Learning for robot navigation presents a critical and challenging task. The
scarcity and costliness of real-world datasets necessitate efficient learning
approaches. In this letter, we exploit Euclidean symmetry in planning for 2D
navigation, which originates from Euclidean transformations between reference
frames and enables parameter sharing. To address the challenges of unstructured
environments, we formulate the navigation problem as planning on a geometric
graph and develop an equivariant message passing network to perform value
iteration. Furthermore, to handle multi-camera input, we propose a learnable
equivariant layer to lift features to a desired space. We conduct comprehensive
evaluations across five diverse tasks encompassing structured and unstructured
environments, along with maps of known and unknown, given point goals or
semantic goals. Our experiments confirm the substantial benefits on training
efficiency, stability, and generalization.

学习机器人导航的关键和挑战性任务是通过欧几里得对称性进行二维导航的规划，以及开发一种等变消息传递网络来进行值迭代。同时，通过可学习的等变层将特征提升到所需空间以处理多相机输入，在固定和无结构环境中的五种任务评估的实验证实了训练效率、稳定性和泛化能力的显著优势。