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Inertial_TEST.cc
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Inertial_TEST.cc
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/*
* Copyright (C) 2015 Open Source Robotics Foundation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*/
#include <gtest/gtest.h>
#include <cmath>
#include "gz/math/Inertial.hh"
using namespace gz;
/////////////////////////////////////////////////
/// \brief Compare quaternions, but allow rotations of PI about any axis.
void CompareModuloPi(const math::Quaterniond &_q1,
const math::Quaterniond &_q2,
const double _tol = 1e-6)
{
const auto rotErrorEuler = (_q1.Inverse() * _q2).Euler();
EXPECT_NEAR(sin(rotErrorEuler.X()), 0.0, _tol);
EXPECT_NEAR(sin(rotErrorEuler.Y()), 0.0, _tol);
EXPECT_NEAR(sin(rotErrorEuler.Z()), 0.0, _tol);
}
/////////////////////////////////////////////////
// Simple constructor, test default values
TEST(Inertiald_Test, Constructor)
{
math::Inertiald inertial;
EXPECT_EQ(inertial.Pose(), math::Pose3d::Zero);
EXPECT_EQ(inertial.MassMatrix(), math::MassMatrix3d());
EXPECT_EQ(inertial.Moi(), math::Matrix3d::Zero);
EXPECT_FALSE(inertial.FluidAddedMass().has_value());
EXPECT_EQ(inertial.BodyMatrix(), math::Matrix6d::Zero);
EXPECT_EQ(inertial.SpatialMatrix(), math::Matrix6d::Zero);
EXPECT_EQ(inertial.BodyMatrix(), inertial.SpatialMatrix());
}
/////////////////////////////////////////////////
// Constructor with default arguments
// Should match simple constructor and with copy constructor
TEST(Inertiald_Test, ConstructorDefaultValues)
{
math::Inertiald inertial(math::MassMatrix3d(), math::Pose3d::Zero);
EXPECT_EQ(inertial, math::Inertiald());
EXPECT_EQ(inertial, math::Inertiald(inertial));
}
/////////////////////////////////////////////////
// Constructor with non-default arguments
TEST(Inertiald_Test, ConstructorNonDefaultValues)
{
const double mass = 5.0;
const math::Vector3d Ixxyyzz(2.0, 3.0, 4.0);
const math::Vector3d Ixyxzyz(0.2, 0.3, 0.4);
math::MassMatrix3d m(mass, Ixxyyzz, Ixyxzyz);
EXPECT_TRUE(m.IsPositive());
EXPECT_TRUE(m.IsValid());
const math::Pose3d pose(1, 2, 3, GZ_PI/6, 0, 0);
math::Inertiald inertial(m, pose);
// Should not match simple constructor
EXPECT_NE(inertial, math::Inertiald());
// Should match with copy constructor
EXPECT_EQ(inertial, math::Inertiald(inertial));
// Test accessors
EXPECT_EQ(inertial.MassMatrix(), m);
EXPECT_EQ(inertial.Pose(), pose);
EXPECT_TRUE(inertial.MassMatrix().IsPositive());
EXPECT_TRUE(inertial.MassMatrix().IsValid());
// Test assignment operator
math::Inertiald inertial2;
EXPECT_NE(inertial, inertial2);
inertial2 = inertial;
EXPECT_EQ(inertial, inertial2);
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, CoverageExtra)
{
// getting full destructor coverage
math::Inertiald *p = new math::Inertiald;
EXPECT_TRUE(p != NULL);
delete p;
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, SetMassMatrix)
{
math::Inertiald inertial;
math::MassMatrix3d m;
// This will be true because the default mass of zero is considered valid
EXPECT_TRUE(inertial.SetMassMatrix(m, 0));
// Set the mass to a negative value, and SetMassMatrix should complain.
