Add option to build composites and compute kinematics

Modifies FrameBodyPoseCache, position kinematics cache,
and velocity kinematics cache. Loosens two tolerances so that Mac CI passes.

Rebased on body->link terminology change.
Rebased on J^T F operator branch

Working on acceleration kinematics.
Working on force elements

Author: sherm1

bindings/generated_docstrings/multibody_plant.h

@@ -3744,7 +3744,7 @@ method computes:
 where ``M(q)`` is the model's mass matrix (including rigid body mass
 properties and reflected_inertia "reflected inertias"), ``C(q, v)v``
 is the bias term for Coriolis and gyroscopic effects and ``tau_app``
-consists of a vector applied generalized forces. The last term is a
+consists of a vector of applied generalized forces. The last term is a
 summation over all bodies in the model where ``Fapp_Bo_W`` is an
 applied spatial force on body B at ``Bo`` which gets projected into
 the space of generalized forces with the transpose of ``Jv_V_WB(q)``
@@ -4620,6 +4620,67 @@ Returns ``L_WSP_W``:
     RuntimeError if model_instances contains an invalid
     ModelInstanceIndex.)""";
         } CalcSpatialMomentumInWorldAboutPoint;
+        // Symbol: drake::multibody::MultibodyPlant::CalcSystemJacobianTransposeTimesF
+        struct /* CalcSystemJacobianTransposeTimesF */ {
+          // Source: drake/multibody/plant/multibody_plant.h
+          const char* doc =
+R"""((Advanced) Computes τ = Jᵀ⋅F, the transpose-times-vector product of
+the System Jacobian against a per-mobilizd body spatial force, in O(n)
+time without forming J.
+
+Here J is the System Jacobian — the block-row-stacked Jacobian
+Jv_V_WB_W whose B-th block is ``∂V_WB_W/∂v``, the Jacobian of
+mobilized body B's spatial velocity in World (at Bo, expressed in W)
+with respect to the generalized velocities v. See
+EvalBlockSystemJacobian() for the matrix-form companion.
+
+Given applied spatial forces ``F_Bo_W_array[k]`` for each mobilized
+body k (about its body origin Bo, expressed in World), this method
+returns
+
+
+.. raw:: html
+
+    <details><summary>Click to expand C++ code...</summary>
+
+.. code-block:: c++
+
+    τ = ∑ₖ J_WBₖᵀ ⋅ F_Boₖ_W                                          (1)
+
+.. raw:: html
+
+    </details>
+
+the generalized forces equivalent to the applied spatial forces.
+
+Warning:
+    The input array ``F_Bo_W_array`` is destroyed during the
+    computation. Callers that need to preserve their input should pass
+    a copy.
+
+Parameter ``context``:
+    The state of the multibody system.
+
+Parameter ``F_Bo_W_array``:
+    Per-mobilized-body applied spatial forces, sized
+    graph().forest().num_mobods(), ordered by MobodIndex (entry 0
+    corresponds to World; it is read but has no effect on τ). **This
+    array is destroyed during the computation**: the operator sweeps
+    tip-to-base, shifting each body's accumulated force into its
+    parent's entry of ``F_Bo_W_array`` in place to avoid allocating a
+    scratch copy.
+
+Parameter ``tau``:
+    On exit, sized num_velocities(), the generalized force equivalent
+    to the applied spatial forces.
+
+Raises:
+    RuntimeError if ``F_Bo_W_array`` or ``tau`` is nullptr or the
+    wrong size.
+
+See also:
+    EvalBlockSystemJacobian(), CalcJacobianSpatialVelocity())""";
+        } CalcSystemJacobianTransposeTimesF;
         // Symbol: drake::multibody::MultibodyPlant::CalcTotalMass
         struct /* CalcTotalMass */ {
           // Source: drake/multibody/plant/multibody_plant.h
@@ -4942,7 +5003,7 @@ be used by Finalize(); post-finalize it returns the joint type that
 *was* used if there were any base bodies in need of a joint.
 
 See also:
-    SetBaseBodyJointType(), Finalize())""";
+    SetBaseBodyJointType(), GetCombineWeldedBodies(), Finalize())""";
         } GetBaseBodyJointType;
         // Symbol: drake::multibody::MultibodyPlant::GetBodiesKinematicallyAffectedBy
         struct /* GetBodiesKinematicallyAffectedBy */ {
@@ -5099,6 +5160,23 @@ geometries for ``body`` previously registered with a SceneGraph.
 See also:
     RegisterCollisionGeometry(), Finalize())""";
         } GetCollisionGeometriesForBody;
+        // Symbol: drake::multibody::MultibodyPlant::GetCombineWeldedBodies
+        struct /* GetCombineWeldedBodies */ {
+          // Source: drake/multibody/plant/multibody_plant.h
+          const char* doc =
+R"""(Returns the currently-set choice for whether welded-together bodies
+should be combined or modeled separately, either for the global
+setting or for a specific model instance. If a model instance is
+provided for which no explicit choice was made, the global setting is
+returned. Any model instance index is acceptable here; if not
+recognized then the global setting is returned. This can be called any
+time -- pre-finalize it returns the setting that will be used by
+Finalize(); post-finalize it returns the setting that *was* used if
+there were any welded-together bodies.
+
+See also:
+    SetCombineWeldedBodies(), GetBaseBodyJointType(), Finalize())""";
+        } GetCombineWeldedBodies;
         // Symbol: drake::multibody::MultibodyPlant::GetConstraintActiveStatus
         struct /* GetConstraintActiveStatus */ {
           // Source: drake/multibody/plant/multibody_plant.h
@@ -6602,8 +6680,30 @@ Parameter ``model_instance``:
     RuntimeError if called after Finalize().
 
 See also:
-    GetBaseBodyJointType(), Finalize())""";
+    GetBaseBodyJointType(), SetCombineWeldedBodies(), Finalize())""";
         } SetBaseBodyJointType;
+        // Symbol: drake::multibody::MultibodyPlant::SetCombineWeldedBodies
+        struct /* SetCombineWeldedBodies */ {
+          // Source: drake/multibody/plant/multibody_plant.h
+          const char* doc =
+R"""(Controls whether welded-together RigidBody elements are to be combined
+into a single composite mobilized body in the generated model. If so,
+the Weld joints will not appear in the post-Finalize() model and there
+will be fewer bodies and joints in the generated model than in the
+user's specification. Results for the original RigidBody elements can
+still be obtained by name or BodyIndex, but no results (in particular,
+no reaction forces) are available for the unmodeled Weld joints.
+
+You can set this globally or on a per-model instance basis.
+
+The default for Drake is *not* to combine welded RigidBody elements.
+
+Raises:
+    RuntimeError if called after Finalize().
+
+See also:
+    GetCombineWeldedBodies(), SetBaseBodyJointType(), Finalize())""";
+        } SetCombineWeldedBodies;
         // Symbol: drake::multibody::MultibodyPlant::SetConstraintActiveStatus
         struct /* SetConstraintActiveStatus */ {
           // Source: drake/multibody/plant/multibody_plant.h