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This research advances robotics by introducing a framework that jointly leverages multiple symmetries across configuration and task spaces, improving policy generalization through unified differential-geometric representations. By composing these symmetries rather than treating them in isolation, the approach enables robots to better exploit structural redundancies inherent in both mechanical design and task properties. The validation on dual-arm systems demonstrates that this mathematical composition yields tangible performance gains in real-world and simulated environments.
Symmetries Here and There, Combined Everywhere: Cross-space Symmetry Compositions in Robotics
arXiv:2605.22639v3 Announce Type: replace 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.
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.
Robotics (cs.RO)
arXiv:2605.22639 [cs.RO]
(or arXiv:2605.22639v3 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2605.22639 Focus to learn more arXiv-issued DOI via DataCite
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