mirror of
https://github.com/wpilibsuite/allwpilib
synced 2026-06-22 01:11:42 +00:00
[wpimath] Add core State-space classes (#2614)
Co-authored-by: Tyler Veness <calcmogul@gmail.com> Co-authored-by: Claudius Tewari <cttewari@gmail.com> Co-authored-by: Declan Freeman-Gleason <declanfreemangleason@gmail.com>
This commit is contained in:
Matt
244
wpimath/src/test/native/cpp/system/DiscretizationTest.cpp
Normal file
244
wpimath/src/test/native/cpp/system/DiscretizationTest.cpp
Normal file
@@ -0,0 +1,244 @@
|
||||
/*----------------------------------------------------------------------------*/
|
||||
/* Copyright (c) 2019-2020 FIRST. All Rights Reserved. */
|
||||
/* Open Source Software - may be modified and shared by FRC teams. The code */
|
||||
/* must be accompanied by the FIRST BSD license file in the root directory of */
|
||||
/* the project. */
|
||||
/*----------------------------------------------------------------------------*/
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include <functional>
|
||||
|
||||
#include "Eigen/Core"
|
||||
#include "frc/system/Discretization.h"
|
||||
#include "frc/system/RungeKutta.h"
|
||||
|
||||
// Check that for a simple second-order system that we can easily analyze
|
||||
// analytically,
|
||||
TEST(DiscretizationTest, DiscretizeA) {
|
||||
Eigen::Matrix<double, 2, 2> contA;
|
||||
contA << 0, 1, 0, 0;
|
||||
|
||||
Eigen::Matrix<double, 2, 1> x0;
|
||||
x0 << 1, 1;
|
||||
Eigen::Matrix<double, 2, 2> discA;
|
||||
|
||||
frc::DiscretizeA<2>(contA, 1_s, &discA);
|
||||
Eigen::Matrix<double, 2, 1> x1Discrete = discA * x0;
|
||||
|
||||
// We now have pos = vel = 1 and accel = 0, which should give us:
|
||||
Eigen::Matrix<double, 2, 1> x1Truth;
|
||||
x1Truth(1) = x0(1);
|
||||
x1Truth(0) = x0(0) + 1.0 * x0(1);
|
||||
|
||||
EXPECT_EQ(x1Truth, x1Discrete);
|
||||
}
|
||||
|
||||
// Check that for a simple second-order system that we can easily analyze
|
||||
// analytically,
|
||||
TEST(DiscretizationTest, DiscretizeAB) {
|
||||
Eigen::Matrix<double, 2, 2> contA;
|
||||
contA << 0, 1, 0, 0;
|
||||
|
||||
Eigen::Matrix<double, 2, 1> contB;
|
||||
contB << 0, 1;
|
||||
|
||||
Eigen::Matrix<double, 2, 1> x0;
|
||||
x0 << 1, 1;
|
||||
Eigen::Matrix<double, 1, 1> u;
|
||||
u << 1;
|
||||
Eigen::Matrix<double, 2, 2> discA;
|
||||
Eigen::Matrix<double, 2, 1> discB;
|
||||
|
||||
frc::DiscretizeAB<2, 1>(contA, contB, 1_s, &discA, &discB);
|
||||
Eigen::Matrix<double, 2, 1> x1Discrete = discA * x0 + discB * u;
|
||||
|
||||
// We now have pos = vel = accel = 1, which should give us:
|
||||
Eigen::Matrix<double, 2, 1> x1Truth;
|
||||
x1Truth(1) = x0(1) + 1.0 * u(0);
|
||||
x1Truth(0) = x0(0) + 1.0 * x0(1) + 0.5 * u(0);
|
||||
|
||||
