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graph_of_convex_sets_test.cc
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graph_of_convex_sets_test.cc
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#include "drake/geometry/optimization/graph_of_convex_sets.h"
#include <forward_list>
#include <gmock/gmock.h>
#include <gtest/gtest.h>
#include "drake/common/test_utilities/eigen_matrix_compare.h"
#include "drake/common/test_utilities/expect_no_throw.h"
#include "drake/common/test_utilities/expect_throws_message.h"
#include "drake/common/yaml/yaml_io.h"
#include "drake/geometry/optimization/hpolyhedron.h"
#include "drake/geometry/optimization/hyperellipsoid.h"
#include "drake/geometry/optimization/point.h"
#include "drake/geometry/optimization/vpolytope.h"
#include "drake/solvers/choose_best_solver.h"
#include "drake/solvers/clarabel_solver.h"
#include "drake/solvers/clp_solver.h"
#include "drake/solvers/csdp_solver.h"
#include "drake/solvers/gurobi_solver.h"
#include "drake/solvers/ipopt_solver.h"
#include "drake/solvers/linear_system_solver.h"
#include "drake/solvers/mosek_solver.h"
#include "drake/solvers/osqp_solver.h"
#include "drake/solvers/solver_options.h"
namespace drake {
namespace geometry {
namespace optimization {
using Eigen::Matrix;
using Eigen::Matrix2d;
using Eigen::Matrix4d;
using Eigen::RowVector2d;
using Eigen::Vector2d;
using Eigen::Vector3d;
using Eigen::Vector4d;
using solvers::Binding;
using solvers::LinearConstraint;
using solvers::LinearCost;
using solvers::LinearEqualityConstraint;
using solvers::MathematicalProgramResult;
using solvers::QuadraticCost;
using solvers::SolutionResult;
using solvers::SolverOptions;
using solvers::internal::CreateBinding;
using symbolic::Environment;
using symbolic::Expression;
using symbolic::Substitution;
using symbolic::Variables;
using Edge = GraphOfConvexSets::Edge;
using EdgeId = GraphOfConvexSets::EdgeId;
using Transcription = GraphOfConvexSets::Transcription;
using Vertex = GraphOfConvexSets::Vertex;
using VertexId = GraphOfConvexSets::VertexId;
using ::testing::AllOf;
using ::testing::HasSubstr;
using ::testing::Not;
const double kInf = std::numeric_limits<double>::infinity();
namespace {
bool MixedIntegerSolverAvailable() {
return (solvers::MosekSolver::is_available() &&
solvers::MosekSolver::is_enabled()) ||
(solvers::GurobiSolver::is_available() &&
solvers::GurobiSolver::is_enabled());
}
} // namespace
GTEST_TEST(GraphOfConvexSetsOptionsTest, Serialize) {
GraphOfConvexSetsOptions options;
options.convex_relaxation = false;
options.max_rounded_paths = false;
options.preprocessing = true;
options.max_rounding_trials = 5;
options.flow_tolerance = 0.01;
options.rounding_seed = 5;
solvers::MosekSolver mosek_solver;
options.solver = &mosek_solver;
options.solver_options = solvers::SolverOptions();
solvers::IpoptSolver ipopt_solver;
options.restriction_solver = &ipopt_solver;
options.restriction_solver_options = solvers::SolverOptions();
options.preprocessing_solver = &mosek_solver;
options.preprocessing_solver_options = solvers::SolverOptions();
const std::string serialized = yaml::SaveYamlString(options);
const auto deserialized =
yaml::LoadYamlString<GraphOfConvexSetsOptions>(serialized);
EXPECT_EQ(deserialized.convex_relaxation, options.convex_relaxation);
EXPECT_EQ(deserialized.preprocessing, options.preprocessing);
EXPECT_EQ(deserialized.max_rounded_paths, options.max_rounded_paths);
EXPECT_EQ(deserialized.max_rounding_trials, options.max_rounding_trials);
EXPECT_EQ(deserialized.flow_tolerance, options.flow_tolerance);
EXPECT_EQ(deserialized.rounding_seed, options.rounding_seed);
// The non-built-in types are not serialized.
EXPECT_EQ(deserialized.solver, nullptr);
EXPECT_EQ(deserialized.restriction_solver, nullptr);
EXPECT_EQ(deserialized.preprocessing_solver, nullptr);
EXPECT_EQ(deserialized.solver_options, solvers::SolverOptions());
EXPECT_FALSE(deserialized.restriction_solver_options.has_value());
EXPECT_FALSE(deserialized.preprocessing_solver_options.has_value());
}
GTEST_TEST(GraphOfConvexSetsTest, AddVertex) {
GraphOfConvexSets g;
Point p(Vector3d(1.0, 2.0, 3.0));
Vertex* v = g.AddVertex(p, "point");
EXPECT_EQ(v->ambient_dimension(), 3);
EXPECT_EQ(v->name(), "point");
EXPECT_EQ(v->x().size(), 3);
EXPECT_EQ(v->x()[0].get_name(), "point(0)");
EXPECT_TRUE(v->set().PointInSet(p.x()));
// Confirm that the vertex set does not refer to the original memory.
