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Eigen 四元数、欧拉角、旋转矩阵、旋转向量相互转换

阅读量:

一、旋转向量

1.0 初始化旋转向量:旋转角为alpha,旋转轴为(x,y,z)

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    Eigen::AngleAxisd rotation_vector(alpha,Vector3d(x,y,z))
    

1.1 旋转向量转旋转矩阵

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 Eigen::Matrix3d rotation_matrix;

    
 rotation_matrix=rotation_vector.matrix();
    
 Eigen::Matrix3d rotation_matrix;
    
 rotation_matrix=rotation_vector.toRotationMatrix();
    
    
    
    
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 inline Eigen::Matrix3d rotationVectorToRotationMatrix(const Eigen::Vector3d& rotation_vector)

    
 {
    
     Eigen::Matrix3d rotation_matrix;
    
     rotation_matrix << 1, -rotation_vector(2), rotation_vector(1), 
    
                    rotation_vector(2), 1, -rotation_vector(0),
    
                    -rotation_vector(1), rotation_vector(0), 1;
    
     return rotation_matrix;
    
 }
    
  
    
 Eigen::Vector3d delta_theta = Eigen::Vector3d::Zero();
    
 Eigen::Matrix3d rotation_delta_base_imu = Eigen::Matrix3d::Identity();
    
 rotation_delta_base_imu = rotationVectorToRotationMatrix(delta_theta);
    
  
    
 Eigen::AngleAxisd angle_axisd_delta_theta(delta_theta.norm(), delta_theta.normalized());
    
 rotation_delta_base_imu = angle_axisd_delta_theta.matrix();
    
    
    
    

1.2 旋转向量转欧拉角(Z-Y-X,即RPY)

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    Eigen::Vector3d eulerAngle=rotation_vector.matrix().eulerAngles(2,1,0);
    

1.3 旋转向量转四元数

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 Eigen::Quaterniond quaternion(rotation_vector);

    
 Eigen::Quaterniond quaternion;
    
 Quaterniond quaternion;
    
 Eigen::Quaterniond quaternion;
    
 quaternion=rotation_vector;
    
  
    
  
    
 Eigen::AngleAxisd angle_axisd(v.norm(),v / v.norm());
    
 Eigen::Quaterniond quaternion(angle_axisd);
    
    
    
    

二、旋转矩阵

2.0 初始化旋转矩阵

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 Eigen::Matrix3d rotation_matrix;

    
 rotation_matrix<<x_00,x_01,x_02,x_10,x_11,x_12,x_20,x_21,x_22;
    
    
    
    

2.1 旋转矩阵转旋转向量

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 Eigen::AngleAxisd rotation_vector(rotation_matrix);

    
 Eigen::AngleAxisd rotation_vector;
    
 rotation_vector=rotation_matrix;
    
 Eigen::AngleAxisd rotation_vector;
    
 rotation_vector.fromRotationMatrix(rotation_matrix);
    
    
    
    

2.2 旋转向量转欧拉角(Z-Y-X,即RPY)

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 Eigen::Vector3d eulerAngle = rotation_matrix.eulerAngles(2,1,0);

    
 (yaw, pitch, roll)
    
    
    
    

2.3 旋转向量转四元数

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 Eigen::Quaterniond quaternion(rotation_matrix);

    
 Eigen::Quaterniond quaternion;
    
 quaternion=rotation_matrix;
    
    
    
    

三、欧拉角

3.0 初始化欧拉角(Z-Y-X,即RPY)

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    Eigen::Vector3d eulerAngle(yaw,pitch,roll);
    

3.1 欧拉角转旋转向量

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 Eigen::AngleAxisd rollAngle(AngleAxisd(eulerAngle(2),Vector3d::UnitX()));

    
 Eigen::AngleAxisd pitchAngle(AngleAxisd(eulerAngle(1),Vector3d::UnitY()));
    
 Eigen::AngleAxisd yawAngle(AngleAxisd(eulerAngle(0),Vector3d::UnitZ()));
    
  
    
 Eigen::AngleAxisd rotation_vector;
    
 rotation_vector=yawAngle*pitchAngle*rollAngle;
    
    
    
    

3.2 欧拉角转旋转矩阵

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 Eigen::AngleAxisd rollAngle(AngleAxisd(eulerAngle(2),Vector3d::UnitX()));

    
 Eigen::AngleAxisd pitchAngle(AngleAxisd(eulerAngle(1),Vector3d::UnitY()));
    
 Eigen::AngleAxisd yawAngle(AngleAxisd(eulerAngle(0),Vector3d::UnitZ()));
    
  
    
 Eigen::Matrix3d rotation_matrix;
    
 rotation_matrix=yawAngle*pitchAngle*rollAngle;
    
    
    
    

3.3 欧拉角转四元数

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 Eigen::AngleAxisd rollAngle(AngleAxisd(eulerAngle(2),Vector3d::UnitX()));

    
 Eigen::AngleAxisd pitchAngle(AngleAxisd(eulerAngle(1),Vector3d::UnitY()));
    
 Eigen::AngleAxisd yawAngle(AngleAxisd(eulerAngle(0),Vector3d::UnitZ()));
    
  
    
 Eigen::Quaterniond quaternion;
    
 quaternion=yawAngle*pitchAngle*rollAngle;
    
    
    
    

四、四元数

4.0 初始化四元数

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    Eigen::Quaterniond quaternion(w,x,y,z);
    

4.1 四元数转旋转向量

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 Eigen::AngleAxisd rotation_vector(quaternion);

    
 Eigen::AngleAxisd rotation_vector;
    
 rotation_vector=quaternion;
    
    
    
    

4.2 四元数转旋转矩阵

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 Eigen::Matrix3d rotation_matrix;

    
 rotation_matrix=quaternion.matrix();
    
 Eigen::Matrix3d rotation_matrix;
    
 rotation_matrix=quaternion.toRotationMatrix();
    
    
    
    

4.4 四元数转欧拉角(Z-Y-X,即RPY)

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    Eigen::Vector3d eulerAngle=quaternion.matrix().eulerAngles(2,1,0);
    

eigen 中四元数、欧拉角、旋转矩阵、旋转向量

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