]) {
+          m->eq_data[mjNEQDATA*i+6]) {
         // normalize quaternion just in case
-        mju_normalize4(m->eq_data+mjNEQDATA*i+6);
+        mju_normalize4(m->eq_data+mjNEQDATA*i+3);
         continue;
       }
 
-      // anchor position is in body2 local frame
+      // data[0-2] = xpos2-xpos1 in body1 local frame
-      mj_local2Global(d, pos, 0, m->eq_data+mjNEQDATA*i, 0, id2, 0);
+      mju_sub3(pos, d->xpos+3*id2, d->xpos+3*id1);
+      mju_rotVecMatT(m->eq_data+mjNEQDATA*i, pos, d->xmat+9*id1);
 
-      // data[3-5] = anchor position in body1 local frame
+      // data[3-6] = neg(xquat1)*xquat2 = "xquat2-xquat1" in body1 local frame
-      mju_subFrom3(pos, d->xpos+3*id1);
-      mju_rotVecMatT(m->eq_data+mjNEQDATA*i+3, pos, d->xmat+9*id1);
-
-      // data[6-9] = neg(xquat1)*xquat2 = "xquat2-xquat1" in body1 local frame
       mju_negQuat(quat, d->xquat+4*id1);
-      mju_mulQuat(m->eq_data+mjNEQDATA*i+6, quat, d->xquat+4*id2);
+      mju_mulQuat(m->eq_data+mjNEQDATA*i+3, quat, d->xquat+4*id2);
     }
   }
 

src/engine/engine_vis_visualize.c

@@ -1606,31 +1606,33 @@ void mjv_addGeoms(const mjModel* m, mjData* d, const mjvOption* vopt,
   objtype = mjOBJ_EQUALITY;
   category = mjCAT_DECOR;
   if (vopt->flags[mjVIS_CONSTRAINT] && (category & catmask) && m->neq) {
-    // connect or weld
+    // connect
     for (int i=0; i<m->neq; i++) {
-      if (m->eq_active[i] && (m->eq_type[i]==mjEQ_CONNECT || m->eq_type[i]==mjEQ_WELD)) {
+      if (m->eq_active[i] && m->eq_type[i]==mjEQ_CONNECT) {
         // compute endpoints in global coordinates
-        int j = m->eq_obj1id[i], k = m->eq_obj2id[i];
+        int j = m->eq_obj1id[i];
-        mju_rotVecMat(vec, m->eq_data+mjNEQDATA*i+3*(m->eq_type[i]==mjEQ_WELD), d->xmat+9*j);
+        int k = m->eq_obj2id[i];
+        mju_rotVecMat(vec, m->eq_data+mjNEQDATA*i, d->xmat+9*j);
         mju_addTo3(vec, d->xpos+3*j);
-        mju_rotVecMat(end, m->eq_data+mjNEQDATA*i+3*(m->eq_type[i]==mjEQ_CONNECT), d->xmat+9*k);
+        mju_rotVecMat(end, m->eq_data+mjNEQDATA*i+3, d->xmat+9*k);
         mju_addTo3(end, d->xpos+3*k);
 
+        // connect endpoints
+        START
+
         // construct geom
         sz[0] = scl * m->vis.scale.constraint;
+        mjv_makeConnector(thisgeom, mjGEOM_CAPSULE, sz[0],
+                          vec[0], vec[1], vec[2],
+                          end[0], end[1], end[2]);
 
-        START
+        f2f(thisgeom->rgba, m->vis.rgba.constraint, 4);
-        mjv_initGeom(thisgeom, mjGEOM_SPHERE, sz, vec, d->xmat+9*j, m->vis.rgba.connect);
+
+        // label flag
         if (vopt->label==mjLABEL_CONSTRAINT) {
           makeLabel(m, mjOBJ_EQUALITY, i, thisgeom->label);
         }
-        FINISH
 
