Morphological Symmetries in Robotics

TL;DR

This paper introduces a comprehensive framework for understanding and utilizing morphological symmetries in robotic systems, enhancing modeling, control, and learning efficiency through symmetry-based methods and harmonic analysis.

Contribution

It presents a novel, physics-informed geometric approach to morphological symmetries, demonstrating their benefits for data-driven and analytical robotics methods.

Findings

Morphological symmetries improve sample efficiency in machine learning models.

Symmetries enable decomposition of robot dynamics into simpler components.

Experiments on real robots validate the theoretical framework.

Abstract

We present a comprehensive framework for studying and leveraging morphological symmetries in robotic systems. These are intrinsic properties of the robot's morphology, frequently observed in animal biology and robotics, which stem from the replication of kinematic structures and the symmetrical distribution of mass. We illustrate how these symmetries extend to the robot's state space and both proprioceptive and exteroceptive sensor measurements, resulting in the equivariance of the robot's equations of motion and optimal control policies. Thus, we recognize morphological symmetries as a relevant and previously unexplored physics-informed geometric prior, with significant implications for both data-driven and analytical methods used in modeling, control, estimation and design in robotics. For data-driven methods, we demonstrate that morphological symmetries can enhance the sample efficiency and generalization of machine learning models through data augmentation, or by applying equivariant/invariant constraints on the model's architecture. In the context of analytical methods, we employ abstract harmonic analysis to decompose the robot's dynamics into a superposition of lower-dimensional, independent dynamics. We substantiate our claims with both synthetic and real-world experiments conducted on bipedal and quadrupedal robots. Lastly, we introduce the repository MorphoSymm to facilitate the practical use of the theory and applications outlined in this work.