p.set_x(Vector3d(4., 5., 6));
EXPECT_FALSE(v->set().PointInSet(p.x()));
auto vertices = g.Vertices();
EXPECT_EQ(vertices.size(), 1);
EXPECT_EQ(vertices.at(0), v);
const GraphOfConvexSets* const_g = &g;
const auto const_vertices = const_g->Vertices();
EXPECT_EQ(const_vertices.size(), 1);
EXPECT_EQ(const_vertices.at(0), v);
}
GTEST_TEST(GraphOfConvexSetsTest, GetVertexSolution) {
GraphOfConvexSets g;
Point p(Vector3d(1.0, 2.0, 3.0));
Vertex* v = g.AddVertex(p, "point");
MathematicalProgramResult result;
std::unordered_map<symbolic::Variable::Id, int> map;
for (int i = 0; i < 3; ++i) {
map.emplace(v->x()[i].get_id(), i);
}
result.set_decision_variable_index(map);
result.set_x_val(p.x());
EXPECT_TRUE(CompareMatrices(v->GetSolution(result), p.x()));
}
GTEST_TEST(GraphOfConvexSetsTest, AddEdge) {
GraphOfConvexSets g;
Point pu(Vector3d(1.0, 2.0, 3.0));
Point pv(Vector2d(4., 5.));
Vertex* u = g.AddVertex(pu, "u");
Vertex* v = g.AddVertex(pv, "v");
Edge* e = g.AddEdge(u, v, "e");
EXPECT_EQ(e->u().name(), u->name());
EXPECT_EQ(e->v().name(), v->name());
EXPECT_EQ(Variables(e->xu()), Variables(u->x()));
EXPECT_EQ(Variables(e->xv()), Variables(v->x()));
}
GTEST_TEST(GraphOfConvexSetsTest, RemoveEdge) {
GraphOfConvexSets g;
Point pu(Vector3d(1.0, 2.0, 3.0));
Point pv(Vector2d(4., 5.));
Vertex* u = g.AddVertex(pu, "u");
Vertex* v = g.AddVertex(pv, "v");
Edge* e1 = g.AddEdge(u, v, "e1");
Edge* e2 = g.AddEdge(v, u, "e2");
EXPECT_EQ(g.Edges().size(), 2);
EXPECT_EQ(u->incoming_edges().size(), 1);
EXPECT_EQ(u->incoming_edges()[0], e2);
EXPECT_EQ(u->outgoing_edges().size(), 1);
EXPECT_EQ(u->outgoing_edges()[0], e1);
EXPECT_EQ(v->incoming_edges().size(), 1);
EXPECT_EQ(v->incoming_edges()[0], e1);
EXPECT_EQ(v->outgoing_edges().size(), 1);
EXPECT_EQ(v->outgoing_edges()[0], e2);
g.RemoveEdge(e1);
auto edges = g.Edges();
EXPECT_EQ(edges.size(), 1);
EXPECT_EQ(edges.at(0), e2);
EXPECT_EQ(u->incoming_edges().size(), 1);
EXPECT_EQ(u->incoming_edges()[0], e2);
EXPECT_EQ(u->outgoing_edges().size(), 0);
EXPECT_EQ(v->incoming_edges().size(), 0);
EXPECT_EQ(v->outgoing_edges().size(), 1);
EXPECT_EQ(v->outgoing_edges()[0], e2);
g.RemoveEdge(e2);
EXPECT_EQ(g.Edges().size(), 0);
EXPECT_EQ(u->incoming_edges().size(), 0);
EXPECT_EQ(u->outgoing_edges().size(), 0);
EXPECT_EQ(v->incoming_edges().size(), 0);
EXPECT_EQ(v->outgoing_edges().size(), 0);
}
GTEST_TEST(GraphOfConvexSetsTest, RemoveVertex) {
GraphOfConvexSets g;
Vertex* v1 = g.AddVertex(Point(Vector2d(3., 5.)));
Vertex* v2 = g.AddVertex(Point(Vector2d(-2., 4.)));
Vertex* v3 = g.AddVertex(Point(Vector2d(5., -2.3)));
Edge* e1 = g.AddEdge(v1, v2);
g.AddEdge(v1, v3);
g.AddEdge(v3, v1);
EXPECT_EQ(v1->incoming_edges().size(), 1);
EXPECT_EQ(v1->outgoing_edges().size(), 2);
EXPECT_EQ(g.Vertices().size(), 3);
EXPECT_EQ(g.Edges().size(), 3);
g.RemoveVertex(v3);
EXPECT_EQ(g.Vertices().size(), 2);
auto edges = g.Edges();
EXPECT_EQ(edges.size(), 1);
EXPECT_EQ(edges.at(0), e1);
EXPECT_EQ(v1->incoming_edges().size(), 0);
g.RemoveVertex(v2);
auto vertices = g.Vertices();
EXPECT_EQ(vertices.size(), 1);
EXPECT_EQ(vertices.at(0), v1);
EXPECT_EQ(g.Edges().size(), 0);
EXPECT_EQ(v1->outgoing_edges().size(), 0);
}
/*
┌───┐ ┌───┐
│ u ├───e──►│ v │
└───┘ └───┘
*/
class TwoPoints : public ::testing::Test {
protected:
TwoPoints() : pu_{Vector2d(1., 2.)}, pv_{Vector3d(3., 4., 5.)} {
u_ = g_.AddVertex(pu_, "u");
v_ = g_.AddVertex(pv_, "v");
e_ = g_.AddEdge(u_, v_, "e");
}
GraphOfConvexSets g_{};
Point pu_;
Point pv_;
Vertex* u_;
Vertex* v_;
Edge* e_;
};
TEST_F(TwoPoints, Basic) {
EXPECT_EQ(e_->name(), "e");
EXPECT_EQ(e_->u().name(), u_->name());
EXPECT_EQ(e_->v().name(), v_->name());
EXPECT_EQ(Variables(e_->xu()), Variables(u_->x()));
EXPECT_EQ(Variables(e_->xv()), Variables(v_->x()));
auto vertices = g_.Vertices();
EXPECT_EQ(vertices.at(0), u_);
EXPECT_EQ(vertices.at(1), v_);
EXPECT_EQ(g_.Edges().at(0), e_);
}
// Confirms that we can add costs (both ways) and get the solution.
