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system_symbolic_inspector_test.cc
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system_symbolic_inspector_test.cc
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#include "drake/systems/framework/system_symbolic_inspector.h"
#include <algorithm>
#include <memory>
#include <gtest/gtest.h>
#include "drake/common/symbolic/polynomial.h"
#include "drake/examples/pendulum/pendulum_plant.h"
#include "drake/systems/framework/leaf_system.h"
namespace drake {
namespace systems {
namespace {
const int kSize = 2;
class SparseSystem : public LeafSystem<symbolic::Expression> {
public:
SparseSystem() {
this->DeclareInputPort(kUseDefaultName, kVectorValued, kSize);
this->DeclareInputPort(kUseDefaultName, kVectorValued, kSize);
this->DeclareVectorOutputPort(kUseDefaultName, kSize,
&SparseSystem::CalcY0);
this->DeclareVectorOutputPort(kUseDefaultName, kSize,
&SparseSystem::CalcY1);
this->DeclareAbstractOutputPort("port_42", 42, &SparseSystem::CalcNothing);
this->DeclareContinuousState(kSize);
this->DeclareDiscreteState(kSize);
this->DeclareEqualityConstraint(&SparseSystem::CalcConstraint, kSize,
"equality constraint");
this->DeclareInequalityConstraint(&SparseSystem::CalcConstraint,
{ Eigen::VectorXd::Zero(kSize),
std::nullopt }, "inequality constraint");
}
void AddAbstractInputPort() {
this->DeclareAbstractInputPort(kUseDefaultName, Value<std::string>{});
}
~SparseSystem() override {}
private:
// Calculation function for output port 0.
void CalcY0(const Context<symbolic::Expression>& context,
BasicVector<symbolic::Expression>* y0) const {
const auto& u0 = this->get_input_port(0).Eval(context);
const auto& u1 = this->get_input_port(1).Eval(context);
const auto& xc = context.get_continuous_state_vector().CopyToVector();
// Output 0 depends on input 0 and the continuous state. Input 1 appears in
// an intermediate computation, but is ultimately cancelled out.
y0->get_mutable_value() = u1;
y0->get_mutable_value() += u0;
y0->get_mutable_value() -= u1;
y0->get_mutable_value() += 12. * xc;
}
// Calculation function for output port 1.
void CalcY1(const Context<symbolic::Expression>& context,
BasicVector<symbolic::Expression>* y1) const {
const auto& u0 = this->get_input_port(0).Eval(context);
const auto& u1 = this->get_input_port(1).Eval(context);
const auto& xd = context.get_discrete_state(0).get_value();
// Output 1 depends on both inputs and the discrete state.
y1->set_value(u0 + u1 + xd);
}
void CalcNothing(const Context<symbolic::Expression>& context, int*) const {}
void CalcConstraint(const Context<symbolic::Expression>& context,
VectorX<symbolic::Expression>* value) const {
*value = context.get_continuous_state_vector().CopyToVector();
}
// Implements a time-varying affine dynamics.
void DoCalcTimeDerivatives(
const Context<symbolic::Expression>& context,
ContinuousState<symbolic::Expression>* derivatives) const override {
const auto& u0 = this->get_input_port(0).Eval(context);
const auto& u1 = this->get_input_port(1).Eval(context);
const auto& t = context.get_time();
const Vector2<symbolic::Expression> x =
context.get_continuous_state_vector().CopyToVector();
const Eigen::Matrix2d A = 2 * Eigen::Matrix2d::Identity();
const Eigen::Matrix2d B1 = 3 * Eigen::Matrix2d::Identity();
const Eigen::Matrix2d B2 = 4 * Eigen::Matrix2d::Identity();
const Eigen::Vector2d f0(5.0, 6.0);
const Vector2<symbolic::Expression> xdot =
A * t * x + B1 * u0 + B2 * u1 + f0;
derivatives->SetFromVector(xdot);
}
void DoCalcDiscreteVariableUpdates(
const systems::Context<symbolic::Expression>& context,
const std::vector<
const systems::DiscreteUpdateEvent<symbolic::Expression>*>&,
systems::DiscreteValues<symbolic::Expression>* discrete_state)
const override {
const auto& u0 = this->get_input_port(0).Eval(context);
const auto& u1 = this->get_input_port(1).Eval(context);
const Vector2<symbolic::Expression> xd =
context.get_discrete_state(0).get_value();
const Eigen::Matrix2d A = 7 * Eigen::Matrix2d::Identity();
const Eigen::Matrix2d B1 = 8 * Eigen::Matrix2d::Identity();
const Eigen::Matrix2d B2 = 9 * Eigen::Matrix2d::Identity();
const Eigen::Vector2d f0(10.0, 11.0);
const Vector2<symbolic::Expression> next_xd =
A * xd + B1 * u0 + B2 * u1 + f0;
discrete_state->set_value(0, next_xd);
}
};
class SystemSymbolicInspectorTest : public ::testing::Test {
public:
SystemSymbolicInspectorTest() : system_() {}
protected:
void SetUp() override {
inspector_ = std::make_unique<SystemSymbolicInspector>(system_);
}
SparseSystem system_;
std::unique_ptr<SystemSymbolicInspector> inspector_;
};
class PendulumInspectorTest : public ::testing::Test {
public:
PendulumInspectorTest() : system_() {}
protected:
void SetUp() override {
inspector_ = std::make_unique<SystemSymbolicInspector>(system_);
}
examples::pendulum::PendulumPlant<symbolic::Expression> system_;
std::unique_ptr<SystemSymbolicInspector> inspector_;
};
// Tests that the SystemSymbolicInspector infers, from the symbolic equations of
// the System, that input 1 does not affect output 0.
