基于eigen实现欧拉角(RPY), 旋转矩阵, 旋转向量, 四元数之间的变换

柔光的暖阳◎ 2022-03-28 03:08 540阅读 0赞

在机器人学中经常会涉及到欧拉角,旋转矩阵,旋转向量,四元数之间的转换,因此基于eigen对变换关系进行实现,以便参考:

#include <iostream>
     
    #include <Eigen/Core>
    #include <Eigen/Geometry>
    
    using namespace std;
    
    #define PI (3.1415926535897932346f)
    
    int main(int argc, char **argv) 
    {
        /**** 1. 旋转向量 ****/
        cout << endl << "********** AngleAxis **********" << endl;
        //1.0 初始化旋转向量,沿Z轴旋转45度的旋转向量
        Eigen::AngleAxisd rotation_vector1 (M_PI/4, Eigen::Vector3d(0, 0, 1)); 
    
        //1.1 旋转向量转换为旋转矩阵
        //旋转向量用matrix()转换成旋转矩阵
        Eigen::Matrix3d rotation_matrix1 = Eigen::Matrix3d::Identity();
        rotation_matrix1 = rotation_vector1.matrix();
        cout << "rotation matrix1 =\n" << rotation_matrix1 << endl;                
        //或者由罗德里格公式进行转换
        rotation_matrix1 = rotation_vector1.toRotationMatrix();
        cout << "rotation matrix1 =\n" << rotation_matrix1 << endl; 
    
        /*1.2 旋转向量转换为欧拉角*/
        //将旋转向量转换为旋转矩阵,再由旋转矩阵转换为欧拉角,详见旋转矩阵转换为欧拉角
        Eigen::Vector3d eulerAngle1 = rotation_vector1.matrix().eulerAngles(2,1,0);
        cout << "eulerAngle1, z y x: " << eulerAngle1 << endl;
    
        /*1.3 旋转向量转四元数*/
        Eigen::Quaterniond quaternion1(rotation_vector1);
        //或者
        Eigen::Quaterniond quaternion1_1;
        quaternion1_1 = rotation_vector1;
        cout << "quaternion1 x: " << quaternion1.x() << endl;
        cout << "quaternion1 y: " << quaternion1.y() << endl;
        cout << "quaternion1 z: " << quaternion1.z() << endl;
        cout << "quaternion1 w: " << quaternion1.w() << endl;
        
        cout << "quaternion1_1 x: " << quaternion1_1.x() << endl;
        cout << "quaternion1_1 y: " << quaternion1_1.y() << endl;
        cout << "quaternion1_1 z: " << quaternion1_1.z() << endl;
        cout << "quaternion1_1 w: " << quaternion1_1.w() << endl;
    
    
        /**** 2. 旋转矩阵 *****/
        cout << endl << "********** RotationMatrix **********" << endl;
        //2.0 旋转矩阵初始化
        Eigen::Matrix3d rotation_matrix2;
        rotation_matrix2 << 0.707107, -0.707107, 0, 0.707107, 0.707107, 0, 0, 0, 1;
    ;
        //或直接单位矩阵初始化
        Eigen::Matrix3d rotation_matrix2_1 = Eigen::Matrix3d::Identity();
    
        //2.1 旋转矩阵转换为欧拉角
        //ZYX顺序，即先绕x轴roll,再绕y轴pitch,最后绕z轴yaw,0表示X轴,1表示Y轴,2表示Z轴
        Eigen::Vector3d euler_angles = rotation_matrix2.eulerAngles(2, 1, 0); 
        cout << "yaw(z) pitch(y) roll(x) = " << euler_angles.transpose() << endl;
    
        //2.2 旋转矩阵转换为旋转向量
        Eigen::AngleAxisd rotation_vector2;
        rotation_vector2.fromRotationMatrix(rotation_matrix2);
        //或者
        Eigen::AngleAxisd rotation_vector2_1(rotation_matrix2);
        cout << "rotation_vector2 " << "angle is: " << rotation_vector2.angle() * (180 / M_PI) 
                                    << " axis is: " << rotation_vector2.axis().transpose() << endl;
    
        cout << "rotation_vector2_1 " << "angle is: " << rotation_vector2_1.angle() * (180 / M_PI) 
                                      << " axis is: " << rotation_vector2_1.axis().transpose() << endl;
    
