Morphological symmetries in robot learning

Daniel Ordonez-Apraez, Antonio Agudo, Mario Martin, Francesc Moreno-Noguer

Keywords: Morphological symmetries, Finite symmetry groups, locomotion, symmetric dynamical systems, symmetric robotic systems, symmetries in robotics

TL;DR: We present a group-theoretic analysis of morphological symmetries of dynamical systems. Characterizing the symmetries of the system's dynamics, control, and proprioceptive/exteroceptive data. And elucidating how to exploit these symmetries in DL

Abstract: This work studies the impact of morphological symmetries in learning applications in robotics. Morphological symmetries are a predominant feature in both biological and robotic systems, arising from the presence of planes/axis of symmetry in the system's morphology. This results in harmonious duplication and distribution of body parts (e.g., humans' sagittal/left-right symmetry). Morphological symmetries become a significant learning prior as they extend to symmetries in the system's dynamics, optimal control policies, and in all proprioceptive and exteroceptive measurements, related to the system's dynamics evolution \cite{ordonez2023discrete}. Exploiting these symmetries in learning applications offers several advantageous outcomes, such as the use of data augmentation to mitigate the cost and challenges of data collection, or the use of equivariant/invariant function approximation models (e.g., neural networks) to improve sample efficiency and generalization, while reducing the number of trainable parameters. Lastly, we provide a video presentation and an open access repository reproducing our experiments and allowing for rapid prototyping in robot learning applications exploiting morphological symmetries.