EXPECT_EQ(x1Truth, x1Discrete);
|
||||
}
|
||||
|
||||
// Test that the discrete approximation of Q is roughly equal to
|
||||
// integral from 0 to dt of e^(A tau) Q e^(A.T tau) dtau
|
||||
TEST(DiscretizationTest, DiscretizeSlowModelAQ) {
|
||||
Eigen::Matrix<double, 2, 2> contA;
|
||||
contA << 0, 1, 0, 0;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> contQ;
|
||||
contQ << 1, 0, 0, 1;
|
||||
|
||||
constexpr auto dt = 1_s;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discQIntegrated = frc::RungeKuttaTimeVarying<
|
||||
std::function<Eigen::Matrix<double, 2, 2>(
|
||||
units::second_t, const Eigen::Matrix<double, 2, 2>&)>,
|
||||
Eigen::Matrix<double, 2, 2>>(
|
||||
[&](units::second_t t, const Eigen::Matrix<double, 2, 2>&) {
|
||||
return Eigen::Matrix<double, 2, 2>(
|
||||
(contA * t.to<double>()).exp() * contQ *
|
||||
(contA.transpose() * t.to<double>()).exp());
|
||||
},
|
||||
Eigen::Matrix<double, 2, 2>::Zero(), 0_s, dt);
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discA;
|
||||
Eigen::Matrix<double, 2, 2> discQ;
|
||||
frc::DiscretizeAQ<2>(contA, contQ, dt, &discA, &discQ);
|
||||
|
||||
EXPECT_LT((discQIntegrated - discQ).norm(), 1e-10)
|
||||
<< "Expected these to be nearly equal:\ndiscQ:\n"
|
||||
<< discQ << "\ndiscQIntegrated:\n"
|
||||
<< discQIntegrated;
|
||||
}
|
||||
|
||||
// Test that the discrete approximation of Q is roughly equal to
|
||||
// integral from 0 to dt of e^(A tau) Q e^(A.T tau) dtau
|
||||
TEST(DiscretizationTest, DiscretizeFastModelAQ) {
|
||||
Eigen::Matrix<double, 2, 2> contA;
|
||||
contA << 0, 1, 0, -1406.29;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> contQ;
|
||||
contQ << 0.0025, 0, 0, 1;
|
||||
|
||||
constexpr auto dt = 5.05_ms;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discQIntegrated = frc::RungeKuttaTimeVarying<
|
||||
std::function<Eigen::Matrix<double, 2, 2>(
|
||||
units::second_t, const Eigen::Matrix<double, 2, 2>&)>,
|
||||
Eigen::Matrix<double, 2, 2>>(
|
||||
[&](units::second_t t, const Eigen::Matrix<double, 2, 2>&) {
|
||||
return Eigen::Matrix<double, 2, 2>(
|
||||
(contA * t.to<double>()).exp() * contQ *
|
||||
(contA.transpose() * t.to<double>()).exp());
|
||||
},
|
||||
Eigen::Matrix<double, 2, 2>::Zero(), 0_s, dt);
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discA;
|
||||
Eigen::Matrix<double, 2, 2> discQ;
|
||||
frc::DiscretizeAQ<2>(contA, contQ, dt, &discA, &discQ);
|
||||
|
||||
EXPECT_LT((discQIntegrated - discQ).norm(), 1e-3)
|
||||
<< "Expected these to be nearly equal:\ndiscQ:\n"
|
||||
<< discQ << "\ndiscQIntegrated:\n"
|
||||
<< discQIntegrated;
|
||||
}
|
||||
|
||||
// Test that the Taylor series discretization produces nearly identical results.