// The correctness of the added costs will be established by the solution tests.
TEST_F(TwoPoints, AddCost) {
auto [ell0, b0] = e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm());
auto cost = std::make_shared<LinearCost>(Vector2d::Zero(), 0.1);
auto [ell1, b1] = e_->AddCost(Binding(cost, e_->xu()));
auto [v_ell0, v_b0] = v_->AddCost((v_->x() + Vector3d::Ones()).squaredNorm());
auto [v_ell1, v_b1] = v_->AddCost(Binding(cost, v_->x().head<2>()));
// Confirm that they are down-castable.
auto quadratic = dynamic_cast<QuadraticCost*>(b0.evaluator().get());
EXPECT_TRUE(quadratic != nullptr);
auto linear = dynamic_cast<LinearCost*>(b1.evaluator().get());
EXPECT_TRUE(linear != nullptr);
quadratic = dynamic_cast<QuadraticCost*>(v_b0.evaluator().get());
EXPECT_TRUE(quadratic != nullptr);
linear = dynamic_cast<LinearCost*>(v_b1.evaluator().get());
EXPECT_TRUE(linear != nullptr);
// Confirm that they are all accessible.
const auto& edge_costs = e_->GetCosts();
EXPECT_EQ(edge_costs[0], b0);
EXPECT_EQ(edge_costs[1], b1);
const auto& vertex_costs = v_->GetCosts();
EXPECT_EQ(vertex_costs[0], v_b0);
EXPECT_EQ(vertex_costs[1], v_b1);
MathematicalProgramResult result;
std::unordered_map<symbolic::Variable::Id, int> map;
map.emplace(ell0.get_id(), 0);
map.emplace(ell1.get_id(), 1);
map.emplace(v_ell0.get_id(), 2);
map.emplace(v_ell1.get_id(), 3);
const Vector4d ell{1.2, 3.4, 5.6, 7.8};
result.set_decision_variable_index(map);
result.set_x_val(ell);
EXPECT_NEAR(e_->GetSolutionCost(result), ell.head<2>().sum(), 1e-16);
EXPECT_NEAR(v_->GetSolutionCost(result), ell.tail<2>().sum(), 1e-16);
symbolic::Variable other_var("x");
DRAKE_EXPECT_THROWS_MESSAGE(e_->AddCost(other_var), ".*IsSubsetOf.*");
DRAKE_EXPECT_THROWS_MESSAGE(v_->AddCost(other_var), ".*IsSubsetOf.*");
// If no transcription is specified, the constraint won't be added.
EXPECT_THROW(e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm(), {}),
std::exception);
EXPECT_THROW(e_->AddCost(Binding(cost, e_->xu()), {}), std::exception);
EXPECT_THROW(u_->AddCost((v_->x() + Vector3d::Ones()).squaredNorm(), {}),
std::exception);
EXPECT_THROW(u_->AddCost(Binding(cost, u_->x()), {}), std::exception);
// By default Edge::AddCost or Vertex::AddCost is adding the binding to all
// transcriptions.
for (const auto& transcription :
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction}) {
const auto transcription_edge_costs = e_->GetCosts({transcription});
EXPECT_EQ(transcription_edge_costs.size(), 2);
EXPECT_EQ(transcription_edge_costs[0], b0);
EXPECT_EQ(transcription_edge_costs[1], b1);
const auto transcription_vertex_costs = v_->GetCosts({transcription});
EXPECT_EQ(transcription_vertex_costs.size(), 2);
EXPECT_EQ(transcription_vertex_costs[0], v_b0);
EXPECT_EQ(transcription_vertex_costs[1], v_b1);
}
// If no transcription is specified, nothing will be returned.
EXPECT_THROW(e_->GetCosts({}), std::exception);
EXPECT_THROW(v_->GetCosts({}), std::exception);
}
// Confirms that we can add constraints (both ways).
// The correctness of the added constraints will be established by the solution
// tests.
TEST_F(TwoPoints, AddConstraint) {
auto b0 = e_->AddConstraint(e_->xv().head<2>() == e_->xu());
auto constraint = std::make_shared<LinearConstraint>(
Matrix2d::Identity(), Vector2d::Zero(), Vector2d{1.2, 3.4});
auto b1 = e_->AddConstraint(Binding(constraint, e_->xu()));
auto u_b0 = u_->AddConstraint(u_->x() == pu_.x());
auto u_b1 = u_->AddConstraint(Binding(constraint, u_->x()));
// If no transcription is specified, the constraint won't be added.
