Beginner Explanation
Imagine you have a toy robot that can move around in your room. You can tell it to go left, right, up, down, and even spin around. The 9-DoF (Degrees of Freedom) Pose Manipulation is like giving your robot the ability to move in all those ways and also change its size. So, if you want the robot to pick up a ball, you can tell it exactly where to go, how to turn, and how big to make its hand to grab the ball. It helps in making the robot understand where it is in the room and how to interact with things around it.Technical Explanation
9-DoF Pose Manipulation refers to controlling an object’s position and orientation in 3D space using nine parameters: three for translation (x, y, z), three for rotation (roll, pitch, yaw), and three for scaling (width, height, depth). This is commonly implemented in robotics and computer graphics. In code, this can be represented using transformation matrices. For example, in Python with NumPy, you can create a transformation matrix as follows: “`python import numpy as np def create_transformation_matrix(translation, rotation, scale): # Create translation matrix translation_matrix = np.array([[1, 0, 0, translation[0]], [0, 1, 0, translation[1]], [0, 0, 1, translation[2]], [0, 0, 0, 1]]) # Create rotation matrix (assuming rotation is in radians) rotation_matrix = np.array([[np.cos(rotation[2]), -np.sin(rotation[2]), 0, 0], [np.sin(rotation[2]), np.cos(rotation[2]), 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) # Create scaling matrix scaling_matrix = np.array([[scale[0], 0, 0, 0], [0, scale[1], 0, 0], [0, 0, scale[2], 0], [0, 0, 0, 1]]) # Combine transformations transformation_matrix = translation_matrix @ rotation_matrix @ scaling_matrix return transformation_matrix “`Academic Context
9-DoF Pose Manipulation is grounded in robotics and computer vision, with significant contributions from kinematics and motion planning. The mathematical foundation involves transformation matrices and homogeneous coordinates, which facilitate the representation of 3D transformations. Key papers include ‘A Survey of Robot Manipulation’ by Siciliano et al., which discusses robotic kinematics, and ‘Geometric Tools for Computer Graphics’ by Philip Schneider and David Eberly, which covers transformations in computer graphics. These works provide a comprehensive understanding of how to manipulate objects in three-dimensional space effectively.Code Examples
Example 1:
import numpy as np
def create_transformation_matrix(translation, rotation, scale):
# Create translation matrix
translation_matrix = np.array([[1, 0, 0, translation[0]],
[0, 1, 0, translation[1]],
[0, 0, 1, translation[2]],
[0, 0, 0, 1]])
# Create rotation matrix (assuming rotation is in radians)
rotation_matrix = np.array([[np.cos(rotation[2]), -np.sin(rotation[2]), 0, 0],
[np.sin(rotation[2]), np.cos(rotation[2]), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
# Create scaling matrix
scaling_matrix = np.array([[scale[0], 0, 0, 0],
[0, scale[1], 0, 0],
[0, 0, scale[2], 0],
[0, 0, 0, 1]])
# Combine transformations
transformation_matrix = translation_matrix @ rotation_matrix @ scaling_matrix
return transformation_matrixExample 2:
# Create translation matrix
translation_matrix = np.array([[1, 0, 0, translation[0]],
[0, 1, 0, translation[1]],
[0, 0, 1, translation[2]],
[0, 0, 0, 1]])
# Create rotation matrix (assuming rotation is in radians)
rotation_matrix = np.array([[np.cos(rotation[2]), -np.sin(rotation[2]), 0, 0],
[np.sin(rotation[2]), np.cos(rotation[2]), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
# Create scaling matrix
scaling_matrix = np.array([[scale[0], 0, 0, 0],
[0, scale[1], 0, 0],
[0, 0, scale[2], 0],
[0, 0, 0, 1]])
# Combine transformations
transformation_matrix = translation_matrix @ rotation_matrix @ scaling_matrix
return transformation_matrixExample 3:
import numpy as np
def create_transformation_matrix(translation, rotation, scale):
# Create translation matrix
translation_matrix = np.array([[1, 0, 0, translation[0]],Example 4:
def create_transformation_matrix(translation, rotation, scale):
# Create translation matrix
translation_matrix = np.array([[1, 0, 0, translation[0]],
[0, 1, 0, translation[1]],
[0, 0, 1, translation[2]],View Source: https://arxiv.org/abs/2511.16666v1