|
||||
TEST(DiscretizationTest, DiscretizeSlowModelAQTaylor) {
|
||||
Eigen::Matrix<double, 2, 2> contA;
|
||||
contA << 0, 1, 0, 0;
|
||||
|
||||
Eigen::Matrix<double, 2, 1> contB;
|
||||
contB << 0, 1;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> contQ;
|
||||
contQ << 1, 0, 0, 1;
|
||||
|
||||
constexpr auto dt = 1_s;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discQTaylor;
|
||||
Eigen::Matrix<double, 2, 2> discA;
|
||||
Eigen::Matrix<double, 2, 2> discATaylor;
|
||||
Eigen::Matrix<double, 2, 1> discB;
|
||||
|
||||
// Continuous Q should be positive semidefinite
|
||||
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> esCont(contQ);
|
||||
for (int i = 0; i < contQ.rows(); i++) {
|
||||
EXPECT_GT(esCont.eigenvalues()[i], 0);
|
||||
}
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discQIntegrated = frc::RungeKuttaTimeVarying<
|
||||
std::function<Eigen::Matrix<double, 2, 2>(
|
||||
units::second_t, const Eigen::Matrix<double, 2, 2>&)>,
|
||||
Eigen::Matrix<double, 2, 2>>(
|
||||
[&](units::second_t t, const Eigen::Matrix<double, 2, 2>&) {
|
||||
return Eigen::Matrix<double, 2, 2>(
|
||||
(contA * t.to<double>()).exp() * contQ *
|
||||
(contA.transpose() * t.to<double>()).exp());
|
||||
},
|
||||
Eigen::Matrix<double, 2, 2>::Zero(), 0_s, dt);
|
||||
|
||||
frc::DiscretizeAB<2, 1>(contA, contB, dt, &discA, &discB);
|
||||
frc::DiscretizeAQTaylor<2>(contA, contQ, dt, &discATaylor, &discQTaylor);
|
||||
|
||||
EXPECT_LT((discQIntegrated - discQTaylor).norm(), 1e-10)
|
||||
<< "Expected these to be nearly equal:\ndiscQTaylor:\n"
|
||||
<< discQTaylor << "\ndiscQIntegrated:\n"
|
||||
<< discQIntegrated;
|
||||
EXPECT_LT((discA - discATaylor).norm(), 1e-10);
|
||||
|
||||
// Discrete Q should be positive semidefinite
|
||||
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> esDisc(discQTaylor);
|
||||
for (int i = 0; i < discQTaylor.rows(); i++) {
|
||||
EXPECT_GT(esDisc.eigenvalues()[i], 0);
|
||||
}
|
||||
}
|
||||
|
||||
// Test that the Taylor series discretization produces nearly identical results.
|
||||
TEST(DiscretizationTest, DiscretizeFastModelAQTaylor) {
|
||||
Eigen::Matrix<double, 2, 2> contA;
|
||||
contA << 0, 1, 0, -1500;
|
||||
|
||||
Eigen::Matrix<double, 2, 1> contB;
|
||||
contB << 0, 1;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> contQ;
|
||||
contQ << 0.0025, 0, 0, 1;
|
||||
|
||||
constexpr auto dt = 5.05_ms;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discQTaylor;
|
||||
Eigen::Matrix<double, 2, 2> discA;
|
||||
Eigen::Matrix<double, 2, 2> discATaylor;
|
||||
Eigen::Matrix<double, 2, 1> discB;
|
||||
|
||||
// Continuous Q should be positive semidefinite
|
||||
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> esCont(contQ);
|
||||
for (int i = 0; i < contQ.rows(); i++) {
|
||||
EXPECT_GT(esCont.eigenvalues()[i], 0);
|
||||
}
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discQIntegrated = frc::RungeKuttaTimeVarying<
|
||||
std::function<Eigen::Matrix<double, 2, 2>(
|
||||
