Yaw, Pitch, Roll的含义

本文介绍了三维空间中的三个基本坐标轴:偏航角-垂直轴、俯仰角-侧轴及翻滚角-纵轴,并展示了这三个轴在空间中的相对位置。

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Yaw – Vertical axis

Pitch – Lateral axis

Roll – Longitudinal axis

The Position of All three axes

 

 

### Yaw, Pitch, and Roll in Computer Graphics and Robotics In both computer graphics and robotics, yaw, pitch, and roll describe rotations around three perpendicular axes. These terms are fundamental for defining orientation changes of objects or robots. #### Definitions - **Yaw**: Rotation about the vertical axis (z-axis). This motion corresponds to turning left or right as seen from above. For instance, a drone changing its heading direction while maintaining altitude involves yaw movement[^2]. - **Pitch**: Rotation about the lateral horizontal axis (y-axis). It describes tilting forward or backward motions such as an airplane ascending or descending without altering course or banking. - **Roll**: Rotation about the longitudinal horizontal axis (x-axis). An example would be an aircraft rolling sideways during turns where one wing drops lower than another. These transformations play crucial roles not only in aviation but also extend into various fields including autonomous vehicles navigation systems like those used by drones or self-driving cars, animation software that simulates realistic movements, virtual reality environments creating immersive experiences, among others. For practical applications within these domains: - In robotics, especially concerning mobile platforms equipped with sensors like LiDAR, understanding how point clouds transform under different orientations becomes essential when implementing algorithms such as Fast Point Feature Histograms (FPFH)[^3]. Properly accounting for yaw, pitch, and roll ensures accurate registration between multiple scans taken at varying angles relative to each other. - Within graphical simulations, applying Euler angle conventions allows developers to manipulate object poses dynamically through scripting languages commonly employed in game engines or CAD programs. ```python import numpy as np def apply_rotation_matrix(yaw_angle, pitch_angle, roll_angle): """ Applies rotation matrices corresponding to yaw, pitch, and roll angles Args: yaw_angle (float): Angle in radians for rotating along Z-axis pitch_angle (float): Angle in radians for rotating along Y-axis roll_angle (float): Angle in radians for rotating along X-axis Returns: ndarray: A 3x3 rotation matrix resulting from combining all individual rotations """ cy = np.cos(yaw_angle) sy = np.sin(yaw_angle) cp = np.cos(pitch_angle) sp = np.sin(pitch_angle) cr = np.cos(roll_angle) sr = np.sin(roll_angle) # Define rotation matrices according to standard convention Ry = np.array([[cy,-sy,0], [sy,cy ,0], [ 0 , 0,1]]) Rp = np.array([[cp ,0,sp ], [ 0 ,1, 0 ], [-sp,0,cp ]]) Rx = np.array([[1, 0 , 0 ], [0,cr ,-sr], [0,sr , cr]]) return Rx @ Rp @ Ry # Example usage demonstrating application of combined rotations rotation_angles = { 'yaw': np.radians(-45), 'pitch': np.radians(30), 'roll': np.radians(60)} final_orientation = apply_rotation_matrix(**rotation_angles) print(final_orientation) ```
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