m.SetMass(-1);
EXPECT_FALSE(inertial.SetMassMatrix(m, 0));
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, Setters)
{
const double mass = 5.0;
const math::Vector3d Ixxyyzz(2.0, 3.0, 4.0);
const math::Vector3d Ixyxzyz(0.2, 0.3, 0.4);
math::MassMatrix3d m(mass, Ixxyyzz, Ixyxzyz);
EXPECT_TRUE(m.IsPositive());
EXPECT_TRUE(m.IsValid());
const math::Pose3d pose(1, 2, 3, GZ_PI/6, 0, 0);
math::Inertiald inertial;
// Initially valid
EXPECT_TRUE(inertial.SetPose(pose));
// Valid once valid mass matrix is set
EXPECT_TRUE(inertial.SetMassMatrix(m));
// Verify values
EXPECT_EQ(inertial.MassMatrix(), m);
EXPECT_EQ(inertial.Pose(), pose);
// Invalid again if an invalid inertia is set
math::MassMatrix3d mInvalid(-1, Ixxyyzz, Ixyxzyz);
EXPECT_FALSE(inertial.SetMassMatrix(mInvalid));
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, MOI_Diagonal)
{
const double mass = 12.0;
const math::Vector3d Ixxyyzz(2.0, 3.0, 4.0);
const math::Vector3d Ixyxzyz(0, 0, 0);
const math::MassMatrix3d m(mass, Ixxyyzz, Ixyxzyz);
EXPECT_TRUE(m.IsPositive());
EXPECT_TRUE(m.IsValid());
// no rotation, expect MOI's to match
{
const math::Pose3d pose(0, 0, 0, 0, 0, 0);
math::Inertiald inertial(m, pose);
EXPECT_EQ(inertial.Moi(), m.Moi());
}
// 90 deg rotation about X axis, expect different MOI
{
const math::Pose3d pose(0, 0, 0, GZ_PI_2, 0, 0);
const math::Matrix3d expectedMOI(2, 0, 0, 0, 4, 0, 0, 0, 3);
math::Inertiald inertial(m, pose);
EXPECT_NE(inertial.Moi(), m.Moi());
EXPECT_EQ(inertial.Moi(), expectedMOI);
}
// 90 deg rotation about Y axis, expect different MOI
{
const math::Pose3d pose(0, 0, 0, 0, GZ_PI_2, 0);
const math::Matrix3d expectedMOI(4, 0, 0, 0, 3, 0, 0, 0, 2);
math::Inertiald inertial(m, pose);
EXPECT_NE(inertial.Moi(), m.Moi());
EXPECT_EQ(inertial.Moi(), expectedMOI);
}
// 90 deg rotation about Z axis, expect different MOI
{
const math::Pose3d pose(0, 0, 0, 0, 0, GZ_PI_2);
const math::Matrix3d expectedMOI(3, 0, 0, 0, 2, 0, 0, 0, 4);
math::Inertiald inertial(m, pose);
EXPECT_NE(inertial.Moi(), m.Moi());
EXPECT_EQ(inertial.Moi(), expectedMOI);
}
// 45 deg rotation about Z axis, expect different MOI
{
const math::Pose3d pose(0, 0, 0, 0, 0, GZ_PI_4);
const math::Matrix3d expectedMOI(2.5, -0.5, 0, -0.5, 2.5, 0, 0, 0, 4);
math::Inertiald inertial(m, pose);
EXPECT_NE(inertial.Moi(), m.Moi());
EXPECT_EQ(inertial.Moi(), expectedMOI);
// double check with a second MassMatrix3 instance
// that has the same base frame MOI but no pose rotation
math::MassMatrix3d m2;
EXPECT_TRUE(m2.SetMass(mass));
EXPECT_TRUE(m2.SetMoi(expectedMOI));
EXPECT_EQ(inertial.Moi(), m2.Moi());
// There are multiple correct rotations due to symmetry
CompareModuloPi(m2.PrincipalAxesOffset(), pose.Rot());
}
}
/////////////////////////////////////////////////
// Base frame MOI should be invariant
void SetRotation(const double _mass,
const math::Vector3d &_ixxyyzz,
const math::Vector3d &_ixyxzyz,
const bool _unique = true)
{
const math::MassMatrix3d m(_mass, _ixxyyzz, _ixyxzyz);
EXPECT_TRUE(m.IsPositive());
EXPECT_TRUE(m.IsValid());
math::Pose3d pose(math::Vector3d::Zero, math::Quaterniond::Identity);
const math::Inertiald inertialRef(m, pose);
const auto moi = inertialRef.Moi();
const std::vector<math::Quaterniond> rotations = {
math::Quaterniond::Identity,
math::Quaterniond(GZ_PI, 0, 0),
math::Quaterniond(0, GZ_PI, 0),
math::Quaterniond(0, 0, GZ_PI),
math::Quaterniond(GZ_PI_2, 0, 0),
