SO(3), SE(3) functionalities

Introduction

• cope provides many tools for working in the space of rigid-body motions SE(3) and the space of rotation group SO(3), including many mathematics operators using Lie Group and Lie algebra.

• It also includes a python implementation of the following paper-Timothy D Barfoot and Paul T Furgale, Associating Uncertainty with Three-Dimensional Poses for use in Estimation Problems. In addition, we extended this framework to the case where poses is seperated into rotation and translation.

Features

• inverse of a homogeneous transformation
• Adjoint of 4x4 transformation matrix
• hat operator - return skew matrix (return 3x3 or 4x4 matrix) from vec
• the matrix log of the transformation matrix T
• the matrix log of the rotation matrix
• so(3) to SO(3), se(3) to SE(3) using the exponential map (closed form and series expansion)
• Jacobian of SO(3), SE(3)
• inverse Jacobian of SO(3), SE(3)
• Adjoint of 4x4 transformation matrix
• uncertainty propagation, uncertainty fusion (for 4x4 transformation matrix)
• uncertainty propagation, uncertainty fusion (where rotation and translation are separated)
• visualize uncertainty

Basic Usage