-        START
-        mjv_initGeom(thisgeom, mjGEOM_SPHERE, sz, end, d->xmat+9*k, m->vis.rgba.constraint);
-        if (vopt->label==mjLABEL_CONSTRAINT) {
-          makeLabel(m, mjOBJ_EQUALITY, i, thisgeom->label);
-        }
         FINISH
       }
     }

src/user/user_objects.cc

@@ -2884,7 +2884,6 @@ mjCEquality::mjCEquality(mjCModel* _model, mjCDef* _def) {
 
   mjuu_zerovec(data, mjNEQDATA);
   data[1] = 1;
-  data[10] = 1;  // torque:force ratio
 
   // clear internal variables
   obj1id = obj2id = -1;
@@ -2972,11 +2971,6 @@ void mjCEquality::Compile(void) {
   if (type==mjEQ_CONNECT) {
     ((mjCBody*)px1)->MakeLocal(anchor, qdummy, data, qunit);
     mjuu_copyvec(data, anchor, 3);
-  } else if (type==mjEQ_WELD) {
-    if (px2) {
-      ((mjCBody*)px2)->MakeLocal(anchor, qdummy, data, qunit);
-      mjuu_copyvec(data, anchor, 3);
-    }
   }
 }
 

src/user/user_objects.h

@@ -752,8 +752,8 @@ class mjCEquality : public mjCBase {
   double data[mjNEQDATA];         // type-dependent data
 
  private:
-  mjCEquality(mjCModel* = 0, mjCDef* = 0);  // constructor
+  mjCEquality(mjCModel* = 0, mjCDef* = 0);// constructor
-  void Compile(void);                       // compiler
+  void Compile(void);                     // compiler
 
   int obj1id;                     // id of object 1
   int obj2id;                     // id of object 2

src/xml/xml_native_reader.cc

@@ -234,8 +234,8 @@ static const char* MJCF[nMJCF][mjXATTRNUM] = {
     {"<"},
         {"connect", "*", "8", "name", "class", "body1", "body2", "anchor",
             "active", "solref", "solimp"},
-        {"weld", "*", "10", "name", "class", "body1", "body2", "relpose", "anchor",
+        {"weld", "*", "8", "name", "class", "body1", "body2", "relpose",
-            "active", "solref", "solimp", "tfratio"},
+            "active", "solref", "solimp"},
         {"joint", "*", "8", "name", "class", "joint1", "joint2", "polycoef",
             "active", "solref", "solimp"},
         {"tendon", "*", "8", "name", "class", "tendon1", "tendon2", "polycoef",
@@ -1310,11 +1310,7 @@ void mjXReader::OneEquality(XMLElement* elem, mjCEquality* pequality) {
     case mjEQ_WELD:
       ReadAttrTxt(elem, "body1", pequality->name1, true);
       ReadAttrTxt(elem, "body2", pequality->name2);
-      ReadAttr(elem, "relpose", 7, pequality->data+3, text);
+      ReadAttr(elem, "relpose", mjNEQDATA, pequality->data, text);
-      ReadAttr(elem, "tfratio", 1, pequality->data+10, text);
-      if (!ReadAttr(elem, "anchor", 3, pequality->data, text)) {
-        mjuu_zerovec(pequality->data, 3);
-      }
       break;
 
     case mjEQ_JOINT:

src/xml/xml_native_writer.cc

@@ -456,9 +456,7 @@ void mjXWriter::OneEquality(XMLElement* elem, mjCEquality* peq, mjCDef* def) {
     case mjEQ_WELD:
       WriteAttrTxt(elem, "body1", peq->name1);
       WriteAttrTxt(elem, "body2", peq->name2);
-      WriteAttr(elem, "anchor", 3, peq->data);
+      WriteAttr(elem, "relpose", 7, peq->data);
-      WriteAttr(elem, "tfratio", 1, peq->data+10);
-      WriteAttr(elem, "relpose", 7, peq->data+3);
       break;
 
     case mjEQ_JOINT:

test/engine/engine_core_smooth_test.cc

@@ -56,9 +56,10 @@ TEST_F(CoreSmoothTest, MjKinematicsWorldXipos) {
 
 // --------------------------- connect constraint ------------------------------
 
-// test that bodies hanging on connects lead to expected force sensor readings
+TEST_F(CoreSmoothTest, RnePostConnectForceSlide) {
-void TestConnect(const char* const filepath) {
+  static const char* const kModelFilePath =
-  const std::string xml_path = GetTestDataFilePath(filepath);
+      "engine/testdata/core_smooth/rne_post/connect/force_slide.xml";
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
   mjModel* model =
       mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
   mjData* data = mj_makeData(model);
@@ -74,46 +75,88 @@ void TestConnect(const char* const filepath) {
 }
 
 
-TEST_F(CoreSmoothTest, RnePostConnectForceSlide) {
-  constexpr char kModelFilePath[] =
-      "engine/testdata/core_smooth/rne_post/connect/force_slide.xml";
-  TestConnect(kModelFilePath);
-}
-
-
 TEST_F(CoreSmoothTest, RnePostConnectForceSlideRotated) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
       "engine/testdata/core_smooth/rne_post/connect/force_slide_rotated.xml";
-  TestConnect(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
+  mjModel* model =
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
+  mjData* data = mj_makeData(model);
+  // settle physics:
+  for (int i=0; i < 1000; i++) {
+    mj_step(model, data);
+  }
+  for (int i=0; i < 3; i++) {
+    EXPECT_NEAR(data->sensordata[i], model->sensor_user[i], 1e-6);
+  }
+  mj_deleteData(data);
+  mj_deleteModel(model);
 }
 
 
 TEST_F(CoreSmoothTest, RnePostConnectForceFree) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
       "engine/testdata/core_smooth/rne_post/connect/force_free.xml";
-  TestConnect(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
+  mjModel* model =
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
+  mjData* data = mj_makeData(model);
+  // settle physics:
+  for (int i=0; i < 1000; i++) {
+    mj_step(model, data);
+  }
+  for (int i=0; i < 3; i++) {
+    EXPECT_NEAR(data->sensordata[i], model->sensor_user[i], 1e-6);
+  }
+  mj_deleteData(data);
+  mj_deleteModel(model);
 }
 
 
 TEST_F(CoreSmoothTest, RnePostConnectTorque) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
       "engine/testdata/core_smooth/rne_post/connect/torque_free.xml";
-  TestConnect(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
+  mjModel* model =
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
+  mjData* data = mj_makeData(model);
+  // settle physics:
+  for (int i=0; i < 1000; i++) {
+    mj_step(model, data);
+  }
+  for (int i=0; i < 3; i++) {
+    EXPECT_NEAR(data->sensordata[i], model->sensor_user[i], 1e-6);
+  }
+  mj_deleteData(data);
+  mj_deleteModel(model);
 }
 
 
 TEST_F(CoreSmoothTest, RnePostConnectMultipleConstraints) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
       "engine/testdata/core_smooth/rne_post/connect/multiple_constraints.xml";
-  TestConnect(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
+  mjModel* model =
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
+  mjData* data = mj_makeData(model);
+  // settle physics:
+  for (int i=0; i < 1000; i++) {
+    mj_step(model, data);
+  }
+  for (int i=0; i < 3; i++) {
+    EXPECT_NEAR(data->sensordata[i], model->sensor_user[i], 1e-6);
+  }
+  mj_deleteData(data);
+  mj_deleteModel(model);
 }
 
 
 // --------------------------- weld constraint ---------------------------------
 
-// test that bodies attached with welds lead to expected force sensor readings
+TEST_F(CoreSmoothTest, RnePostWeldForceFree) {
-void TestWeld(const char* const filepath) {
+  static const char* const kModelFilePath =
-  const std::string xml_path = GetTestDataFilePath(filepath);
+      "engine/testdata/core_smooth/rne_post/weld/force_free.xml";
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
   mjModel* model =
       mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
   mjData* data = mj_makeData(model);
@@ -134,65 +177,75 @@ void TestWeld(const char* const filepath) {
 }
 
