Geometric Algebra For RObotics in Python

This library provides a geometric algebra tools targeted towards robotics applications. It includes various computations for the kinematics and dynamics of serial manipulators as well as optimal control.

It is based on gafro, a C++ library relying on templates to efficiently implement the geometric algebra operations.

Please visit https://gitlab.com/gafro in order to find the entire gafro software stack.

Installation using pip

Requirements:

• Eigen 3.4+

Due to the template-based nature of gafro (see Differences between gafro and pygafro below), the compilation of pygafro can take a long time. Additionally, using clang instead of gcc is highly recommended: gcc requires more memory resources when compiling pygafro, which can become problematic on lower-end computers.

Using the default compiler of your computer

pip install pygafro

Forcing the usage of clang

(assuming that clang is installed at /usr/bin/clang)

export CC=/usr/bin/clang
export CXX=/usr/bin/clang++
pip install pygafro

Installation from source

(works either in a conda or virtual environment)

Requirements:

• Eigen 3.4+
• numpy

Due to the template-based nature of gafro (see Differences between gafro and pygafro below), the compilation of pygafro can take a long time. Additionally, using clang instead of gcc is highly recommended: gcc requires more memory resources when compiling pygafro, which can become problematic on lower-end computers.

Using the default compiler of your computer

git clone --recurse-submodules https://github.com/idiap/pygafro.git
mkdir build && cd build
cmake ..
make # or for example "make -j4" if you have enough resources
make install

Forcing the usage of clang

(assuming that clang is installed at /usr/bin/clang)

git clone --recurse-submodules https://github.com/idiap/pygafro.git
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/usr/bin/clang++ -DCMAKE_C_COMPILER=/usr/bin/clang ..
make # or for example "make -j4" if you have enough resources
make install

Usage

Multivectors

from pygafro import Multivector
from pygafro import Point
from pygafro import Motor

# create a multivector that corresponds to a Euclidean vector
vector = Multivector.create(['e1', 'e2', 'e3'], [1.0, 2.0, 3.0])

# create a point (a specialized multivector subclass)
point = Point(1.0, 2.0, 3.0)

# create a random motor
motor = Motor.Random()

# apply the motor to our multivectors
vector2 = motor.apply(vector)
point2 = motor.apply(point)

# geometric product
result = vector * point

# inner product
result = vector | point

# outer product
result = vector ^ point

Robots

from pygafro import FrankaEmikaRobot

panda = FrankaEmikaRobot()

position = panda.getRandomConfiguration()

# forward kinematics: compute the motor at the end-effector
ee_motor = panda.getEEMotor(position)

Differences between gafro and pygafro

gafro being based on C++ templates, only the classes and operations you are effectively using are compiled into your software.

This versatility cannot be achieved in a Python library: we cannot instantiate the templates at runtime, nor can we realistically instantiate all the possible combinations at compile time.

A compromise was choosen: a subset of multivectors (using sensible blades combinations) are instantiated and compiled, and other blades combinations are supported through a Python class that internally use a C++ multivector with more blades and transparently use a mask to only expose the blades requested by the user.

Thus, creating a multivector is done using the following helper function:

# using values
vector = Multivector.create(['e1', 'e2', 'e3'], [1.0, 2.0, 3.0])

# using only the list of blades
vector = Multivector.create(['e1', 'e2', 'e3', 'ei', 'e123i'])

Background

You can find the accompanying article here and more information on our website.

How to cite

If you use gafro in your research, please cite the

@article{loewGeometricAlgebraOptimal2023,
  title = {Geometric {{Algebra}} for {{Optimal Control}} with {{Applications}} in {{Manipulation Tasks}}},
  author = {L\"ow, Tobias and Calinon, Sylvain},
  date = {2023},
  journal = {IEEE Transactions on Robotics},
  doi = {10.1109/TRO.2023.3277282}
}