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

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.

8 pages, 4 figures, 7 optional appendix pages, 4 appendix figures

References in corpus (8)

• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
• Chirality Nets for Human Pose Regression
• Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
• An Adaptable Approach to Learn Realistic Legged Locomotion without Examples
• Benchmarking Structured Policies and Policy Optimization for Real-World Dexterous Object Manipulation
• Legged Robot State Estimation using Invariant Kalman Filtering and Learned Contact Events
• Residual Pathway Priors for Soft Equivariance Constraints

Cited by in corpus (3)

• Leveraging Symmetry in RL-based Legged Locomotion Control
• Morphological Symmetries in Robotics
• Breaking Symmetries Leads to Diverse Quadrupedal Gaits