Symmetries Here and There, Combined Everywhere: Cross-space Symmetry Compositions in Robotics

TL;DR

This paper presents a framework for learning robot policies that are jointly equivariant to multiple symmetries across configuration and task spaces, improving generalization in robotic tasks.

Contribution

It introduces cross-space symmetry compositions, leveraging differential geometry to combine symmetries from configuration and task spaces within a unified framework.

Findings

Jointly leveraging multiple symmetries improves generalization.

Framework validated on simulated and real-world dual-arm robot experiments.

Symmetry composition enhances policy learning efficiency.

Abstract

Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in isolation, failing to exploit their combined potential. This paper introduces cross-space symmetry compositions, a framework for learning robot policies that are jointly equivariant to multiple symmetries across configuration and task spaces. Leveraging the differential-geometric structure of the forward kinematics map, we both descend symmetries from configuration to task space and lift symmetries from task to configuration space, enabling their composition within a unified representation space. We validate our framework on simulated and real-world experiments on a dual-arm robot, demonstrating that jointly leveraging multiple symmetries yields improved generalization.