Add Expression Costs and Formula Constraints to Subgraphs in GcsTraje…

…ctoryOptimization (#22091)

Adds placeholder variables to subgraphs, that can be used to construct costs and constraints to each vertex or edge.

Note that this includes the fix  Fix a Bug in GCS When Passing in a Trivially-Infeasible Upper Bound #22090, since the conjunctive formula used in a test case creates an instance of this bug.

Co-Authored-By: Russ Tedrake <[email protected]>

planning/trajectory_optimization/gcs_trajectory_optimization.cc

@@ -29,9 +29,6 @@ namespace trajectory_optimization {
 using Subgraph = GcsTrajectoryOptimization::Subgraph;
 using EdgesBetweenSubgraphs = GcsTrajectoryOptimization::EdgesBetweenSubgraphs;
 
-using drake::solvers::MathematicalProgram;
-using drake::solvers::Solve;
-using drake::solvers::VectorXDecisionVariable;
 using Eigen::MatrixXd;
 using Eigen::SparseMatrix;
 using Eigen::VectorXd;
@@ -65,11 +62,17 @@ using solvers::L2NormCost;
 using solvers::LinearConstraint;
 using solvers::LinearCost;
 using solvers::LinearEqualityConstraint;
+using solvers::MathematicalProgram;
+using solvers::MatrixXDecisionVariable;
 using solvers::QuadraticCost;
+using solvers::Solve;
+using solvers::VectorXDecisionVariable;
 using symbolic::DecomposeLinearExpressions;
 using symbolic::Expression;
+using symbolic::Formula;
 using symbolic::MakeMatrixContinuousVariable;
 using symbolic::MakeVectorContinuousVariable;
+using symbolic::Variable;
 using trajectories::BezierCurve;
 using trajectories::CompositeTrajectory;
 using trajectories::PiecewiseTrajectory;
@@ -316,6 +319,16 @@ Subgraph::Subgraph(
         path_continuity_constraint,
         {GetControlPoints(*u).col(order), GetControlPoints(*v).col(0)}));
   }
+
+  // Construct placeholder variables.
+  placeholder_vertex_duration_var_ = symbolic::Variable("t");
+  placeholder_vertex_control_points_var_ =
+      MakeMatrixContinuousVariable(num_positions(), order + 1, "x");
+  placeholder_edge_durations_var_ =
+      std::make_pair(symbolic::Variable("tu"), symbolic::Variable("tv"));
+  placeholder_edge_control_points_var_ = std::make_pair(
+      MakeMatrixContinuousVariable(num_positions(), order + 1, "xu"),
+      MakeMatrixContinuousVariable(num_positions(), order + 1, "xv"));
 }
 
 Subgraph::~Subgraph() = default;
@@ -638,6 +651,9 @@ void Subgraph::AddPathContinuityConstraints(int continuity_order) {
 }
 
 void Subgraph::AddContinuityConstraints(int continuity_order) {
+  // TODO(cohnt): Rewrite to use the generic AddCost and AddConstraint
+  // interfaces.
+
   if (continuity_order == 0) {
     throw std::runtime_error(
         "Path continuity is enforced by default. Choose a higher order.");
@@ -739,6 +755,161 @@ symbolic::Variable Subgraph::GetTimeScaling(
   return v.x()(v.x().size() - 1);
 }
 
