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

TL;DR

This paper investigates discrete morphological symmetries in dynamical systems, especially in robotics, and develops a framework for identifying and exploiting these symmetries to improve data efficiency and model generalization.

Contribution

It introduces a theoretical and practical framework for identifying morphological symmetry groups and leveraging them with data augmentation and equivariant neural networks in robotics.

Findings

Symmetry-aware methods improve sample efficiency.

Exploiting symmetries enhances model generalization.

Symmetry-based approaches reduce model complexity.

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.