math::Quaterniond(0, GZ_PI_2, 0),
math::Quaterniond(0, 0, GZ_PI_2),
math::Quaterniond(GZ_PI_4, 0, 0),
math::Quaterniond(0, GZ_PI_4, 0),
math::Quaterniond(0, 0, GZ_PI_4),
math::Quaterniond(GZ_PI/6, 0, 0),
math::Quaterniond(0, GZ_PI/6, 0),
math::Quaterniond(0, 0, GZ_PI/6),
math::Quaterniond(0.1, 0.2, 0.3),
math::Quaterniond(-0.1, 0.2, -0.3),
math::Quaterniond(0.4, 0.2, 0.5),
math::Quaterniond(-0.1, 0.7, -0.7)};
for (const auto &rot : rotations)
{
{
auto inertial = inertialRef;
const double tol = -1e-6;
EXPECT_TRUE(inertial.SetMassMatrixRotation(rot, tol));
EXPECT_EQ(moi, inertial.Moi());
if (_unique)
{
CompareModuloPi(rot, inertial.MassMatrix().PrincipalAxesOffset(tol));
}
EXPECT_TRUE(inertial.SetInertialRotation(rot));
EXPECT_EQ(rot, inertial.Pose().Rot());
EXPECT_EQ(moi, inertial.Moi());
}
{
auto inertial = inertialRef;
EXPECT_TRUE(inertial.SetInertialRotation(rot));
EXPECT_EQ(rot, inertial.Pose().Rot());
EXPECT_EQ(moi, inertial.Moi());
const double tol = -1e-6;
EXPECT_TRUE(inertial.SetMassMatrixRotation(rot, tol));
EXPECT_EQ(moi, inertial.Moi());
if (_unique)
{
CompareModuloPi(rot, inertial.MassMatrix().PrincipalAxesOffset(tol));
}
}
}
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, SetRotationUniqueDiagonal)
{
SetRotation(12, math::Vector3d(2, 3, 4), math::Vector3d::Zero);
SetRotation(12, math::Vector3d(3, 2, 4), math::Vector3d::Zero);
SetRotation(12, math::Vector3d(2, 4, 3), math::Vector3d::Zero);
SetRotation(12, math::Vector3d(3, 4, 2), math::Vector3d::Zero);
SetRotation(12, math::Vector3d(4, 2, 3), math::Vector3d::Zero);
SetRotation(12, math::Vector3d(4, 3, 2), math::Vector3d::Zero);
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, SetRotationUniqueNondiagonal)
{
SetRotation(12, math::Vector3d(2, 3, 4), math::Vector3d(0.3, 0.2, 0.1));
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, SetRotationNonuniqueDiagonal)
{
SetRotation(12, math::Vector3d(2, 2, 2), math::Vector3d::Zero, false);
SetRotation(12, math::Vector3d(2, 2, 3), math::Vector3d::Zero, false);
SetRotation(12, math::Vector3d(2, 3, 2), math::Vector3d::Zero, false);
SetRotation(12, math::Vector3d(3, 2, 2), math::Vector3d::Zero, false);
SetRotation(12, math::Vector3d(2, 3, 3), math::Vector3d::Zero, false);
SetRotation(12, math::Vector3d(3, 2, 3), math::Vector3d::Zero, false);
SetRotation(12, math::Vector3d(3, 3, 2), math::Vector3d::Zero, false);
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, SetRotationNonuniqueNondiagonal)
{
SetRotation(12, math::Vector3d(4, 4, 3), math::Vector3d(-1, 0, 0), false);
SetRotation(12, math::Vector3d(4, 3, 4), math::Vector3d(0, -1, 0), false);
SetRotation(12, math::Vector3d(3, 4, 4), math::Vector3d(0, 0, -1), false);
SetRotation(12, math::Vector3d(4, 4, 5), math::Vector3d(-1, 0, 0), false);
SetRotation(12, math::Vector3d(5, 4, 4), math::Vector3d(0, 0, -1), false);
SetRotation(12, math::Vector3d(5.5, 4.125, 4.375),
0.25*math::Vector3d(-sqrt(3), 3.0, -sqrt(3)/2), false);
SetRotation(12, math::Vector3d(4.125, 5.5, 4.375),
0.25*math::Vector3d(-sqrt(3), -sqrt(3)/2, 3.0), false);
}
/////////////////////////////////////////////////
// test for diagonalizing MassMatrix
// verify MOI is conserved
// and that off-diagonal terms are zero
void Diagonalize(
const double _mass,
const math::Vector3d &_ixxyyzz,
const math::Vector3d &_ixyxzyz)
{
const math::MassMatrix3d m(_mass, _ixxyyzz, _ixyxzyz);
EXPECT_TRUE(m.IsPositive());