 
-TEST_F(CoreSmoothTest, RnePostWeldForceFree) {
+TEST_F(CoreSmoothTest, RnePostWeldForceFreeRotatoed) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
-      "engine/testdata/core_smooth/rne_post/weld/force_free.xml";
-  TestWeld(kModelFilePath);
-}
-
-
-TEST_F(CoreSmoothTest, RnePostWeldForceFreeRotated) {
-  constexpr char kModelFilePath[] =
       "engine/testdata/core_smooth/rne_post/weld/force_free_rotated.xml";
-  TestWeld(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
+  mjModel* model =
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
+  mjData* data = mj_makeData(model);
+  // settle physics:
+  for (int i=0; i < 1000; i++) {
+    mj_step(model, data);
+  }
+  for (int sensor_index=0; sensor_index < model->nsensor; sensor_index++) {
+    for (int i=0; i < 3; i++) {
+      EXPECT_NEAR(
+          data->sensordata[model->sensor_adr[sensor_index] + i],
+          model->sensor_user[model->nuser_sensor*sensor_index + i],
+          1e-6);
+    }
+  }
+  mj_deleteData(data);
+  mj_deleteModel(model);
 }
 
 
 TEST_F(CoreSmoothTest, RnePostWeldForceTorqueFree) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
       "engine/testdata/core_smooth/rne_post/weld/force_torque_free.xml";
-  TestWeld(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
+  mjModel* model =
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
+  mjData* data = mj_makeData(model);
+  // settle physics:
+  for (int i=0; i < 1000; i++) {
+    mj_step(model, data);
+  }
+  for (int sensor_index=0; sensor_index < model->nsensor; sensor_index++) {
+    for (int i=0; i < 3; i++) {
+      EXPECT_NEAR(
+          data->sensordata[model->sensor_adr[sensor_index] + i],
+          model->sensor_user[model->nuser_sensor*sensor_index + i],
+          1e-6);
+    }
+  }
+  mj_deleteData(data);
+  mj_deleteModel(model);
 }
 
 
 TEST_F(CoreSmoothTest, RnePostWeldForceTorqueFreeRotated) {
-  constexpr char kModelFilePath[] =
+  static const char* const kModelFilePath =
       "engine/testdata/core_smooth/rne_post/weld/force_torque_free_rotated.xml";
-  TestWeld(kModelFilePath);
+  const std::string xml_path = GetTestDataFilePath(kModelFilePath);
-}
+  mjModel* model =
-
+      mj_loadXML(xml_path.c_str(), nullptr, 0, 0);
-
+  mjData* data = mj_makeData(model);
-TEST_F(CoreSmoothTest, WeldRatioForceFree) {
+  // settle physics:
-  constexpr char kModelFilePath[] =
+  for (int i=0; i < 1000; i++) {
-      "engine/testdata/core_smooth/rne_post/weld/tfratio0_force_free.xml";
+    mj_step(model, data);
-  TestConnect(kModelFilePath);
+  }
-}
+  for (int sensor_index=0; sensor_index < model->nsensor; sensor_index++) {
-
+    for (int i=0; i < 3; i++) {
-
+      EXPECT_NEAR(
-TEST_F(CoreSmoothTest, WeldRatioForceSlide) {
+          data->sensordata[model->sensor_adr[sensor_index] + i],
-  constexpr char kModelFilePath[] =
+          model->sensor_user[model->nuser_sensor*sensor_index + i],
-      "engine/testdata/core_smooth/rne_post/weld/tfratio0_force_slide.xml";
+          1e-6);
-  TestConnect(kModelFilePath);
+    }
-}
+  }
-
+  mj_deleteData(data);
-
+  mj_deleteModel(model);
-TEST_F(CoreSmoothTest, WeldRatioTorqueFree) {
-  constexpr char kModelFilePath[] =
-      "engine/testdata/core_smooth/rne_post/weld/tfratio0_torque_free.xml";
-  TestConnect(kModelFilePath);
-}
-
-
-TEST_F(CoreSmoothTest, WeldRatioForceSlideRotated) {
-  constexpr char kModelFilePath[] =
-      "engine/testdata/core_smooth/rne_post/weld/tfratio0_force_slide_rotated.xml";
-  TestConnect(kModelFilePath);
-}
-
-TEST_F(CoreSmoothTest, WeldRatioMultipleConstraints) {
-  constexpr char kModelFilePath[] =
-      "engine/testdata/core_smooth/rne_post/weld/tfratio0_multiple_constraints.xml";
-  TestConnect(kModelFilePath);
 }
 
