void transformOrientationToGroundFrame(const VirtualRobot::RobotPtr& robot,
const Eigen::Matrix6Xf& leftFootTrajectory,
const VirtualRobot::RobotNodePtr& leftFoot,
const VirtualRobot::RobotNodePtr& rightFoot,
const VirtualRobot::RobotNodeSetPtr& bodyJoints,
const Eigen::MatrixXf& bodyTrajectory,
const Eigen::Matrix3Xf& trajectory,
const std::vector<SupportInterval>& intervals,
Eigen::Matrix3Xf& relativeTrajectory)
{
Eigen::Matrix4f leftInitialPose = bodyJoints->getKinematicRoot()->getGlobalPose();
int N = trajectory.cols();
int M = trajectory.rows();
relativeTrajectory.resize(M, N);
BOOST_ASSERT(M > 0 && M <= 3);
auto intervalIter = intervals.begin();
for (int i = 0; i < N; i++)
{
while (i >= intervalIter->endIdx)
{
intervalIter = std::next(intervalIter);
}
// Move basis along with the left foot
Eigen::Matrix4f leftFootPose = Eigen::Matrix4f::Identity();
VirtualRobot::MathTools::posrpy2eigen4f(1000 * leftFootTrajectory.block(0, i, 3, 1),
leftFootTrajectory.block(3, i, 3, 1), leftFootPose);
robot->setGlobalPose(leftFootPose);
bodyJoints->setJointValues(bodyTrajectory.col(i));
Eigen::Matrix3f worldToRef = computeGroundFrame(leftFoot->getGlobalPose(),
rightFoot->getGlobalPose(),
intervalIter->phase).block(0, 0, 3, 3);
relativeTrajectory.block(0, i, M, 1) = worldToRef.colPivHouseholderQr().solve(trajectory.col(i)).block(0, 0, M, 1);
}
}
{
Eigen::Matrix3f mM3;
Eigen::Vector3f x3NL;
x3NL(0) = dMt.x03(0,1);
x3NL(1) = dMt.x03(1,1);
x3NL(2) = dMt.x03(2,1);
// c0 + c1*nl + c2*nl^2
mM3 <<
1, 0, 0,
1, 2, 4,
1, 4, 16;
Eigen::Vector3f ci3 = pow(4,-3)*mM3.colPivHouseholderQr().solve(x3NL);
// NL^0
REQUIRE( ci3(0) == Approx( -198.7068 ) );
// NL^1
REQUIRE( ci3(1) == Approx( 26.9239 ) );
// NL^2
REQUIRE( ci3(2) == Approx( -0.65269 ) );
}
SECTION( "Four-loop zm4 = c0 + c1*L + c2*L^2 + c3*L^3 + c4*L^4" )
{
////
/// 4-loop
//
int main(int argc, char** argv) {
ros::init(argc, argv, "eigen_test");
ros::NodeHandle nh_jntPub; // node handle for joint command publisher
// ros::Publisher pub_joint_commands; //
// pub_joint_commands = nh_jntPub.advertise<atlas_msgs::AtlasCommand>("/atlas/atlas_command", 1, true);
ROS_INFO("test eigen program");
Eigen::Matrix3f A;
Eigen::Vector3f b;
A << 1,2,3, 4,5,6, 7,8,10;
A(1,2)=0; // how to access one element of matrix; start from 0; no warning out of range...
b << 3,3,4;
std::cout <<"b = "<<b <<std::endl;
// column operaton: replace first column of A with vector b:
A.col(0)= b; // could copy columns of matrices w/ A.col(0) = B.col(0);
std::cout <<"A = "<<A <<std::endl;
Eigen::MatrixXd mat1 = Eigen::MatrixXd::Zero(6, 6); //6x6 matrix full of zeros
Eigen::MatrixXd mat2 = Eigen::MatrixXd::Identity(6, 6); //6x6 identity matrix
std::cout<<mat1<<std::endl;
std::cout<<mat2<<std::endl;
Eigen::Vector3f xtest = A.colPivHouseholderQr().solve(b);
std::cout<<"soln xtest = "<<xtest<<std::endl;
Eigen::Vector3f x = A.partialPivLu().solve(b); //dec.solve(b); //A.colPivHouseholderQr().solve(b);
std::cout<<"soln x = "<<x<<std::endl;
Eigen::Vector3f btest = A*x;
std::cout<<"test soln: A*x = " <<btest<<std::endl;
//extend to 6x6 test: v = M*z, find z using 2 methods
// use double-precision matrices/vectors
Eigen::MatrixXd M = Eigen::MatrixXd::Random(6,6);
std::cout<<"test 6x6: M = "<<M<<std::endl;
Eigen::VectorXd v(6);
v << 1,2,3,4,5,6;
std::cout<<"v = "<<v<<std::endl;
Eigen::VectorXd z(6);
Eigen::VectorXd ztest(6);
ztest = M.colPivHouseholderQr().solve(v);
std::cout<<"soln ztest = "<<ztest<<std::endl;
z = M.partialPivLu().solve(v);
std::cout<<"soln 6x6: z = "<<z<<std::endl;
Eigen::VectorXd vtest(6);
vtest = M*z;
std::cout<<"test soln: M*z = "<<vtest<<std::endl;
// .norm() operator...