EXPECT_TRUE(m.IsValid());
math::Pose3d pose(math::Vector3d::Zero, math::Quaterniond::Identity);
math::Inertiald inertial(m, pose);
const auto moi = inertial.Moi();
EXPECT_TRUE(inertial.SetMassMatrixRotation(math::Quaterniond::Identity));
EXPECT_EQ(moi, inertial.Moi());
EXPECT_EQ(inertial.MassMatrix().OffDiagonalMoments(), math::Vector3d::Zero);
// try again with negative tolerance
EXPECT_TRUE(
inertial.SetMassMatrixRotation(math::Quaterniond::Identity, -1e-6));
EXPECT_EQ(moi, inertial.Moi());
EXPECT_EQ(inertial.MassMatrix().OffDiagonalMoments(), math::Vector3d::Zero);
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, Diagonalize)
{
Diagonalize(12, math::Vector3d(2, 3, 4), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(3, 2, 4), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(2, 4, 3), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(3, 4, 2), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(4, 2, 3), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(4, 3, 2), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(2, 3, 4), math::Vector3d(0.3, 0.2, 0.1));
Diagonalize(12, math::Vector3d(2, 2, 2), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(2, 2, 3), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(2, 3, 2), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(3, 2, 2), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(2, 3, 3), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(3, 2, 3), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(3, 3, 2), math::Vector3d::Zero);
Diagonalize(12, math::Vector3d(4, 4, 3), math::Vector3d(-1, 0, 0));
Diagonalize(12, math::Vector3d(4, 3, 4), math::Vector3d(0, -1, 0));
Diagonalize(12, math::Vector3d(3, 4, 4), math::Vector3d(0, 0, -1));
Diagonalize(12, math::Vector3d(4, 4, 5), math::Vector3d(-1, 0, 0));
Diagonalize(12, math::Vector3d(5, 4, 4), math::Vector3d(0, 0, -1));
Diagonalize(12, math::Vector3d(5.5, 4.125, 4.375),
0.25*math::Vector3d(-sqrt(3), 3.0, -sqrt(3)/2));
Diagonalize(12, math::Vector3d(4.125, 5.5, 4.375),
0.25*math::Vector3d(-sqrt(3), -sqrt(3)/2, 3.0));
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, AdditionSubtraction)
{
// Add two half-cubes together and
// Subtract one half-cube from a full cube
{
const double mass = 12.0;
const math::Vector3d size(1, 1, 1);
math::MassMatrix3d cubeMM3;
EXPECT_TRUE(cubeMM3.SetFromBox(mass, size));
const math::Inertiald cube(cubeMM3, math::Pose3d::Zero);
math::MassMatrix3d half;
const math::Vector3d half_size(0.5, 1, 1);
EXPECT_TRUE(half.SetFromBox(0.5*mass, half_size));
math::Inertiald left(half, math::Pose3d(-0.25, 0, 0, 0, 0, 0));
math::Inertiald right(half, math::Pose3d(0.25, 0, 0, 0, 0, 0));
EXPECT_EQ(cube, left + right);
EXPECT_EQ(cube, right + left);
EXPECT_EQ(right, cube - left);
EXPECT_EQ(left, cube - right);
// test += operator
{
math::Inertiald tmp = left;
tmp += right;
EXPECT_EQ(cube, tmp);
}
{
math::Inertiald tmp = right;
tmp += left;
EXPECT_EQ(cube, tmp);
}
// test -= operator
{
math::Inertiald tmp = cube;
tmp -= right;
EXPECT_EQ(left, tmp);
}
{
math::Inertiald tmp = cube;
tmp -= left;
EXPECT_EQ(right, tmp);
}
// Test EquivalentBox
{
math::Vector3d size2;
math::Quaterniond rot2;
EXPECT_TRUE((left + right).MassMatrix().EquivalentBox(size2, rot2));
EXPECT_EQ(size, size2);
EXPECT_EQ(rot2, math::Quaterniond::Identity);
}
{
math::Vector3d size2;
math::Quaterniond rot2;
