On discrete symmetries of robotics systems: A group-theoretic and data-driven analysis
This work addresses the challenge of leveraging symmetries for better performance in robotics and AI systems, offering a domain-specific solution that is incremental in nature.
The paper tackles the problem of discrete morphological symmetries in robotics systems by characterizing how these symmetries extend to dynamics and measurements, and presents a framework to exploit them using data augmentation and equivariant neural networks, resulting in improved sample efficiency, generalization, and parameter reduction.
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.