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GAFRO: Geometric Algebra For RObotics


Toolbox for efficient learning and control in robotics by relying on geometric algebra


Löw, T. and Calinon, S. (2023). Geometric Algebra for Optimal Control with Applications in Manipulation Tasks. IEEE Transactions on Robotics (T-RO).


  • Geometric algebra provides a unification of various frameworks such as screw theory, Lie algebra or dual quaternions, while offering greater generalization and extension perspectives.
  • It provide a single algebra for geometric reasoning, alleviating the need of utilizing multiple algebras to express geometric relations.
  • Geometric algebra operations typically allow translations and rotations to be treated in the same way, without requiring us to switch between different algebras.
  • Geometric algebra allows geometric operations to be computed in a very fast way, with compact codes.


  • Robotics
  • Geometric problems

Oriented pointmass

An oriented pointmass system.

Tracking point

System tracking a point target.

Tracking pointing point

Pointing task, i.e. system tracking a point target using a line.

Tracking line

System tracking a line target. It can be seen that the system is compliant if moved along the line and stiff if moved away from the line.

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