EXPECT_TRUE((right + left).MassMatrix().EquivalentBox(size2, rot2));
EXPECT_EQ(size, size2);
EXPECT_EQ(rot2, math::Quaterniond::Identity);
}
{
math::Vector3d size2;
math::Quaterniond rot2;
EXPECT_TRUE((cube - right).MassMatrix().EquivalentBox(size2, rot2));
EXPECT_EQ(half_size, size2);
EXPECT_EQ(rot2, math::Quaterniond::Identity);
}
{
math::Vector3d size2;
math::Quaterniond rot2;
EXPECT_TRUE((cube - left).MassMatrix().EquivalentBox(size2, rot2));
EXPECT_EQ(half_size, size2);
EXPECT_EQ(rot2, math::Quaterniond::Identity);
}
}
// Add two rotated half-cubes together and
// Subtract a rotated half-cube from rotated full-cube
{
const double mass = 12.0;
const math::Vector3d size(1, 1, 1);
math::MassMatrix3d cubeMM3;
EXPECT_TRUE(cubeMM3.SetFromBox(mass, size));
const math::Inertiald cube(cubeMM3, math::Pose3d(0, 0, 0, GZ_PI_4, 0, 0));
math::MassMatrix3d half;
EXPECT_TRUE(half.SetFromBox(0.5*mass, math::Vector3d(0.5, 1, 1)));
math::Inertiald left(half, math::Pose3d(-0.25, 0, 0, GZ_PI_4, 0, 0));
math::Inertiald right(half, math::Pose3d(0.25, 0, 0, GZ_PI_4, 0, 0));
// objects won't match exactly
// since inertia matrices will all be in base frame
// but mass, center of mass, and base-frame MOI should match
// +operator
EXPECT_NE(cube, left + right);
EXPECT_NE(cube, right + left);
EXPECT_DOUBLE_EQ(cubeMM3.Mass(), (left + right).MassMatrix().Mass());
EXPECT_DOUBLE_EQ(cubeMM3.Mass(), (right + left).MassMatrix().Mass());
EXPECT_EQ(cube.Pose().Pos(), (left + right).Pose().Pos());
EXPECT_EQ(cube.Pose().Pos(), (right + left).Pose().Pos());
EXPECT_EQ(cube.Moi(), (left + right).Moi());
EXPECT_EQ(cube.Moi(), (right + left).Moi());
// -operator
EXPECT_NE(left, cube - right);
EXPECT_NE(right, cube - left);
EXPECT_DOUBLE_EQ(left.MassMatrix().Mass(),
(cube - right).MassMatrix().Mass());
EXPECT_DOUBLE_EQ(right.MassMatrix().Mass(),
(cube - left).MassMatrix().Mass());
EXPECT_EQ(left.Pose().Pos(), (cube - right).Pose().Pos());
EXPECT_EQ(right.Pose().Pos(), (cube - left).Pose().Pos());
EXPECT_EQ(left.Moi(), (cube - right).Moi());
EXPECT_EQ(right.Moi(), (cube - left).Moi());
}
// Add eight cubes together into larger cube and
// Subtract seven cubes from larger cube
{
const double mass = 12.0;
const math::Vector3d size(1, 1, 1);
math::MassMatrix3d cubeMM3;
EXPECT_TRUE(cubeMM3.SetFromBox(mass, size));
const math::Inertiald sevenCubes =
math::Inertiald(cubeMM3, math::Pose3d(-0.5, -0.5, -0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(-0.5, 0.5, -0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(0.5, -0.5, -0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(0.5, 0.5, -0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(-0.5, -0.5, 0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(-0.5, 0.5, 0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(0.5, -0.5, 0.5, 0, 0, 0));
const math::Inertiald lastCube =
math::Inertiald(cubeMM3, math::Pose3d(0.5, 0.5, 0.5, 0, 0, 0));
const math::Inertiald addedCube = sevenCubes + lastCube;
math::MassMatrix3d trueCubeMM3;
EXPECT_TRUE(trueCubeMM3.SetFromBox(8*mass, 2*size));
EXPECT_EQ(addedCube, math::Inertiald(trueCubeMM3, math::Pose3d::Zero));
EXPECT_EQ(lastCube, addedCube - sevenCubes);
EXPECT_EQ(sevenCubes, addedCube - lastCube);
}
// Add eight rotated cubes together into larger cube and
// Subtract seven rotated cubes from larger cube
{
const double mass = 12.0;
const math::Vector3d size(1, 1, 1);
