c++ - 使用特征值的欧拉到四元数/四元数到欧拉

Question

我正在尝试实现一项功能，该功能可以使用 Eigen 将欧拉角转换为四元数并返回“YXZ”约定。稍后这应该用于让用户给你欧拉角并作为四元数旋转并为用户转换回。事实上，我的数学很差，但我尽力了。我不知道这个矩阵是否正确或任何东西。代码有效，但我想我的结果很糟糕。知道我在哪里走错了吗？这是我的 Quat.cpp 的样子:

#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;
}

输入:x = 55.0，y = 80.0，z = 12.0 四元数:w:0.872274，x:-0.140211，y:0.447012，z:-0.140211 返回值:x:-55.5925，y:-6.84901，z:-21.8771 忽略前缀，X 值似乎是正确的，但 Y 和 z 是关闭的。

Answer 1

从欧拉到四元数:

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;

从四元数到欧拉:

auto euler = q.toRotationMatrix().eulerAngles(0, 1, 2);
std::cout << "Euler from quaternion in roll, pitch, yaw"<< std::endl << euler << std::endl;

取自https://eigen.tuxfamily.org/dox/classEigen_1_1AngleAxis.html