EXPECT_THROW(e_->AddConstraint(e_->xv().head<2>() == e_->xu(), {}),
std::exception);
EXPECT_THROW(e_->AddConstraint(Binding(constraint, e_->xu()), {}),
std::exception);
EXPECT_THROW(u_->AddConstraint(u_->x() == pu_.x(), {}), std::exception);
EXPECT_THROW(u_->AddConstraint(Binding(constraint, u_->x()), {}),
std::exception);
// Confirm that they are down-castable.
auto linear_equality =
dynamic_cast<LinearEqualityConstraint*>(b0.evaluator().get());
EXPECT_TRUE(linear_equality != nullptr);
auto linear = dynamic_cast<LinearConstraint*>(b1.evaluator().get());
EXPECT_TRUE(linear != nullptr);
linear_equality =
dynamic_cast<LinearEqualityConstraint*>(u_b0.evaluator().get());
EXPECT_TRUE(linear_equality != nullptr);
linear = dynamic_cast<LinearConstraint*>(u_b1.evaluator().get());
EXPECT_TRUE(linear != nullptr);
// Confirm that they are all accessible.
const auto& all_edge_constraints = e_->GetConstraints();
EXPECT_EQ(all_edge_constraints.size(), 2);
EXPECT_EQ(all_edge_constraints[0], b0);
EXPECT_EQ(all_edge_constraints[1], b1);
const auto& all_vertex_constraints = u_->GetConstraints();
EXPECT_EQ(all_vertex_constraints.size(), 2);
EXPECT_EQ(all_vertex_constraints[0], u_b0);
EXPECT_EQ(all_vertex_constraints[1], u_b1);
// By default Edge::AddConstraint or Vertex::AddConstraint is adding the
// binding to all transcriptions.
for (const auto& transcription :
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction}) {
const auto edge_constraints = e_->GetConstraints({transcription});
EXPECT_EQ(edge_constraints.size(), 2);
EXPECT_EQ(edge_constraints[0], b0);
EXPECT_EQ(edge_constraints[1], b1);
const auto vertex_constraints = u_->GetConstraints({transcription});
EXPECT_EQ(vertex_constraints.size(), 2);
EXPECT_EQ(vertex_constraints[0], u_b0);
EXPECT_EQ(vertex_constraints[1], u_b1);
}
// If no transcription is specified, nothing will be returned.
EXPECT_THROW(e_->GetConstraints({}), std::exception);
EXPECT_THROW(u_->GetConstraints({}), std::exception);
symbolic::Variable other_var("x");
DRAKE_EXPECT_THROWS_MESSAGE(e_->AddConstraint(other_var == 1),
".*IsSubsetOf.*");
DRAKE_EXPECT_THROWS_MESSAGE(u_->AddConstraint(other_var == 1),
".*IsSubsetOf.*");
}
// Verifies that the correct solver is used for the MIP, relaxation,
// preprocessing, and restriction.
TEST_F(TwoPoints, ReportCorrectSolverId) {
e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm());
GraphOfConvexSetsOptions options;
// Define a different solver for the restriction.
solvers::ClarabelSolver clarabel;
options.solver = &clarabel;
solvers::ClpSolver clp;
options.restriction_solver = &clp;
options.convex_relaxation = true;
options.preprocessing = false;
// When solving the convex relaxation with no rounded paths, we expect the
// options.solver to be used.
options.max_rounded_paths = 0;
auto result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_TRUE(result.is_success());
EXPECT_EQ(result.get_solver_id(), options.solver->solver_id());
// The convex restriction should use the restriction solver.
result = g_.SolveConvexRestriction({e_}, options);
EXPECT_TRUE(result.is_success());
EXPECT_EQ(result.get_solver_id(), options.restriction_solver->solver_id());
// With the rounding on, the reported solver should be the restriction solver
options.max_rounded_paths = 1;
result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_TRUE(result.is_success());
EXPECT_EQ(result.get_solver_id(), options.restriction_solver->solver_id());
// Even if we add a constraint that makes only the rounding fail, the
// reported solver should still be the restriction solver.
u_->AddConstraint(u_->x()[0] == 0.0, {Transcription::kRestriction});
result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_FALSE(result.is_success());
EXPECT_EQ(result.get_solver_id(), options.restriction_solver->solver_id());
// Adding infeasible constraints to the relaxation should fail the relaxation,
// hence solving the restriction will never be reached and the reported solver
// should be the solver used in the relaxation.
e_->AddConstraint(e_->xv()[0] == 0.0, {Transcription::kRelaxation});
result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_FALSE(result.is_success());
EXPECT_EQ(result.get_solver_id(), options.solver->solver_id());
// Since we haven't added any infeasible constraints to the MIP transcription,
// we expect the solve to be successful and the reported solver to be the MIP
// solver.
if (solvers::MosekSolver::is_available() &&
solvers::MosekSolver::is_enabled()) {
solvers::MosekSolver mosek;
options.solver = &mosek;
options.convex_relaxation = false;
result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_TRUE(result.is_success());
EXPECT_EQ(result.get_solver_id(), options.solver->solver_id());
}
// Test the preprocessing solver. Since the results of these solves are not
// reported, we call the OSQP solver and expect an error -- this solver cannot
// handle LPs, the preprocessing problems are LPs.
solvers::OsqpSolver osqp;
options.preprocessing = true;
options.preprocessing_solver = &osqp;
EXPECT_THROW(g_.SolveShortestPath(*u_, *v_, options), std::exception);
}
// Verify that assigning a transcription to a cost adds it to the correct
// problem.