double relative_error = (M*z - v).norm() / v.norm(); // norm() is L2 norm
std::cout << "The relative error is:\n" << relative_error << std::endl;
std::cout<<"dot prod, v, z: "<< v.dot(z)<<std::endl;
std::cout<<"cross prod, b-cross-x: " << b.cross(x)<<std::endl;
return 0;
}
template <typename PointInT, typename PointNT, typename PointOutT, typename IntensitySelectorT> void
pcl::IntensityGradientEstimation <PointInT, PointNT, PointOutT, IntensitySelectorT>::computePointIntensityGradient (
const pcl::PointCloud <PointInT> &cloud, const std::vector <int> &indices,
const Eigen::Vector3f &point, float mean_intensity, const Eigen::Vector3f &normal, Eigen::Vector3f &gradient)
{
if (indices.size () < 3)
{
gradient[0] = gradient[1] = gradient[2] = std::numeric_limits<float>::quiet_NaN ();
return;
}
Eigen::Matrix3f A = Eigen::Matrix3f::Zero ();
Eigen::Vector3f b = Eigen::Vector3f::Zero ();
for (size_t i_point = 0; i_point < indices.size (); ++i_point)
{
PointInT p = cloud.points[indices[i_point]];
if (!pcl_isfinite (p.x) ||
!pcl_isfinite (p.y) ||
!pcl_isfinite (p.z) ||
!pcl_isfinite (intensity_ (p)))
continue;
p.x -= point[0];
p.y -= point[1];
p.z -= point[2];
intensity_.demean (p, mean_intensity);
A (0, 0) += p.x * p.x;
A (0, 1) += p.x * p.y;
A (0, 2) += p.x * p.z;
A (1, 1) += p.y * p.y;
A (1, 2) += p.y * p.z;
A (2, 2) += p.z * p.z;
b[0] += p.x * intensity_ (p);
b[1] += p.y * intensity_ (p);
b[2] += p.z * intensity_ (p);
}
// Fill in the lower triangle of A
A (1, 0) = A (0, 1);
A (2, 0) = A (0, 2);
A (2, 1) = A (1, 2);
//*
Eigen::Vector3f x = A.colPivHouseholderQr ().solve (b);
/*/
Eigen::Vector3f eigen_values;
Eigen::Matrix3f eigen_vectors;
eigen33 (A, eigen_vectors, eigen_values);
b = eigen_vectors.transpose () * b;
if ( eigen_values (0) != 0)
b (0) /= eigen_values (0);
else
b (0) = 0;
if ( eigen_values (1) != 0)
b (1) /= eigen_values (1);
else
b (1) = 0;
if ( eigen_values (2) != 0)
b (2) /= eigen_values (2);
else
b (2) = 0;
Eigen::Vector3f x = eigen_vectors * b;
// if (A.col (0).squaredNorm () != 0)
// x [0] /= A.col (0).squaredNorm ();
// b -= x [0] * A.col (0);
//
//
// if (A.col (1).squaredNorm () != 0)
// x [1] /= A.col (1).squaredNorm ();
// b -= x[1] * A.col (1);
//
// x [2] = b.dot (A.col (2));
// if (A.col (2).squaredNorm () != 0)
// x[2] /= A.col (2).squaredNorm ();
// Fit a hyperplane to the data
//*/
// std::cout << A << "\n*\n" << bb << "\n=\n" << x << "\nvs.\n" << x2 << "\n\n";
// std::cout << A * x << "\nvs.\n" << A * x2 << "\n\n------\n";
// Project the gradient vector, x, onto the tangent plane
gradient = (Eigen::Matrix3f::Identity () - normal*normal.transpose ()) * x;
}