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 = ;
%欧拉角转旋转矩阵
Rx = [1 0 0;
cos(x) -sin(x);
sin(x) cos(x)];
Ry = [cos(y)0 sin(y);
1 0;
-sin(y) 0 cos(y)];
Rz = [cos(z) -sin(z) 0;
sin(z) cos(z)0;
0 1];
R = Rz*Ry*Rx;
R1 = R;
%旋转矩阵转欧拉角
x = atan2(R(3,2),R(3,3));
y = atan2(-R(3,1),sqrt(R(3,2)^2+R(3,3)^2));
z = atan2(R(2,1),R(1,1));
Ang2 = ;
%旋转矩阵转四元数
t=sqrt(1+R(1,1)+R(2,2)+R(3,3))/2;
q=;
Q1 = q;
%四元数转旋转矩阵
R=[ 2*q(1).^2-1+2*q(2)^2 2*(q(2)*q(3)-q(1)*q(4)) 2*(q(2)*q(4)+q(1)*q(3));
2*(q(2)*q(3)+q(1)*q(4)) 2*q(1)^2-1+2*q(3)^2 2*(q(3)*q(4)-q(1)*q(2));
2*(q(2)*q(4)-q(1)*q(3)) 2*(q(3)*q(4)+q(1)*q(2)) 2*q(1)^2-1+2*q(4)^2];
R2 = R;
%欧拉角转四元数
q = [cos(x/2)*cos(y/2)*cos(z/2) + sin(x/2)*sin(y/2)*sin(z/2) ...
sin(x/2)*cos(y/2)*cos(z/2) - cos(x/2)*sin(y/2)*sin(z/2) ...
cos(x/2)*sin(y/2)*cos(z/2) + sin(x/2)*cos(y/2)*sin(z/2) ...
cos(x/2)*cos(y/2)*sin(z/2) - sin(x/2)*sin(y/2)*cos(z/2)];
Q2 = q;
%四元数转欧拉角
x = atan2(2*(q(1)*q(2)+q(3)*q(4)),1 - 2*(q(2)^2+q(3)^2));
y = asin(2*(q(1)*q(3) - q(2)*q(4)));
z = atan2(2*(q(1)*q(4)+q(2)*q(3)),1 - 2*(q(3)^2+q(4)^2));
Ang3 = ;
Ang1
Ang2
Ang3
R1
R2
Q1
Q2
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