TEST_F(TwoPoints, VerifyCostTranscriptionAssignment) {
const double kCostRelaxation = 1.23;
const double kCostRestriction = 4.56;
const double kCostMIP = 7.89;
// We add each cost four times, once for each AddCost entry point.
for (const auto& [transcription, cost] :
{std::pair<Transcription, double>{Transcription::kMIP, kCostMIP},
std::pair<Transcription, double>{Transcription::kRelaxation,
kCostRelaxation},
std::pair<Transcription, double>{Transcription::kRestriction,
kCostRestriction}}) {
auto [ell, e_b] = e_->AddCost(cost, {transcription});
e_->AddCost(e_b, {transcription});
auto [v_ell, v_b] = v_->AddCost(cost, {transcription});
v_->AddCost(v_b, {transcription});
}
GraphOfConvexSetsOptions options;
options.preprocessing = false;
// The convex relaxation should be successful.
options.convex_relaxation = true;
options.max_rounded_paths = 0;
auto result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_TRUE(result.is_success());
EXPECT_NEAR(result.get_optimal_cost(), 4 * kCostRelaxation, 1e-6);
// The restriction, also in the rounding, should be successful.
options.convex_relaxation = true;
options.max_rounded_paths = 1;
result = g_.SolveConvexRestriction({e_}, options);
EXPECT_TRUE(result.is_success());
EXPECT_NEAR(result.get_optimal_cost(), 4 * kCostRestriction, 1e-6);
result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_TRUE(result.is_success());
EXPECT_NEAR(result.get_optimal_cost(), 4 * kCostRestriction, 1e-6);
// The MIP should be successful as well.
options.convex_relaxation = false;
if (MixedIntegerSolverAvailable()) {
result = g_.SolveShortestPath(*u_, *v_, options);
EXPECT_TRUE(result.is_success());
EXPECT_NEAR(result.get_optimal_cost(), 4 * kCostMIP, 1e-6);
}
}
// Verify that assigning a transcription to a constraint adds it to the correct
// problem. This test will be split into multiple cases.
TEST_F(TwoPoints, VerifyTranscriptionAssignmentBaseline) {
// We will be adding a few feasible constraints to all transcriptions, even
// though there are redundant with the set constraint. It is expected that
// solving the individual problems will be successful.
e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm());
e_->AddConstraint(e_->xv()[0] == 3.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
u_->AddConstraint(u_->x()[0] == 1.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
GraphOfConvexSetsOptions options;
options.preprocessing = false;
// The convex relaxation should be successful.
options.convex_relaxation = true;
options.max_rounded_paths = 0;
EXPECT_TRUE(g_.SolveShortestPath(*u_, *v_, options).is_success());
// The restriction, also in the rounding, should be successful.
options.convex_relaxation = true;
options.max_rounded_paths = 1;
EXPECT_TRUE(g_.SolveConvexRestriction({e_}, options).is_success());
EXPECT_TRUE(g_.SolveShortestPath(*u_, *v_, options).is_success());
// The MIP should be successful as well.
options.convex_relaxation = false;
if (MixedIntegerSolverAvailable()) {
EXPECT_TRUE(g_.SolveShortestPath(*u_, *v_, options).is_success());
}
}
TEST_F(TwoPoints, VerifyTranscriptionAssignmentkMIP) {
// We will be adding a few feasible constraints to all transcriptions, even
// though there are redundant with the set constraint.
// Further, we will add an infeasible constraint to the relaxation and the
// restriction, but not the MIP.
e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm());
e_->AddConstraint(e_->xv()[0] == 3.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
u_->AddConstraint(u_->x()[0] == 1.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
GraphOfConvexSetsOptions options;
options.preprocessing = false;
// The MIP should be successful.
e_->AddConstraint(e_->xv()[0] == 0.0,
{Transcription::kRelaxation, Transcription::kRestriction});
u_->AddConstraint(u_->x()[0] == 0.0,
{Transcription::kRelaxation, Transcription::kRestriction});
if (MixedIntegerSolverAvailable()) {
options.convex_relaxation = false;
EXPECT_TRUE(g_.SolveShortestPath(*u_, *v_, options).is_success());
}
// Ensure the relaxation fails.
options.convex_relaxation = true;
options.max_rounded_paths = 0;
EXPECT_FALSE(g_.SolveShortestPath(*u_, *v_, options).is_success());
// Ensure the restriction fails.
EXPECT_FALSE(g_.SolveConvexRestriction({e_}, options).is_success());
}
TEST_F(TwoPoints, VerifyTranscriptionAssignmentkRelaxation) {
// We will be adding a few feasible constraints to all transcriptions, even
// though there are redundant with the set constraint.
