[geometry] Add optional MuJoCo multi-point contact for convex meshes

[xuchenhan-lbm]

Summary

This pull request adds a second narrowphase for point contact. The new
narrowphase uses MuJoCo's convex collision detection, and it gives a pair of
convex meshes up to four contact points. The feature is off by default. A user
turns it on with a new proximity property.

The problem

Drake's point contact model gives each colliding geometry pair one contact
point, which is the deepest point. Two flat faces that overlap thus touch at a
single point. A box on a table has one support point, and that point moves from
one corner of the box to another corner between time steps.

The usual solution is to add several small spheres to the body. This pull
request adds a second solution. A geometry pair can report a contact manifold.

What the pull request does

A new proximity property ("material", "point_contact_algorithm") selects the
narrowphase for one geometry. It has two values:

• "single_point" is the default. It keeps the existing behavior. Every
  penetrating geometry pair reports one contact point.
• "mujoco_multipoint" selects the new narrowphase. A geometry pair reports up
  to four contact points, and each point carries its own depth.

DefaultProximityProperties::point_contact_algorithm sets the property for a
whole scene.

A geometry pair uses the new narrowphase only when both geometries select
"mujoco_multipoint" and both geometries are Convex or Mesh shapes. Every
other pair keeps the existing behavior, and so does every scalar type that is
not double. Both ComputePointPairPenetration() and the point contact
fallback of ComputeContactSurfacesWithFallback() use the property.

MuJoCo computes the manifold with GJK, EPA, and contact polygon clipping. A
face-face contact and an edge-face contact give up to four points. A
vertex-face contact gives one point.

The commits

The five commits build on each other. Please read them in order.

1. [workspace] adds the mujoco_internal external. Its license is
   Apache-2.0. The externals dm_control_internal and ccd_internal are
   precedents. The external pins the MuJoCo 3.12.0 release, and it compiles
   only src/engine/engine_collision_gjk.c and two small utility files. The
   commit also adds the LICENSE install rule and the mirror metadata.
2. [geometry] adds the wrapper. mujoco_ccd_mesh_data builds the mesh
   polygon tables that MuJoCo's model compiler would build, from Drake's qhull
   convex hulls. mujoco_ccd_penetration runs MuJoCo's mjc_ccd() and makes
   one PenetrationAsPointPair from each witness pair. When MuJoCo's GJK or
   EPA is degenerate, the wrapper reports the pair as unresolved, so that the
   caller can use a different algorithm.
3. [multibody] repairs a meshcat defect that this feature made visible. The
   point contact visualizer made the path of each arrow from the names of the
   two bodies, so several contacts of one body pair drew one arrow. The
   visualizer now gives a number to each repeated contact.
4. [geometry] connects the feature to the proximity engine. This commit
   adds the property, the validation in AssignRole(), the table cache, the
   callback dispatch with the single-point fallback, and a stable result sort.
5. [examples] adds examples/multibody/multipoint_contact. Two Convex
   boxes fall onto a Convex slab, and each box uses a different narrowphase. At
   a time step of 1 ms the single-point box turns at about 0.23 rad/s and sinks
   5.5 mm into the slab in five seconds. At a time step of 10 ms it falls
   through the slab. The multipoint box stays at its exact rest height at every
   time step.

Validation

The face-face, rotated, edge-face, and vertex-face results of the wrapper are
identical to the results of pip mujoco==3.12.0, which is the release that the
external pins. The tests in mujoco_ccd_penetration_test hold these expected
values.

An internal corpus of 153 manipulation scenes showed no change in the median
cost. The largest improvement was a scene with a stack of rigid meshes. That
scene ran 1.46 times faster, and its settled penetration decreased from 53 mm
to 4.5 mm.

Known limitations

• The feature works for the double scalar type only. Other scalar types keep
  the existing behavior. They do not support penetration queries between Convex
  or Mesh shapes.
• The feature works for Convex and Mesh pairs only. A primitive shape still reports
  just a single contact point.
• The support function is a linear scan of the vertices. This is MuJoCo's own
  choice below 10 vertices. A large hull needs MuJoCo's hill climbing variant,
  which needs mesh graph preprocessing that this port does not include.
• A mesh whose convex hull has no volume, such as a planar mesh, reports one
  point.
• mujoco_ccd_mesh_data.cc documents one deliberate difference from MuJoCo.
  This port does not copy the three-edge shortcut in MeshPolygon::Paths(),
  which can give a triangle with reversed winding.

---

This change is 

[xuchen-han]

+(status: do not merge) +a:@SeanCurtis-TRI for a design review. I have gone through the non-test non-example files to clean things up and I'm hoping to find a path and get this feature merged upstream (in pieces of course).

@xuchen-han made 1 comment.
Reviewable status: LGTM missing from assignee SeanCurtis-TRI(platform), needs at least two assigned reviewers, labeled "do not merge", commits need curation (https://drake.mit.edu/reviewable.html#curated-commits), missing label for release notes (waiting on SeanCurtis-TRI).