本节介绍了旋转运动的表示方法——旋转矩阵,以及如何创建较为复杂的旋转矩阵。
In the field of robotics there are many possible ways of representing orientations of which the most common are:
- orthonormal rotation matrices (3x3),
- three angles (1x3), and
- quaternions.
在机器人学领域,有许多不同的方法来表示方位。最常见的有:
-标准正交旋转矩阵
-三个方向角
-四元数
A rotation of pi/2 about the x-axis can be represented as an orthonormal rotation matrix
>> R = rotx(pi/2)
R =
1.0000 0 0
0 0.9996 -0.0274
0 0.0274 0.9996
which we can see is a 3x3 matrix.
例如:绕x轴旋转pi/2的旋转运动,可以用方向旋转矩阵表示为:
>> R = rotx(pi/2)
R =
1.0000 0 0
0 0.9996 -0.0274
0 0.0274 0.9996
可以看出,这是一个3x3的矩阵。
Such a matrix has the property that it's columns (and rows) are sets of orthogonal unit vectors. The determinant of such a matrix is always 1
>> det(R)
ans =
1.0000
这种矩阵有一个特点:它的行和列都是单位正交向量。这样的矩阵,其行列式的值恒为1。
>> det(R)
ans =
1.0000
Let's create a more complex rotation
>> R = rotx(30, 'deg') * roty(50, 'deg') * rotz(10, 'deg')
创建一个更为复杂的旋转矩阵的示例如下:
>> R = rotx(30, 'deg') * roty(50, 'deg') * rotz(10, 'deg')
(本节完)
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