 

test/engine/testdata/core_smooth/rne_post/weld/tfratio0_force_free.xml

@@ -1,43 +0,0 @@
-<!-- Copyright 2021 DeepMind Technologies Limited
-     Licensed under the Apache License, Version 2.0 (the "License");
-     you may not use this file except in compliance with the License.
-     You may obtain a copy of the License at
-         http://www.apache.org/licenses/LICENSE-2.0
-     Unless required by applicable law or agreed to in writing, software
-     distributed under the License is distributed on an "AS IS" BASIS,
-     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-     See the License for the specific language governing permissions and
-     limitations under the License.
--->
-
-<mujoco>
-  <!--
-  body2 is held by body1 through the weld constraint, so the force sensor on body1
-  should register -2*gravity (for the weight of both bodies).
-  -->
-  <option gravity="1 2 3"/>
-
-  <default>
-    <!-- A cube of size 0.1^3 with density of 1000 has mass of 1. -->
-    <geom density="1000" size="0.05 0.05 0.05" type="box"/>
-  </default>
-
-  <worldbody>
-    <body name="body1">
-      <geom/>
-      <site name="sensor"/>
-    </body>
-    <body name="body2" pos="1 2 3">
-      <joint type="free"/>
-      <geom/>
-    </body>
-  </worldbody>
-
-  <equality>
-    <weld body1="body1" body2="body2" anchor="0 0 0" tfratio="0"/>
-  </equality>
-
-  <sensor>
-    <force site="sensor" user="-2 -4 -6"/>
-  </sensor>
-</mujoco>

test/engine/testdata/core_smooth/rne_post/weld/tfratio0_force_slide.xml

@@ -1,43 +0,0 @@
-<!-- Copyright 2021 DeepMind Technologies Limited
-     Licensed under the Apache License, Version 2.0 (the "License");
-     you may not use this file except in compliance with the License.
-     You may obtain a copy of the License at
-         http://www.apache.org/licenses/LICENSE-2.0
-     Unless required by applicable law or agreed to in writing, software
-     distributed under the License is distributed on an "AS IS" BASIS,
-     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-     See the License for the specific language governing permissions and
-     limitations under the License.
--->
-
-<mujoco>
-  <!--
-  body2 is held by body1 through the weld constraint, so the force sensor on body1
-  should register 20 (for the weight of both bodies).
-  -->
-  <option gravity="0 0 -1"/>
-
-  <default>
-    <!-- A cube of size 0.1^3 with density of 1000 has mass of 1. -->
-    <geom size="0.05 0.05 0.05" type="box"/>
-  </default>
-
-  <worldbody>
-    <body name="body1">
-      <geom/>
-      <site name="sensor"/>
-    </body>
-    <body name="body2" pos="0 0 -0.1">
-      <joint type="slide" axis="0 0 1"/>
-      <geom/>
-    </body>
-  </worldbody>
-
-  <equality>
-    <weld body1="body1" body2="body2" anchor="0 0 0" tfratio="0"/>
-  </equality>
-
-  <sensor>
-    <force site="sensor" user="0 0 2"/>
-  </sensor>
-</mujoco>