units::second_t, const Eigen::Matrix<double, 2, 2>&)>,
|
||||
Eigen::Matrix<double, 2, 2>>(
|
||||
[&](units::second_t t, const Eigen::Matrix<double, 2, 2>&) {
|
||||
return Eigen::Matrix<double, 2, 2>(
|
||||
(contA * t.to<double>()).exp() * contQ *
|
||||
(contA.transpose() * t.to<double>()).exp());
|
||||
},
|
||||
Eigen::Matrix<double, 2, 2>::Zero(), 0_s, dt);
|
||||
|
||||
frc::DiscretizeAB<2, 1>(contA, contB, dt, &discA, &discB);
|
||||
frc::DiscretizeAQTaylor<2>(contA, contQ, dt, &discATaylor, &discQTaylor);
|
||||
|
||||
EXPECT_LT((discQIntegrated - discQTaylor).norm(), 1e-3)
|
||||
<< "Expected these to be nearly equal:\ndiscQTaylor:\n"
|
||||
<< discQTaylor << "\ndiscQIntegrated:\n"
|
||||
<< discQIntegrated;
|
||||
EXPECT_LT((discA - discATaylor).norm(), 1e-10);
|
||||
|
||||
// Discrete Q should be positive semidefinite
|
||||
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> esDisc(discQTaylor);
|
||||
for (int i = 0; i < discQTaylor.rows(); i++) {
|
||||
EXPECT_GT(esDisc.eigenvalues()[i], 0);
|
||||
}
|
||||
}
|
||||
|
||||
// Test that DiscretizeR() works
|
||||
TEST(DiscretizationTest, DiscretizeR) {
|
||||
Eigen::Matrix<double, 2, 2> contR;
|
||||
contR << 2.0, 0.0, 0.0, 1.0;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discRTruth;
|
||||
discRTruth << 4.0, 0.0, 0.0, 2.0;
|
||||
|
||||
Eigen::Matrix<double, 2, 2> discR = frc::DiscretizeR<2>(contR, 500_ms);
|
||||
|
||||
EXPECT_LT((discRTruth - discR).norm(), 1e-10)
|
||||
<< "Expected these to be nearly equal:\ndiscR:\n"
|
||||
<< discR << "\ndiscRTruth:\n"
|
||||
<< discRTruth;
|
||||
}
|
||||
77
wpimath/src/test/native/cpp/system/LinearSystemIDTest.cpp
Normal file
77
wpimath/src/test/native/cpp/system/LinearSystemIDTest.cpp
Normal file
@@ -0,0 +1,77 @@
|
||||
/*----------------------------------------------------------------------------*/
|
||||
/* Copyright (c) 2020 FIRST. All Rights Reserved. */
|
||||
/* Open Source Software - may be modified and shared by FRC teams. The code */
|
||||
/* must be accompanied by the FIRST BSD license file in the root directory of */
|
||||
/* the project. */
|
||||
/*----------------------------------------------------------------------------*/
|
||||
|
||||
#include <frc/system/LinearSystem.h>
|
||||
#include <frc/system/plant/DCMotor.h>
|
||||
#include <frc/system/plant/LinearSystemId.h>
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include <iostream>
|
||||
|
||||
#include "frc/StateSpaceUtil.h"
|
||||
#include "frc/system/plant/LinearSystemId.h"
|
||||
#include "units/length.h"
|
||||
#include "units/mass.h"
|
||||
|
||||
TEST(LinearSystemIDTest, IdentifyDrivetrainVelocitySystem) {
|
||||
auto model = frc::LinearSystemId::DrivetrainVelocitySystem(
|
||||
frc::DCMotor::NEO(4), 70_kg, 0.05_m, 0.4_m, 6.0_kg_sq_m, 6.0);
|
||||
|
||||
ASSERT_TRUE(model.A().isApprox(
|
||||
frc::MakeMatrix<2, 2>(-10.14132, 3.06598, 3.06598, -10.14132), 0.001));
|
||||
ASSERT_TRUE(model.B().isApprox(
|
||||
frc::MakeMatrix<2, 2>(4.2590, -1.28762, -1.2876, 4.2590), 0.001));
|
||||
ASSERT_TRUE(