math::MassMatrix3d cubeMM3;
EXPECT_TRUE(cubeMM3.SetFromBox(mass, size));
const math::Inertiald sevenCubes =
math::Inertiald(cubeMM3, math::Pose3d(-0.5, -0.5, -0.5, 0, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(-0.5, 0.5, -0.5, GZ_PI_2, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(0.5, -0.5, -0.5, 0, GZ_PI_2, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(0.5, 0.5, -0.5, 0, 0, GZ_PI_2)) +
math::Inertiald(cubeMM3, math::Pose3d(-0.5, -0.5, 0.5, GZ_PI, 0, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(-0.5, 0.5, 0.5, 0, GZ_PI, 0)) +
math::Inertiald(cubeMM3, math::Pose3d(0.5, -0.5, 0.5, 0, 0, GZ_PI));
const math::Inertiald lastCube =
math::Inertiald(cubeMM3, math::Pose3d(0.5, 0.5, 0.5, 0, 0, 0));
const math::Inertiald addedCube = sevenCubes + lastCube;
math::MassMatrix3d trueCubeMM3;
EXPECT_TRUE(trueCubeMM3.SetFromBox(8*mass, 2*size));
EXPECT_EQ(addedCube, math::Inertiald(trueCubeMM3, math::Pose3d::Zero));
EXPECT_EQ(lastCube, addedCube - sevenCubes);
EXPECT_EQ(sevenCubes, addedCube - lastCube);
}
// Add two cubes with diagonal corners touching at one point
// ┌---------┐
// | |
// | |
// | |
// | |
// ┌---------+---------┘
// | |
// | |
// | |
// | |
// └---------┘
{
// properties of each cube to be added
// side length: 1
// mass: 6
// diagonal moment of inertia values: 1
// off-diagonal moment of inertia values: 0
const double mass = 6.0;
const math::Vector3d size(1, 1, 1);
math::MassMatrix3d cubeMM3;
EXPECT_TRUE(cubeMM3.SetFromBox(mass, size));
EXPECT_EQ(
math::Vector3d::One,
cubeMM3.DiagonalMoments());
EXPECT_EQ(
math::Vector3d::Zero,
cubeMM3.OffDiagonalMoments());
const math::Inertiald cube1 =
math::Inertiald(cubeMM3, math::Pose3d(-0.5, -0.5, -0.5, 0, 0, 0));
const math::Inertiald cube2 =
math::Inertiald(cubeMM3, math::Pose3d(0.5, 0.5, 0.5, 0, 0, 0));
const math::Inertiald diagonalCubes = cube1 + cube2;
// lumped mass = 6 + 6 = 12
// lumped center of mass at (0, 0, 0)
// lumped Moment of inertia:
// for each cube
// [ 1 0 0 ] [ 0.5^2 + 0.5^2 -0.5*0.5 -0.5*0.5 ]
// [ 0 1 0 ] + 6 * [ -0.5*0.5 0.5^2 + 0.5^2 -0.5*0.5 ]
// [ 0 0 1 ] [ -0.5*0.5 -0.5*0.5 0.5^2 + 0.5^2 ]
//
// [ 1 0 0 ] [ 0.5 -0.25 -0.25 ]
// [ 0 1 0 ] + 6 * [ -0.25 0.5 -0.25 ]
// [ 0 0 1 ] [ -0.25 -0.25 0.5 ]
//
// [ 1 0 0 ] [ 3.0 -1.5 -1.5 ]
// [ 0 1 0 ] + [ -1.5 3.0 -1.5 ]
// [ 0 0 1 ] [ -1.5 -1.5 3.0 ]
//
// [ 4.0 -1.5 -1.5 ]
// [ -1.5 4.0 -1.5 ]
// [ -1.5 -1.5 4.0 ]
//
// then double it to account for both cubes
EXPECT_EQ(math::Pose3d::Zero, diagonalCubes.Pose());
EXPECT_DOUBLE_EQ(mass * 2.0, diagonalCubes.MassMatrix().Mass());
EXPECT_EQ(
math::Vector3d(8, 8, 8),
diagonalCubes.MassMatrix().DiagonalMoments());
EXPECT_EQ(
math::Vector3d(-3, -3, -3),
diagonalCubes.MassMatrix().OffDiagonalMoments());
// -operator
EXPECT_EQ(cube1.Pose(), (diagonalCubes - cube2).Pose());
EXPECT_EQ(cube2.Pose(), (diagonalCubes - cube1).Pose());
EXPECT_DOUBLE_EQ(mass, (diagonalCubes - cube2).MassMatrix().Mass());
EXPECT_DOUBLE_EQ(mass, (diagonalCubes - cube1).MassMatrix().Mass());
EXPECT_EQ(
cubeMM3.DiagonalMoments(),
(diagonalCubes - cube2).MassMatrix().DiagonalMoments());
EXPECT_EQ(
cubeMM3.DiagonalMoments(),
(diagonalCubes - cube1).MassMatrix().DiagonalMoments());
EXPECT_EQ(
cubeMM3.OffDiagonalMoments(),
(diagonalCubes - cube2).MassMatrix().OffDiagonalMoments());
EXPECT_EQ(
cubeMM3.OffDiagonalMoments(),
(diagonalCubes - cube1).MassMatrix().OffDiagonalMoments());
