Euler to Quaternion / Quaternion to Euler using Eigen - c++

Question

I'm trying to implement a functionality that can convert an Euler angle into an Quaternion and back "YXZ"-convention using Eigen. Later this should be used to let the user give you Euler angles and rotate around as Quaternion and convert Back for the user. In fact i am realy bad at math but tried my best. I have no Idea if this matrices are correct or anything. The code Works, but my results are way to off, i suppose. Any idea where i take the wrong turn? This is what my Quat.cpp looks like:
#include "Quat.h"
#include <Eigen/Geometry>
#include <Eigen/Dense>
#include <cmath>
#include <iostream>
using namespace Eigen;
Vector3f Quat::MyRotation(const Vector3f YPR)
{
Matrix3f matYaw(3, 3), matRoll(3, 3), matPitch(3, 3), matRotation(3, 3);
const auto yaw = YPR[2]*M_PI / 180;
const auto pitch = YPR[0]*M_PI / 180;
const auto roll = YPR[1]*M_PI / 180;
matYaw << cos(yaw), sin(yaw), 0.0f,
-sin(yaw), cos(yaw), 0.0f, //z
0.0f, 0.0f, 1.0f;
matPitch << cos(pitch), 0.0f, -sin(pitch),
0.0f, 1.0f, 0.0f, // X
sin(pitch), 0.0f, cos(pitch);
matRoll << 1.0f, 0.0f, 0.0f,
0.0f, cos(roll), sin(roll), // Y
0.0f, -sin(roll), cos(roll);
matRotation = matYaw*matPitch*matRoll;
Quaternionf quatFromRot(matRotation);
quatFromRot.normalize(); //Do i need to do this?
return Quat::toYawPitchRoll(quatFromRot);
}
Vector3f Quat::toYawPitchRoll(const Eigen::Quaternionf& q)
{
Vector3f retVector;
const auto x = q.y();
const auto y = q.z();
const auto z = q.x();
const auto w = q.w();
retVector[2] = atan2(2.0 * (y * z + w * x), w * w - x * x - y * y + z * z);
retVector[1] = asin(-2.0 * (x * z - w * y));
retVector[0] = atan2(2.0 * (x * y + w * z), w * w + x * x - y * y - z * z);
#if 1
retVector[0] = (retVector[0] * (180 / M_PI));
retVector[1] = (retVector[1] * (180 / M_PI))*-1;
retVector[2] = retVector[2] * (180 / M_PI);
#endif
return retVector;
}
Input: x = 55.0, y = 80.0, z = 12.0
Quaternion: w:0.872274, x: -0.140211, y:0.447012, z:-0.140211
Return Value: x:-55.5925, y: -6.84901, z:-21.8771
The X-Value seems about right disregarding the prefix, but Y and z are off.

Answer 1

From Euler to Quaternion:
using namespace Eigen;
//Roll pitch and yaw in Radians
float roll = 1.5707, pitch = 0, yaw = 0.707;
Quaternionf q;
q = AngleAxisf(roll, Vector3f::UnitX())
* AngleAxisf(pitch, Vector3f::UnitY())
* AngleAxisf(yaw, Vector3f::UnitZ());
std::cout << "Quaternion" << std::endl << q.coeffs() << std::endl;
From Quaternion to Euler:
auto euler = q.toRotationMatrix().eulerAngles(0, 1, 2);
std::cout << "Euler from quaternion in roll, pitch, yaw"<< std::endl << euler << std::endl;
Taken from https://eigen.tuxfamily.org/dox/classEigen_1_1AngleAxis.html

Answer 2

Here's one approach (not tested):
Vector3d euler = quaternion.toRotationMatrix().eulerAngles(2, 1, 0);
yaw = euler[0]; pitch = euler[1]; roll = euler[2];

Answer 3

The Quaternation to Euler solution didnt work for me, so i researched and modified the code, now it works for my purpose:
Vector3f ToEulerAngles(const Eigen::Quaternionf& q) {
Vector3f angles; //yaw pitch roll
const auto x = q.x();
const auto y = q.y();
const auto z = q.z();
const auto w = q.w();
// roll (x-axis rotation)
double sinr_cosp = 2 * (w * x + y * z);
double cosr_cosp = 1 - 2 * (x * x + y * y);
angles[2] = std::atan2(sinr_cosp, cosr_cosp);
// pitch (y-axis rotation)
double sinp = 2 * (w * y - z * x);
if (std::abs(sinp) >= 1)
angles[1] = std::copysign(M_PI / 2, sinp); // use 90 degrees if out of range
else
angles[1] = std::asin(sinp);
// yaw (z-axis rotation)
double siny_cosp = 2 * (w * z + x * y);
double cosy_cosp = 1 - 2 * (y * y + z * z);
angles[0] = std::atan2(siny_cosp, cosy_cosp);
return angles;
}
I was inspired by this wiki entry and did some bench marking with the presented solution here.
Checkout the wiki:
https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles

Answer 4

When I use
auto euler = q.toRotationMatrix().eulerAngles(0, 1, 2)
It can not work perfectly all the time, the euler angle always has a regular beat (the actual value and the calculated value have a deviation of ±π).
For example, read and show yaw angle by rqt
picture.
I have no idea about this, but I find ros tf::getYaw() also can achieve "Quaternion to Euler" (because I just need yaw angle).

Answer 5

Without Eigen (just in case), I did:
tf2::Matrix3x3 ( quat ) . getEulerYPR( &roll, &pitch, &yaw );
// and
tf2::Matrix3x3 ( quat ) . getRPY( &roll, &pitch, &yaw );
Though, these can give only two of the 24 configurations possible.