|
||||
model.C().isApprox(frc::MakeMatrix<2, 2>(1.0, 0.0, 0.0, 1.0), 0.001));
|
||||
ASSERT_TRUE(
|
||||
model.D().isApprox(frc::MakeMatrix<2, 2>(0.0, 0.0, 0.0, 0.0), 0.001));
|
||||
}
|
||||
|
||||
TEST(LinearSystemIDTest, ElevatorSystem) {
|
||||
auto model = frc::LinearSystemId::ElevatorSystem(frc::DCMotor::NEO(2), 5_kg,
|
||||
0.05_m, 12);
|
||||
ASSERT_TRUE(model.A().isApprox(
|
||||
frc::MakeMatrix<2, 2>(0.0, 1.0, 0.0, -99.05473), 0.001));
|
||||
ASSERT_TRUE(model.B().isApprox(frc::MakeMatrix<2, 1>(0.0, 20.8), 0.001));
|
||||
ASSERT_TRUE(model.C().isApprox(frc::MakeMatrix<1, 2>(1.0, 0.0), 0.001));
|
||||
ASSERT_TRUE(model.D().isApprox(frc::MakeMatrix<1, 1>(0.0), 0.001));
|
||||
}
|
||||
|
||||
TEST(LinearSystemIDTest, FlywheelSystem) {
|
||||
auto model = frc::LinearSystemId::FlywheelSystem(frc::DCMotor::NEO(2),
|
||||
0.00032_kg_sq_m, 1.0);
|
||||
ASSERT_TRUE(model.A().isApprox(frc::MakeMatrix<1, 1>(-26.87032), 0.001));
|
||||
ASSERT_TRUE(model.B().isApprox(frc::MakeMatrix<1, 1>(1354.166667), 0.001));
|
||||
ASSERT_TRUE(model.C().isApprox(frc::MakeMatrix<1, 1>(1.0), 0.001));
|
||||
ASSERT_TRUE(model.D().isApprox(frc::MakeMatrix<1, 1>(0.0), 0.001));
|
||||
}
|
||||
|
||||
TEST(LinearSystemIDTest, IdentifyPositionSystem) {
|
||||
// By controls engineering in frc,
|
||||
// x-dot = [0 1 | 0 -kv/ka] x = [0 | 1/ka] u
|
||||
double kv = 1.0;
|
||||
double ka = 0.5;
|
||||
auto model = frc::LinearSystemId::IdentifyPositionSystem(kv, ka);
|
||||
|
||||
ASSERT_TRUE(model.A().isApprox(frc::MakeMatrix<2, 2>(0.0, 1.0, 0.0, -kv / ka),
|
||||
0.001));
|
||||
ASSERT_TRUE(model.B().isApprox(frc::MakeMatrix<2, 1>(0.0, 1.0 / ka), 0.001));
|
||||
}
|
||||
|
||||
TEST(LinearSystemIDTest, IdentifyVelocitySystem) {
|
||||
// By controls engineering in frc,
|
||||
// V = kv * velocity + ka * acceleration
|
||||
// x-dot = -kv/ka * v + 1/ka \cdot V
|
||||
double kv = 1.0;
|
||||
double ka = 0.5;
|
||||
auto model = frc::LinearSystemId::IdentifyVelocitySystem(kv, ka);
|
||||
|
||||
std::cout << model.A() << std::endl << model.B() << std::endl;
|
||||
|
||||
ASSERT_TRUE(model.A().isApprox(frc::MakeMatrix<1, 1>(-kv / ka), 0.001));
|
||||
ASSERT_TRUE(model.B().isApprox(frc::MakeMatrix<1, 1>(1.0 / ka), 0.001));
|
||||
}
|
||||
68
wpimath/src/test/native/cpp/system/NumericalJacobianTest.cpp
Normal file
68
wpimath/src/test/native/cpp/system/NumericalJacobianTest.cpp
Normal file
@@ -0,0 +1,68 @@
|
||||
/*----------------------------------------------------------------------------*/
|
||||
/* Copyright (c) 2019-2020 FIRST. All Rights Reserved. */
|
||||
/* Open Source Software - may be modified and shared by FRC teams. The code */
|
||||
/* must be accompanied by the FIRST BSD license file in the root directory of */
|
||||
/* the project. */
|
||||
/*----------------------------------------------------------------------------*/
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include "frc/system/NumericalJacobian.h"
|
||||
|
||||
Eigen::Matrix<double, 4, 4> A = (Eigen::Matrix<double, 4, 4>() << 1, 2, 4, 1, 5,