        //2.3 旋转矩阵转换为四元数
        Eigen::Quaterniond quaternion2(rotation_matrix2);
        //或者
        Eigen::Quaterniond quaternion2_1;
        quaternion2_1 = rotation_matrix2;
        cout << "quaternion2 x: " << quaternion2.x() << endl;
        cout << "quaternion2 y: " << quaternion2.y() << endl;
        cout << "quaternion2 z: " << quaternion2.z() << endl;
        cout << "quaternion2 w: " << quaternion2.w() << endl;
        
        cout << "quaternion2_1 x: " << quaternion2_1.x() << endl;
        cout << "quaternion2_1 y: " << quaternion2_1.y() << endl;
        cout << "quaternion2_1 z: " << quaternion2_1.z() << endl;
        cout << "quaternion2_1 w: " << quaternion2_1.w() << endl;
    
    
        /**** 3. 欧拉角 ****/
        cout << endl << "********** EulerAngle **********" << endl;
        //3.0 初始化欧拉角(Z-Y-X，即RPY, 先绕x轴roll,再绕y轴pitch,最后绕z轴yaw)
        Eigen::Vector3d ea(0.785398, -0, 0);
    
        //3.1 欧拉角转换为旋转矩阵
        Eigen::Matrix3d rotation_matrix3;
        rotation_matrix3 = Eigen::AngleAxisd(ea[0], Eigen::Vector3d::UnitZ()) * 
                           Eigen::AngleAxisd(ea[1], Eigen::Vector3d::UnitY()) * 
                           Eigen::AngleAxisd(ea[2], Eigen::Vector3d::UnitX());
        cout << "rotation matrix3 =\n" << rotation_matrix3 << endl;   
    
        //3.2 欧拉角转换为四元数,
        Eigen::Quaterniond quaternion3;
        quaternion3 = Eigen::AngleAxisd(ea[0], Eigen::Vector3d::UnitZ()) * 
                      Eigen::AngleAxisd(ea[1], Eigen::Vector3d::UnitY()) * 
                      Eigen::AngleAxisd(ea[2], Eigen::Vector3d::UnitX());
        cout << "quaternion3 x: " << quaternion3.x() << endl;
        cout << "quaternion3 y: " << quaternion3.y() << endl;
        cout << "quaternion3 z: " << quaternion3.z() << endl;
        cout << "quaternion3 w: " << quaternion3.w() << endl;
    
        //3.3 欧拉角转换为旋转向量
        Eigen::AngleAxisd rotation_vector3;
        rotation_vector3 = Eigen::AngleAxisd(ea[0], Eigen::Vector3d::UnitZ()) * 
                           Eigen::AngleAxisd(ea[1], Eigen::Vector3d::UnitY()) * 
                           Eigen::AngleAxisd(ea[2], Eigen::Vector3d::UnitX());  
        cout << "rotation_vector3 " << "angle is: " << rotation_vector3.angle() * (180 / M_PI) 
                                    << " axis is: " << rotation_vector3.axis().transpose() << endl;
    
    
        /**** 4.四元数 ****/
        cout << endl << "********** Quaternion **********" << endl;
        //4.0 初始化四元素,注意eigen Quaterniond类四元数初始化参数顺序为w,x,y,z
        Eigen::Quaterniond quaternion4(0.92388, 0, 0, 0.382683);
    
        //4.1 四元数转换为旋转向量
        Eigen::AngleAxisd rotation_vector4(quaternion4);
        //或者
        Eigen::AngleAxisd rotation_vector4_1;
        rotation_vector4_1 = quaternion4;
        cout << "rotation_vector4 " << "angle is: " << rotation_vector4.angle() * (180 / M_PI) 
                                    << " axis is: " << rotation_vector4.axis().transpose() << endl;
    
        cout << "rotation_vector4_1 " << "angle is: " << rotation_vector4_1.angle() * (180 / M_PI) 
                                      << " axis is: " << rotation_vector4_1.axis().transpose() << endl;
    
        //4.2 四元数转换为旋转矩阵
        Eigen::Matrix3d rotation_matrix4;
        rotation_matrix4 = quaternion4.matrix();
        Eigen::Matrix3d rotation_matrix4_1;
        rotation_matrix4_1 = quaternion4.toRotationMatrix();
        cout << "rotation matrix4 =\n" << rotation_matrix4 << endl;
        cout << "rotation matrix4_1 =\n" << rotation_matrix4_1 << endl;      
    
    
        //4.4 四元数转欧拉角(Z-Y-X，即RPY)
        Eigen::Vector3d eulerAngle4 = quaternion4.matrix().eulerAngles(2,1,0);
        cout << "yaw(z) pitch(y) roll(x) = " << eulerAngle4.transpose() << endl;
    
    
        return 0;
    }

终端输出:

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaWNhbzE5OTA_size_16_color_FFFFFF_t_70][]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaWNhbzE5OTA_size_16_color_FFFFFF_t_70]: /images/20220328/54f40b865c26441185302cd7790f0819.png