Makes multibody/constraint private within examples/rod2d (RobotLocomo…

…tion#21445)

We move the entire multibody/constraint into the only place it gets used examples/rod2d.
Along with this, we properly deprecate the original constraint_solver for removal, leaving the original files as copies in `multibody/constraint` simply to provide a proper deprecation window.

The docs are removed from our public Doxygen modules to avoid this old confusion users have that we have an LCP solver in Drake. The docs are now a local README file in examples/rod2d/constraint.

Co-authored-by: Jeremy Nimmer <[email protected]>

doc/doxygen_cxx/doxygen.h

@@ -167,11 +167,6 @@ namespace solvers {
 */
 } // namespace solvers
 
-/**
-  @defgroup constraint_overview Multibody Dynamics Constraints
-  @ingroup multibody
-*/
-
 // TODO(russt): Take a thorough pass through the algorithms group
 // documentation, adding brief descriptions of each and tagging the relevant
 // algorithms throughout the code.

examples/rod2d/BUILD.bazel

@@ -8,6 +8,19 @@ load(
 
 package(default_visibility = ["//visibility:private"])
 
+drake_cc_library(
+    name = "constraint_solver",
+    srcs = ["constraint_solver.cc"],
+    hdrs = [
+        "constraint_problem_data.h",
+        "constraint_solver.h",
+    ],
+    deps = [
+        "//common:essential",
+        "//solvers:moby_lcp_solver",
+    ],
+)
+
 drake_cc_library(
     name = "rod2d_state_vector",
     srcs = ["rod2d_state_vector.cc"],
@@ -45,11 +58,10 @@ drake_cc_library(
     hdrs = [
         "rod2d.h",
     ],
-    visibility = ["//multibody/constraint:__pkg__"],
     deps = [
+        ":constraint_solver",
         ":rod2d_state_vector",
         "//common:essential",
-        "//multibody/constraint",
         "//solvers:mathematical_program",
         "//systems/framework:leaf_system",
     ],
@@ -77,16 +89,26 @@ drake_cc_library(
 
 # === test/ ===
 
+drake_cc_googletest(
+    name = "constraint_solver_test",
+    deps = [
+        ":constraint_solver",
+        ":rod2d",
+        "//solvers:moby_lcp_solver",
+        "//solvers:unrevised_lemke_solver",
+    ],
+)
+
 drake_cc_googletest(
     name = "rod2d_test",
     deps = [
+        ":constraint_solver",
         ":rod2d",
         "//common:essential",
         "//common/test_utilities:eigen_matrix_compare",
         "//common/test_utilities:expect_no_throw",
-        "//multibody/constraint",
         "//systems/analysis:simulator",
     ],
 )
 
-add_lint_tests(enable_clang_format_lint = False)
+add_lint_tests()

examples/rod2d/constraint_solver.cc

@@ -0,0 +1,11 @@
+#include "drake/examples/rod2d/constraint_solver.h"
+
+namespace drake {
+namespace examples {
+namespace rod2d {
+
+template class ConstraintSolver<double>;
+
+}  // namespace rod2d
+}  // namespace examples
+}  // namespace drake