On discrete symmetries of robotics systems: A group-theoretic and data-driven analysis

Daniel F Ordonez-Apraez
Italian Institute of Technology
Martin, Mario
Antonio Agudo
Francesc Moreno
Paper Website

Paper ID 53

Session 7. Mobile Manipulation and Locomotion

Poster Session Wednesday, July 12

Poster 21

Abstract: We present a comprehensive study on discrete morphological symmetries of dynamical systems, which are commonly observed in biological and artificial locomoting systems, such as legged, swimming, and flying animals/robots/virtual characters. These symmetries arise from the presence of one or more planes/axis of symmetry in the system’s morphology, resulting in harmonious duplication and distribution of body parts. Significantly, we characterize how morphological symmetries 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. In the context of data-driven methods, symmetry represents an inductive bias that justifies the use of data augmentation or symmetric function approximators. To tackle this, we present a theoretical and practical framework for identifying the system’s morphological symmetry group $\G$ and characterizing the symmetries in proprioceptive and exteroceptive data measurements. We then exploit these symmetries using data augmentation and $\G$-equivariant neural networks. Our experiments on both synthetic and real-world applications provide empirical evidence of the advantageous outcomes resulting from the exploitation of these symmetries, including improved sample efficiency, enhanced generalization, and reduction of trainable parameters.