+namespace {
+
+std::vector<Variable> FlattenVariables(
+    const std::vector<Variable>& scalar_variables,
+    const std::vector<VectorXDecisionVariable>& vector_variables,
+    const std::vector<MatrixXDecisionVariable>& matrix_variables) {
+  std::vector<Variable> all_variables;
+
+  // Append scalar variables.
+  all_variables.insert(all_variables.end(), scalar_variables.begin(),
+                       scalar_variables.end());
+
+  // Flatten vector variables.
+  for (const auto& vector_variable : vector_variables) {
+    for (int i = 0; i < vector_variable.size(); ++i) {
+      all_variables.push_back(vector_variable(i));
+    }
+  }
+
+  // Flatten matrix variables.
+  for (const auto& matrix_variable : matrix_variables) {
+    for (int i = 0; i < matrix_variable.rows(); ++i) {
+      for (int j = 0; j < matrix_variable.cols(); ++j) {
+        all_variables.push_back(matrix_variable(i, j));
+      }
+    }
+  }
+
+  return all_variables;
+}
+
+template <typename T>
+T SubstituteAllVariables(
+    T e, std::vector<Variable> old_scalar_variables = {},
+    std::vector<Variable> new_scalar_variables = {},
+    std::vector<VectorXDecisionVariable> old_vector_variables = {},
+    std::vector<VectorXDecisionVariable> new_vector_variables = {},
+    std::vector<MatrixXDecisionVariable> old_matrix_variables = {},
+    std::vector<MatrixXDecisionVariable> new_matrix_variables = {}) {
+  DRAKE_DEMAND(old_scalar_variables.size() == new_scalar_variables.size());
+  DRAKE_DEMAND(old_vector_variables.size() == new_vector_variables.size());
+  DRAKE_DEMAND(old_matrix_variables.size() == new_matrix_variables.size());
+
+  std::vector<Variable> old_variables = FlattenVariables(
+      old_scalar_variables, old_vector_variables, old_matrix_variables);
+  std::vector<Variable> new_variables = FlattenVariables(
+      new_scalar_variables, new_vector_variables, new_matrix_variables);
+  DRAKE_DEMAND(old_variables.size() == new_variables.size());
+
+  symbolic::Variables e_vars = e.GetFreeVariables();
+  for (int i = 0; i < ssize(old_variables); ++i) {
+    if (e_vars.include(old_variables[i])) {
+      e = e.Substitute(old_variables[i], new_variables[i]);
+    }
+  }
+  return e;
+}
+
+template <typename T>
+void ThrowIfContainsVariables(const T& e, const std::vector<Variable>& vars,
+                              const std::string& error_message) {
+  symbolic::Variables e_vars = e.GetFreeVariables();
+  for (const auto& var : vars) {
+    if (e_vars.include(var)) {
+      throw(std::runtime_error(error_message));
+    }
+  }
+}
+
+}  // namespace
+
+template <typename T>
+T Subgraph::SubstituteVertexPlaceholderVariables(T e,
+                                                 const Vertex& vertex) const {
+  // Check that a user hasn't used the edge placeholder variables.
+  const std::string error_message =
+      "Edge placeholder variables cannot be used to add vertex costs or "
+      "constraints.";
+  ThrowIfContainsVariables(
+      e,
+      FlattenVariables({placeholder_edge_durations_var_.first,
+                        placeholder_edge_durations_var_.second},
+                       {},
+                       {placeholder_edge_control_points_var_.first,
+                        placeholder_edge_control_points_var_.second}),
+      error_message);
+
+  return SubstituteAllVariables(
+      e, {placeholder_vertex_duration_var_}, {GetTimeScaling(vertex)}, {}, {},
+      {placeholder_vertex_control_points_var_}, {GetControlPoints(vertex)});
+}
+
+template <typename T>
+T Subgraph::SubstituteEdgePlaceholderVariables(T e, const Edge& edge) const {
+  // Check that a user hasn't used the vertex placeholder variables.
+  const std::string error_message =
+      "Vertex placeholder variables cannot be used to add edge costs or "
+      "constraints.";
+  ThrowIfContainsVariables(
+      e,
+      FlattenVariables({placeholder_vertex_duration_var_}, {},
+                       {placeholder_vertex_control_points_var_}),
+      error_message);
+
+  const Vertex& v1 = edge.u();
+  const Vertex& v2 = edge.v();
+
+  return SubstituteAllVariables(e,
+                                {placeholder_edge_durations_var_.first,
+                                 placeholder_edge_durations_var_.second},
+                                {GetTimeScaling(v1), GetTimeScaling(v2)}, {},
+                                {},
+                                {placeholder_edge_control_points_var_.first,
+                                 placeholder_edge_control_points_var_.second},
+                                {GetControlPoints(v1), GetControlPoints(v2)});
+}
+
+void Subgraph::AddVertexCost(
+    const Expression& e,
+    const std::unordered_set<Transcription>& used_in_transcription) {
+  for (Vertex*& vertex : vertices_) {
+    Expression post_substitution =
+        SubstituteVertexPlaceholderVariables(e, *vertex);
+    vertex->AddCost(post_substitution, used_in_transcription);
+  }
+}
+
+void Subgraph::AddVertexConstraint(
+    const Formula& e,
+    const std::unordered_set<Transcription>& used_in_transcription) {
+  for (Vertex*& vertex : vertices_) {
+    Formula post_substitution =
+        SubstituteVertexPlaceholderVariables(e, *vertex);
+    vertex->AddConstraint(post_substitution, used_in_transcription);
+  }
+}
+
+void Subgraph::AddEdgeCost(
+    const Expression& e,
+    const std::unordered_set<Transcription>& used_in_transcription) {
+  for (Edge*& edge : edges_) {
+    Expression post_substitution = SubstituteEdgePlaceholderVariables(e, *edge);
+    edge->AddCost(post_substitution, used_in_transcription);
+  }
+}
+
+void Subgraph::AddEdgeConstraint(
+    const symbolic::Formula& e,
+    const std::unordered_set<Transcription>& used_in_transcription) {
+  for (Edge*& edge : edges_) {
+    Formula post_substitution = SubstituteEdgePlaceholderVariables(e, *edge);
+    edge->AddConstraint(post_substitution, used_in_transcription);
+  }
+}
+
 EdgesBetweenSubgraphs::EdgesBetweenSubgraphs(
     const Subgraph& from_subgraph, const Subgraph& to_subgraph,
     const ConvexSet* subspace, GcsTrajectoryOptimization* traj_opt,