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.

翻译：机器人导航学习是一项关键且具有挑战性的任务。真实世界数据集的稀缺性和高成本要求采用高效的学习方法。在本信中，我们利用二维导航规划中的欧几里得对称性——这种对称性源于参考系间的欧几里得变换，并允许参数共享。为应对非结构化环境的挑战，我们将导航问题建模为几何图上的规划问题，并开发了一种等变消息传递网络来执行值迭代。此外，为处理多相机输入，我们提出了一种可学习的等变层，将特征提升至所需空间。我们在涵盖结构化与非结构化环境、已知与未知地图、点目标与语义目标的五项不同任务中进行了全面评估。实验证实了该方法在训练效率、稳定性和泛化能力方面的显著优势。