|
||||
2, 3, 4, 5, 1, 3, 2, 1, 1, 3, 7)
|
||||
.finished();
|
||||
|
||||
Eigen::Matrix<double, 4, 2> B =
|
||||
(Eigen::Matrix<double, 4, 2>() << 1, 1, 2, 1, 3, 2, 3, 7).finished();
|
||||
|
||||
// Function from which to recover A and B
|
||||
Eigen::Matrix<double, 4, 1> AxBuFn(const Eigen::Matrix<double, 4, 1>& x,
|
||||
const Eigen::Matrix<double, 2, 1>& u) {
|
||||
return A * x + B * u;
|
||||
}
|
||||
|
||||
// Test that we can recover A from AxBuFn() pretty accurately
|
||||
TEST(NumericalJacobianTest, Ax) {
|
||||
Eigen::Matrix<double, 4, 4> newA = frc::NumericalJacobianX<4, 4, 2>(
|
||||
AxBuFn, Eigen::Matrix<double, 4, 1>::Zero(),
|
||||
Eigen::Matrix<double, 2, 1>::Zero());
|
||||
EXPECT_TRUE(newA.isApprox(A));
|
||||
}
|
||||
|
||||
// Test that we can recover B from AxBuFn() pretty accurately
|
||||
TEST(NumericalJacobianTest, Bu) {
|
||||
Eigen::Matrix<double, 4, 2> newB = frc::NumericalJacobianU<4, 4, 2>(
|
||||
AxBuFn, Eigen::Matrix<double, 4, 1>::Zero(),
|
||||
Eigen::Matrix<double, 2, 1>::Zero());
|
||||
EXPECT_TRUE(newB.isApprox(B));
|
||||
}
|
||||
|
||||
Eigen::Matrix<double, 3, 4> C =
|
||||
(Eigen::Matrix<double, 3, 4>() << 1, 2, 4, 1, 5, 2, 3, 4, 5, 1, 3, 2)
|
||||
.finished();
|
||||
|
||||
Eigen::Matrix<double, 3, 2> D =
|
||||
(Eigen::Matrix<double, 3, 2>() << 1, 1, 2, 1, 3, 2).finished();
|
||||
|
||||
// Function from which to recover C and D
|
||||
Eigen::Matrix<double, 3, 1> CxDuFn(const Eigen::Matrix<double, 4, 1>& x,
|
||||
const Eigen::Matrix<double, 2, 1>& u) {
|
||||
return C * x + D * u;
|
||||
}
|
||||
|
||||
// Test that we can recover C from CxDuFn() pretty accurately
|
||||
TEST(NumericalJacobianTest, Cx) {
|
||||
Eigen::Matrix<double, 3, 4> newC = frc::NumericalJacobianX<3, 4, 2>(
|
||||
CxDuFn, Eigen::Matrix<double, 4, 1>::Zero(),
|
||||
Eigen::Matrix<double, 2, 1>::Zero());
|
||||
EXPECT_TRUE(newC.isApprox(C));
|
||||
}
|
||||
|
||||
// Test that we can recover D from CxDuFn() pretty accurately
|
||||
TEST(NumericalJacobianTest, Du) {
|
||||
Eigen::Matrix<double, 3, 2> newD = frc::NumericalJacobianU<3, 4, 2>(
|
||||
CxDuFn, Eigen::Matrix<double, 4, 1>::Zero(),
|
||||
Eigen::Matrix<double, 2, 1>::Zero());
|
||||
EXPECT_TRUE(newD.isApprox(D));
|
||||
}
|
||||
71
wpimath/src/test/native/cpp/system/RungeKuttaTest.cpp
Normal file
71
wpimath/src/test/native/cpp/system/RungeKuttaTest.cpp
Normal file
@@ -0,0 +1,71 @@
|
||||
/*----------------------------------------------------------------------------*/
|
||||
/* Copyright (c) 2019-2020 FIRST. All Rights Reserved. */
|
||||
/* Open Source Software - may be modified and shared by FRC teams. The code */
|
||||
/* must be accompanied by the FIRST BSD license file in the root directory of */
|
||||
/* the project. */
|
||||
/*----------------------------------------------------------------------------*/
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include <cmath>
|
||||
|
||||
#include "frc/system/RungeKutta.h"
|
||||
|
||||
// Tests that integrating dx/dt = e^x works.
