pymatlie 0.0.1a1

pymatlie provides an implementation of Matrix Lie Groups (MLG) used in robotics.

PyMatLie

Installation

Either install via pip through

pip install pymatlie

or, for development, clone the repository and install in editable mode using

$ python -m venv venv
$ source venv/bin/activate
$ pip install -e ".[dev]"

Usage

We use $g \in G$ for a group element, where $G$ is the Matrix Lie Group, $\xi \in \mathbb R^m$ for a column vector in the Lie Algebra and $\xi^\wedge \in \mathfrak g$ for the matrix representation of said vector.

from pymatlie.se2 import SE2

g = SE2.random() # Sample random group element

# Moving from the Group to the Lie Algebra
xi_hat = SE2.log(g)
xi     = SE2.vee(xi_hat)
# or alternatively
xi     = SE2.Log(g)

# Moving from the Lie Algebra to the Group
xi_hat = SE2.hat(xi) # Or SE3.wedge(xi)
g       = SE2.expm(xi_hat)
# or alternatively
g       = SE2.exp(xi)

# There are methods for generating common matrices
e       = SE2.get_identity()
Jl      = SE2.left_jacobian(xi)
Jr      = SE2.right_jacobian(xi)
Ad      = SE2.adjoint_matrix(g)
ad      = SE2.ad_operator(g)

Features

• Implemented SO(2), SE(2)
• Batched
• Euler-Poincare and Euler-Poincare-Suslov