End-to-end learning for visual robotic manipulation is known to suffer from sample inefficiency, requiring a large number of demonstrations. The spatial roto-translation equivariance, or the SE(3)-equivariance can be exploited to improve the sample efficiency for learning robotic manipulation. In this paper, we present fully end-to-end SE(3)-equivariant models for visual robotic manipulation from a point cloud input. By utilizing the representation theory of the Lie group, we construct novel SE(3)-equivariant energy-based models that allow highly sample efficient end-to-end learning. We show that our models can learn from scratch without prior knowledge yet is highly sample efficient (~10 demonstrations are enough). Furthermore, we show that the trained models can generalize to tasks with (i) previously unseen target object poses, (ii) previously unseen target object instances of the category, and (iii) previously unseen visual distractors. We experiment with 6-DoF robotic manipulation tasks to validate our models' sample efficiency and generalizability. Codes are available at: https://github.com/tomato1mule/edf

本文利用李群的表示理论构建了新的 SE(3) - 等变能量模型，允许高样本的端到端学习。我们证明这些模型可以从头开始学习，但具有很高的样本效率，并且可以推广到具有不同要求的任务中。

等变描述符场：SE（3）等变能量模型用于端到端的视觉机器人操作学习