|
||||
TEST(RungeKuttaTest, Exponential) {
|
||||
Eigen::Matrix<double, 1, 1> y0;
|
||||
y0(0) = 0.0;
|
||||
|
||||
Eigen::Matrix<double, 1, 1> y1 = frc::RungeKutta(
|
||||
[](Eigen::Matrix<double, 1, 1> x) {
|
||||
Eigen::Matrix<double, 1, 1> y;
|
||||
y(0) = std::exp(x(0));
|
||||
return y;
|
||||
},
|
||||
y0, 0.1_s);
|
||||
EXPECT_NEAR(y1(0), std::exp(0.1) - std::exp(0), 1e-3);
|
||||
}
|
||||
|
||||
// Tests that integrating dx/dt = e^x works when we provide a U.
|
||||
TEST(RungeKuttaTest, ExponentialWithU) {
|
||||
Eigen::Matrix<double, 1, 1> y0;
|
||||
y0(0) = 0.0;
|
||||
|
||||
Eigen::Matrix<double, 1, 1> y1 = frc::RungeKutta(
|
||||
[](Eigen::Matrix<double, 1, 1> x, Eigen::Matrix<double, 1, 1> u) {
|
||||
Eigen::Matrix<double, 1, 1> y;
|
||||
y(0) = std::exp(u(0) * x(0));
|
||||
return y;
|
||||
},
|
||||
y0, (Eigen::Matrix<double, 1, 1>() << 1.0).finished(), 0.1_s);
|
||||
EXPECT_NEAR(y1(0), std::exp(0.1) - std::exp(0), 1e-3);
|
||||
}
|
||||
|
||||
namespace {
|
||||
Eigen::Matrix<double, 1, 1> RungeKuttaTimeVaryingSolution(double t) {
|
||||
return (Eigen::Matrix<double, 1, 1>()
|
||||
<< 12.0 * std::exp(t) / (std::pow(std::exp(t) + 1.0, 2.0)))
|
||||
.finished();
|
||||
}
|
||||
} // namespace
|
||||
|
||||
// Tests RungeKutta with a time varying solution.
|
||||
// Now, lets test RK4 with a time varying solution. From
|
||||
// http://www2.hawaii.edu/~jmcfatri/math407/RungeKuttaTest.html:
|
||||
// x' = x (2 / (e^t + 1) - 1)
|
||||
//
|
||||
// The true (analytical) solution is:
|
||||
//
|
||||
// x(t) = 12 * e^t / ((e^t + 1)^2)
|
||||
TEST(RungeKuttaTest, RungeKuttaTimeVarying) {
|
||||
Eigen::Matrix<double, 1, 1> y0 = RungeKuttaTimeVaryingSolution(5.0);
|
||||
|
||||
Eigen::Matrix<double, 1, 1> y1 = frc::RungeKuttaTimeVarying(
|
||||
[](units::second_t t, Eigen::Matrix<double, 1, 1> x) {
|
||||
return (Eigen::Matrix<double, 1, 1>()
|
||||
<< x(0) * (2.0 / (std::exp(t.to<double>()) + 1.0) - 1.0))
|
||||
.finished();
|
||||
},
|
||||
y0, 5_s, 1_s);
|
||||
EXPECT_NEAR(y1(0), RungeKuttaTimeVaryingSolution(6.0)(0), 1e-3);
|
||||
}
|
||||
Reference in New Issue
Block a user