matlab练习程序（旋转矩阵、欧拉角、四元数互转）

欧拉角转旋转矩阵公式：

旋转矩阵转欧拉角公式：

旋转矩阵转四元数公式，其中1+r11+r22+r33>0：

四元数转旋转矩阵公式，q0^2+q1^2+q2^2+q3^2=1：

欧拉角转四元数公式：

四元数转欧拉角公式：

matlab代码如下：

clear all;
close all;
clc;

%欧拉角
x = 0.5;
y = 0.6;
z = 0.7;
Ang1 = [x y z];

%欧拉角转旋转矩阵
Rx = [            ;
     cos(x) -sin(x);
     sin(x) cos(x)];
Ry = [cos(y)   sin(y);
                 ;
    -sin(y)  cos(y)];
Rz = [cos(z) -sin(z) ;
    sin(z) cos(z)  ;
                 ];
R = Rz*Ry*Rx;
R1 = R;

%旋转矩阵转欧拉角
x = atan2(R(,),R(,));
y = atan2(-R(,),sqrt(R(,)^+R(,)^));
z = atan2(R(,),R(,));
Ang2 = [x y z];

%旋转矩阵转四元数
t=sqrt(+R(,)+R(,)+R(,))/;
q=[t (R(,)-R(,))/(*t) (R(,)-R(,))/(*t) (R(,)-R(,))/(*t)];
Q1 = q;

%四元数转旋转矩阵
R=[ *q().^-+*q()^    *(q()*q()-q()*q()) *(q()*q()+q()*q());
    *(q()*q()+q()*q()) *q()^-+*q()^     *(q()*q()-q()*q());
    *(q()*q()-q()*q()) *(q()*q()+q()*q()) *q()^-+*q()^];
R2 = R;

%欧拉角转四元数
q = [cos(x/)*cos(y/)*cos(z/) + sin(x/)*sin(y/)*sin(z/) ...
    sin(x/)*cos(y/)*cos(z/) - cos(x/)*sin(y/)*sin(z/) ...
    cos(x/)*sin(y/)*cos(z/) + sin(x/)*cos(y/)*sin(z/) ...
    cos(x/)*cos(y/)*sin(z/) - sin(x/)*sin(y/)*cos(z/)];
Q2 = q;

%四元数转欧拉角
x = atan2(*(q()*q()+q()*q()), - *(q()^+q()^));
y = asin(*(q()*q() - q()*q()));
z = atan2(*(q()*q()+q()*q()), - *(q()^+q()^));
Ang3 = [x y z];

Ang1
Ang2
Ang3

R1
R2

Q1
Q2

参考：

https://blog.csdn.net/lql0716/article/details/72597719

https://www.cnblogs.com/21207-iHome/p/6894128.html