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基于Matlab现有函数下的内容
Matlab ——旋转矩阵，四元数，欧拉角之间的转换
旋转矩阵 dcm R
四元数 quat q = [q0 q1 q2 q3]
欧拉角 angle [row,pitch,yaw]/[r1,r2,r3]
注：以上表格是为了帮助理解的表示
roll(横滚) –X pitch（俯仰）–Y yaw（偏航/航向）– Z
– – – – – – – – – – – – – – – – – – – – – – — – – — – – – – – – – – – – – – – – — – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
转四元数
旋转矩阵转四元数
q =dcm2quat(R)；
欧拉角转四元数
q=angle2quat(r1,r2,r3，S)；
– – – – – – – – – – – – – – – – – – – – – – — – – — – – – – – – – – – – – – – – — – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
转欧拉角
旋转矩阵转欧拉角
[r2,r2,r3]=dcm2angle(R, S)
注：得到的结果为弧度，若需要角度需进一步转化
四元数转欧拉角
[r1,r2,r3]=quat2angle([q0 q1 q2 q3]，S)
注：S 的选择有12种，【’ZYX’,’ZYZ’,‘ZXY’,‘ZXZ’,‘YXZ’,‘YXY’,‘YZX’,‘YZY’,‘XYZ’,‘XYX’,‘XZY’,‘XZX’】
S 默认 ‘ZYX’
– – – – – – – – – – – – – – – – – – – – – – — – – — – – – – – – – – – – – – – – — – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
转旋转矩阵
四元数转旋转矩阵
R=quat2dcm([q0 q1 q2 q3])
欧拉角转旋转矩阵
R=angle2dcm(r1,r2,r3,S);
R=angle2dcm(yaw/180*pi,pitch/180*pi,roll/180*pi)
注：根据欧拉角是弧度/角度，选择以上操作
– – – – – – – – – – – – – – – – – – – – – – — – – — – – – – – – – – – – – – – – — – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
若已知旋转矩阵R，求四元数[q0 q1 q2 q2]
R=⎡⎣⎢r11r21r31r12r22r32r13r23r33⎤⎦⎥
则对应的四元数为：
q0=121+r11+r22+r33−−−−−−−−−−−−−−√
q1=r32−r234q0
q2=r13−r314q0
q3=r21−r124q0
– – – – – – – – – – – – – – – – – – – – – – — – – — – – – – – – – – – – – – – – — – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
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