让机器人同时利用多种对称性，提升泛化能力
Symmetries Here and There, Combined Everywhere: Cross-space Symmetry Compositions in Robotics
- 通过跨空间对称性组合，统一建模配置与任务空间的对称性
- 在双臂机器人上验证，联合使用对称性显著提升泛化性能
- 适合研究机器人学习、对称性建模与具身智能的学者
机器人因其机械结构和任务特性展现出丰富的对称性。尽管许多机器人问题同时存在多种对称性，现有方法通常将其孤立处理，未能挖掘其协同潜力。本文提出跨空间对称性组合框架，学习在配置空间与任务空间中共同具备等变性的机器人策略。基于正向运动学映射的微分几何结构，我们实现了从配置空间到任务空间的对称性下推，以及从任务空间到配置空间的对称性上提，使不同对称性可在统一表示空间中组合。在模拟与真实双臂机器人上的实验验证表明，联合利用多重对称性可显著提升策略泛化能力。
原文摘要 · Abstract (English)
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.
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