}
}
/////////////////////////////////////////////////
// Addition operator has different behavior if mass is non-positive
TEST(Inertiald_Test, AdditionInvalid)
{
// inertias all zero
const math::MassMatrix3d m0(0.0, math::Vector3d::Zero, math::Vector3d::Zero);
EXPECT_FALSE(m0.IsPositive());
EXPECT_TRUE(m0.IsNearPositive());
EXPECT_TRUE(m0.IsValid());
// both inertials with zero mass
{
math::Inertiald left(m0, math::Pose3d(-1, 0, 0, 0, 0, 0));
math::Inertiald right(m0, math::Pose3d(1, 0, 0, 0, 0, 0));
// expect sum to equal left argument
EXPECT_EQ(left, left + right);
EXPECT_EQ(right, right + left);
{
math::Inertiald tmp = left;
tmp += right;
EXPECT_EQ(tmp, left);
}
{
math::Inertiald tmp = right;
tmp += left;
EXPECT_EQ(tmp, right);
}
}
// one inertial with zero inertias should not affect the sum
{
math::MassMatrix3d m(12.0,
math::Vector3d(2, 3, 4),
math::Vector3d(0.1, 0.2, 0.3));
EXPECT_TRUE(m.IsPositive());
EXPECT_TRUE(m.IsValid());
math::Inertiald i(m, math::Pose3d(-1, 0, 0, 0, 0, 0));
math::Inertiald i0(m0, math::Pose3d(1, 0, 0, 0, 0, 0));
// expect i0 to not affect the sum
EXPECT_EQ(i, i + i0);
EXPECT_EQ(i, i0 + i);
{
math::Inertiald tmp = i;
tmp += i0;
EXPECT_EQ(tmp, i);
}
{
math::Inertiald tmp = i0;
tmp += i;
EXPECT_EQ(tmp, i);
}
EXPECT_TRUE((i + i0).MassMatrix().IsPositive());
EXPECT_TRUE((i0 + i).MassMatrix().IsPositive());
EXPECT_TRUE((i + i0).MassMatrix().IsValid());
EXPECT_TRUE((i0 + i).MassMatrix().IsValid());
}
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, SubtractionInvalid)
{
const double mass = 12.0;
{
math::MassMatrix3d m1, m2;
EXPECT_TRUE(m1.SetFromBox(0.5*mass, math::Vector3d(0.5, 1, 1)));
EXPECT_TRUE(m1.IsPositive());
EXPECT_TRUE(m1.IsValid());
EXPECT_TRUE(m2.SetFromBox(mass, math::Vector3d(0.5, 0.25, 0.25)));
EXPECT_TRUE(m2.IsValid());
EXPECT_TRUE(m2.IsPositive());
// two inertials with i2 having higher mass than i1
math::Inertiald i1(m1, math::Pose3d(-0.25, 0, 0, 0, 0, 0));
math::Inertiald i2(m2, math::Pose3d(0.25, 0, 0, 0, 0, 0));
// expect subtraction to equal left argument
EXPECT_EQ(i1, i1 - i2);
{
math::Inertiald tmp = i1;
tmp -= i2;
EXPECT_EQ(tmp, i1);
}
}
// one inertial with zero inertias should not affect the subtraction
{
const math::MassMatrix3d m1(mass,
math::Vector3d(2, 3, 4),
math::Vector3d(0.1, 0.2, 0.3));
EXPECT_TRUE(m1.IsPositive());
EXPECT_TRUE(m1.IsValid());
const math::MassMatrix3d m2(0.0,
math::Vector3d::Zero, math::Vector3d::Zero);
EXPECT_FALSE(m2.IsPositive());
EXPECT_TRUE(m2.IsNearPositive());
EXPECT_TRUE(m2.IsValid());
// i2 with zero inertia
math::Inertiald i1(m1, math::Pose3d(-1, 0, 0, 0, 0, 0));
math::Inertiald i2(m2, math::Pose3d(1, 0, 0, 0, 0, 0));
// expect i2 to not affect the subtraction
EXPECT_EQ(i1, i1 - i2);
{
math::Inertiald tmp = i1;
tmp -= i2;
EXPECT_EQ(tmp, i1);
}
EXPECT_TRUE((i1 - i2).MassMatrix().IsPositive());
EXPECT_FALSE((i2 - i1).MassMatrix().IsPositive());
EXPECT_TRUE((i1 - i2).MassMatrix().IsValid());
EXPECT_TRUE((i2 - i1).MassMatrix().IsValid());
}
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, BodyMatrix)
{
math::MassMatrix3d massMatrix(100, {2.0, 3.0, 4.0}, {0.2, 0.3, 0.4});
math::Pose3d com{7, 8, 9, 0, 0, GZ_PI * 0.5};
math::Inertiald inertial(massMatrix, com);
auto bodyMatrix = inertial.BodyMatrix();
EXPECT_EQ(bodyMatrix, inertial.SpatialMatrix());
// Mass diagonal
EXPECT_EQ(math::Matrix3d(
100, 0, 0,
0, 100, 0,
0, 0, 100),