TEST_F(SystemSymbolicInspectorTest, InputToOutput) {
// Only input 0 affects output 0.
EXPECT_TRUE(inspector_->IsConnectedInputToOutput(0, 0));
EXPECT_FALSE(inspector_->IsConnectedInputToOutput(1, 0));
// Both inputs affect output 1.
EXPECT_TRUE(inspector_->IsConnectedInputToOutput(0, 1));
EXPECT_TRUE(inspector_->IsConnectedInputToOutput(1, 1));
// All inputs are presumed to affect output 2, since it is abstract.
EXPECT_TRUE(inspector_->IsConnectedInputToOutput(0, 2));
EXPECT_TRUE(inspector_->IsConnectedInputToOutput(1, 2));
}
// Tests that, if the System has an abstract input, the SystemSymbolicInspector
// conservatively reports that every output might depend on every input.
TEST_F(SystemSymbolicInspectorTest, AbstractContextThwartsSparsity) {
system_.AddAbstractInputPort();
inspector_ = std::make_unique<SystemSymbolicInspector>(system_);
for (int i = 0; i < system_.num_input_ports(); ++i) {
for (int j = 0; j < system_.num_output_ports(); ++j) {
EXPECT_TRUE(inspector_->IsConnectedInputToOutput(i, j));
}
}
}
TEST_F(SystemSymbolicInspectorTest, ConstraintTest) {
const auto& constraints = inspector_->constraints();
const std::vector<std::string> expected{
"((xc0 == 0) and (xc1 == 0))",
"((xc0 >= 0) and (xc1 >= 0) and (xc0 <= inf) and (xc1 <= inf))",
};
std::vector<std::string> actual;
std::transform(
constraints.begin(), constraints.end(), std::back_inserter(actual),
[](const auto& item) { return item.to_string(); });
EXPECT_EQ(actual, expected);
}
TEST_F(SystemSymbolicInspectorTest, IsTimeInvariant) {
// The derivatives depends on t.
EXPECT_FALSE(inspector_->IsTimeInvariant());
}
TEST_F(PendulumInspectorTest, IsTimeInvariant) {
EXPECT_TRUE(inspector_->IsTimeInvariant());
}
TEST_F(SystemSymbolicInspectorTest, HasAffineDynamics) {
EXPECT_TRUE(inspector_->HasAffineDynamics());
}
TEST_F(PendulumInspectorTest, HasAffineDynamics) {
EXPECT_FALSE(inspector_->HasAffineDynamics());
}
TEST_F(SystemSymbolicInspectorTest, IsAbstract) {
auto context = system_.CreateDefaultContext();
EXPECT_FALSE(SystemSymbolicInspector::IsAbstract(system_, *context));
system_.AddAbstractInputPort();
auto context2 = system_.CreateDefaultContext();
EXPECT_TRUE(SystemSymbolicInspector::IsAbstract(system_, *context2));
}
TEST_F(PendulumInspectorTest, SymbolicParameters) {
auto params = inspector_->numeric_parameters(0);
using examples::pendulum::PendulumParamsIndices;
EXPECT_EQ(params.size(), PendulumParamsIndices::kNumCoordinates);
// Test that the damping parameter appears with the correct order in the
// derivatives and output methods.
symbolic::Variables v({params[PendulumParamsIndices::kDamping]});
auto derivatives = inspector_->derivatives();
EXPECT_EQ(symbolic::Polynomial(derivatives[0], v).TotalDegree(), 0);
EXPECT_EQ(symbolic::Polynomial(derivatives[1], v).TotalDegree(), 1);
auto output = inspector_->output(0);
EXPECT_EQ(symbolic::Polynomial(output[0], v).TotalDegree(), 0);
EXPECT_EQ(symbolic::Polynomial(output[1], v).TotalDegree(), 0);
}
} // namespace
} // namespace systems
} // namespace drake