Python 代码:计算欧拉角从旋转矩阵
由于欧拉角的计算方式有多种,所以以下提供其中一种常见的计算方法的代码。
首先,需要定义三个旋转角度(pitch、yaw、roll)和一个旋转矩阵(rotation matrix):
import numpy as np
pitch = 0.1
yaw = 0.2
roll = 0.3
rotation_matrix = np.array([
[np.cos(yaw)*np.cos(roll), np.cos(yaw)*np.sin(roll), -np.sin(yaw)],
[np.sin(pitch)*np.sin(yaw)*np.cos(roll)-np.cos(pitch)*np.sin(roll), np.sin(pitch)*np.sin(yaw)*np.sin(roll)+np.cos(pitch)*np.cos(roll), np.sin(pitch)*np.cos(yaw)],
[np.cos(pitch)*np.sin(yaw)*np.cos(roll)+np.sin(pitch)*np.sin(roll), np.cos(pitch)*np.sin(yaw)*np.sin(roll)-np.sin(pitch)*np.cos(roll), np.cos(pitch)*np.cos(yaw)]
])
然后,可以根据旋转矩阵计算欧拉角:
# 计算yaw角
if rotation_matrix[0, 1] > 0.98 or rotation_matrix[0, 1] < -0.98:
yaw = 0
else:
yaw = np.arctan2(rotation_matrix[0, 1], rotation_matrix[0, 0])
# 计算pitch角
pitch = np.arctan2(-rotation_matrix[0, 2], np.sqrt(rotation_matrix[1, 2]**2+rotation_matrix[2, 2]**2))
# 计算roll角
roll = np.arctan2(rotation_matrix[1, 2], rotation_matrix[2, 2])
其中,由于计算过程中可能会遇到除数为0的情况,需要进行特判。此外,由于arctan2函数的返回值范围是[-pi, pi],需要根据具体情况进行调整,以保证yaw角的范围在[0, 2*pi]之间。
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