// Further, we will add an infeasible constraint to the MIP and the
// restriction, but not the relaxation.
e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm());
e_->AddConstraint(e_->xv()[0] == 3.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
u_->AddConstraint(u_->x()[0] == 1.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
GraphOfConvexSetsOptions options;
options.preprocessing = false;
// The relaxation should be successful.
e_->AddConstraint(e_->xv()[0] == 0.0,
{Transcription::kMIP, Transcription::kRestriction});
u_->AddConstraint(u_->x()[0] == 0.0,
{Transcription::kMIP, Transcription::kRestriction});
options.convex_relaxation = true;
options.max_rounded_paths = 0;
EXPECT_TRUE(g_.SolveShortestPath(*u_, *v_, options).is_success());
// Ensure the mip fails.
if (MixedIntegerSolverAvailable()) {
options.convex_relaxation = false;
EXPECT_FALSE(g_.SolveShortestPath(*u_, *v_, options).is_success());
}
// Ensure the restriction fails.
EXPECT_FALSE(g_.SolveConvexRestriction({e_}, options).is_success());
// Ensure the restriction called in the rounding fails.
options.convex_relaxation = true;
options.max_rounded_paths = 1;
EXPECT_FALSE(g_.SolveShortestPath(*u_, *v_, options).is_success());
}
TEST_F(TwoPoints, VerifyTranscriptionAssignmentkRestriction) {
// We will be adding a few feasible constraints to all transcriptions, even
// though there are redundant with the set constraint.
// Further, we will add an infeasible constraint to the MIP and the
// relaxation, but not the restriction.
e_->AddCost((e_->xv().head<2>() - e_->xu()).squaredNorm());
e_->AddConstraint(e_->xv()[0] == 3.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
u_->AddConstraint(u_->x()[0] == 1.0,
{Transcription::kMIP, Transcription::kRelaxation,
Transcription::kRestriction});
GraphOfConvexSetsOptions options;
options.preprocessing = false;
// The restriction should be successful.
e_->AddConstraint(e_->xv()[0] == 0.0,
{Transcription::kMIP, Transcription::kRelaxation});
u_->AddConstraint(u_->x()[0] == 0.0,
{Transcription::kMIP, Transcription::kRelaxation});
EXPECT_TRUE(g_.SolveConvexRestriction({e_}, options).is_success());
// Ensure the mip fails.
if (MixedIntegerSolverAvailable()) {
options.convex_relaxation = false;
EXPECT_FALSE(g_.SolveShortestPath(*u_, *v_, options).is_success());
}
// Ensure the and relaxation fails.
options.convex_relaxation = true;
options.max_rounded_paths = 0;
EXPECT_FALSE(g_.SolveShortestPath(*u_, *v_, options).is_success());
}
GTEST_TEST(GraphOfConvexSetsTest, InitialGuess) {
GraphOfConvexSets gcs;
// A source (with 1 free variable) and a target (a fixed point), with an edge
// between them.
Vertex* s = gcs.AddVertex(HPolyhedron::MakeUnitBox(1));
Vertex* t = gcs.AddVertex(Point(Vector1d(1.0)));
Edge* e = gcs.AddEdge(s, t);
using std::pow;
const double kMinima = 0.8;
// A quartic cost function w/ minima at 0 and kMinima.
s->AddCost(pow(s->x()[0], 2) * pow(s->x()[0] - kMinima, 2));
// Solving with no initial guess is like using an initial guess of zero.
auto result = gcs.SolveConvexRestriction({e});
EXPECT_TRUE(result.is_success());
EXPECT_NEAR(result.GetSolution(s->x())[0], 0.0, 1e-6);
GraphOfConvexSetsOptions options;
MathematicalProgramResult initial_guess = result;
initial_guess.SetSolution(s->x()[0], kMinima);
result = gcs.SolveConvexRestriction({e}, options, &initial_guess);
EXPECT_TRUE(result.is_success());
EXPECT_NEAR(result.GetSolution(s->x())[0], kMinima, 1e-6);
}
GTEST_TEST(GraphOfConvexSetsTest, TwoNullPointsConstraint) {
GraphOfConvexSets g;
Point pu(Eigen::VectorXd::Zero(0));
Point pv(Eigen::VectorXd::Zero(0));
Vertex* u = g.AddVertex(pu, "u");
Vertex* v = g.AddVertex(pv, "v");
Edge* e = g.AddEdge(u, v, "e");
DRAKE_EXPECT_THROWS_MESSAGE(e->AddConstraint(symbolic::Formula::True()),
".*total.*ambient.*dimension.*");
}
/* A graph with one edge definitely on the optimal path, and one definitely off
it.
┌──────┐ ┌──────┐
│source├──e_on──►│target│
└───┬──┘ └──────┘
│e_off
│
┌───▼──┐
│ sink │
└──────┘
*/
class ThreePoints : public ::testing::Test {
protected:
ThreePoints()
: p_source_{Vector2d(3., 5.)},
p_target_{Vector2d(-2., 4.)},
p_sink_{Vector2d(5., -2.3)} {
source_ = g_.AddVertex(p_source_);
target_ = g_.AddVertex(p_target_);
sink_ = g_.AddVertex(p_sink_);
e_on_ = g_.AddEdge(source_, target_);
e_off_ = g_.AddEdge(source_, sink_);
subs_on_off_.emplace(e_on_->xv()[0], e_off_->xv()[0]);
subs_on_off_.emplace(e_on_->xv()[1], e_off_->xv()[1]);
options_.preprocessing = false;
options_.convex_relaxation = true;
}
void CheckConvexRestriction(const MathematicalProgramResult& result) {
MathematicalProgramResult restriction_result =
g_.SolveConvexRestriction(std::vector<const Edge*>({e_on_}), options_);
log()->info("Solved convex restriction with {}",
restriction_result.get_solver_id().name());
// Confirm that we get a convex solver (not an NLP solver).