test/engine/testdata/core_smooth/rne_post/weld/tfratio0_force_slide_rotated.xml

@@ -1,43 +0,0 @@
-<!-- Copyright 2021 DeepMind Technologies Limited
-     Licensed under the Apache License, Version 2.0 (the "License");
-     you may not use this file except in compliance with the License.
-     You may obtain a copy of the License at
-         http://www.apache.org/licenses/LICENSE-2.0
-     Unless required by applicable law or agreed to in writing, software
-     distributed under the License is distributed on an "AS IS" BASIS,
-     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-     See the License for the specific language governing permissions and
-     limitations under the License.
--->
-
-<mujoco>
-  <!--
-  body2 is held by body1 through the weld constraint, so the force sensor on body1
-  should register 20 (for the weight of both bodies), rotated into the y-z plane.
-  -->
-  <option gravity="0 0 -1"/>
-
-  <default>
-    <!-- A cube of size 0.1^3 with density of 1000 has mass of 1. -->
-    <geom size="0.05 0.05 0.05" type="box"/>
-  </default>
-
-  <worldbody>
-    <body name="body1" euler="0 45 0">
-      <geom/>
-      <site name="sensor" euler="0 0 90"/>
-    </body>
-    <body name="body2" pos="0 0 -0.2">
-      <joint type="slide" axis="0 0 1"/>
-      <geom/>
-    </body>
-  </worldbody>
-
-  <equality>
-    <weld body1="body1" body2="body2" anchor="0 0 0" tfratio="0"/>
-  </equality>
-
-  <sensor>
-    <force site="sensor" user="0 1.41421356237 1.41421356237"/>
-  </sensor>
-</mujoco>

test/engine/testdata/core_smooth/rne_post/weld/tfratio0_multiple_constraints.xml

@@ -1,59 +0,0 @@
-<!-- Copyright 2021 DeepMind Technologies Limited
-     Licensed under the Apache License, Version 2.0 (the "License");
-     you may not use this file except in compliance with the License.
-     You may obtain a copy of the License at
-         http://www.apache.org/licenses/LICENSE-2.0
-     Unless required by applicable law or agreed to in writing, software
-     distributed under the License is distributed on an "AS IS" BASIS,
-     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-     See the License for the specific language governing permissions and
-     limitations under the License.
--->
-
-<mujoco>
-  <!--
-  Same as force_free.xml, but with a distractor constraint.
-  -->
-  <option gravity="1 2 3"/>
-
-  <default>
-    <!-- A cube of size 0.1^3 with density of 1000 has mass of 1. -->
-    <geom size="0.05 0.05 0.05" type="box"/>
-  </default>
-
-  <worldbody>
-    <body name="body0" pos="-3 0 0">
-      <joint name="joint0" type="slide" axis="0 0 1"/>
-      <geom/>
-    </body>
-    <body name="body1">
-      <geom/>
-      <site name="sensor"/>
-    </body>
-    <body name="body2" pos="1 2 3">
-      <joint type="free"/>
-      <geom/>
-    </body>
-    <body name="body3" pos="3 0 0">
-      <geom/>
-      <body name="body3b" pos="3 0 -1">
-        <joint type="slide" axis="0 0 1" frictionloss="9"/>
-        <geom/>
-      </body>
-    </body>
-    <body name="body4" pos="4 0 0">
-      <joint type="free"/>
-      <geom/>
-    </body>
-  </worldbody>
-
-  <equality>
-    <joint joint1="joint0"/>
-    <weld body1="body3" body2="body4"/>
-    <weld body1="body1" body2="body2" anchor="0 0 0" tfratio="0"/>
-  </equality>
-
-  <sensor>
-    <force site="sensor" user="-2 -4 -6"/>
-  </sensor>
-</mujoco>