bodyMatrix.Submatrix(math::Matrix6d::TOP_LEFT));
// CoM translational offset
EXPECT_EQ(math::Matrix3d(
0, 100 * 9, -100 * 8,
-100 * 9, 0, 100 * 7,
100 * 8, -100 * 7, 0),
bodyMatrix.Submatrix(math::Matrix6d::TOP_RIGHT));
// Transpose of TOP_RIGHT
EXPECT_EQ(math::Matrix3d(
0, -100 * 9, 100 * 8,
100 * 9, 0, -100 * 7,
-100 * 8, 100 * 7, 0),
bodyMatrix.Submatrix(math::Matrix6d::BOTTOM_LEFT));
EXPECT_EQ(bodyMatrix.Submatrix(math::Matrix6d::BOTTOM_LEFT).Transposed(),
bodyMatrix.Submatrix(math::Matrix6d::TOP_RIGHT));
// Moments of inertia with CoM rotational offset
// 90 deg yaw:
// * xx <- (-1)*(-1)*yy
// * xy <- (-1)*xy
// * xz <- (-1)*yz
// * yy <- xx
// * yz <- xz
// * zz <- zz
EXPECT_EQ(math::Matrix3d(
3.0, -0.2, -0.4,
-0.2, 2.0, 0.3,
-0.4, 0.3, 4.0),
bodyMatrix.Submatrix(math::Matrix6d::BOTTOM_RIGHT));
}
/////////////////////////////////////////////////
TEST(Inertiald_Test, FluidAddedMass)
{
math::MassMatrix3d massMatrix(100, {1, 2, 3}, {4, 5, 6});
math::Pose3d com{7, 8, 9, 0, 0, 0};
math::Matrix6d addedMass{
0.1, 0.2, 0.3, 0.4, 0.5, 0.6,
0.2, 0.7, 0.8, 0.9, 1.0, 1.1,
0.3, 0.8, 1.2, 1.3, 1.4, 1.5,
0.4, 0.9, 1.3, 1.6, 1.7, 1.8,
0.5, 1.0, 1.4, 1.7, 1.9, 2.0,
0.6, 1.1, 1.5, 1.8, 2.0, 2.1};
math::Inertiald inertial(massMatrix, com, addedMass);
EXPECT_TRUE(inertial.FluidAddedMass().has_value());
EXPECT_EQ(addedMass, inertial.FluidAddedMass());
auto spatialMatrix = inertial.SpatialMatrix();
EXPECT_EQ(math::Matrix3d(
100 + 0.1, 0.2, 0.3,
0.2, 100 + 0.7, 0.8,
0.3, 0.8, 100 + 1.2),
spatialMatrix.Submatrix(math::Matrix6d::TOP_LEFT));
EXPECT_EQ(math::Matrix3d(
0.4, 0.5 + 100 * 9, 0.6 - 100 * 8,
0.9 - 100 * 9, 1.0, 1.1 + 100 * 7,
1.3 + 100 * 8, 1.4 - 100 * 7, 1.5),
spatialMatrix.Submatrix(math::Matrix6d::TOP_RIGHT));
EXPECT_EQ(math::Matrix3d(
0.4, 0.9 - 100 * 9, 1.3 + 100 * 8,
0.5 + 100 * 9, 1.0, 1.4 - 100 * 7,
0.6 - 100 * 8, 1.1 + 100 * 7, 1.5),
spatialMatrix.Submatrix(math::Matrix6d::BOTTOM_LEFT));
EXPECT_EQ(math::Matrix3d(
1.6 + 1, 1.7 + 4, 1.8 + 5,
1.7 + 4, 1.9 + 2, 2.0 + 6,
1.8 + 5, 2.0 + 6, 2.1 +3),
spatialMatrix.Submatrix(math::Matrix6d::BOTTOM_RIGHT));
// Set new added mass
math::Matrix6d notSymmetric;
notSymmetric(1, 2) = 100;
EXPECT_FALSE(inertial.SetFluidAddedMass(notSymmetric));
math::Matrix6d newAddedMass{
0.01, 0.02, 0.03, 0.04, 0.05, 0.06,
0.02, 0.07, 0.08, 0.09, 1.00, 1.01,
0.03, 0.08, 1.02, 1.03, 1.04, 1.05,
0.04, 0.09, 1.03, 1.06, 1.07, 1.08,
0.05, 1.00, 1.04, 1.07, 1.09, 2.00,
0.06, 1.01, 1.05, 1.08, 2.00, 2.01};
EXPECT_TRUE(inertial.SetFluidAddedMass(newAddedMass));
EXPECT_EQ(newAddedMass, inertial.FluidAddedMass());
auto newSpatialMatrix = inertial.SpatialMatrix();
EXPECT_NE(newSpatialMatrix, spatialMatrix);
EXPECT_EQ(math::Matrix3d(
100 + 0.01, 0.02, 0.03,
0.02, 100 + 0.07, 0.08,
0.03, 0.08, 100 + 1.02),
newSpatialMatrix.Submatrix(math::Matrix6d::TOP_LEFT));
EXPECT_EQ(math::Matrix3d(
0.04, 0.05 + 100 * 9, 0.06 - 100 * 8,
0.09 - 100 * 9, 1.00, 1.01 + 100 * 7,
1.03 + 100 * 8, 1.04 - 100 * 7, 1.05),
newSpatialMatrix.Submatrix(math::Matrix6d::TOP_RIGHT));
EXPECT_EQ(math::Matrix3d(
0.04, 0.09 - 100 * 9, 1.03 + 100 * 8,
0.05 + 100 * 9, 1.00, 1.04 - 100 * 7,
0.06 - 100 * 8, 1.01 + 100 * 7, 1.05),
newSpatialMatrix.Submatrix(math::Matrix6d::BOTTOM_LEFT));
EXPECT_EQ(math::Matrix3d(
1.06 + 1, 1.07 + 4, 1.08 + 5,
1.07 + 4, 1.09 + 2, 2.00 + 6,
1.08 + 5, 2.00 + 6, 2.01 +3),
newSpatialMatrix.Submatrix(math::Matrix6d::BOTTOM_RIGHT));
}