if (MixedIntegerSolverAvailable()) {
EXPECT_TRUE(
restriction_result.get_solver_id() == solvers::MosekSolver::id() ||
restriction_result.get_solver_id() == solvers::GurobiSolver::id());
}
EXPECT_TRUE(restriction_result.is_success());
EXPECT_NEAR(result.get_optimal_cost(),
restriction_result.get_optimal_cost(), 1e-4);
for (const auto* v : {source_, target_, sink_}) {
EXPECT_TRUE(CompareMatrices(result.GetSolution(v->x()),
restriction_result.GetSolution(v->x()),
1e-6));
}
}
GraphOfConvexSets g_;
Point p_source_;
Point p_target_;
Point p_sink_;
Vertex* source_{nullptr};
Vertex* target_{nullptr};
Vertex* sink_{nullptr};
Edge* e_on_{nullptr};
Edge* e_off_{nullptr};
Substitution subs_on_off_{};
GraphOfConvexSetsOptions options_;
};
// Confirms that we get a helpful error message when we try to solve a problem
// and no MIP solver is available.
TEST_F(ThreePoints, NoMixedIntegerSolverAvailable) {
if (MixedIntegerSolverAvailable()) {
return;
}
options_.convex_relaxation = false;
// Note: DRAKE_EXPECT_THROWS_MESSAGE fails to match the error message even
// when the regex is ".*". So we implement a simpler a regex-free version
// here.
try {
g_.SolveShortestPath(*source_, *target_, options_);
GTEST_NONFATAL_FAILURE_("Should have thrown.");
} catch (const std::exception& err) {
EXPECT_NE(
std::string(err.what())
.find(
"no solver available that can solve the mixed-integer version"),
std::string::npos);
} catch (...) {
GTEST_NONFATAL_FAILURE_("Should have thrown std::exception.");
}
}
TEST_F(ThreePoints, LinearCost1) {
e_on_->AddCost(1.0);
e_off_->AddCost(1.0);
source_->AddCost(1.0);
auto result = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result.is_success());
EXPECT_NEAR(e_on_->GetSolutionCost(result), 1.0, 1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result), 1.0, 1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_TRUE(
CompareMatrices(e_on_->GetSolutionPhiXu(result), p_source_.x(), 1e-6));
EXPECT_TRUE(
CompareMatrices(e_on_->GetSolutionPhiXv(result), p_target_.x(), 1e-6));
EXPECT_TRUE(CompareMatrices(e_off_->GetSolutionPhiXu(result),
0 * p_source_.x(), 1e-6));
EXPECT_TRUE(
CompareMatrices(e_off_->GetSolutionPhiXv(result), 0 * p_sink_.x(), 1e-6));
CheckConvexRestriction(result);
options_.solver_options = SolverOptions();
auto result4 = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result4.is_success());
EXPECT_NEAR(e_on_->GetSolutionCost(result4), 1.0, 1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result4), 0.0, 1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result4), 1.0, 1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result4), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result4), 0.0, 1e-6);
EXPECT_TRUE(
CompareMatrices(source_->GetSolution(result4), p_source_.x(), 1e-6));
EXPECT_TRUE(
CompareMatrices(target_->GetSolution(result4), p_target_.x(), 1e-6));
EXPECT_TRUE(sink_->GetSolution(result4).hasNaN());
if (solvers::ClpSolver::is_available()) {
solvers::ClpSolver clp;
options_.solver = &clp;
auto result3 = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result3.is_success());
EXPECT_NEAR(e_on_->GetSolutionCost(result3), 1.0, 1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result3), 0.0, 1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result3), 1.0, 1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result3), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result3), 0.0, 1e-6);
}
}
TEST_F(ThreePoints, ConvexRelaxation) {
e_on_->AddCost(1.0);
e_off_->AddCost(1.0);
source_->AddCost(1.0);
e_on_->AddConstraint(e_on_->xv()[0] <= 0.0);
source_->AddConstraint(source_->x()[0] >= 1.0);
auto result = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result.is_success());
EXPECT_NEAR(result.GetSolution(e_on_->phi()), 1.0, 1e-6);
EXPECT_NEAR(result.GetSolution(e_off_->phi()), 0.0, 1e-6);
if (!MixedIntegerSolverAvailable()) {
return;
}
options_.convex_relaxation = false;
auto result2 = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result2.is_success());
EXPECT_NEAR(result2.GetSolution(e_on_->phi()), 1.0, 1e-6);
EXPECT_NEAR(result2.GetSolution(e_off_->phi()), 0.0, 1e-6);
EXPECT_NEAR(e_on_->GetSolutionCost(result), e_on_->GetSolutionCost(result2),
1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result), e_off_->GetSolutionCost(result2),
1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result),
source_->GetSolutionCost(result2), 1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result),
target_->GetSolutionCost(result2), 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result), sink_->GetSolutionCost(result2),