test/engine/testdata/core_smooth/rne_post/weld/tfratio0_torque_free.xml

@@ -1,43 +0,0 @@
-<!-- Copyright 2021 DeepMind Technologies Limited
-     Licensed under the Apache License, Version 2.0 (the "License");
-     you may not use this file except in compliance with the License.
-     You may obtain a copy of the License at
-         http://www.apache.org/licenses/LICENSE-2.0
-     Unless required by applicable law or agreed to in writing, software
-     distributed under the License is distributed on an "AS IS" BASIS,
-     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-     See the License for the specific language governing permissions and
-     limitations under the License.
--->
-
-<mujoco>
-  <!--
-  body2 is free, but because it's offset on y it wants to rotate about x due to gravity on z. The
-  connect prevents that, so the torque sensor should record the weight*offset of the second body.
-  -->
-  <option gravity="0 0 -1"/>
-
-  <default>
-    <!-- A cube of size 0.1^3 with density of 1000 has mass of 1. -->
-    <geom size="0.05 0.05 0.05" type="box"/>
-  </default>
-
-  <worldbody>
-    <body name="body1">
-      <geom/>
-      <site name="sensor"/>
-    </body>
-    <body name="body2" pos="0 2 0">
-      <freejoint/>
-      <geom/>
-    </body>
-  </worldbody>
-
-  <equality>
-    <weld body1="body1" body2="body2" anchor="0 0 0" tfratio="0"/>
-  </equality>
-
-  <sensor>
-    <torque site="sensor" user="2 0 0"/>
-  </sensor>
-</mujoco>

test/engine/testdata/weld.xml

@@ -1,58 +0,0 @@
-<mujoco>
-  <option>
-    <flag contact="disable"/>
-  </option>
-
-  <default>
-    <default class="static">
-      <geom size=".5 .1 .5" rgba=".5 .7 .5 .3"/>
-    </default>
-    <default class="free">
-      <geom type="box" size=".2" fromto="0 0 0 0 -2 0" rgba=".4 .7 .6 .3"/>
-    </default>
-  </default>
-
-  <worldbody>
-    <geom pos="0 0 -2" type="plane" size="10 10 .01"/>
-    <light pos="0 0 20"/>
-
-    <body name="box1" pos="-3 0 0">
-      <geom type="box" class="static"/>
-    </body>
-    <body name="beam1" pos="-3 0 0">
-      <freejoint/>
-      <geom class="free"/>
-    </body>
-
-    <body name="box2" pos="-1 0 0">
-      <geom type="box" class="static"/>
-    </body>
-    <body name="beam2" pos="-1 0 0">
-      <freejoint/>
-      <geom class="free"/>
-    </body>
-
-    <body name="box3" pos="1 0 0">
-      <geom type="box" class="static"/>
-    </body>
-    <body name="beam3" pos="1 0 0">
-      <freejoint/>
-      <geom class="free"/>
-    </body>
-
-    <body name="box4" pos="3 0 0">
-      <geom type="box" class="static"/>
-    </body>
-    <body name="beam4" pos="3 0 0">
-      <freejoint/>
-      <geom class="free"/>
-    </body>
-  </worldbody>
-
-  <equality>
-    <weld name="weak torques"      body1="box1" body2="beam1" tfratio="0.002"/>
-    <weld name="anchor no torques" body1="box2" body2="beam2" tfratio="0" anchor="0 -2 0"/>
-    <weld name="relpose"           body1="box3" body2="beam3" relpose="0 0 0 1 -.3 0 0"/>
-    <weld name="relpose+anchor"    body1="box4" body2="beam4" relpose="0 0 0 1 -.3 0 0" anchor="0 0 -1"/>
-  </equality>
-</mujoco>

unity/Runtime/Bindings/MujocoBindings.cs

@@ -40,7 +40,7 @@ public const double mjMAXIMP = 0.9999;
 public const int mjMAXCONPAIR = 50;
 public const int mjMAXVFS = 2000;
 public const int mjMAXVFSNAME = 1000;
-public const int mjNEQDATA = 11;
+public const int mjNEQDATA = 7;
 public const int mjNDYN = 10;
 public const int mjNGAIN = 10;
 public const int mjNBIAS = 10;