1e-6);
}
TEST_F(ThreePoints, LinearCost2) {
const Vector0<double> a;
const double b = 1.23;
auto cost = std::make_shared<solvers::LinearCost>(a, b);
e_on_->AddCost(solvers::Binding(cost, {}));
e_off_->AddCost(solvers::Binding(cost, {}));
source_->AddCost(solvers::Binding(cost, {}));
auto result = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result.is_success());
EXPECT_NEAR(e_on_->GetSolutionCost(result), b, 1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result), b, 1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result), 0.0, 1e-6);
CheckConvexRestriction(result);
}
TEST_F(ThreePoints, LinearCost3) {
const Vector2d a{2.3, 4.5};
const double b = 1.23;
e_on_->AddCost(a.dot(e_on_->xu()) + b);
e_off_->AddCost(a.dot(e_off_->xu()) + b);
source_->AddCost(a.dot(source_->x()) + b);
auto result = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result.is_success());
EXPECT_NEAR(e_on_->GetSolutionCost(result), a.dot(p_source_.x()) + b, 1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result), a.dot(p_source_.x()) + b, 1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result), 0.0, 1e-6);
CheckConvexRestriction(result);
}
TEST_F(ThreePoints, LinearCost4) {
const double b = -1.23;
e_on_->AddCost(b);
DRAKE_EXPECT_THROWS_MESSAGE(
g_.SolveShortestPath(*source_, *target_, options_),
"Constant costs must be non-negative.*");
}
TEST_F(ThreePoints, LinearCost5) {
const double b = -1.23;
source_->AddCost(b);
DRAKE_EXPECT_THROWS_MESSAGE(
g_.SolveShortestPath(*source_, *target_, options_),
"Constant costs must be non-negative.*");
}
TEST_F(ThreePoints, MultipleVertexCosts) {
source_->AddCost(1.0);
source_->AddCost(1.0);
DRAKE_EXPECT_NO_THROW(g_.SolveShortestPath(*source_, *target_, options_));
}
TEST_F(ThreePoints, QuadraticCost) {
e_on_->AddCost((e_on_->xu() - e_on_->xv()).squaredNorm());
e_off_->AddCost((e_off_->xu() - e_off_->xv()).squaredNorm());
source_->AddCost(
static_cast<const VectorX<Expression>>(source_->x()).squaredNorm());
auto result = g_.SolveShortestPath(*source_, *target_, options_);
if (result.get_solver_id() == solvers::IpoptSolver::id()) {
return; // See IpoptTest for details.
}
ASSERT_TRUE(result.is_success());
EXPECT_NEAR(e_on_->GetSolutionCost(result),
(p_source_.x() - p_target_.x()).squaredNorm(), 1e-6);
EXPECT_NEAR(e_off_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(source_->GetSolutionCost(result), p_source_.x().squaredNorm(),
1e-6);
EXPECT_NEAR(target_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result), 0.0, 1e-6);
CheckConvexRestriction(result);
}
TEST_F(ThreePoints, QuadraticCost2) {
Matrix2d A;
A << 4.3, .5, -.4, 1.2;
// Make an arbitrary non-negative quadratic form, which goes to zero at a
// point.
Expression cost = (A * (e_on_->xu() - Vector2d{.54, -.23}) +
A * (e_on_->xv() - Vector2d{7.2, -.73}))
.squaredNorm();
e_on_->AddCost(cost);
e_off_->AddCost(cost.Substitute(subs_on_off_));
Expression vertex_cost =
(A * (source_->x() - Vector2d{.54, -.23})).squaredNorm();
source_->AddCost(vertex_cost);
auto result = g_.SolveShortestPath(*source_, *target_, options_);
if (result.get_solver_id() == solvers::IpoptSolver::id()) {
return; // See IpoptTest for details.
}
ASSERT_TRUE(result.is_success());
Environment env{};
env.insert(e_on_->xu(), p_source_.x());
env.insert(e_on_->xv(), p_target_.x());
EXPECT_NEAR(e_on_->GetSolutionCost(result), cost.Evaluate(env), 2e-5);
EXPECT_NEAR(e_off_->GetSolutionCost(result), 0.0, 4e-6);
EXPECT_NEAR(source_->GetSolutionCost(result), vertex_cost.Evaluate(env),
2e-5);
EXPECT_NEAR(target_->GetSolutionCost(result), 0.0, 1e-6);
EXPECT_NEAR(sink_->GetSolutionCost(result), 0.0, 1e-6);
CheckConvexRestriction(result);
}
TEST_F(ThreePoints, QuadraticCost3) {
Matrix2d A;
A << 4.3, .5, -.4, 1.2;
// Make an arbitrary positive quadratic form (by adding a constant).
Expression cost = (A * (e_on_->xu() - Vector2d{.54, -.23}) +
A * (e_on_->xv() - Vector2d{7.2, -.73}))
.squaredNorm() +
4.2;
e_on_->AddCost(cost);
e_off_->AddCost(cost.Substitute(subs_on_off_));
Expression vertex_cost =
(A * (source_->x() - Vector2d{.54, -.23})).squaredNorm() + 4.2;
source_->AddCost(vertex_cost);
auto result = g_.SolveShortestPath(*source_, *target_, options_);
ASSERT_TRUE(result.is_success());
Environment env{};
env.insert(e_on_->xu(), p_source_.x());
env.insert(e_on_->xv(), p_target_.x());
EXPECT_NEAR(e_on_->GetSolutionCost(result), cost.Evaluate(env), 5e-5);
EXPECT_NEAR(e_off_->GetSolutionCost(result), 0.0, 4e-6);
EXPECT_NEAR(source_->GetSolutionCost(result), vertex_cost.Evaluate(env),